Untitled - Blake Education

Natural Maths Strategies – Beginning level Written by Ann Baker BPhil, DipRdg and Johnny Baker BScHons, PhD Copyright © 2007 Ann & Johnny Baker and Blake Education First published 2007 Blake Education Pty Ltd ABN 50 074 266 023 108 Main Rd Clayton South VIC 3168 Ph: (03) 9558 4433 Fax: (03) 9558 5433 www.blake.com.au Publisher: Lynn Dickinson Series editor: Sante D’Ettorre Designer: Domani Design Illustrations: Shiloh Gordon and Oscar Brown Cover design: Domani Design Typesetter: Post Pre-press Group Printed by Tara TPS, Korea. This publication is © copyright. No part of this book may be reproduced by any means without written permission from the publisher. COPYING OF THIS BOOK BY EDUCATIONAL INSTITUTIONS A purchasing educational institution may only photocopy pages within this book in accordance with The Australian Copyright Act 1968 (the Act) and provided the educational institution (or body that administers it) has given a remuneration notice to the Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions, contact: Copyright Agency Limited Level 19, 157 Liverpool St Sydney, NSW, 2000 COPYING BY INDIVIDUALS OR NON-EDUCATIONAL INSTITUTIONS Except as permitted under the Act (for example for fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, or transmitted in any form by any means, without the prior written approval of the publisher. All enquiries should be made to the publisher.

National Library of Australia ISBN: 978-1-921143-57-1 1. Mathematics – Study and teaching (Primary). I. Title 372.7

Contents

CONTENTS Introduction

vi

Unit 1: All Sorts

2

Unit 2: Toy Town

16

Unit 3: Fish Eyes

30

Unit 4: Pattern Play

44

Unit 5: Number Crunching

58

Unit 6: Shaping Up

72

Unit 7: Measuring Up

86

Unit 8: Shop ’til you drop

100

Activity Sheets

114

Song Sheets

150

Resource cards

155

Beginning Level Maths CD-ROM The CD-ROM provided at the back of this book has WORD, Excel and .pdf documents that support the integration of the Natural Maths Strategies material into your curriculum. The CDROM contains the following files: ✒ letters to parents and carers about each unit ✒ the focus, context and developmental sequence for each unit ✒ the activity sheets, song sheets and resource cards ✒ a student profile chart ✒ a preparation and resources list for each unit ✒ a picture of Tess for each unit.

© 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

C o n t e n t s

iii

Big Ideas in Maths

Big Ideas in Maths The mathematical content of this Natural Maths Strategies series is organised around 12 big ideas that are relevant to teaching maths at the beginning level. At this level, not all of the 12 big ideas are appropriate. However, below we have listed the relevant big ideas and left gaps to show where future development will take place.

B i g i d e a s i n M a t h s

iv

N0.1

Number Sense

N0.2

Addition & Subtraction

N0.3

Multiplication & Division

N0.4

Money

M0.1

Measurement

M0.2

Time

S0.1

Shape

S0.2

Position in Space

CD0.1

Chance

CD0.2

Data

PA0.1

Pattern

PA0.2

Equivalence

Unit 1

Unit 2

Unit 3

Unit 4

All Sorts

Toy Town

Fish Eyes

Pattern Play


Big Ideas in Maths

Big Ideas in Maths

Unit 5

Unit 6

Unit 7

Unit 8

Number Crunching

Shaping Up

Measuring Up

Shop ’til You Drop

Subitising and counting small groups of objects using number names.

Understanding that groups can be joined to make larger groups and separated to make smaller groups.

Understanding that money is used to buy things.

Using informal and comparative language to describe size and mass.

Identifying and sequencing events by familiar times.

B i g i d e a s

Recognising 2-D and 3-D shapes by name.

Using positional language in everyday contexts.

Matching objects one-to-one and comparing group size.

Making patterns by attributes and actions.


i n M a t h s

v

Introduction

Introduction This book provides starting points for three-part lessons that focus on the big ideas for teaching maths to 4 to 5-year-olds. It is organised into 8 units, with each unit containing mental routines, problematised situations and assessment activities to match the big ideas for this level, as well as investigations and games that engage the children in mathematical activity. The units are intended as starting points for teachers to build on, so they may bring their own flair and ideas to the classroom. New maths curricula are frequently divided into 5 strands: ✒ Number (including Money) ✒ Space ✒ Measurement ✒ Chance and Data ✒ Patterns and Algebra

i n t r o d u c t i o n

Within each of the strands there are a number of big ideas on which the units for the Beginning Level are based.

Links to imaginative event-based play At this early stage in their development children learn through play. With this in mind the units have been designed to allow for free play at the beginning of the unit. Through free play children will explore the possibilities for the situations and materials presented. Scaffolding and immersion in the related vocabulary, concepts and ways of thinking about the big ideas presented in the units will lay the foundation for the activities that follow on from the free-play situations. The contexts provide rich scope for the children to develop related imaginative and event-based play situations. The Toy Town unit for instance culminates in the creation of a road map and buildings that can be set out on the floor in a myriad of different ways. Children will be able to plan trips and routes to places of special interest that they add to their town. The links to their everyday life ensure that learning about numeracy is always connected to their experiences of the real world. As the children play and interact with the activities there will be many opportunities presented through their interests and questions to extend and challenge the mathematical learning, and to make connections with other curriculum strands, especially literacy and technology.

Engagement through narrative The introduction of the character, Tess, into the units is a device that can be used to engage interest and curiosity. Tess could be an imaginary friend or child in another school. She could, for example, send letters with problems and photos, and the children could reply with letters and photos. With a little imagination and dramatisation Tess could become a feature of the day that the children really look forward to, solving her problems or responding to her challenges and then awaiting her reactions. Tess may have lots of stories to share with the children and the children with her. You may select another character or a real character that you prefer to substitute for Tess, and that is fine too as long as the “magic” is kept alive.

vi


Introduction Introduction

Incidental learning It is impossible to include in one volume all of the experiences that children need to become mathematical thinkers. In particular, the activities on counting and number recognition complement the common sense incidental mathematical learning that teachers engage in naturally. There are many opportunities during the day for incidental learning and you need to capitalise on these. There are also many odd moments that can be filled with useful mathematical activity. Counting for instance is something that children need to be engaged and immersed in every day. When counting is tied to everyday situations, it is made meaningful for the children. Counting the number of students present or absent, counting the steps to the music room and filling in odd moments with number rhymes are activities that do not need to be included explicitly in this book although they do need to be included in your daily program. Incidental learning brings with it mathematical ideas that lay good foundations and connections with other mathematical ideas. An example would be counting down while tidying up – “Let’s see if you can tidy the floor and come back to the carpet by the time we have counted down from 10/20” – which combines passage of time with a useful counting strategy. Similarly counting the number of giant steps to the end of the school block and then taking tiny steps back introduces aspects of measurement of distance, and provides some experiences for proportional reasoning required in the future.

Three-part lessons This book is much more than a resource to help teachers meet their syllabus requirements. The activities provide the type of resource needed to implement a three-part lesson process. In outline, a three-part lesson includes: ✒ a mental routine to develop the child’s self-confidence and repertoire in mathematical thinking ✒ a problematised situation where the child applies their own thinking to a situation that they can engage with ✒ a time for reflection in which strategies and solutions are shared, compared and formalised, through which: 1. we begin from where the children are 2. we build on their understanding through the sharing of ideas This approach to the teaching and learning of mathematics has its roots in research findings, and brings these findings to life through activities that have been found to fully engage children in mathematical discovery, discussion and understanding. Children learn to value each other’s ideas, working as a community of learners rather than as individuals.



vii

Introduction

Part 1: Mental Routines

Part 2: Problematised Situations

Part 3: Reflection

Number sense, fluency with mathematical and strategic thinking and estimation skills are the foundational building blocks of all later mathematics. Worksheets and mental arithmetic tests are anathema to risk-taking, reflective thinking and seeking out efficient strategies that will develop automaticity in number facts based on deep understanding.

P a r t 1

Five years ago we began to question the relevance of paper and pencil, worksheets and “drill and kill” methods in the development of foundational basic number facts and understandings. We began by testing a few mental activities that involved the children simultaneously in fun and relevant activities. As we did so, we observed that when children are engaged in mental activities, certain conditions need to be present for them to obtain maximum benefits. These are: ✒ Concrete materials need to be provided for children to be used as tools. ✒ Feedback is immediate, and involves sharing and discussing strategies as well as showing equal respect for all children. ✒ Errors are seen as learning opportunities for all. ✒ Questions provide success for all as well as challenges for some. ✒ All children need to be engaged at their own level during the process. ✒ Children see themselves as a community of learners where everyone has a role to play in the development of thinking and learning. It was with these criteria in mind that we began to explore the potential of “mental routines” as we have chosen to call them. The purpose of mental routines is to develop useful strategies that will lead to mastery and a solid foundation in basic maths concepts. Mental strategies as far as possible should relate to the methods that children develop intuitively and within their own culture. They should also relate as far as possible to the ways in which those strategies are applied in the real world. This means that mathematics instruction must use contexts and pedagogies that allow children to use their own cultural, ethnic and gender preferences and approaches. Ladson-Billings, 1994 When we refer to the conditions that need to be present for the effective development of mental strategies, we see that this view is clearly reflected. The mental routines make an excellent lesson starter as they arouse enthusiasm and encourage the children to feel part of a learning community. They need last no more than ten minutes, but during that time every child would be engaged and challenged to take risks with their current understanding.

viii


Introduction

Classroom management For each mental routine, provide a laminated mini-whiteboard of the resource card for each student and suitable writing materials. We call these “mini-whiteboards”, as normal felt pens can be used to ring or mark ideas on them. The teacher begins by posing simple, closed questions that enable everyone to be successful. Soon the questions change to a more open type, where more than one answer can be found. This enables the children to begin to work at their own level. Finally, the process is flipped, and the children ask the questions, trying to determine a solution to the problem that the teacher has posed.

COLLECTIONS Target strategies give a focus to the lesson.

Target strategies ✒ Identifying characteristics and properties

Card masters are provided for the mini-whiteboards.

Resource Card 1 Collections

Resource card 1

✒ Sorting by characteristics and properties

M e n t a l Open questions

Closed questions enable the teacher to see who has “got it” and which strategies are being used.

show the students that there is often more than one method and more than one right answer to a question.

r o u t i n Flip questions give the students e the opportunity to s practise the language of maths.

✒ Knowing that an object can be classified in many different ways ✒ Identifying categories for sorting

Closed questions I am thinking of something that a dog would like? I am thinking of two round things. What are they? The thing I am thinking of is bouncy. What is it?

© 2007 Blake Education – Natural Maths Strategies – Beginning Level

157

Both of these things are animals. What are they?

Open questions I am thinking of something furry. What might it be?

P a r t 1

You could eat this. What might it be? It is round. What might it be? It is a fruit. What might it be?

Flip questions We are going to play a game where you try to guess which one of the things on the card I am thinking of. This is tricky though because you can’t simply ask “Is it a dog?” If you want to find out if I am thinking of the dog, you might ask: “Is the thing you are thinking of furry?” “Does the thing you are thinking of eat bones?” You can cross things off the board as you go; we’ll do this first one together. The children may play the game with a partner or in a small group, in which case they choose the object and answer the questions.

Note: Each laminated mini-whiteboard can be reused for up to two weeks by changing the level of the question content as the students’ vocabulary, skills and strategies improve.


ix

Introduction



Part 3: Reflection

We use the term problematised situation to describe the type of activities that will allow the children to engage with realistic (to them) situations as described in the research from the Freudenthal Institute. The situations provide the kinds of challenges that encourage children to construct their own ideas, strategies and mathematical understandings as they grapple with them. The children, as described earlier, are developing their own mathematical tools, which can be formalised by the teachers when appropriate.

P a r t 2

x

The problematised situations provided have multiple entry points and many methods of solution. If the numbers are too hard, they can be reduced; if they are too easy, they can be increased. Some children will draw pictures or act out the solution with objects whereas others may use a more symbolic approach using numbers or tallies. Some will present solutions in an organised fashion whereas other solutions will be more muddled. It is the sharing and reflecting on the range of strategies that will broaden the possibilities for the children and allow them to enter into mathematical thinking from their very first experiences. The focus in the primary classroom is shifting towards an emphasis on mathematical reasoning and problem solving in a true sense. This new focus helps the children learn how to describe, compare and discuss their multiple approaches to solving real problems. In the classrooms where we have been working, we have noted that the children have engaged with the problems and have shown an increased interest in maths along with a really firm conceptual understanding. The reflection, as described further on and included in each of the presented problematised situations, is central to this approach. Part of the preparation for the reflection is the process of observing the strategies that the children use and of listening to their explanations. From the information gathered, it is possible to extend, consolidate and formalise learning during the reflection process. While the children are working, it is possible to gather information about what they do know and what they can do. For instance when a child is touch counting all the things drawn or set out, a simple question such as “Do you have to count them all or is there something else you can do?” may act as a prompt from which the children can demonstrate that they can subitise and count on. Annotating the work samples makes it possible to record this information so that decisions about future planning can be made. A range of work samples will eventually give a clear picture of a child's progress towards understanding the big ideas.


Introduction

Classroom management The body of a three-part lesson is often taken up with a problematised situation in which the activity is introduced with as little scaffolding as possible. The activity can be structured to enable the children to work independently, in small groups or collaboratively in larger groups, either as they wish or to suit the teacher’s assessment purposes. The problematised situations require the children to work mathematically, draw on their own experiences and often to invent their own methods of recording and finding a solution.

WHAT’S INSIDE THE BOX? We give a specification of the problem that can be photocopied and displayed for all to refer to.

The resources list is a suggestion only – it needs to be tailored to your class’s needs.

you’ll never guess. t be I x? bo e th e id ins t’s Wha you some clues. Listen carefully while I give It is wooden. sides. It does not have straight middle. It has a hole through the g. You can thread it on a strin Activity Sheet 1

Resources

Activity Sheet 1

Objects to match those on Activity Sheet 1 to hide in a box; boxes with lids so that the children may prepare clues too; magazine cut-outs prepared ahead of time to ensure that a good mix of objects is ready to select from.

The activity guide makes suggestions for running the activity.

After the investigation, each situation leads on to the final part of the lesson – the reflection stage.

Name

Tess’s mess

The activity Explain to the children that you have hidden an object in the box and that you will give them clues so that they can work out what it is. Read the clues; do not say Yes or No if a child makes a guess before sufficient clues have been given for a correct guess to be made. Review the clues one by one at the end after a correct guess has been made. When reviewing the clues, ask questions such as:

P a r t 2

A link to the most relevant big idea helps to provide “What did you know after you were told it was wooden?” a focus for “What did you know after you heard that it did not have straight sides?” observation during Explain to the children that they are going to paste pictures of objects onto paper so that they the activity. can make up clues for others to guess their mystery object. 116


Allow time for them to try out their clues on a friend or an adult and make changes, as needed, before presenting to a group or the class.

Reflection Ask the children to comment on different clues in terms of which clues are too easy and give the game away, and which clues are not very helpful.

and M0.1 Using informal e to ag gu lan ive rat compa ss. describe size and ma

As the children are working on the problem, the teacher has opportunities to observe methods of recording, strategies used, problems encountered and fix-up strategies used. This is important preparation for the final reflection stage.


xi

Introduction


P a r t 3


Part 3: Reflection

In the busy classroom the end of the lesson approaches all too quickly and as a result the reflection is often neglected. And yet the reflection is the most important part of the lesson. It is the time when the children use mathematical language to explain what they have done and they see that there are many strategies for solving problems, and that some are more effective than others. It is also the time when the teacher can formalise a particular idea, concept or process and scaffold the children to the next level. In fact there are some who go so far as to say that if you don’t hold a reflection then the children will probably retain nothing. The development of a community of learners who share, listen and learn from each other is at the heart of this approach to mathematics. The reflection time sets up the mathematical culture of the classroom with its tight-knit community of learners. It allows for mathematical mind journeys and adds to the excitement of learning mathematics. The principles of rigorous reflection are: ✒ the identification of a range of strategies to share and discuss ✒ the use of one or more errors to show the value of checking results and of developing a fix-up strategy ✒ celebrating risk-taking, inventiveness, mathematical reasoning and learning from mistakes ✒ building on, extending and presenting more formal methods of recording as the children demonstrate readiness for them ✒ positive, constructive feedback with a focus on feed forward – what you will do next time. Through the dialogues and participation of all the children in the class, the reflection stage becomes crucial to the development of a community of learners, through which active involvement in learning mathematics is successfully fostered.

xii


Introduction

OTHER CONSIDERATIONS Concrete materials The mental routines provided in this book are actually very “hands on”. The children may be sitting with concrete materials as in the “Shop ‘til You Drop” unit, or with cards made from the resource cards as in the “Pattern Play” unit, or they may be writing and drawing on laminated resource cards. The children will actively engage in acting out or in marking on their boards which means that visual imagery is combined with the verbal instructions helping the children to chunk information into a meaningful whole. So there are two points to keep in mind as we discuss the uses of tools: First, meaning is not inherent in the tool; students construct meaning for it. Second, meaning developed for tools and meaning developed with tools both result from actively using tools. Teachers don't need to provide long demonstrations before allowing students to use tools; teachers just need to be aware that when students are using tools, they are working on two fronts simultaneously: what the tool means and how it can be used effectively to understand something else. Heibert, J. et al. 1997 This use of invented tools is equally important when the children are working on the problematised situations described below. You will notice that we have provided hands-on resources for each mental routine. These can be photo-enlarged, reduced or copied as appropriate. We laminate ours because we know that they will be used time and time again, and we want students to interact with them. They are used repeatedly and have uses outside those initially presented. The children enjoy using water-soluble felt pens and a tissue to clean them. The use of darker coloured pens means that we can see what the children record and also follow their thinking as they find their answers. The children can hold their cards up for everyone to see and this means that they see a broad range of possible answers during the open questions. The resources are also used to develop adaptive reasoning during the flip questioning.

Feedback, assessment and student profile Feedback at this early stage needs to be immediate and very positive. Sometimes we need to remind ourselves that unexpected answers or responses to what we think are fairly straightforward questions or instructions will have a logical foundation in the minds of the children. We need to find out exactly what question the children think they have answered and why they gave the response that they did. Only through observation, prompts and questioning on the job can we find out exactly what the children are thinking, understand and able to do. The annotation and collection of work samples will provide documentary evidence and show the journey of each child. The problematised situation together with the big ideas and reflection suggestions on the page help the busy teacher to maximise their observations and make records on the matching Student Profile Sheets supporting each unit. The mental routines clearly specify particular target strategies and also offer opportunities to observe the children’s responses.


There are many references to the digital camera. A model can be photographed to create a permanent record of an achievement and then added to an e-portfolio.


xiii

Introduction

Engagement The ten or so minutes set aside for mental routines are fast and pacy. They may involve concrete materials, number cards, coins or other materials. The children engage with the activities because they are different to the rest of the lesson. When we first began exploring the mental activities that we suggest here, we had no idea how much fun and, of course, how much learning would flow from them. We soon realised that we didn't need to make up a new mental activity every day because the nature of the tasks and the children’s interest in them meant that they could be used and easily adapted over several days, hence the term “mental routines”. We now use the routines for several consecutive days, all the time watching to see the level of engagement and of course we switch to a new routine if we think the interest is dwindling.


xiv

As we introduce each routine, we use the meta-language of the strategies or process that go with it. At first it was our intention to simply immerse the children in the meta-language but they were so captivated by words such as subitising and eliminating, they soon wanted to use them too. Watching the children engage with the activities has been rewarding for us and for them too. When the children are having fun and are engaged, they seem to be hungry for more. We have seen even the switched-off learners re-engage through the mental routines.

Community of learners To gain the most from these activities, the children need to become a community of learners. They need to really listen to the ideas of others, give positive feedback, ask questions, make suggestions and comparisons, and finally to evaluate the strategies presented by others. They need to feel safe to take a risk, present their ideas, comment on the ideas of others and learn to justify their viewpoints and stick with them. Learning to be a member of a mathematical community means taking ownership of the goals and accepting the norms of social interaction. Why is it important that classrooms become mathematical communities and that all students participate? Because such communities provide rich environments for developing deep understandings of mathematics. Heibert, J. et al. 1997


Introduction

REFERENCES The references given below are the key sources for our explanation of the developmental sequence associated with topics at this level. 1.

Checkley, K. (1999) Math in the early grades: Laying a foundation for later learning. Curriculum Magazine.

2.

Copley, J.V. (2000) The Young Student and Mathematics. National Association for the Education of Young Children, Washington DC.

3.

Heibert, J. et al. (1997) Making Sense: Teaching and Learning Mathematics with Understanding. Heinemann, NH.

4.

Hunt, J. (1999) “Maths in the Early Grades”. Curriculum Journal, ASCD.

5.

Kamii, C. (1989) Young Children Continue to Reinvent Arithmetic: Implications of Piaget’s Theory of Developmental Sequence. Teacher’s College Press, N.Y.

6.

National Research Council (2001) Adding It Up: Helping Children Learn Mathematics. The National Academies Press, Washington DC.

7.

Russell, S.J. (2001) “Changing the Elementary Mathematics Curriculum: Obstacles And Challenges”, in D. Zhang, T. Sawada & J.P. Becker (eds) Proceedings of the China–Japan–U.S. Seminar on Mathematics Education.

8.

Trafton, P.R. & Thiessen, D. (1999) Learning Through Problems: Number Sense and Computational Strategies. Heinemann, NH.

9.

van Hiele, P.M. (1999) “Developing geometric thinking through activities that begin with play”, Teaching Children Mathematics, 5 (6), pp. 310–316.



Unit 1 All Sorts

Focus For their introduction to maths young children need opportunities to play with man-made and natural materials. As they sort and explore materials, they learn about the physical properties of shapes (hard, soft, rigid, smooth, rough, straight sides, curved sides) and the ways in which shapes behave (rolls, slides, bounces, stacks, joins). By direct comparison they also learn that some shapes are bigger, longer and shorter, and that some are different colours and textures. As they play with materials in a structured environment, early vocabulary related to the properties (size, colour and shape) begins to develop. As children engage in the activities presented in this unit, they will: ✒ explore the properties of a range of materials and objects ✒ sort and classify by many properties ✒ count and label different groups ✒ use the comparative language of size, shape and other properties ✒ compare group size by counting and one-to-one match-

2


Context The context for this unit is All sorts. This will lead into informal sorting and describing, and then into more formal sorting activities using a wide range of materials. As the children sort and describe materials, they will initially identify one category to sort by (for example, red things) but with experience they will begin to extend their sorting to two or more characteristics (small red buttons with 4 holes). Also as they sort, they will identify descriptors for categories that allow them to understand that an object can belong to more than one category (an orange will fit into the category “round” when being sorted by shape but also into the category “fruit” when foods are sorted). The children may also engage in sorting themselves (girls/boys or blue eyes/brown eyes). The children will develop basic mathematical vocabulary as they use the language of colour, shape, size and other properties to compare, sort and label objects. Concepts of direct comparison, that is, similarities, differences and opposites, will be developed during the sorting activities.

Developmental sequence Children at this very early stage of their development are beginning to understand that: 1. materials and objects can be sorted by many different attributes 2. some materials and objects fit into many different categories 3. direct comparisons can be made between objects to identify similarities and differences 4. sorting and labelling is a natural part of many aspects of everyday life 5. comparative language can be used to describe size (big/bigger/biggest) and properties (soft, softer, softest) 6. collections can be counted and labelled.


3

UNIT 1 All Sorts

P R E P A R A T I O N A N D

PREPARATION AND RESOURCES You will need: 1. collections of materials for sorting (maths materials, scrap materials, picture cut-outs, found and natural materials) 2. items to match or replace those presented in the mental routines and problematised situations, if you wish the children to use a hands-on approach, or from time to time change the objects used 3. several printed name labels for each child 4. suitable objects to use with Activity Sheet 1 and a box to hide them in 5. a picture photograph to match the problem on page 11.

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) The following picture books are closely related to the ideas presented in this unit and may spark additional ideas for sorting and imaginative free play. A Picture Book of Animal Opposites, Walker Books Ltd. Dr Seuss Lift-The-Flap-Books: Silly Opposites, Dr Seuss, HarperCollins Publishers. Elephant, Elephant: A Book of Opposites, Pittau and Gervais, HNA Books. Kipper’s Book of Opposites, Mick Inkpen, Hodder Children’s Books. Opposites, John Burningham, Walker Books. The Foot Book, Dr Seuss, HarperCollins Publishers.

R E S O U R C E S 4


All Sorts 1 1 UNIT UNIT

FREE PLAY Target strategies ✒ Identifying the properties of materials by feeling, touching and playing freely with them ✒ Naming the characteristics of materials handled (soft, warm, shiny, long, round) ✒ Identifying categories through free sorting (toys, animals, shapes)

The activity Gather an absolute mass of objects to tip out and surprise the children with. They will then want to sort through, play with and freely sort the materials before you introduce more formal activities, so allow time for this. As the children play, immerse them in the types of comparisons that can be made – shape, size, colour, texture and use – according to the sorting materials available. Also introduce generic terms such as farm animals, cars, round things, building things, foods and so on. As the children play, pose questions such as: “Which of these things do we find outdoors?” “Which of these things do we use when we are building models?”

F R E E

“Which of these things would roll/stack?” “Which of these things are red/blue/smaller than the building block?” Provide several boxes for the children to sort the objects into at packing up time but do not give instructions for which things to put into which boxes. If the children randomly pack things into any box, wait till next time to ask “Would there be a good way of sorting these so that we won’t have such a mixed-up collection next time?”

Observation

P L A Y

As the children play and talk, note: ✒ the range of properties used for sorting and the vocabulary used ✒ which colours and shapes are known ✒ whether the children recognise that an object can be classified in many ways and belong to more than one category (for example, does a big blue object belong to the group of blue things as well as the group of big things). The observations that you make will inform planning in terms of: ✒ materials to use next time ✒ focus concepts and vocabulary ✒ further sorting experience needed.


5

UNIT 1 All Sorts

COLLECTIONS Target strategies ✒ Identifying characteristics and properties

Resource Card 1 Collections

Resource card 1

✒ Sorting by characteristics and properties

M e n t a l r o u t i n e s

6

✒ Knowing that an object can be classified in many different ways ✒ Identifying categories for sorting

Closed questions I am thinking of something that a dog would like? I am thinking of two round things. What are they? The thing I am thinking of is bouncy. What is it?


157

Both of these things are animals. What are they?

Open questions I am thinking of something furry. What might it be? You could eat this. What might it be? It is round. What might it be? It is a fruit. What might it be?

Flip questions We are going to play a game where you try to guess which one of the things on the card I am thinking of. This is tricky though because you can’t simply ask “Is it a dog?” If you want to find out if I am thinking of the dog, you might ask: “Is the thing you are thinking of furry?” “Does the thing you are thinking of eat bones?” You can cross things off the board as you go; we’ll do this first one together. The children may play the game with a partner or in a small group, in which case they choose the object and answer the questions.


All Sorts

1 UNIT

OPPOSITES Target strategies ✒ Identifying similarities and differences in shape/size and other properties

Resource Card 2 Opposites poster

Resource card 2

✒ Using the language of opposites (straight sides/round sides, short/tall) ✒ Using the measurement language of comparison

Closed questions I am thinking of an animal that is the opposite of tall. What is it? The thing I am thinking of is the opposite of cold. What is it? I am thinking of a plant that is the opposite of small. What is it?


159

Open questions I am not a hot or a cold object. What might I be? You might find me in the garden. What might I be? I don’t have any leaves and you wouldn’t eat me. What might I be? I smell nice. What might I be?

Flip questions This is a game called Opposites where you ask opposites questions to find out what I am. My answers may be a bit tricky, though. If you ask if I am hot, I might answer with the opposite: “No I am not the cold thing. What would you cross off the picture then?” Help the children with the questions and elimination process initially until they are able to use their adaptive reasoning.



7

UNIT 1 All Sorts

P R O B L E M A T I S E D S I T U A T I O N S 8

TESS’S MESS er little h f o ll a t u o t r o s to r e h Tess’s mum told ted the r o s e h s e m ti y r e v E . s e c bits and pie started d n a y a w r e tt e b a f o t h g u pieces, she tho all over again. rent fe if d t a h W ? s g in th r e h t r How should she so sort them? ways can you find to Activity Sheet 1

Resources

Activity Sheet 1

Name

Tess’s mess

Activity sheet cards or a set of objects for sorting; glue if using the cut-outs; digital camera (optional) if using real materials.

The activity Read Tess’s problem to the children. Ask them to describe the special characteristics of each object before they begin sorting. The children may work alone, in pairs or threes for this activity. Explain to the children that you want to keep a record of each method of sorting, so they need to glue their first sorting on the page before sorting in a different way. Ask the children to name the sorted groups that they have made. Give a suggestion to help them get started if necessary. Ask the children which group has the most/least things. They may subitise (just know by visual comparison), count or make a direct one-to-one match to answer such questions. 116


The children can then repeat the process to find a different way of sorting and paste these onto another page.

Reflection

g Subitising and countin

N0.1 Use several examples from different groups s using small groups of object for comparison. Ask the children which samnumber names. ples had some of the same categories and labels. Ask why some things fitted into many different categories. Relate the situation back to Tess and ask the children how they would like Tess to sort her objects and to say why.


All Sorts 1 UNIT

WHAT’S INSIDE THE BOX? er guess. v e n ’ll u yo t e b I ? x o b e th What’s inside s. e lu c e m o s u yo e iv g I ile h Listen carefully w It is wooden. es. id s t h ig a tr s e av h t o n s e It do dle. id m e th h g u o r th le o h a s It ha . g in tr s a n o it d a e r th n a c You Activity Sheet 1

Resources

Activity Sheet 1

Name

Tess’s mess

Objects to match those on Activity Sheet 1 to hide in a box; boxes with lids so that the children may prepare clues too; magazine cut-outs prepared ahead of time to ensure that a good mix of objects is ready to select from.

The activity Explain to the children that you have hidden an object in the box and that you will give them clues so that they can work out what it is. Read the clues; do not say Yes or No if a child makes a guess before sufficient clues have been given for a correct guess to be made. Review the clues one by one at the end after a correct guess has been made. When reviewing the clues, ask questions such as:

116


“What did you know after you were told it was wooden?” “What did you know after you heard that it did not have straight sides?” Explain to the children that they are going to paste pictures of objects onto paper so that they can make up clues for others to guess their mystery object. Allow time for them to try out their clues on a friend or an adult and make changes, as needed, before presenting to a group or the class.

Reflection Ask the children to comment on different clues in terms of which clues are too easy and give the game away, and which clues are not very helpful.

and M0.1 Using informal to comparative language s. describe size and mas



UNIT 1 All Sorts


TESS’S COLLECTION s a h e h S . s d in f e h s t a th s Tess collects thing stic toys, shapes and all many shells, twigs, pla . sorts of other things ways e m o s t s e g g u s to s s la c r She would like ou ts about in h ts n a w e h S . n o ti c lle o c to sort her oup. what should be in each gr garden

Resources Objects for sorting, for example, leaves, twigs, shells, bottle tops and other small found objects; glue.

The activity

beach long round

Brainstorm with the children and record a short list to match several of the sorting materials. As you create the list, make it into a chart as shown with a small space for the label and a larger space to write or draw the things that belong in that group. The children can then work in small groups to sort and label their materials to make a similar chart. Explain that if they put the things into the groups on the chart, you will help them write the label for each group. As you label the groups, encourage the children to think about whether that is the most appropriate label or whether some things fit into more than one group. They may want to move objects around at this stage. When the children think they have made the best labels and groupings possible, it is time to paste the items onto the chart for display. Encourage the children to join in and count how many objects there are in each group so that the number can be used as a label too. Encourage the children to compare group size in terms of: lots of

not many of

Reflection

more than/less than

same amount

objects one-to-one

CD0.2 Matching Present each group’s pasted sorting and size. compare the labels and properties used to and comparing group sort by. Discuss reasons why some similar things have been put into different groups on each poster. Use this opportunity to create a red beads large beads Venn diagram with two overlapping circles labelled “red beads” and “large beads”. Use some beads or similar objects to show how the large red beads fit inside the intersection of the two circles, the small red beads fit in the first circle and all other large beads fit in the second circle. The remaining small beads that are not red are outside both circles.


All Sorts 1 UNIT

TESS’S ALL SORTS HUNT ind on f to d te n a w e h s s g in th f Tess made a list o en she went and found her all sorts hunt. Th ws what she found. them. This picture sho sorts? ll a r e h t u o b a e c ti o n u yo What do l way like ia c e p s a in t r o s n a c u yo Find things that Tess did. Activity Sheet 2

Resources

Activity Sheet 2

Name

Scatter objects around the room that can be sorted by length, mass, size, thickness, shininess, roughness and other attributes.

Tess’s list

long short

The activity Show the children the picture. Then use the activity sheet to stimulate comparative discussions about the length, thickness and mass of the items collected by Tess.

heavy light

Discuss and demonstrate some of the possible comparisons that can be made with the available objects before the children begin their own all sorts hunt. Explain that their groups of objects each need three things in them so that comparisons similar to Tess’s (for example, long, longer, longest) can be made. Involve the children in the direct comparisons by asking questions such as: © 2007 Blake Education – Natural Maths Strategies – Beginning Level

117

“Which object is short?” “Is this one shorter or longer than that one?” “Which is the shortest?” Together with the children, put the three objects in the sequence shortest, shorter, short. Explain to the children that they will need to draw pictures of the things that they make into groups of three so that other children will be able to find them too. Encourage them to draw the objects in sequence if they can.

Reflection

1 Using informal and

M0. During the reflection, compare some of the to comparative language groups of three objects and the sequences. s. describe size and mas Note the comparative terms used by the children as well as whether they were able to compare and describe comparatively only two or possibly three objects. Use the recordings in the same way, asking the children to explain what was being compared and how. Match the actual objects to the pictures and involve the children in the direct comparisons and labelling.



UNIT 1 All Sorts

BINGO ALL SORTS A game for 4 players

Resources

Activity Sheets 3, 4, 5

Four sets of laminated playing cards made by photocopying Activity Sheet 3 onto one each of red, green, yellow and blue card; game boards on Activity Sheets 4 and 5 which have a piece of card of the appropriate colour stuck over each colour name. A bag to put the cards in.

Activity Sheet 5

4 yellow Activity blue Sheet red

Name

Shape game boards (1)

Activity Sheet 3

Name

blue

red

120

How to play

yellow

green

blue

red

Shape cards

Note: There are only three positions for the colours while the cards will be copied onto four colours of card. This gives the game an extra level of interest when the card has the right shape, but not the right colour.

g a m e s

Name


yellow

118

green



On their turn, the player takes a card without looking into the bag. If the card matches a category on their board, they keep it and place it on the grid. If it does not match, it is put back into the bag. The first player with a full board calls “bingo”.

green

119


ALL SORTS SNAP A game for 2 to 4 players

Resources Two complete sets of cards made from Activity Sheet 3.

How to play Begin by giving each player only 6 cards and then increase to 12 or 18 cards as the children’s proficiency at the game develops. All the cards are dealt face-down in piles in front of the players. As with regular Snap, players take turns to turn over their top card and place it on the middle pile. When an identical card is placed on top of a card in the pile, the first player to call “snap” wins the pile and places those cards aside (they are not put back into play). When no more playing cards are left, the player who collected the most cards wins. The children may count their cards or lay them in a line for direct one-to-one comparison with the cards won by other players.

12


All AllSorts Sorts

1 UNIT

SELF-SORTS Resources Print several name labels for each child; glue.

The investigation This investigation asks the children to think of things that they can compare about themselves – eye colour, hair colour, height, numbers of brothers and sisters, pets such as a dog/cat/fish and so on. This activity will work most effectively if even-sized groups are used because at the beginning of the investigation every child will have a partner. Explain to the children that they are going to work in small groups for the next few days to compare themselves in many ways. They will sort themselves into groups by a variety of personal features such as eye colour or who has a dog, or they might have some suggestions for things to sort by. Assist with the first sort by asking the children to arrange themselves so that all the boys are in one line and the girls in another line. Ask the boys and girls to join hands so that everyone has a partner. Ask the children to compare group sizes in terms of more than, less than or the same as. “What will happen if all the children with blue eyes stand in a line and children with other eye colours stand in another line?” “Will there be more people with blue eyes or less people with blue eyes?” Ask the children to suggest ways in which the name tags can be used to make a record of what they have found, prompting, if necessary, that they make an informal block graph. Encourage the children to suggest other ways that the groups can be sorted and allow time over the next few days for them to investigate the different sorts. If they do not suggest sorting and lining up by height and creating sets of short and tall people, suggest it at some stage. They should suggest sorting into groups of different eye colours as well.

Reflection Ask the children to comment on their groupings and to show their recordings. Allow time for the children to compare the results for their groups with the results for other groups, asking questions such as “Did every group have the same number of blue-eyed people as other colours?” and ask the children to say why and how groups were different.


I n v e s t i g a t i o n

13

UNIT 1 All Sorts

MAKING GROUPS A S S E S S M E N T A C T I V I T I E S

14

up. o r g h c a e in s g in th e r o m Draw up? o r g h c a e to e iv g e w ld u o What name c ? it in s g in th t s o m e th s a h Which group Activity Sheet 6

Resources

Activity Sheet 6

Name

Coloured pencils; magazine cut-outs and glue or Kid Pix (if motor coordination and drawing is a problem).

Making groups Draw more things in each group.

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ sorting a wide range of materials ✒ naming groups made ✒ making direct comparison of group size with or without actual counting


121

Observer’s guide Explain to the children that they are to add some more things to each group. Ask them what is special about the things already drawn in each group and to suggest something else that could go in that group. Also encourage them to suggest a name or label for the group (write the label for them). Observe the children as they add to the groups and ask them to explain why something does or does not belong to a group. Occasionally there will be reasons that make sense to the child even if they don’t make sense to you. Their ideas need to be respected. When the children give names for the groups, note which criteria they were based on. If necessary, ask the children to say what category or type of thing a particular item belongs to (for example, these are both bugs, or this is a piece of clothing). When the children answer questions about which group has the least/most or same number as, note how they work out their answers. For instance they might: ✒ just guess by appearance without conservation of number (saying that a group of large things has more in it than a group that has a larger number of small things) ✒ match one-to-one to make a comparison ✒ count or subitise to make a comparison.

unting N0.1 Subitising and co s using small groups of object number names.


All Sorts

1 UNIT

FILL THE GRID Resources

Activity Sheet 7 Name

Fill the grid

small

Several objects that match the criteria presented on the grid on the activity sheet.

Activity Sheet 7

blue

Prior experiences ✒ sorting by two characteristics

big

✒ direct comparison of size ✒ naming groups ✒ comparing group size

122

small

red

The children will be ready for this activity if they have had experiences with:


Observer’s guide Show the children the grid and ask them what they think the labels are for and what would go in the first empty box. Point at the top and side label with a finger of each hand, read both labels and then pull the fingers together into that first box. Ask the children to sort the materials provided so that they match the labels on the grid. They will need to draw each object on the grid if you want to keep a permanent record of this activity. As the children sort, note the ease with which they compare size and the decisions they are making. It is arbitrary where the cut-off of small and large would be for them and you may want to probe to find out why they make the decisions that they do. When the sorting is complete, ask the children questions about which group has the most/least or same number of objects than another group and observe their methods of comparing.

cts one-to-one CD0.2 Matching obje size. and comparing group


A S S E S S M E N T A C T I V I T I E S

15

Unit 2 Toy Town

Focus At this stage the children are very much at Level 0 in their geometric thinking, according to Pierre van Hiele. That is, they are beginning to make links between common shapes by their appearance, not by their properties, and will relate shapes to everyday objects. To move towards Level 1, where the characteristics and isolated properties of shapes are identified, children need opportunities to investigate and use the properties of shapes by constructing and creating a range of model buildings and designs. As they do so, they will find out which shapes join well and which do not. They need to see that some things roll and others only slide. By using 3-D materials, they will also begin to identify the related 2-D shapes on the faces of the solids. Position and number will be integrated as the children plan and predict what will happen as their constructions develop. When playing with the materials in a structured environment, the children will hear and use the language of shape, position and quantity in meaningful situations. As the children engage with the activities in this unit, they will: ✒ experience hands-on manipulating and constructing with 3-D and 2-D shapes ✒ use the language of shape (square, circle, round, sides, joins, stacks, rolls) ✒ think spatially as they visualise the effects of manipulating materials to fit them together ✒ use positional concepts and language (on top of, next to, in front of, across) ✒ solve design and construction problems as they arise ✒ translate models into draw-

16


Context The context for this unit is making a Toy Town. For this concept the children will create buildings from 3-D materials which will eventually form part of a floor map that they can drive cars around and construct free play with. For instance they might go driving to the shops or the park, or visit a friend who lives at No. 7. As the children engage in the problems of joining, stacking and manipulating shapes, there will be opportunities to scaffold and extend geometric understandings of space and position and to immerse them in the language of shape, location and movement. Although their drawings at this stage may be barely recognisable, it is still useful to ask the children to draw models of what they intend to build or models they have completed. Their verbal explanations will help clarify and support their thinking.

Developmental sequence Children at this stage of their development are beginning to understand that: 1. some solid shapes stack and join 2. some solid shapes do not stack or join well 3. shapes have specific names 4. 3-D shapes can be matched to objects in the environment 5. 3-D shapes each have special properties (straight sides, curved sides, points, corners, faces) 6. mental pictures of shapes can be made 7. words can be used to identify location and position (on top, over there).


17

UNIT 2 Toy Town

P R E P A R A T I O N A N D R E S O U R C E S 18

PREPARATION AND RESOURCES In this unit you will see that with some help the children will be expected to create their own toy town models. This will require a number of building materials as well as collaborative group work.

You will need: 1. building materials and junk construction materials suitable for making a toy town 2. glue and paint to decorate the models that the children make 3. Montessori-sized blocks (usually in the ratio 2:1:1 or 1:1:1) blocks and cylinders) 4. small play characters (preferably sorting teddies to match the activity titles) 5. cardboard boxes with one side cut out to make a barrier.

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) The following picture books are closely related to the Toy Town theme of this unit and may be a source of new ideas and challenges for the free play and construction activities. The children will have great fun matching blocks with those used in the book Changes, Changes and with recreating and extending the story with blocks. Changes, Changes, Pat Hutchins, Simon & Schuster Children’s Publishing. Danny’s Dilemma, John Tarlton, Scholastic New Zealand. I can build a house, Shigeo Watanabe, Red Fox Picture Books. Teddy Bears’ Moving Day, Suzanna Gretz, A & C Black Publishers Ltd. Song Sheet 1 song Sheet 1

Building Rhymes

Rhymes

Build it Up Build it up, build it up, build it high, (use fists to model building high) Build it high, high, high into the sky. (involve the children in counting how many fists have been used)

The rhymes on Song Sheet 1 may be used at odd moments and provide on opportunity for the children to chant numbers as they count the number of fists or blocks used.

Tower Block I am going to build a tower block (use blocks to model building) Very, very high. I am going to keep on building Until I reach the sky. (indicate how high you think it might grow) Can you count my building blocks To see how high it grows? (involve the children in chanting the count) Oh No, It’s getting wobbly . . . And over it goes. (nudge the tower over) Crash, crash, crash.

150



Toy Town

UNIT 22 UNIT

FREE PLAY Target strategies ✒ Describing 3-D shapes and the process of building with them ✒ Applying positional language to constructions with 3-D shapes ✒ Describing changes made to shapes as constructions develop (“I am going to make it taller/wider/stronger”)

Resources Building blocks that are proportional as they will lead to more mathematical discoveries (for example, sets where two cubes are the same size as the rectangular prism and two triangular blocks fit together to match the cube); repeat this activity with different scales of blocks as each will stimulate different ways of constructing.

The activity As the children play and build with the blocks, ask “What if” questions to challenge their thinking and immerse them in positional and shape language, for instance: “What if you wanted to put this long flat block on the top?” “What if you wanted to make a bridge over your road?” “What if your house needed a roof?” “What if you wanted to make a space where the bear could hide?” “What if I put this cylinder on the top?” “What if you wanted a tower as tall as you are?” When the children have made a construction they are proud of, ask them to keep a record of it by drawing their model. Surprisingly some children are very good at translating their models to drawings; for others, being asked to attempt the drawing will help them focus on the shapes, even if they are poorly represented.

F R E E P L A Y

Observation As the children play and talk, note: ✒ the shape and positional language used ✒ the choices and reasons for using particular blocks for particular purposes ✒ the problem solving strategies applied to “tricky” situations (for example, selecting a different block or stabilising a weak link). The observations that you make will inform planning in terms of: ✒ challenges and “What ifs” to pose next time ✒ vocabulary and concepts that are needed or ready to be developed further.


19

UNIT 2 Toy Town

BUILD IT UP Target strategies ✒ Following simple building and positional instructions ✒ Comparing towers by height, width, colour

M e n t a l

Preparation

r o u t i n e s

Open questions

Use unifix cubes or other stacking materials to make 4 or 5 towers and base the questions below on those towers.

Closed questions I am thinking of the tallest tower. Which is it? The tower I am thinking of is two blocks wide. Which is it? I am thinking of the middle-sized tower. Which is it? The tower I am thinking of is made of more than just one colour. Which is it?

The tower I am thinking of is not the tallest. Which one might it be? My tower is not as tall as the red one. Which one might it be? I am not thinking of the first or the last tower. Which one might it be? The tower I am thinking of is not multi-coloured. Which one might it be? My tower is not the red one. Which one might it be?

Flip questions Tell the children that you are thinking of one of the towers and they may ask questions to find out which one it is. Explain that you will give only Yes or No answers. Model some question starters, such as: “Is your tower taller than the red one?” “Is your tower the shortest one?” “Is your tower all one colour?” “Does your tower come after the red one?” Involve the children in removing the eliminated towers each time.

20


Toy Town

2 UNIT

SHAPES IN THE ROOM Target strategies ✒ Making connections between solid shapes and their use in the environment ✒ Using direct comparison to identify size (tall, high, tallest, highest) ✒ Using a range of characteristics and properties to identify particular objects (size, colour, position)

Preparation A collection of everyday objects and matching 3-D solid shapes and use the questions below as models for questions to match the collection.

Closed questions The block I am thinking of is the same shape as the tissue box. Which shape is it? The shape I am thinking of is round and will roll. Which one is it? My shape has a round top and bottom but is curved on the sides just like this mug. Which one is it? My block would make a good roof on a little house. Which one is it? The shape I am thinking of reminds me of an ice-cream. What is it?

Open questions The shape I am thinking of does not have straight sides and curved sides. Which one might it be? The shape I am thinking of is not the same as the tissue box. What might it be? The shape I am thinking of is not like a ball. What might it be?

Flip questions Show the children four or five objects (for example, a tin, ball, tissue box, toblerone box, a die, a domino) and matching solid shapes and tell them that they will need to ask questions about the solid shapes to guess which object you are thinking of.


Model some questions to begin the activity, such as: “Is the object you are thinking of the same shape as . . .?” “Is the block you are thinking of the same shape as . . . ?” Involve the children in the elimination process each time.


21

UNIT 2 Toy Town


TESS’S TEDDY NEEDS A HOUSE dy. d te r e h r fo e s u o h a ild u Tess wants to b (Show them a teddy.) h just it w ild u b to s e c ie p d n a s She has lots of bit ld she do? like these. What shou

Resources Empty packaging such as soap powder or cereal boxes, kitchen roll holders, margarine tubs; a small teddy, scissors, glue, adhesive tape, newspaper, paint, collage materials, digital camera (optional). Note: Assistance may be needed with cutting, in which case the teacher may use a sharp pair of scissors or cutting knife.

The activity Read the problem to the children and show them the materials that are available to them. Before they begin working on their houses, ask them what special features they might give the house. These could include windows, a door, a chimney, decorations and furnishings. Draw attention to the size of the teddy that you are using and remind the children that the teddy must fit inside the house, as well as stand up, sit down and lie down in the house. Suggest to the children that they might want to draw their teddy’s house before they begin building it. Although the drawings may not be very clear, it will help the children generate some ideas before they begin and will lead in some cases to more successful houses. As the children are building, ask them questions to scaffold their thinking, for instance: “What will you use to make the roof?” “Where would be a good place for a window?” “Will the teddy be able to lie down in there?” “Which packaging would join together well to make the walls?”

Reflection

and 3-D S0.1 Recognising 2-D shapes by name.

Compare three or four houses, asking the children to comment on the differences and similarities between them. They may refer to the materials used, joining methods, strength of the construction and size and fit, as well as the features and decoration. This is not meant to be competitive, so ensure that comments about each house are positive. Finally, photograph the houses to be sent to Tess and ask the children to comment on what Tess might think of their ideas for a teddy house.


Toy Town 2 UNIT

TESS’S MODELS y k ic tr e m o s f o s e r tu ic p s Tess has sent u k in th t o n s e o d e h S . e d a m models that she has y them. I think you can copy you will be able to copr some tricky model them. We will send he she goes with them. pictures and see how

Resources Digital camera, pictures of Tess’s buildings (made from materials that you have in your classroom), materials to match the photos you have taken. Note: The models are not intended to be permanent. For instance they could include a simple tower with 6 blocks for the base, 4 on the next layer and then a stack of 5 single blocks. They can increase in complexity and include towers with spaces in them or bridges with spaces to go through. Match these to your observations of the children’s level of development.

The activity For this activity, make models with readily available materials. Photograph each model from several angles so that the children will be able to see quite clearly how they were constructed and what materials and how many of each were used. Present Tess’s first challenge (one set of photographs) with the necessary materials and allow time for the children to have a go at copying the models with the materials provided. As they work, draw attention, if necessary, to the number or the position of the materials used and assist the children to match them. Check their progress as they go. The children can then make constructions of their own. Make a big fuss about photographing them so they can be sent to Tess to challenge her.

Reflection As the children copy the constructions, observe the: ✒ way they match (or don’t manage to match) the shapes and materials to use each time


✒ effectiveness of the sequence of actions that they take to copy the constructions

P R O B L E M A T I S E D S I T U A T I O N S

✒ range of shape and positional language used.


23

UNIT 2 Toy Town


TESS’S TOY TOWN e teddy th ll a h it w d e s s e r p im o s Tess was make a to d e id c e d e h s t a th e d a houses you m de a a m e h S . m e th h it w s e s u o whole street of h as a h o ls a e h S . g n lo a e iv r d road too for cars to in each house and each little toy person living s. Tess says we should do has their own addres the same.

Resources Junk materials and/or building blocks such as Duplo or Lego; long strips of paper or card (straight and curved) to make road sections, grey and white paint, twigs, cotton wool balls and empty cotton reels to make trees; scissors and collage materials; sample characters; laminating materials (optional) for making a durable set of road sections and traffic signs.

The activity Ask the children to brainstorm the sorts of buildings and other things that they will need to make for their toy town (houses, apartment blocks, shops, parks . . .). Show them the characters (whatever small characters you have available) that will live in the town. Tell the children that they will also need to make some road strips that can be arranged in different ways. Allow time for the children to experiment with the available materials for making buildings and additional features needed for their town. Encourage them to add features to their buildings and help them to write shop names for their shops. Before the road pieces are painted, ask the children what things might be needed to make the roads look realistic. Suggest road markings if necessary. When everything is painted and dry, set up the toy town and ask the children to explain what an address is and how addresses work. Spend some time creating and naming addresses for the toy town, relating this to environmental uses of number. Keep all of the pieces for free play and other activities and for the investigation in this unit. The children may want to add to them as the days go by.

Reflection As the children work, you will be able to observe their:

language in S0.2 Using positional everyday contexts.

✒ construction and design strategies ✒ understanding of street names and numbers ✒ positional language and ordinal numbers.

24


Toy Town 2 UNIT

TESS’S MAP ts you to n a w e h S . n w to y to r u yo n Tess has see the ke a m n a c e h s t a th o s r e make a map for h same town that you did. t. s r fi t a k o lo to p a m a s u t She has sen Activity Sheet 8

Resources Road pieces, buildings and accessories made in the previous activity, coloured pencils.

Activity Sheet 8

Name

Tess’s map TOY SHOP

BOUTIQUE

BUTCHER

The activity

BAKER

NEWSAGENT

Read the problem to the children and ask them to identify the features and places on the map. If necessary, prompt with questions such as: “What will you need to do first?” “Will you have many streets in your town?”


123

“What are some places to visit in your town?” “What does a map look like?” Allow time for the children to set out their town and be prepared to scaffold the children’s earliest attempts at creating a map. You may want to suggest, for instance, that the road be drawn in first so that the buildings can be marked next. Expect a range of developmental levels to be visible in this activity; it is not about a brilliant map but about engaging in the processes of looking, describing and explaining, visualising and translating ideas from one medium into another. Encourage the children to include as much detail as they can into their maps.

Reflection

positional language in

S0.2 Using Use two or three of the maps for the refleceveryday contexts. tion, asking the children to show where one of the buildings in the town is shown on the maps, or matching one street with a street on the maps. Talk about the features and places that have been included on the maps as well as the ones that may have been missed out. Ask the children to give instructions or trace routes for getting from A to B on the maps.



UNIT 2 Toy Town

TEDDY ON THE BLOCKS A game for small groups of children

Resources Create a barrier (for example, an open box with one side cut off) to hide the actions of one player from those trying to follow the clues; a tiny teddy and at least three blocks for each group.

How to play Player 1 places the blocks in a line with spaces between them. The teddy is then positioned on top, in front of, behind or between the blocks. Player 1 gives clues such as those below. Time is allowed for the other players to match the instructions for each clue. “I have set the blocks in a line so they go red, blue, green.” “My teddy is not on top of a block. It is not in front of the blocks. It is between two blocks.”

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“It is not between the red and the blue block. Where is my teddy?” When the other players have an answer, the barrier is removed and they look to see if they followed the clues correctly. The clues can be as simple or as complex as needed to match the development of the players.

Variation 1 The game can also be played like the flip games in the mental routines, in which case the players behind the barrier ask questions to locate the teddy.

Variation 2 Player 1 makes a model tower or building and gives instructions for the other players to create the identical model. In the first instance, limit the number of blocks to four, but extend this as the children get better at giving and following clues.

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Toy Toy Town Town

2 UNIT

WHERE IS TINY TEDDY? Seek. d n a e id H y la p to s e lik e h s Tess says that in e r e h w e m o s y d d te ny ti a She wants you to hidede. She also needs clues the town you have ma to help her find it.

Resources The road map and buildings (from a previous activity) set up as a town; tiny teddy.

The investigation Remind the children of their earlier map making and what worked well when making the maps. Explain that the clues Tess wants need to show the route to the hiding place. Allow time for them to set up the town, hide the teddy and create a map. Ask the children to suggest ways that the route could be shown on the maps. They might suggest little footprints or dotted lines. If no suggestions are made, prompt by asking: “How are we going to make sure that Tess knows which marks show the route and which ones show the roads and the buildings?” As the children create their routes, ask them to say the route out loud and encourage or scaffold as much positional language as possible. If the route is not very adventurous, suggest some extra ideas such as going behind, over and around something on the map. Encourage the children to test each others’ maps and hiding places and to make changes if they need to before finalising the maps that they are going to send to Tess.

Reflection Select three or four maps and allow time for the children to hide the teddy as planned on their maps. Using some of the maps, follow the clues to the hiding place and ask the children to comment on:


✒ how easy it was to find places on the maps ✒ how easy or tricky it was to actually find the teddy’s hiding place ✒ what else could have been added to the map or directions.


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UNIT 2 Toy Town

MAKING BUILDINGS FROM PLANS A S S E S S M E N T A C T I V I T I E S

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Resources

Activity Sheet 9

Building blocks to match those on Activity Sheet 10 which uses standard Montessori sizes.

Activity Sheet 9

Name

Making buildings from plans Find a block to match each of these blocks.

Prior experiences The children will be ready for this activity if they have had experiences with:

Use your blocks to make this building

✒ matching 3-D blocks to 2-D pictures of them ✒ making simple structures shown in pictures and plans ✒ constructing and building with 3-D blocks 124

Observer’s guide


Explain to the children that you want them to find one block to match every block shown at the top of the page. When they have done that, they should make a building to match the one pictured. As the children work, observe and note: ✒ strategies for matching the blocks to the ones pictured ✒ strategies for copying the simple building pictured ✒ language used to describe or explain their thinking. Ask questions to find out what the children are doing/thinking and why. Questions could include: “How do you know that this block exactly matches the one in the picture?” “Why did you start with that piece?” “What would have happened if you had used this piece first?” When the first part of the activity is complete, ask the children to use the same blocks but to make a completely different building. Ask questions to find out why they chose particular blocks or made specific changes. When complete, ask the children to say how they can check that no pieces have been left out and to say which pieces, if any, are in the same position in the new model as in the original. Ask the children to draw a picture of the model that they made so that they can make it again at a later stage if they want to. Note the range of shape and positional language used as well as the ease or otherwise with which the blocks were manipulated, visualised, rotated and selected for the job intended.



Toy Town 2 UNIT

FINDING AND HIDING TEDDIES Prior experiences

Activity Sheets 10, 11

The children will be ready for this page if they have had experiences with: ✒ playing Hide and Seek

Activity Sheet 11

Name

Hiding teddies Show where teddy could hide in this room.

Activity Sheet 10

Name

Finding teddies Where is the teddy hiding in this room?

✒ using the language of position (on top of, next to, behind, between, under) ✒ giving and following simple positional instructions

Observer’s guide Show the children Activity Sheet 10 and ask them to describe where the 5 teddies are hiding. The children may want to point to the hiding teddy but explain that they have to say in words where each one is hiding. Encourage the use of positional language by asking questions such as:

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“For this teddy, tell me if you think he is on top of, at the side of or underneath the cupboard.” When appropriate, give the children a copy of Activity Sheet 11 and ask them to hide some teddies in the picture. Explain that they should choose a different type of hiding place each time and that under, behind, beside, on top and next to are all good clues. As the children work on this activity, note: ✒ how easily they can use positional clues to locate a particular teddy ✒ the range of vocabulary used to describe position ✒ the range of hiding places suggested ✒ whether the child can check by counting that all teddies have been found.

language in S0.2 Using positional everyday contexts.



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Unit 3 Fish Eyes

Focus Children at this stage need opportunities to use the properties of materials and shapes as they make play things and then engage in directed or invented play based on them. They also need opportunities to match their actions to words, numbers and rhymes. The activities in this unit provide opportunities for the children to subitise (look at and visualise or suddenly know how many in a small group) and to rote count, touch count and count out. As they engage in these activities, they will: ✒ explore and utilise the characteristics of circles and be immersed in the appropriate shape language ✒ cover an area as they decorate their round fish ✒ observe and describe movement and position ✒ subitise different-sized groupings ✒ count and label different-sized groupings ✒ identify and recognise numbers.

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Context The context for this make-and-count unit Fish eyes is based on a rhyme. The children will (with assistance) follow a simple procedure to make a paper plate fish. The fish are then used to create mobiles and puppets. As the air currents blow the fish in different directions, endless opportunities for subitising, estimating, counting and talking about position and direction will emerge. The rhyme itself allows opportunities for children to match actions to rhymes and to count and use the language of position and location. Throughout this unit children will be immersed in opportunities to hear and use counting sequences, subitise, estimate and match numerals to groups of fish. The suggested fish books and counting books will provide ideas for invented event-based play, incidental art and language activities. Tess has provided problematised situations based on counting fish to engage and challenge the children’s thinking and imagination.

Developmental sequence The foundations of number sense will be laid in this unit. For this to be successful, children need opportunities for: 1. touch counting and counting out 2. subitising 3. comparing group size. These experiences also need to be embedded in the child’s world and will entail: 4. using materials for construction 5. matching actions to rhymes 6. using the language of spatial and directional movement 7. comparative language (big, bigger, biggest, small, smaller, smallest, long, middle-sized, short).


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UNIT 3 Fish Eyes

P R E P A R A T I O N A N D

PREPARATION AND RESOURCES You will need to: 1. make several laminated number strips from Resource Card 3 and cut up and laminate the number cards from Resource Card 4 2. colour, cut out and laminate several copies of each fish on Resource Card 5; glue magnetic strips onto the back of each fish if you have a magnetic surface or whiteboard; alternatively, Velcro dots work on some surfaces 3. attach a cloth or large sheet of paper to cover the magnetic surface to act as a screen for hiding some fish 4. Photo reduce the fish on Resource Card 5 to make Tess’s Counting Book (see page 38) 5. draw, cut out and label the outline of a child’s left and right hands, laminate it and attach a magnetic strip 6. provide: string and coat hanger wire to make mobiles and sticks to make puppets; paper plates, cotton balls, google-eyes and tissue paper to make the fish mobiles 7. make a fish tank from a cardboard box with painted backdrop, hanging fish, sand, pebbles and shells.

Related picture books and DVDs (some of the following books are no longer in print but may be available second-hand or from your library) Fish Eyes: A Book You Can Count On, Lois Ehlert, Harcourt Children’s Books. One Fish, Two Fish, Red Fish, Blue Fish, Dr Seuss, HarperCollins. One Lonely Seahorse, Saxton Freymann and Joost Elffers, Arthur A. Levine Books/Scholastic Press.

Song Sheets 2, 3, 4, 5 song Sheet 5

Rainbow Fish, Marcus Pfister, Nord Süd Verlag AG.

R E S O U R C E S 32

Fish Eyes Fish eyes here, fish eyes there. song Sheet 4 Fish eyes looking everywhere. (teachers sheet)

Finding Nemo (DVD), Walt Disney Pictures, 2003.

Fish rhymes Copy the rhymes on Song Sheets onto coloured card and laminate for the children to refer to as they wish. Song Sheet 5 can be photo enlarged, coloured and laminated to make a focal point for the activities in this unit. Introduce a rhyme, actions and counting at times that seem appropriate and be sure to develop a rhythm and change expression to emphasise the repeating pattern in the rhyme. For example, with the rhyme Fish Eyes, set up the magnetic fish on the whiteboard ready for counting. Three to the left, three to the right and one facing straight ahead will be plenty at first. As the counting progresses, change the numbers and even omit one of the directions to introduce the idea of none going left/right.

Fish Eyes

Fish eyes, eyes looking left. Fish eyes here, fishfish eyes there. song SheetFish 3 eyes How manyeverywhere. fish eyes do you see? (look all around) looking Fish eyes, fish eyes looking left. Fish Alive

Fish eyes, fish eyes looking(hands right. swimming left) One, two, three, four, five. song 2 How many do you see? How many fish eyesfish do eyes you Sheet see? (show the fingers of left hand) (count 1,2,3,4 eyes looking left) Once I saw a fish alive. Five Little Fishes Fish eyes, fish eyes looking straight at me. Six, seven, eight, ten. Under the ocean green andnine, deep, How many eyes right. do you see? Fish eyes, fish eyesfish looking (show the fingers of the right hand) Lie five little fishes fast asleep. (hands swimming right) Then I let him go again. (fingers on theeyes leftlooking hand) everywhere. Fish eyes, How many fish eyesfish do you see? Along came a bigger fish out of the blue.fish eyes do you see? How many (count 1,2,3,4 eyes looking right) Why did you let him go? (the right hand) Fish eyes, fish eyes looking straight at me. Because he bit my finger so. (shake all fingers) Swim little fish or he’ll catch you. (hands swimming straight ahead) Which finger did he bite? (right hand moves around the left) How many fish eyes do you see? This little finger on the right. (show little finger) Swim little fish, swim to the left, (count 1,2,3,4 eyes looking straight at me) (wiggle left fingers, move to the left) Swim little fish, swim to the right, Fish eyes, fish eyes looking everywhere. (wiggle left fingers, move to right) Swim little fish with all your might. How many fish eyes do you see? (move all around)

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(look all around)

(count all the eyes)



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You could create mobiles with the paper plate fish (from Activity Sheet 17) and substitute these for the magnetic fish when counting. The variety will offer a challenge.


Fish Eyes 3 3 UNIT UNIT

FISHY FREE PLAY Target strategies

Resource Cards 3, 4, 5 Magnetic Fish

✒ Counting

Resources Number strips from Resource Card 3, Number cards from Resource Card 4, Magnetic fish from Resource Card 5.

Resource card 3

1 2 3

4 5 6 7 8 9

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The activity

Number cards

1 2 3 4 5 6 7 8 9

✒ Matching actions to rhymes and stories

Number Strips

1 2 3 4 5 6 7 8 9

✒ Using the language more than/less than/the same

Resource card 4

1 2 3 4 5 6 7 8 9

✒ Subitising

Resource card 5


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Place the magnetic fish and number strips near to the magnetic surface and encourage a small group of children to use them for free play. The children may act out the rhymes that they have learnt or they may count or create story-like environments with the fish. As the children play, scaffold their developing number sense by introducing comparative, part and whole-part questions and ideas, for instance: “What if some fish swam away? How many would be left then?” “What if every fish wanted to swim with a friend? Would that work out with the fish you have got there?” “What if a shark came along and the fish swam off in groups to hide?” “It looks like there are more big fish than little fish. What do you think? How could we find out?”

F R E E P L A Y

Through play, immerse the children in the language of number and in comparison of group size. “Is there a group of fish to match the number on this card?”

Observation As the children play, count and respond to questions, note: ✒ how far they can rote count ✒ whether they can subitise small groups ✒ whether they have one-to-one correspondence as they count ✒ what strategies they have for comparing group size ✒ whether they recognise any numbers and if so, which ones.


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UNIT 3 Fish Eyes

MAGNETIC FISH 1 Target strategies ✒ Touch counting ✒ Subitising small groups ✒ Counting on 1, 2 or 3 more

M e n t a l

Resources Magnetic fish made from Resource Card 5).

Closed questions Familiarise the children with the fish and identify which ones are swimming left, right and straight ahead. Tell the children that you have hidden some fish behind the flap and that you are going to lift the flap for them to have a quick look to see how many fish there are. Begin by hiding only 2, 3 or 4 fish and asking: “How many do you think you saw?”

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“Were they all swimming in the same direction?” “Were all the fish the same size?” “How many big/small fish did you see?” Accept all answers without saying Yes or No. Then unveil the fish and ask the children how you could check together how many there are. Model subitising and counting on each time. “So there are 2 fish swimming left here and 2 more swimming right over here, so that’s 2, 3, 4 altogether.” Repeat the process with different arrangements and numbers of fish each time matched to the children’s developmental level.

Open questions Tell the children that you have hidden some fish and that you will lift the flap a little way so that they can see some of the fish. Their task then is to say how many fish they think you may have hidden altogether. Use the opportunity to count on from the number of fish first shown as the children work out how many altogether.

Flip questions To play a game of Guess How Many Fish? with the children, hide some fish behind the screen but give them an idea of the range. For example, “There are less than 6 fish hidden.” Encourage the children to ask questions to find out how many are hidden. Answer questions with “there are more than/less than that” rather than just Yes or No.

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Fish Eyes

3 UNIT

MAGNETIC FISH 2 Target strategies ✒ Touch counting ✒ Subitising small groups ✒ Counting on 1, 2 or 3 more

Resources Magnetic fish Resource card 5.

Closed questions Hide 2, 3 or 4 fish. Tell the children that they are so smart that you have a tricky one for them because this time they need to look and see how many eyes, not fish, they can see altogether. Use the suggested layouts for this activity. “Why can you see 2 eyes on some fish and only 1 eye on others?” “Do all fish have 2 eyes?” “How many eyes did you see altogether?” “How many fish have 2 eyes looking at you?” “Did any fish have only 1 eye looking at you?” “How many fish have only 1 eye looking at you?” “Does the longest fish look at you with 2 eyes?” Unveil the fish and check the number of eyes together. You could introduce counting by 2s to 6 or 8 for those children who are ready for another strategy.

Open questions I have hidden 2 fish. How many eyes do you think we will see? I can see 4 eyes looking at me. How many fish do you think I can see? There are 3 fish hiding. How many eyes might we see?


Extension Increase the number of fish and/or the number of fish with 2 eyes looking straight ahead to match the range of learners. Allow time over the next few days for the children to hide groups of fish and ask questions too.

Flip questions There are two parts to this Hidden Fish game. First the children need to find out how many fish are hidden and then how many eyes that might be. Reply with yes/no and more than/less than answers. Keep the numbers manageable and matched to the children’s development. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

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UNIT 3 Fish Eyes


HOW MANY EYES? s with 4 d r a c h is f e e r th d ke ic p e Tess says sh do that? e h s id d w o H r. e th e g o lt a fish eyes yes she e f o r e b m u n r e th o t a h w She wonders . s d r a c e e r th h it w ke a m n a c ase? le p t u o it k r o w r e h lp e h Can you

Resources Magnetic fish made from Resource Cards 5 and 6 and number strips from Resource Card 3.

The activity Set out the fish cards so that they are clearly visible and then read Tess’s problem to the children. Allow time for guess and check as the children try to find three cards that match the description (3 fish with 4 eyes visible). Ask the children which number matches the number of eyes. Counting along the strip to find the number gives the children a strategy that they can use independently later. Ask the children to pick sets of 3 fish and find out how many eyes are showing. Encourage the children to record by drawing the fish and the eyes, and to have a go at matching the number counted with the number on the strip so that they can attempt to write the matching number on their pictures. Some children will respond well to the challenge of finding all of the different possibilities (3, 4, 5 and 6 eyes are all possible). Encourage the children to move beyond touching and counting to subitising 2 eyes and breaking the counting sequence and counting on from 2. Rather than asking the children to touch and count every time, ask them: “Is there a quicker way of counting?” “Do you have to count them all every time?” Some children may not understand the concept of “altogether” and will count the eyes on each fish separately so offer prompts and modelling, for example: “Yes this fish has 2 eyes and this fish has 2 eyes. Let’s count them all now to see how many eyes altogether.”

Reflection


There are two aspects to focus on during the reflection. For children who could not draw the fish each time, invite them to show what strategies they used for working out how many visible eyes on their three cards. For those who did manage to label their fish, use their drawings and ask the rest of the class to suggest ways of working out how many eyes. Select three or four clear drawings and ask the children to comment on which have more than/less than or the same number of eyes and to explain their thinking. During the reflection, immerse the children in subitising, breaking the counting sequence and counting on but do not necessarily expect them all to adopt this strategy immediately. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

Fish Eyes

3 UNIT

THE FISH TANK p a r c s h it w k n ta h is f a ke a Tess wants to m ys a s e h S . w o h w o n k ’t n s e o materials but she d ld make a fish tank and you can help. You cou some instructions. send her a photo or

Resources Cardboard boxes with a window in the front already cut out, paint, string, see-through plastic, scissors, scrap materials, lightweight card. Note: You might like to make a simple fish tank to present as a model.

The activity Read Tess’s problem to the children and either show them the model or the cut-out boxes. Engage them in suggestions for making a fish tank. Allow time for the children to brainstorm what to include in the tank and what materials to use for each before they begin work. As the children create fish for their tanks, they may not think through aspects such as size of fish to fit the tank and other aspects that require careful planning. Allow them to make mistakes and to talk about why something is not working out the way they expected. This is all a natural part of the learning process. The intention is not to have every child with an identical fish tank. Encourage the use of comparative language and fix-up strategies and select some examples for the reflection. Comments such as “My fish are too small for this tank” or “My string is too long and the fish are lying on the bottom” indicate that the children are beginning to think about size, scale and position and the problems that they present.

Reflection

1 Using informal and

M0. At the reflection, first ask the children to to comparative language comment on what they think worked well in s. describe size and mas the making of their fish tanks and what features look good. Then ask them what some of the problems were. When they explain what didn’t work, ask them to comment on some fix-up strategies and what they would do next time they make a model. Create plenty of excitement about photographing the models to send to Tess and of jointly writing down some suggestions and instructions to send to her.



UNIT 3 Fish Eyes


TESS’S COUNTING BOOK he S . k o o b g n ti n u o c y h is f a Tess has sent you to subitise the number of says you may be able count them. fish on each page or ng ti n u o c y h is f a ke a m to u She then wants yo try and work out how many book for her. She willeach page. fish you have put on

Resources Make Tess’s fishy counting book with fish copied and laminated from Resource Card 4 so that the fish are arranged for subitising in groups of, say, 2, 3 or 4 and with up to 6 fish on a page (depending on your learners) or use fish stamps and stencils or KidPix on the computer as an alternative for children with poor motor control; laminated number strips made from Resource Card 3.

The activity Introduce this activity by showing the children the counting book that Tess has sent. Show each page quickly, too quickly for the children to count all the fish on the page and then hide it. Ask the children how many fish they thought they saw. Review possible ways of counting which could include counting all, subitising small groups and counting on. Repeat this process on each page and then revisit the pages drawing attention to the clever way in which Tess had drawn the fish to make them easy to count. For example, point out a group of 2 or 3 fish that can be easily subitised. Demonstrate how easy it is to count on from 3 without having to begin back at 1 each time. Each child could make just one page for a class book or a book of their own. Encourage the children to use their number strips to find the number to match each page. They will write the number on each page and may make a little flap over it so that Tess must count first and check the answer afterwards. As the children make their pages, ask them how they would work out how many on each page and prompt to see if they have included any groups of 2 or 3 that Tess will be able to subitise.

Reflection Share the pages over a few days, involving the children in fast ways of working out how many on each page. Really focus on subitising and ask the children each time:


“Do we need to count this group again now that we know how many there are or can we just count on?”


Fish Eyes

3 UNIT

THE FISHY PUPPET SHOW make a to h is f te la p r e p a p r e h d Tess has use counting puppet show. u to yo e lik ld u o w e h S . n fu f o She says its lots make one too. Activity Sheet 12

Resources

Activity Sheet 12

Name

Tess’s paper plate fish

The children should make their own paper-plate fish using the procedure on Activity Sheet 12 in preparation for this activity.

The activity

You will need: 2 paper plates 2 fluffy eyes 2 google eyes Paper and scraps of paper Glue and a stapler

What to do: Make two fins and a tail. Staple the plates and the fins together.

Ask several children to hold the puppet plates while acting out the fish rhymes presented in the unit. Then make up a story about two or three of the fish or act out a part of the Rainbow Fish storybook. Explain to the children that Tess has made a puppet theatre and number story and thinks that it would be fun for them to do the same.

Decorate the fish. Give the fish a mouth. Stick on the fluffy eyes. Stick on the google eyes.


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Allow time for the children to try creating stories with the puppets and making settings for them before reminding them, if necessary, that Tess made a counting puppet story. Tell the children that you will write their script (story) for them if they want to send it to Tess. Alternatively you could tell the children that when the puppet show is ready, you will record it for Tess. As the children are working, ask questions to focus on the number aspects, such as: “How many fish does the show open with?” “How many are left after the first one leaves?” “Do the fish have to swim away one at a time or could more swim away each time?” “How many fish are there altogether now?”

Reflection Encourage some of the children to present their puppet shows to the class and then involve the class in recounting the story in terms of how many fish, how many coming and going, how many left and how many


altogether. If some children did not engage in the puppetry before, allow time for them to use the puppets now that they have some extra ideas.



UNIT 3 Fish Eyes

GONE FISHING A game for 2 to 4 players

Resources 2 sets of laminated fish cards cut from Resource Card 6 with magnetic tape on the backs; fishing rods made with string, sticks and magnets; laminated blue paper cut out to make a pond for the fish or make a tank from a cardboard box as in the earlier activity “The Fish Tank”.

How to play For this simplest form of the game the fish cards are placed face-down on the pond and the players take turns to catch a fish with their rod. The player with the most dots on their fish wins that round. To increase the complexity of the game, the players catch 2 fish and the winner is the one with the greatest number of spots altogether.

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To further increase the complexity, players can choose a target number, for example 5, and whoever is closest to the target number wins.

FISH MEMORY A game for 2 to 4 players

Resources 2 to 4 sets of laminated fish cards made from Resource Card 6 depending on the number of players.

How to play The cards are placed face-down on the table. Players take turns to turn over two cards. If the number of dots on the two cards matches, the player keeps that pair. If the cards do not match, they are turned face-down again and play passes to the next person. After matching a pair successfully, the player takes another turn. When all the pairs have been made, the player with the greatest number of matching pairs wins.

Variation To increase the complexity of the game, the players must make pairs with a difference of 1.

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Fish Fish Eyes Eyes

3 UNIT

FISH NUMBERS POSTER he says S r. te s o p r e b m u n is th s u Tess has sent out b a l ia c e p s is t a h w t u o d in she wants you to f u to make a special number it. Then she wants yo . poster for her to see Activity Sheet 13

Resources


Fish number poster

Photo-enlarge Activity Sheet 13 to use as a poster. Provide rubber or foam stamps or stencils of fish or Kid Pix.

The investigation Show the children the poster and ask them to look very quickly before you hide it and ask them some questions such as: “Did every tank have the same or a different number of fish in it?” “How could you check your thinking?”

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Note: Some children will say that the tank where the fish are well-spaced or where the fish are bigger holds more fish than the other tanks. Show the poster again and ask the children how many fish in each tank and to explain their method of working it out. They may have counted one by one, subitised, or subitised and counted on. Draw attention to the fact that each tank has the same number of fish in it but that they all look different. Ask the children how there can be the same number in each tank and yet all be swimming in different groupings. The children should now be able to identify that the special feature of Tess’s poster is that every tank has the same number of fish in it. Explain to the children that they will choose a number and make a fish tank poster for it. You may want to cap the numbers for some children but allow others to experiment with larger than expected numbers if they want to. Remind them that each tank has to have the same number of fish in it but that the groupings or the size of the fish should be different each time. As the children work on their posters, ask questions about how they are deciding what to change each time. Some children will be using trial and error but some might be systematically changing only one fish each time.


Reflection Use the fish posters in the same way as you did Tess’s so that the children feel success and purpose in their work. Reflect on the different groupings for each number and use appropriate language, scaffolding it as you do so, for example: “This one looks like double 2, there are 2 here and 2 here, and 2 and 2 make 4 altogether.” “I can see 3 here so I can subitise 3 and count on 2 more, 3, 4, 5 altogether.”


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UNIT 3 Fish Eyes

TESS’S SPOTTED FISH A S S E S S M E N T

ta u p e h S . e s e th e lik t s ju h is Tess drew 4 f he S . h is f h c a e n o ts o p s f o different number . wrote some numbers too on each t u p e h s k in th u yo o d ts o How many sp fish? Activity Sheet 14

Resources

Activity Sheet 14

Name

Tess’s spotted fish

Coloured pencils, number strips (card masters).

Add some spots to the fish and show how many spots each fish has.

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ touch counting ✒ subitising small groups

A C T I V I T I E S

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✒ counting out ✒ matching numerals to small groups


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Observer’s guide Tell the children about Tess putting spots on the fish and writing numbers to say how many there were each time. Ask them to do the same. As the children work on their page, observe, note and prompt to find out whether they: ✒ plan to draw a particular number of dots ✒ draw some dots and then count them ✒ use a fix-up strategy (adding more or crossing some off to reach their target number) ✒ draw and count as they go ✒ use the number strips to count and find the number that they want ✒ write the number from memory ✒ use the number to label the last dot counted or to say how many dots on that fish altogether. Also note the range of numbers that the children are confidently using.



Fish Eyes 3 UNIT

FISHY PARTNERS Prior experiences

Activity Sheets 15, 16

The children will be ready for this page if they have had experiences with:

Activity Sheet 16

Name

Fishy partners (2) Give each fish a partner.


✒ counting small groups of objects

Fishy partners (1) Find each fish a partner.

✒ comparing group size by direct comparison ✒ subitising and counting on ✒ identifying whether same-sized groupings that are arranged differently still have the same number of objects in them

Observer’s guide Explain to the children that each fish has a partner that has the same number of spots. Unfortunately the fish have got mixed up and need to find their proper partners. Suggest that the children join the pairs of fish as they find them. Also encourage them to make their own fish partners with matching numbers of dots on the copy that has no dots. Since the numbers of dots on the activity sheet are quite small, you might want to challenge some children to use larger numbers of dots when they make their own “Fishy Partners” sheet. © 2007 Blake Education – Natural Maths Strategies – Beginning Level

130

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As the children work, note the strategies used to compare the number of dots each time. Some children will count the dots on one fish and then without really thinking will count the dots on a different fish even though it obviously has more or fewer dots. This may indicate lack of conservation (dots that are spread out look like more in number than dots close together). Alternatively it may indicate lack of visual comparison. In the latter case, suggest scanning the page to see if any groups look like they have the same number of dots. Then the children may check by counting.




43

Unit 4 Pattern Play

Focus Children at this stage will be noticing patterns in the world around them. It is time now to draw more formal attention to patterns and sequences in their everyday life so they can describe patterns and changes, and make predictions based on the patterns they encounter. The children will have encountered the recurring nature of day and night, light and dark, sun and moon. They know that certain routines and rituals occur in their life: they get up, get dressed, have breakfast, go to school, and so on. These are patterns that they live by. They will have noticed patterns in nature too; when the sun shines and it rains at the same time, a rainbow forms. Rainbows have a special colour sequence too. Familiarity with patterns and the language to describe and explain them lays the foundation for later work with patterns, functions and algebra. As the children work on the activities presented in this unit, they will: ✒ use the properties of shape, size and colour to create patterns ✒ describe patterns and their repeats ✒ create rhythmic, physical and concrete patterns of their own ✒ follow and give pattern instructions ✒ use the language and concepts of the passage of time and its predictable cycles.

44


Context The context for this unit is Pattern play. This will engage the children in generating their own patterns and pattern rules using materials, actions and words. Dance and music are familiar situations where patterns and sequence are recognisable and memorable to children. The natural sense of rhythm is reflected in the patterning activities. Cycles in the days of the week and in the hours of the day also provide opportunities for the children to recognise and work with simple durations of time. They will also familiarise themselves with time language such as Monday, Tuesday, weekend, before school, after school, morning tea, and so on. Tess is featured in some problems and the unit introduces her friend Fred who needs a quilt.

Developmental sequence Children at this stage of their development are beginning to: 1. recognise the way in which a sequence of objects can follow a short, repeating pattern 2. clap simple rhythms 3. create action patterns (hop, skip, hop, skip) 4. identify and describe pattern elements and repeats 5. make simple patterns with objects 6. continue patterns started by others 7. apply number to patterns (2 red, 1 yellow, 2 red, 1 yellow) 8. use shape, colour, size or position as pattern descriptions.


45

UNIT 4 Pattern Play


PREPARATION AND RESOURCES You need to collect: 1. found and commercially produced patterning materials (pattern blocks, tiles, sorting sets) 2. coloured counters and matchsticks 3. coloured straws cut into three different lengths 4. coloured gummed paper shapes.

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) Busy Bugs: A Book About Patterns, Jayne Harvey, Sagebrush Education Resources. Cookie’s Week, Cindy Ward and Tomie dePaola, Penguin Publishing. Seven More Sleeps, Margaret Wild and Donna Rawlins, Working Title Press. The Very Blue Thingamajig, Narelle Oliver, Scholastic Australia.

Related rhymes The Wheels on the Bus Heads and Shoulders Mary, Mary Quite Contrary

Related dance Hokey Kokey You put your right arm in, you put your right arm out In out in out and shake it all about You do the Hokey Kokey you turn around. That's what it's all about. Repeat for the left arm, right leg, left leg, right side, left side, and finish with: You put your whole self in, you put your whole self out In out in out and shake it all about You do the Hokey Kokey you turn around. That's what it's all about.


Pattern Play 4 4 UNIT UNIT

FREE PLAY Target strategies ✒ Identifying, creating and continuing simple patterns ✒ Matching actions and rhythms to patterns ✒ Applying number to patterns ✒ Using shape and position to create simple patterns

The activity Provide a range of patterning materials over a period of time (commercially produced art materials such as stamps, stencils and cut-outs, found objects such as shells, leaves and twigs, and consumable materials such as bottle tops, bread tags). Tell the children that you have collected these materials (or take them outside to collect their own twigs and leaves) because you thought they would be fun to make patterns with. Allow time for the children to manipulate and play with the materials and to experiment with patterning activities. As the children begin to create patterns, ask them: ✒ Where does the pattern begin and end?

F R E E

✒ Which part repeats? ✒ What would come next? ✒ How can number be used to describe patterns, for example, the number of blue and red counters in the pattern? If consumable materials such as bottle tops have been used, they can be taped or stuck onto paper for show and tell during the reflection. They can also be displayed.

Observation

P L A Y

As the children play, note: ✒ whether they create repeating patterns ✒ whether they can explain why a pattern is a pattern and not just a random line of objects ✒ the range and complexity of the patterns made (colour, shape, position) ✒ whether number is applied to the pattern rules or descriptions (2 red, 3 blue, 2 red, 3 blue) The patterns created will inform decisions about what materials and further opportunities for free play with patterns are needed.


47

UNIT 4 Pattern Play

AUDITORY PATTERNS Target strategies ✒ Listen to and continue a rhythmic sequence ✒ Identify the repeating element within a clapping sequence ✒ Create and present clapping patterns


Closed questions I am going to make some sound patterns. Listen to my clapping pattern. Can you clap it back to me? Listen to my pattern. What was the first part? What was the second part? What would it sound like if I just kept clapping the two parts non-stop? Listen to my clicks and claps pattern. How many clicks each time? How many claps each time? Listen to my clapping pattern. Can you play it back to me by stamping your feet? I am going to clap the rhythm pattern of one of our favourite nursery rhymes. Listen and see if you can guess what it is.

Open questions I am going to clap the first three claps of a pattern. What do you think I should make the next part of my clapping pattern? I want to make a pattern with claps and stamps. What should it start like? I want to make a pattern with clicks, claps and stamps. How should I begin? I am going to use three claps and two clicks to make a pattern. What could it be like?

Flip questions Begin by acting out a few examples of a three-part pattern unit, such as stamp, stamp, clap, or clap, stamp, clap. Encourage the children to join in. You are now ready for a game of Guess my Pattern. I made three claps or stamps altogether to make a pattern. You can guess my pattern by making your own pattern and I will tell you how close it is to mine. I will let you know how close you are to my pattern by telling you that: “My pattern unit does not have a stamp at the beginning.” “My pattern does not have two claps in it.” As the children begin to understand and respond well to the game, increase the complexity by allowing four elements in the pattern unit or by including clicks as part of three actions in the pattern unit.

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Pattern Play

4 UNIT

ALL SORTS PATTERNS Target strategies ✒ Spotting the repeating unit in patterns

Activity Sheet 3 Activity Sheet 3

Name

Shape cards

✒ Identifying the changing characteristic in a pattern ✒ Applying number to patterns Note: Use the shape cards from Activity Sheet 3 to make the patterns for this routine. Provide the children with the cards to show their answers to your questions.

Closed questions So far my pattern goes star, star, circle, star, star, circle. Which three cards come next? My pattern is square, triangle, square, triangle. How should my pattern continue?

118


My pattern uses all the shapes that have four sides. Which ones did I use? I have used all triangles. The first sits on a point and the next sits on a base (bottom). What comes next in my pattern?

Open questions My pattern only uses these rectangles. It is made by turning the rectangle each time. What might my pattern look like? My pattern uses stars and diamonds. What might it look like? There are four shapes in my pattern unit. What might my pattern look like?

Flip questions I have made a pattern using two shapes. You may ask me questions to find out what my pattern looks like, for example: “Do you have a triangle in your pattern?” “Is the square the first shape in your pattern?”


Start with a really easy AB, AB, AB pattern. Model some questions for the children initially. The complexity can increase over time as the children’s patterning ability and vocabulary develop.


49

UNIT 4 Pattern Play


ALL IN A ROW r “Mary, fo s d r o w w e n p u g in k a m Tess has been y r a M r e h t n e s s a h e h S ”. y Mary, Quite Contrar s she y a s e h S t. u o t c a to s u r Mary pattern fo rs too. u yo f o e m o s r e h d n e s wants you to Here’s her verse: Mary, Mary, quite contrary ? d n ta s n e r ild h c r u yo o d w Ho nd a ile m s a h it w e n o n, w o fr One with a one with a waving hand.

Resources Digital camera to send photos to Tess (optional).

The activity Introduce or review “Mary, Mary Quite Contrary” with the children so that it is familiar to them when you introduce the variation. Sit the children in a circle around you while you read the problem to them. When they have heard the verse, involve the whole class in creating the pattern for Tess’s verse. Ask the children to sit down again and involve them in deciding how you could draw the pattern for Tess’s verse so that you will remember it. As you do so, focus on the fact that there were three things in the original rhyme – silver bells and cockle shells and pretty maids all in a row – as well as in Tess’s variation of it. Explain to the children that they can invent three actions for their pattern variation of the verse but that they will need to draw it as a repeating pattern to send to Tess.

Reflection

aking patterns by

PA0.1 M Use the actual pattern drawings and over a . attributes and actions few days involve the whole class in carrying out the patterns. Take some photos to “send to Tess”. Involve the children in creating the words to match the patterns so that Tess can have words, drawings and pictures. Lucky Tess! As the patterns are presented, discuss the similarities and differences between them.


Pattern Play

4 UNIT

TESS’S PATTERN DANCE made e h S t. h ig n t s la s s la c e c n I saw Tess at da nt: e w it d n a e c n a d n w o r e h up p m ta s , p te s e id s , p m ta s , p Side ste Jump, jump, jump shake Side step shake, side step Wiggle, wiggle, wiggle. attern p e c n a d a p u ke a m to n r Now it is your tu w. of steps for Tess to follo

Resources A large space to dance in, video camera (optional) to record some dances to send to Tess.

The activity Teach the class Tess’s dance. When they are able to match the actions to the words and remember the words and rhythm, ask them how they think Tess invented her dance. If necessary, prompt so that they talk about the need to: ✒ think of actions that can be incorporated into a pattern ✒ name the actions ✒ create patterns and rhythms in the words and actions. Try out a few simple suggestions and then allow time for the children to work with some friends to create a pattern sequence of their own. Join in with them and be prepared to make a few suggestions or positive criticisms such as: “Do you think everyone will be able to hop 6 times?” “It’s not easy to switch from stamp to hop is it, so should we change that bit?” “Is this pattern too long for people to be able to remember it?”

Reflection Allow time for the children to share their pattern dances and teach them to the other children. Encourage the children to say which actions, sequences or patterns they liked and why.

s by PA0.1 Making pattern . attributes and actions



UNIT 4 Pattern Play


FOLLOW THE LEADER h fun c u m w o h g in y a s e g a s s e Tess sent me a m e said I h S . e b n a c ” r e d a e L n r e tt “Follow the Pa you s y a s e h S . it y la p to w o h should teach you the n e h T r. e d a le e th d in h e b stand in one long line pattern and everyone else leader has to invent aern. follows the same patt

Resources A large area outside, a parent helper (if possible) to help guide the children as they follow the leader.

The activity In the first instance you or another chosen person will need to be the leader. The leader thinks of a pattern and performs the pattern sequence, for example, step forward 1, 2, 3 jump, step forward 1, 2, 3 jump but the pattern is not said out loud. The children need to observe and follow on behind. When the pattern has become well-established, the leader stops and asks: “What is my pattern?” Any child may become the leader when they have thought of a pattern that they can do. Patterns can include any action that can be carried out while moving forward, for example, arms out, up, left, right or skip, hop, waddle . . . Continue this pattern walk for as long as the children are enjoying it.

Reflection Review each pattern by asking the children to name the patterns and say how they are the same or different. Encourage the use of number in the comparisons, for example:


“This one had 3 hops but the other one had only 2 hops.” “For each pattern this time we had to remember 3 things, hop, skip, bob, but the other pattern had only 2 things, step, hop, step, hop.”


Pattern Play

PATTERNS IN OUR SCHOOL DAYS ys at a d r e h in n r e tt a p a is e r Tess says the ek at e w r e h r fo t r a h c is th s u school. She sent s in your n r e tt a p e av h u yo if d ke s school. She a her a d n e s n a c u yo if ks s a s s week at school. Te u do. yo t a h w e e s n a c e h s o s t char Activity Sheet 17

The activity


Patterns in our day

It is expected that this activity will stretch across the whole school week. Use Tess’s chart to talk about the days of the school week and why Saturday and Sunday are not shown on her chart. Also draw attention to the times on her chart.

Monday puzzles

big books

dance

painting

puzzles

construction

singing

sport

storytelling

swimming

cooking

library

puzzles

big books

computers

sport

Tuesday

Focus on Monday (start on an actual Monday). Ask questions that will show the similarities and differences between what Tess does on Monday at different times during the day and what the class does.

Wednesday

Thursday

Ask the children to draw some of the things that they do every Monday and to make sure they include something that they greatly enjoy.

Friday puzzles 132

construction storytelling

painting

Use the drawings from each day for the reflection so that as the week goes by, the children might begin to:

P R O B L E M A T I S E D


Repeat this process every day of the week after reminding the children what needs to be done each time. On Friday ask the children to suggest ways in which the pattern in the week can be shown on an individual or class poster for Tess.

Reflection

4 UNIT

sequencing M0.2 Identifying and es. events by familiar tim

✒ follow the normal sequence of the day rather than simply random sequences ✒ explore new ways of visually showing an event (for example, drawing a puzzle piece to show puzzle time) ✒ include made-up times or attempts at clocks on the pages.


S I T U A T I O N S 53

UNIT 4 Pattern Play

WHAT’S MISSING? A game for small groups or pairs of children

Resources

Activity Sheet 3

Shape cards made from Activity Sheet 3, coloured counters or matchsticks.

Activity Sheet 3

Name

Shape cards

How to play

g a m e s

One player makes a pattern with at least four repeats. Extra cards are placed face-up on the table for all to see. The other players close their eyes while the pattern originator removes 1 or 2 cards from the pattern. The other players then look at the pattern, find the missing card/s and complete the pattern. Players take a counter or matchstick for each correct card that they place in the pattern. At the end of the game the player with the most counters is the winner.

118


The complexity of this game will change as the children make more complex patterns or remove trickier cards.

PATTERN RACE A game for 2 or 3 players

Resources Shape cards made from Activity Sheet 3.

How to play For 2 players, use two sets of four of the shape cards; for 3 players, use two full sets of shape cards. For this activity, AB pattern units are set out to match the cards being used, for example, star, circle; or triangle, rectangle; or square, diamond pattern units could be made. The cards are shuffled and the players are dealt the rest of the cards. Players take turns to add a card to the patterns; they must keep the patterns going. If a player cannot place a card, they miss that turn. The player to use all their cards first is the winner.

54


Pattern Pattern Play Play

4 UNIT

THE BEADED CURTAIN traws. s d e r u lo o c t u c e s e th s u Tess has sent ws. a tr s f o t u o in ta r u c d e d a She has made a be pattern for every string. Tess used a different t different pattern strings She wants to see whauld like a picture of your you can make. She wo hed. curtain when it is finis

Resources Straws in 6 colours or stripes (cut each straw into 3 different lengths so that there are identical short, medium and long straws in each variety), string. Note: Tie a straw onto the beginning of each string ready for the children to thread.

The investigation Review some of the patterns that the children have made earlier, including some tricky ones, before asking the children what sorts of patterns they think they can make with the straws. If necessary, draw attention to the colours and the lengths and ask the children to suggest some pattern possibilities. Ask the children whether they think it is possible to make every beaded string different. Ask them what they might need to do to make that happen. As the children make their pattern strings, ask them to make comments about the patterns being made and whether they are the same or different to others already made. Encourage direct comparison of the beaded strings. Suggest that they use their comparisons to help them create new and perhaps more complex beaded strings. Some children may use two characteristics at a time when making their patterns, for instance, short red, middle-sized green, long blue. When all of the strings are complete, send them off to Tess for a couple of days. When she has sent them back, the children could use them to construct a curtain across a doorway, window or other area.


Reflection Involve the children in describing the patterns and in saying why some are trickier than others. Create a real element of surprise about how many different patterns are possible; you could even sound impressed as you count the number of different patterns.


55

UNIT 4 Pattern Play

A QUILT FOR FRED A S S E S S M E N T A C T I V I T I E S

ilt. u q a ts n a w d e Fr . d e Fr d Tess has a friend callepattern rows, with a He said he wants it in ach row. Tess asks could different pattern in e design a quilt for Fred? you please help her to Activity Sheet 18

Resources

Activity Sheet 18

Name

Fred’s quilt

Coloured gummed paper pre-cut into shapes for patterning or the shapes from Activity Sheet 3 (if using the shapes, you may want to take digital pictures of the designs).

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ making and describing patterns ✒ describing patterns © 2007 Blake Education – Natural Maths Strategies – Beginning Level

✒ applying number to patterns

Observer’s guide Show the quilt to the children and explain that Fred wants a different pattern on each stripe of his quilt. Show the children the resources that are available for them to use and review some patterns that they have made earlier. Allow time for the children to make and describe their first pattern stripe and then ask them what they think they will do for the next stripe. If they suggest a similar pattern such as an AB pattern, ask them if they could make a pattern that has 3 shapes in it this time. For each successive stripe, prompt to see if the children can increase the complexity. Also, ask the children how many of each shape they used in each stripe and note their strategies for working it out. As the children complete their quilts, you will have opportunities to note: ✒ the types of patterns used ✒ how confidently they describe their patterns ✒ whether they can name the shapes that they are working with


✒ whether number is spontaneously applied to pattern descriptions ✒ strategies used to count the number of items in a pattern or the number of each shape used.

56

133


Pattern Play

4 UNIT

PATTERN STARTER CARDS cards to n r e tt a p e m o s g in n ig s e d Tess has been . go with the pattern blocks tterns? a p r e h e u n ti n o c d n a w llo Can you fo ss. Te r fo d r a c n r e tt a p a ke a Please m Activity Sheet 19

Resources


Pattern starter cards

Pattern blocks, coloured pencils.

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ making and describing patterns

A S S E S S M E N T

✒ continuing patterns ✒ applying number to patterns 134


Observer’s guide Read Tess’s request to the children and ask them to match the shapes with the pattern blocks that are available. The children can then continue Tess’s patterns. Allow time for the children to colour Tess’s patterns to match the pattern blocks that they are using. As the children continue the patterns, observe the strategies that they are using and also note whether they: ✒ identify the pattern unit ✒ correctly continue the sequence ✒ describe out loud the pattern items, number and sequence as they continue the patterns (2 triangles, 1 square, 2 triangles, 1 square, and so on).


The children should plan the pattern they are going to send to Tess before they draw it on the sheet. This will allow for planning but also for you to ask questions about their thinking prior to making a permanent record. Questions such as the following might help some children with fix-up strategies and provide a challenge to others: “What makes this a pattern?”

A C T I V I T I E S

“What comes next in your pattern?” “Will this pattern be too easy for Tess?” “What if you used 3 triangles each time instead of just 1. Would that work?”


57

Unit 5 Number Crunching

Focus The activities presented in this unit provide opportunities for the children to have fun and play games while they develop counting, number recognition and number formation skills. The intention is to develop strong number sense at this level. All too often, number recognition activities are mundane with the numbers atomised and removed from any real purpose or meaning for the children. Children need to see they can do a lot with numbers and that they have many meanings. For instance 3 can mean 3 objects, the third thing counted, the number in the group, 3 times, 3 o’clock or 3 minutes. It can be written in numbers or words and can be shown in different ways, as part-part-whole, with objects, pictures and numbers (1 + 1 + 1, 1 + 2, 2 + 1 or 3 altogether). Understanding that 3 is 1 more than 2, the number after 2, the number before 4 and 1 less than 4 are all part of the development of number sense at this level. Knowing that 3 objects can be put together and then taken apart again (part-whole relationships) also develops intuitively at this level. As the children engage with the activities in this unit, they will: ✒ make connections between their intuitive thinking and more formal number concepts ✒ subitise, count all, count on and intuitively use part-part-whole relationships (for example, there are 2 fish there and 3 fish here so that’s 5 fish altogether) ✒ begin to recognise numbers and use them as labels to name the last item counted and later as quantities (how many in the group altogether) ✒ consolidate and extend their counting sequences to 10 and well beyond for some ✒ develop understandings of cardinality as well as acquire conservation of number.

58


Context This unit has been called Number crunching to create the image of children absolutely loving number sense at this level. Finger rhymes, number clues, number stories and games are the central feature of this unit. When the children engage in fun games and activities, they are more likely to make connections between their intuitive thinking about number and how number is used in everyday life. While they play, they will be solving problems for themselves using available resources, and work out what a number looks like and how to write it. This allows them to actively think about what a number looks like rather than mindlessly tracing over a number already named and given to them as an exercise.

Developmental sequence Children at this early stage in their development of number sense will be moving through the following developmental sequence: 1. random counting, knowing that numbers exist but without knowing the sequence of them 2. perceptual subitising small groups of 3 or 4 objects without any counting involved 3. rote counting, counting fluently but without ascribing any meaning to the numbers (parroting) 4. touch counting, matching the counting sequence to the objects touched (when they are presented in a linear or systematically grouped arrangement) 5. counting out a given number of objects, matching counting to actions and remembering to stop at the designated number 6. developing strategies to avoid double dipping or omissions when counting a random arrangement of objects or dots 7. perceptual subitising, automatically recognising 5 objects or dots when presented as 3 and 2 (part-part-whole) 8. when using numbers to say how many counted, the number is used as a label for the last item counted not for the number in the group altogether 9. using number to show the quantity in the group altogether 10. conservation of number, knowing that 5 objects close together are still the same number when they have been spaced out to look like more.


59

UNIT 5 Number Crunching

P R E P A R A T I O N

PREPARATION AND RESOURCES You will need to: 1. laminate a copy of Resource Card 7 for each child; this can be used as a reference by the children at any stage, helping them to become independent readers and writers of numbers

Resource Card 7 Number formation

2. collect a large bag or box of sorting animals 3. prepare 4 small identical boxes, such as matchboxes or mint tins, each with a different number of small objects in it. 4. make a class number frieze.

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) 1 2 3, Mike Brown, Kingfisher Books. 1 Hunter, Pat Hutchins, Greenwillow Books.

A N D

10 Little Rubber Ducks, Eric Carle, HarperCollins. Mouse Count, Ellen Stoll Walsh, Harcourt Children’s Books. One Bear at Bedtime, Mick Inkpen, Hodder Children’s Books. One White Crocodile Smile, Richard Heffer, Thomas Nelson Australia. Ten Sleepy Sheep, Phyllis Root, Walker Books. The Rainforest Counts! Lisa McCourt, Hinkler Books.

R E S O U R C E S 60

Resource card 7

Related rhymes One, Two Buckle My Shoe Finger Fun



167

Number Crunching

UNIT 55 UNIT

TESS’S PLAY BOX Target strategies ✒ Touch counting and counting out

Resource Card 4 Resource card 4

✒ Numeral and number name recognition

1 2 3

✒ Matching numerals and number names to groups of objects ✒ Comparing group size (more than, less than)

4 5 6

Resources A large box or bag “from Tess” with objects that can be sorted (multiples of farm/zoo animals or plastic sorting toys that can be made into groups of 1–9), number cards, access to a class number frieze.

Number cards

7 8 9 162


Note: New boxes can arrive as necessary for the concepts to begin to develop; you may decide to reduce or extend the numbers being worked with to suit the needs of the children.

The activity Take out the box/bag “from Tess” and create some excitement about this surprise parcel and its contents, particularly the number cards and what they might be for. Allow time for the children to play with the materials with a view to finding out what’s so special about Tess’s surprise box. As the children play, introduce the concept of number if they do not start sorting and comparing, for instance: “What a lot of cows! Do you think there are more cows than any other animal there?” “Which animal do you think there are most of? How could we find out?” “What do you think the number cards are for?”

F R E E P L A Y

Encourage the children to invent and pack their own parcels for other children to try out and send to Tess. Explain that they must have the right quantities and matching number cards in their boxes or Tess will be confused.

Observation As the children sort and play with the materials, observe and note: ✒ the range, efficiency and accuracy of the counting ✒ emerging numeral and number name recognition ✒ language of comparison, more than/less than and methods for checking.


61


NUMBER CARDS Note: Either use only the 1–5 cards on Resource Card 8 to make laminated whiteboards, or use all the cards and extend the questions below to cover 1–9.

Target strategies

r o u t i n e s

2

two

✒ Knowing or being able to find the number before/after/between or 1 more than/1 less than a given number

9

nine

8

eight

7

seven

3

✒ Recognising small groups by their part-part-whole configuration or by their shape configuration

6

three

4

✒ Looking for and describing recognisable shapes in the numerals 1 to 5

six

four

5

✒ Using the 1 to 5 counting sequence to solve number and word recognition questions

Number and Dice

1

one

M e n t a l

Resource card 8

five

✒ Knowing that numbers can be shown pictorially, with numerals or with words

Resource Card 8

168


Closed questions The number I am thinking of has just one straight line. What is it? The die number I am thinking of has a dot in every corner but no dot in the middle. What is it? The number I am thinking of is made from three straight lines. What is it? The die number I am thinking of has a dot in two of its corners as well as one in the middle. What is it? I am thinking of the number after 4. What is it? I am thinking of the number that comes between 2 and 4. What is it?

Open questions The die number I am thinking of has a dot in the middle. What might it be? The number name I am thinking of has 4 letters in it. What might it be? The number I am thinking of has straight and curved lines in it. What might it be? The number I am thinking of comes after 1 but before 5. What might it be?

Flip questions We are going to play a game where you try to find out which die, number or number name I am thinking of. You can ask me questions such as: “Are you thinking of a number die?” “Are you thinking of a number name?” “Is the number you are thinking of between 3 and 5?”

62


Number Crunching

5 UNIT

SPOT COUNT Target strategies

Resource Card 9 Spot count

✒ Subitising and/or touch counting

Resource card 9

✒ Numeral recognition and writing ✒ Comparing group size (more than, less than, most, least, same as)

1st spots

✒ Using part-part-whole to say how many altogether ✒ Ordinal numbers 1st, 2nd and 3rd

2nd spots

Closed questions The first prize cow had 2 spots. Can you draw the spots and write the number 2 in the box?

3rd spots

1

2

3

4

5

6

7


8

9 169

The second prize cow had 1 less spot. How many spots should you draw and write for her? The third prize cow had 2 more spots than the second prize cow. How many spots should you draw and write for her?

M e n t a l

How many spots were there altogether? Can you circle the matching number?

Open questions The first prize cow had more than 4 spots. How many might she have had? The third prize cow had the least number of spots. How many might she have had? How many spots might the second prize cow have? Can you write the numbers to match each cow? How many spots do your cows have altogether?

Flip questions We are going to play a game. First you need to draw spots on the cows and write the numbers to match. Put 3 spots on the first prize cow. Put 4 dots on the third prize cow. Give the second prize cow 5 spots. You may now ask me number questions to find out which cow I am thinking of.

r o u t i n e s

Model questions such as: “Does the cow you are thinking of have the most spots?” “Does the cow you are thinking of have 1 more spot than the first prize cow?”


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GUESS AND CHECK k” boxes. c e h c d n a s s e u “g e m o s t Tess has sen small e m o s n e d id h s a h e h s x o Inside each b to try and s xe o b e th le tt a r y a m u o things. Y we n e h T . e n o h c a e in e r a s g guess how many thin nd check how close your can open the boxes a guesses were. ess and u “g n w o r u yo r e h d n e s ill Then you w trick her. n a c u yo if e e s to s xe o b check” Activity Sheet 20

Resources Four small boxes with lids, small objects for each box such as counters, cotton wool balls (tricky! as it makes no noise) and Unifix cubes; tiny teddies or other plastic counting toys, play money or real coins.

The activity

Activity Sheet 20

Name

Guess and check

Guess

Look

Check

Guess

Look

Check

Guess

Look

Check

1

2

3 Create plenty of intrigue about what objects and how many could be inside the boxes. Make sure that the children know Guess Look Check that guesses are not meant to be right answers and may be 4 a long way off actual answers. Allow time for the children to rattle the boxes and write their guesses. Encourage them to use available resources if they need help writing the numbers for their guesses. The boxes can then be opened one at a time and the surprise enjoyed before checking how many and writing the numbers. Encourage the children to make comments such as “way more”, “way less” and “close” about their guesses. © 2007 Blake Education – Natural Maths Strategies – Beginning Level

135

Remind the children that Tess is expecting to see their guess and check lists so they need to write the actual numbers and draw the correct number of objects in the spaces on the page. Encourage the children to think carefully about what they will pack in the boxes for Tess. Ask them to pack some boxes and trial them on some friends before the boxes are sent off to Tess.

Reflection

unting N0.1 Subitising and co

Ask the children to comment on how close s using small groups of object their guesses were and why some were closer number names. than others. Ask them to listen again to the rattling of the different objects. Ask questions such as “Do the bigger things make it sound like there are more, even though there are not as many of them?” Ask them to predict which objects and numbers of objects might be difficult for Tess to guess easily and to say why. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

Number Crunching 5 UNIT

LIFT-THE-FLAP POSTER ster o p is th d n u fo I , g in n r o m When I came in this bout it waiting for you all. and some questions acame from? How do you Where do you think it ut anyone noticing? think it got here withobeen busy!) (Obviously Tess has Activity Sheets 21, 22

Resources

Activity Sheet 22

Name

Follow the instructions on Activity Sheet 21 to make the poster, rubber or foam stamps, paint, scissors.

Lift-the-flap poster (2) Activity Sheet 21 Name

Lift-the-flap 1oster (1)

The activity Show the poster to the children, demonstrating the way in which ducks are hidden behind each flap. Involve the children in the questions about the poster, lifting the flaps to find combinations of birds that are equivalent to, say, 4. Ask the children to look for a way that lifts only 1, 2, 3 or 4 flaps. Enjoy the children’s surprise as they realise that there is more than one way of lifting the flaps to show 4 birds. Engage them in describing what is under the flaps in terms of part-part-whole statements, for instance:

Cut around the black outlines of the previous activity sheet and paste the whole sheet onto this sheet to make a lift-the-flap poster. © 2007 Blake Education – Natural Maths Strategies – Beginning Level

136

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“There are 2 farm birds here and here’s 1 and here’s another 1 so that makes 4 altogether.” If necessary, encourage counting on rather than counting all by pointing at the first 2 and saying “Here’s 2, (counting on) 3, 4.” Ask the children to make predictions about the following: “How many or in what different ways do you think you could find 3/5 birds?” “How could you keep a record of the ones we have found so that we will know when we have found all the ways?” The children may suggest drawing the birds for each with numbers, or with numbers alone. Allow time for them to try out their methods. Suggest to the children that the class should make and test some lift-the-flap posters. They could leave them out one night to see if a certain somebody collects their posters in exchange.

Reflection When using the original poster or the ones that the children have made, focus on: ✒ how easily some groupings are to “subitise”

P R O B L E M A T I S E D

that groups N0.2 Understanding e larger can be joined to mak to make groups and separated smaller groups.

✒ count-on strategies

S I T U A T I O N S

✒ describing the combinations and emphasising “how many altogether” about the questions.


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JUMPING FROGS e m o s d n a s d r a c e r tu ic p e Tess has sent us thes to know if you are as tricky clues. She wantsu are. smart as I told her yo Clues: . d r a c e th n o s g o fr r u fo n There are more tha Three frogs are jumping. Two frogs are sitting. Activity Sheets 23, 24

Resources

Frogs Activity Sheet 23 Name

Cards cut from Activity Sheet 23, scissors, glue.

Jumping frogs

The activity Display the cards and read the clues to the children one at a time allowing them to talk about which card might be eliminated or the correct card and to say why. Continue reading the clues until the children have identified the correct one. Repeat the process a few times with another card/s. Then invite the children to make up clues so others may guess their card.


139

When the children are ready, explain that Tess has also sent some frog sheets for them to cut out and make their own clue cards with. The children will choose their own number of frogs for each card. Explain that you will write their clues for each card for them when they are ready. Then the cards will go to Tess for her to try out. Remind the children that the jumping frogs are up in the air and the sitting frogs are down on the ground which makes it easy to see how many of each are on each card. 138

Reflection Use the children’s cards and clues at the reflection. Ask the children: “What were some of the useful clues?” “Which clues didn’t help?”


that groups N0.2 Understanding e larger can be joined to mak to make groups and separated smaller groups.

“How did you know which ones to eliminate?” “What were some of the fast counting strategies you used?”

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Activity Sheet 24

Name



TESS’S FINGER FUN e has sent h s ” n Fu r e g in “F e m y h r e Tess loves th we try ll a h S . it h it w ys la p e h s e to us and the gam with it? Tess wants to know it and see how we go vourite finger numbers are. what some of your fa Activity Sheet 25

The activity


Finger Fun

Introduce the first part of the rhyme to the children and involve them in explaining quick ways of working out how many fingers. Encourage subitising and counting on rather than counting all the fingers one by one. With this in mind, begin with small numbers such as 2, 3 and 4 altogether. This will allow the introduction of terms such as:

Part 1 Fingers like to play,

(wiggle the fingers of both hands)

Fingers like to hide,

(hide fingers behind your back)

Fingers like to give us all A great big surprise!

(hands to front, all fingers showing) (hide hands behind back)

Watch very carefully when fingers come out to play.

(bend some fingers down and bring fingers out now)

How many fingers? Can you say?

(This part can be repeated until the children are subitising the number of fingers)

“It’s a double!”

Part 2

“Double two is 4.”

Fingers like to give us all

Fingers like to play,




A great big surprise!

The intention is to immerse the children in early strategies for combining small groups so that they do not rely on or overvalue counting all.

(hands to front, all fingers showing) (hide hands behind back)

Ready now to guess As fingers come back into sight. Show how many fingers! Were you right?

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(bend some fingers down and bring fingers out now)


Introduce the second part when the children are ready. There is a variation here because the children try to guess how many fingers the speaker will put out. After the line “Show how many fingers!” they put their fingers out and compare whether they are the same number, more or less than the speaker put out. Some children will be able to say that they were 1 away or 2 away. You might want to give clues so that the children can work it out. Clues could include, less than 5, more than 5, between 4 and 8. As the children improve with this, be a little tricky and hold up no fingers on one hand. Note the children’s responses. Tell the children that Tess wants them to send some finger fun pictures. Their task will be to choose a favourite number and a favourite way of showing that with fingers, to write the number and draw the picture. Some children will want to do several numbers and ways of showing them.

Reflection Use the children’s work samples for the reflection and encourage them to talk about:


✒ what the most popular numbers were ✒ different ways of showing the same number ✒ fast ways of working out how many fingers are showing in each picture.




RACE TO 9 Note: The games given below cover the numbers 1 to 9. They can be restricted to a smaller range if necessary. A game for 2 to 4 players

Resource Cards 10, 11

Resources

Resource card 11

Sets of laminated cards made from Resource Cards 10 and 11 (3 sets for 2 players, 4 sets for 3 players or 5 sets for 4 players).

How to play

Words, numbers and dice cards (1)

six

Resource card 10

6

one 1 seven

7

two 2 eight

8

three 3 The object of this game is to be the first player to have nine 9 collected all of the numbers 1 to 9 and to have placed them in the correct sequence 1 to 9 in front of them. four 4 The cards are spread face-down in a pool on the table, and overlaps and pile ups do not matter. Players take five 5 turns to pick a card and, if it is one they need, put it face-up in front of them in the place where it belongs in their sequence. As the children gain experience with this game, encourage them to count places to find the position for a card even if it is the 7 and only the 2 has been placed so far. This will encourage them to be systematic as they play. 172

g a m e s




171

If a card is not needed, it can go back into the pool which is given a swirl around.

Variation If the children are able to count down from 9, the sequence can be reversed so 9 is placed in the beginning position of the sequence each time.

A FULL SET A game for 2 to 4 players

Resources 1 set of laminated cards made from Resource Cards 10 and 11 for 2 players (3 or 4 players will need two sets).

How to play The object of this game is to be the first player with a full number family set, that is, any number and its matching number name and dot picture. The players are each dealt 4 cards. The pool of cards is placed face-down in a pile on the table. Players take turns to pick up a card from the pack, decide whether to swap it for one in their hand or to discard it as they try to make a matching set of 3 cards. The discard pile is set to one side for reuse if necessary after the pack has been used up.

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Number Number Crunching Crunching

5 UNIT

FILL THE BOX Resources A small box (matchbox or mint tin size) for each child, another small box filled with up to 5 small objects so that there is room for the children to increase the number in their own boxes later.

The investigation Tell the children that Tess has sent this box with small objects in it. She wants to know if they can pack more small things into a matchbox than she can. She says we could have a class record for the most things inside the box. Pass the box around so that the children can feel how heavy it is and listen to it rattle. Ask them how many things they think Tess managed to pack into her box. Open the box, count the things and make a pictorial list of the objects with the total beside it. Brainstorm with the children what small objects can be found around the room, focussing on comparative size with comments such as: “There must be something even smaller.” “That’s the smallest thing yet.” Explain to the children that they will investigate different combinations of things inside their boxes until they are happy that they have packed the most things possible in a box. Suggest that they keep a record of their attempts by making a pictorial list of the items and their number each time, in case they forget what their best attempt was. Explain that their best box will be sent to Tess.

Reflection Use the children’s recordings rather than their actual boxes for the reflection, if possible. Ask them to look at the written numbers to compare group sizes initially, encouraging comments such as: “8 is more than 6.”


“7 is one less than 8.” Use the pictorial lists as a check that the numbers are correct and engage the children in strategies for: ✒ counting all without missing any or double dipping when using a disorganised list (this could include making a small mark on the objects counted) ✒ subitising (if the layout permits) and then counting on.


69


HANDFULS A S S E S S M E N T

w how a r D . s y to g n ti r o s f o l fu d Take a small han number. e th e it r w d n a g in ld o h e r many you a er this w fe r o e r o m ke ta u yo if Try again and see time. Activity Sheet 26

Resources Small sorting toys such as counters, tiny teddies, Unifix cubes or anything that is not so small that the children will have too many to count.

Handfuls

Prior experiences

How many?

How many?

The children will be ready for this activity if they have had experiences with: ✒ guessing how many objects in a small group ✒ touch counting and counting out ✒ subitising and counting on

A C T I V I T I E S

Activity Sheet 26

Name


141

✒ writing numbers

Observer’s guide Explain to the children that they will take a handful of small objects in their left hand (not a big grab), have a quick look and guess how many before working out how many. Then they will draw the objects, add colour and write how many. Then they will do it again and compare both handfuls. Observe the children as they estimate and ask them how they know they made a good guess. They may look at the size of the objects, how much space they occupy in their hand or subitise the actual amount. Observe as they draw and work out how many objects, as this will give insights into their counting strategies. Some children may sort before they draw or arrange them into easy-to-count groups (for example, 3 in a row on top and 3 in a row underneath). As the children work, ask questions such as: “If I spread these out a bit like this, is there the same number now or more? How do you know?” “Why did you set the objects out in that way?” “Is there another way you could count them?”


“Do you have more/less or the same number in your second handful? How do you know?” “Can you tell me without having to count whether there are more red things in this handful or this one?”

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MAKING SNOWMEN Prior experiences

Activity Sheet 27



Making snowmen Each snowman needs:

✒ comparing group size by counting or one-to-one matching

A hat

A cane

A bow tie

Two buttons

✒ identifying how many more than/less than ✒ writing numbers What extra items do the snowmen need?

Observer’s guide Show the children the activity sheet and read it to them. Ask them which snowmen already have a hat and which ones are still waiting for hats. Explain that their task is to find out and to show what other items are needed to complete Tess’s snowmen.

142


There are several ways of completing this activity but do not suggest any to the children until they have had time to think for themselves. They might: ✒ draw some extra hats and then match lines to the snowmen, adding more hats or crossing off hats if they have drawn too many ✒ draw the missing items twice, once onto the actual snowmen and once in the box ✒ count the snowmen, count each item and draw the missing ones by counting up from the starting number, for example, from 2 hats, 3 hats, 4 hats, 5 hats ✒ simply write the numbers of missing items with pictures or words as shown in the list on the page. As the children work, observe their counting strategies, comparison skills and descriptions of differences. For example: “The snowmen only need 2 more bow ties.”




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Unit 6 Shaping Up

Focus Children at this stage are still at Level 0 in their geometric thinking, according to Pierre van Hiele. Although they may be beginning to name 2-D shapes and identify where they occur in the environment, they are not really focussing on their properties. The children will have sorted by shape in the sorting and pattern units, however they still need a nudge towards noticing what makes two shapes different or the same as each other. Using explicit language to describe examples of a particular shape will focus attention on the actual properties of a shape. Comparisons and descriptions of number of sides, number of corners and length of sides will help move the children towards level 1 of van Hiele’s developmental sequence of geometric thinking. As the children begin to manipulate, fold, cut, draw and observe changes made to shapes, they will: ✒ explore the properties of 2-D shapes ✒ use the language of 2-D shapes (circle, round, square, rectangle, straight, diamond, corner) ✒ apply number to the description of shapes ✒ experiment with ways of changing shapes ✒ begin to create mental images of shapes and actions on them ✒ identify the main shapes in pictures ✒ copy and draw shapes.

72


Context The context for this this unit is Shaping up. The children will be given opportunities to manipulate shapes, rotating them, flipping them and looking at them from many angles. They will be encouraged to copy and draw shapes, fold them to create new shapes and to cut them to change the shapes. Incidental learning will include matching shapes to everyday objects that have those shapes. All too often when children engage in shape activities, they focus on the general rather than the specific properties of shape. Visualising images of shapes and changes to them is an important aspect that needs to be developed. Involving the children also in drawing shapes and shape pictures from observation and from memory will help develop their ability to create mental images.

Developmental sequence Children at this stage of their development are beginning to: 1. know the names of common 2-D shapes 2. notice the specific properties of 2-D shapes 3. make connections between 2-D shapes and where they occur in the environment 4. create mental pictures of shapes and changes to them after folding, cutting and manipulating them 5. make reasonable attempts at drawing circles and squares, triangles and diamonds 6. select and arrange shapes to make shape pictures.


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UNIT 6 Shaping Up


PREPARATION AND RESOURCES You will need to: 1. collect pattern blocks, attribute blocks, tessellating tiles, gummy paper shapes, stencils, templates and stamps 2. make paper squares approximately half an A4 sheet in size and prepare a square folded a few times with the shapes coloured in 3. prepare a shape card cut in the shape of a circle or triangle with shape pictures on it and an envelope obviously made by just folding and sticking to make a pocket with a flap (not professional looking) with a drawn stamp at the top right-hand corner

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) Shapes, Shapes, Shapes, Tana Hoban, Sagebrush Education Resources. Ship Shapes, Stella Blackstone and Siobhan Bell, Barefoot Books. The Shape of Me and Other Stuff, Dr Seuss, Random House Children’s Books. The Surprise Party, Pat Hutchins, Simon & Schuster. When a Line Bends – A Shape Begins, Rhonda Gowler Greene, Turtleback Books.

Related rhymes Square

Circle

I have four sides

I’m made from one line

They’re all the same,

That goes round and round,

Yes you have guessed it

I’ve got no corners

I’m a square.

Where am I found?

Use your hands, Make two corners and you will see,

I’m made from one line

You can make a square just like me.

That goes round and round, I’ve got no corners Now you can trace me on the ground.


Shaping Up

UNIT 66 UNIT

FREE PLAY Target strategies ✒ Naming and recognising common 2-D shapes ✒ Selecting and arranging shapes to make designs and shape pictures ✒ Tracing around shapes and stencils

Resources An assortment of shapes and shape materials such as pattern blocks, attribute blocks, tessellating tiles, gummy cut-out shapes, templates and stencils.

The activity Encourage the children to play with the materials and to make pictures and designs with them informally. As the children play, scaffold their learning by immersing them in the names of the shapes and pointing out their properties as well as new shapes that are made by joining two or more shapes together. Challenge the children’s play and thinking by asking “What if” questions such as: “What if we join these two rectangles along the long edge? What will the new shape be?” “What if we join four of these squares together? What different ways could we do that?” “What if we wanted to make a robot/house/truck? Which shapes would we use?” “What if we turn this triangle so that the point is at the bottom? Will it still be a triangle?” “What if we join all of these squares at the corners instead of along the sides?” Encourage the children to suggest some “What ifs” to investigate too. As the children play with the shapes, encourage them to make a copy of any design or picture that they are satisfied with by using sticky gummed shapes or by drawing it, or alternatively, a digital photograph can be used to keep a record.

F R E E P L A Y

Observation As the children play and talk, observe and note: ✒ the shapes that they recognise and can name ✒ which properties of the shapes they refer to and describe ✒ how responsive they were to the “What ifs” posed to them ✒ decisions that they make when creating shape pictures and designs. The observations that you make will inform planning in terms of: ✒ challenges and “What ifs” to pose next time ✒ vocabulary and properties needing to be addressed next time.


75

UNIT 6 Shaping Up

SHAPES ALL AROUND US Target strategies ✒ Recognising and naming 2-D shapes

Resource Card 12 Shapes all around us

Resource card 12

✒ Connecting 2-D shapes with shapes in the environment ✒ Identifying and naming the properties of 2-D shapes


76

Closed questions I am thinking of a rectangle that you use to pay for things. What is it?

11

12

1

10

2

9

3 4

8 7

6

5

I am thinking of a triangle that tells us there are men at work. Which one is it? I am thinking of a circle. I have one in my pocket. What is it? © 2007 Blake Education – Natural Maths Strategies – Beginning Level

173

The shape of this object is a rectangle. I would use it when I go shopping. What is it? I am thinking of a square that you could look through. What is it?

Open questions The shape I am thinking of is a triangle/square/rectangle/circle. What might it be? I am thinking of a shape that has 4 sides all the same length. What might it be? I am thinking of some money. What shape might it be? I have only 3 sides and 3 corners. What might I be?

Flip questions I am thinking of one of the objects on this card. You may ask me questions to find out what it is. Questions could include: “Is it a triangular shape?” “Does it have 4 sides and 4 corners?” Before letting the children ask their own questions in this way, model the types of questions and how to cross off the items eliminated.


Shaping Up

6 UNIT

SHAPE PICTURES Target strategies ✒ Recognising and naming 2-D shapes

Resource Card 13 Shape pictures

Resource card 13

✒ Noticing and identifying shapes in a range of orientations in shape pictures ✒ Combining number with shape to identify shapes and shape pictures

Closed questions I am thinking of a part of the horse’s body. It has no corners or straight edges. What is it? I am thinking of the big diamond shape. Where is it?


175

I am thinking of a big triangle made from two smaller triangles. Where is it? I am looking at three small rectangles all in a row. Where are they?

Open questions I am thinking of a four-sided shape. What might it be? I am thinking of a shape with three corners. What might it be? I am not a small rectangle. Which rectangle might I be? I am a small shape on the boat. Which shape might I be?

Flip questions I am thinking of one of the pictures on the page (horse, kite or boat). You may ask me questions about the shapes and the number of shapes to find out which picture I am thinking of. Model questions such as: “Does the picture you are thinking of have more than two circles in it?” “Does the picture you are thinking of have more than two diamonds in it?”



77

UNIT 6 Shaping Up


FOLDING PAPER SQUARES ut o it s n e p o n e th d n a e r a u Tess folds a paper sqhe has made. Then she to see what shapes s fold lines. She opens it up refolds it to make newe what new shapes she has and looks again to se hat she has made she now. When she likes w he sent us this one. colours the shapes. S

Resources Squares of white paper (15 cm squares will allow 2 to be made from a sheet of A4 paper), coloured pencils, black felt pen, a sample of Tess’s paper folding with black outlines and coloured shapes.

The activity Tell the children about Tess’s paper folding and show them her coloured sample. Demonstrate the process of folding and opening the paper to see what new shapes have been made by the folds. Engage the children in trying to visualise and predict what new shapes there might be. Their guesses might be inaccurate because the children will not be experienced at this. It is important that you model this thinking and visualising process which the children need to adopt when they make their own paper folds. There will be shapes that the children have not seen before, so demonstrate the process of looking at and counting the number of sides and corners each time. If appropriate point out the long sides and short sides of the shapes. Name the shapes even though you do not expect the children to remember the names. Suggest to the children that they use a black felt pen to draw the fold lines before they colour in just like Tess did. Allow time for the children to fold and refold, and to colour the shapes so that they can send them to Tess.

Reflection Share the folded designs and compare two at a time in terms of:


✒ whether they have any of the same shapes in them ✒ how many shapes they each have ✒ the size of the shapes made, particularly in relation to the number of folds (some children will think that more means bigger and expect more folds to result in bigger not smaller shapes being made) ✒ whether any are the same on one side (half) as the other (some children will notice simple symmetry in the designs).


Shaping Up 6 UNIT

TESS’S SHAPE PICTURE s made a h e h s t a th e r tu ic p is th Tess sent us make n a c e w if w o n k to ts n a w from shapes. She a picture like this.

Resources Make a shape picture to match the one on Activity Sheet 28 or make up one of your own to match the materials at hand but make sure that some shapes are put on top of others, gummy paper shapes or felt shapes and a felt board.

Activity Sheet 28 Activity Sheet 28

Name

Tess’s shape picture

The activity Show the children the shape picture. Ask them the names of the shapes used and which shapes were used first. In effect this is helping the children to see which shapes are the most important and need to be used first when planning their own shape pictures.


143

Encourage the children to match the shapes that Tess has used and to have a go at copying her picture before they try one of their own. This will allow you to observe how well they match the shapes. It will also allow insights into the effectiveness or otherwise of their planning processes. Some children will need assistance to work out that the two most important shapes to find and use first are the 2 large squares. Be prepared to make suggestions if the children cannot think of something to create a picture of. Trucks and boats are fairly simple to visualise, whereas finding shapes to create an animal or a fish may be more difficult. If felt shapes are used, you may want to take digital photos of the finished products for the e-portfolio.

Reflection

ising 2-D and 3-D

S0.1 Recogn When using the children’s pictures for the shapes by name. reflection, focus on the identifiable shapes and the ways in which some shapes have been used to match an aspect of the object depicted, for example, a triangle used for a roof. Also ask the children to guess which shape was placed on a picture first and to say why.



UNIT 6 Shaping Up


SQUARES AND TRIANGLES cks. She lo b n r e tt a p e m o s h it w g in Tess was play res and a u q s d e s u e h s n e h w t a noticed th with no r e th e g to d e tt fi s e p a h s triangles, the she if d e r e d n o w e h s n e h T . n spaces in betwee ern with just squares and could make a big patt u think? triangles. What do yo

Resources Pattern blocks, digital camera for record keeping (optional). Note: The example given starts with an inside shape (which can be just about anything you like made with squares and triangles) and then a ring of squares and triangles added around the edge. A simpler alternative would be to join strips made alternately with squares and triangles, but that is rather restrictive and doesn’t lead to much variation.

The activity Show the children the way to join the triangles and squares with no gaps. Ask the children whether they think the mixing of squares and triangles would allow a big area (show something about A4 size) without ever leaving a gap. Ask for reasons to support their comments. The options are: ✒ squares on their own joining without leaving gaps ✒ triangles on their own joining without leaving any gaps ✒ strips of squares and triangles (as mentioned above). Allow time for the children to explore ways of joining the triangles and the squares and to see if the joins will work over a larger area. When a method does not work, discourage the children from scrapping the design before they have back-tracked a few steps. Most times it will be easy to remove a few blocks and to find a way in which the existing design can be fixed up. You might assist by asking “What if” questions: “What if you took this triangle away?” “What if you put a triangle just here instead of a square?” A permanent record of the designs can be made with the digital camera. The photos will make an excellent resource for the reflection, and the blocks can be packed neatly away.

Reflection Ask the children to comment on what they discovered and to demonstrate their methods of joining squares and triangles. They may be surprised by the many different ways of combining the two shapes, so make the most of this by referring to what they have discovered about squares and triangles. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

Shaping Up 6 UNIT

THANK YOU TESS ld all u o h s e w k in th I ? k in th I t a Do you know wh r all fo u yo k n a th y a s to d r a c send Tess a shape as that she sends to us. the problems and ide

Resources Gummy paper shapes, shape stencils, stamps, templates or pattern blocks, coloured pencils or felt pens, paper for a card or an envelope, prepared shape card with shape pictures and roughly folded envelope with a flap and drawn stamp.

The activity Explain to the children that they are each going to make a shape card that you will be sending to Tess. Show them the one that you have made and also the envelope. Explain that you just folded it carefully to fit the card inside and left a flap to close it with. Explain that the children can select from the available resources to design and create their own cards and not to worry if they make a mistake because there are plenty of materials. The intention is not for the cards to look alike but rather for the children to experiment with using shape to create designs and fold paper to make an envelope. A wide range of skills and expertise will be employed so all efforts should be appreciated. Be prepared to assist some children to get started on the card or the envelope by asking questions such as: “What shape will you make your card?” “What picture did you make with shapes the other day?” “Where could you fold the paper to make the pocket part of the envelope?”

Reflection

gnising 2-D and 3-D

S0.1 Reco Share the results and focus on the shapes shapes by name. and designs made. Ask the children to talk about any problems they had when designing and making their card and envelope. Also ask them to comment on the ways in which some of the envelopes were folded. Try testing some of the envelopes. Ask the children if there were any ideas they liked. Then, if they wish, they may like to make shape cards for their friends over the next few days.



UNIT 6 Shaping Up

FILL THE SHAPES A game for 2 to 4 players

Resources

Resource Cards 14, 15

Tiles made of card cut from Resource Card 14, a game board for each player made from laminated Resource Card 15, a shape die made by sticking 2 of each tile onto a wooden block.

Resource card 15

Tile shapes

Shapes game board

Resource card 14

How to play

g a m e s

The object of the game is to be the first person with all the shapes on their boards filled. Players take turns to throw the die and take a tile to match the shape showing. They may then place that tile onto one of the shapes on the board. As the children get the hang of the game, encourage them to think carefully about where to place each tile. Triangles can be used to fill up little spaces but the rectangle can only be used in a big space so it makes sense to try to wait for a rectangle for the big spaces.

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Note: You will need to allow time for the children to cover the shapes in different ways and to make some relationships, such as two squares make a rectangle, before they begin to play.

FILL THE BORDER A game for 3 or 4 players

Resources Tiles as above and a game board (Resource Card 15) for each player, feely bag with one of each tile in it.

How to play The object of this game rather like the earlier game is to be the first player to fill their board. One player is the caller. That player puts their hand into the feely bag, quickly pulls out a tile without showing it to the other players and names and describes it to the other players. The shape is then replaced in the feely bag. The players take a matching tile and place it on their game board. As they become adept at this game, they may make strategic decisions as to where to place their tiles. You may want to sit in as a player and think aloud about where or where not to place a tile. Again the triangles can fill up small spaces but the rectangles will have to be placed carefully.

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Shaping Shaping Up Up

6 UNIT

THE SHAPE HUNT ll a g in w o h s t r a h c r e v -o ld Tess has sent us this efofound on her detective of the shapes that sh we won’t know what shape hunt. She says use they are hidden behind objects she saw beca know what shapes we the fold. She wants toon a detective shape hunt. would see if we went Resource Card 16

Resources

Shapes and objects card

Resource card 16

Photo-enlarge Resource Card 16 to make an A3 size chart, detective props if necessary to increase interest, large sheets of paper.

The investigation Show the children the back of the chart after folding the shapes back so that the actual objects are not visible to the children.

Happy Birthday

Ask the children to predict where Tess might have seen each of the shapes or what objects they might have been. There are some new shapes here, so allow time for the children to talk about them and their properties (the spiral goes round and round). Uncover the actual things seen by Tess and enjoy any surprises, similarities and differences between what she saw and what the children might see when they are being shape detectives. fold line


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Give the children large sheets of paper but do not create a chart for them; see if they do this for themselves. Remind the children that Tess found some unusual shapes as well as the ones we have been looking at. The children can become shape detectives and go on their own hunt now and create their charts.


Reflection Use two or three work samples for the reflection and ask the children to: ✒ comment on what shapes are the same and different in each one ✒ say where in the room or outside they think the shapes were found ✒ comment on what unusual shapes were found, where they were found and to describe them in terms of their properties.


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UNIT 6 Shaping Up

COPY THAT TRUCK A S S E S S M E N T A C T I V I T I E S

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Prior experiences

Activity Sheet 29



Copy that truck fold back

✒ drawing shapes ✒ making shape pictures ✒ copying shape pictures

fold over

✒ naming and recognising 2-D shapes

Observer’s guide Show the children the picture of the truck on the activity sheet that was drawn by Tess. Ask them to name the shapes and to say which shape they think Tess drew first and why. Ask them to copy the truck into the first space that Tess has left for them.

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Talk about what was easy and what was hard about copying it. For some children planning which shape to start with will be hard. They may, for instance, draw the wheels first and then have difficulty organising the small square and the large square to join up properly. They will learn from this experience and probably fix up their mistake in the second part of the activity. Some children will have difficulty with their fine motor skills and find it hard to draw the shapes. Some children will draw disconnected shapes, in which case there is no way they will manage the second part of the activity. Instead, help them look to find which shapes are connected to each other, which is the biggest shape and so on. Some students will need ongoing help learning to identify the key features and connect shapes one to another. You may also need to assist some to draw their truck. Fold over the top part of the page along the dotted line so that both trucks are hidden. Now ask the children to draw the truck from memory in the bottom box. For many children this will be an improvement on their first attempt. Ask the children to explain what they were thinking and remembering as they drew the truck the second time. They will make interesting comments about shapes, sizes, position and joining.



Shaping Up 6 UNIT

FAVOURITE SHAPES ide an s e b s e p a h s e it r u o v fa r e Tess has drawn h object that she likes. s and e p a h s e it r u o v fa r u yo f o Show some objects. Activity Sheet 30

Prior experiences

Activity Sheet 30

Name

Favourite shapes


I like triangles and circles.

That’s why I like Ice-cream

✒ naming and recognising 2-D shapes ✒ matching 2-D with shapes in the environment

Draw your own favourite shapes and objects.

✒ drawing shapes and shape pictures

Observer’s guide Read the information on the activity sheet to the children and talk about the shapes that Tess has drawn to show her ice-cream. Ask them to think about some of the shapes they like and where they are found. Allow time for them to go for a walk around and remind them of the shape detective investigation if necessary. For some children, identifying just one shape and its location will be enough but for others challenge them to think of more than just one favourite shape. © 2007 Blake Education – Natural Maths Strategies – Beginning Level

As the children think, talk and draw, you will be able to note: ✒ which shapes they do recognise and can name ✒ how effectively they describe the properties of the shapes that they identify ✒ whether they can describe irregular shapes in terms of straight sides, curved sides, number of corners and numbers of sides and corners ✒ whether they can draw reasonable copies of the shapes and objects that they identify.



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85

Unit 7 Measuring Up

Focus It is second nature for even young children to want to measure and to compare things by size – heavy/light, long/short, full/empty, deep/shallow and bigger/smaller. Often as they play, they can be heard making comments such as “This one’s bigger”, “I want the long one” or “Mine is the widest”. At this stage children need opportunities to compare size by direct comparison and by using informal units. Usually as they make comparisons and judgements, young children use only one attribute. A tall, thin container is deemed to be bigger than a larger, short wide one. Similarly a large box is judged to be heavy even without hefting whereas a smaller box is deemed to be lighter even though it might have a heavy object inside it. Conservation is slow to develop and children need many hands-on opportunities with materials to develop this concept. As the children engage in the activities presented in this unit, they will: ✒ use direct comparison to compare size ✒ use informal units to measure ✒ fill and empty containers ✒ explore best fit ✒ pick up and heft items to compare mass ✒ discover that there are many things to measure and many ways of measuring them ✒ begin to use comparative language such as big, bigger, biggest.

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Context The context for this unit is Measuring up. As the title suggests, the children will engage in a range of comparison and measuring activities. They will explore what can be measured, (mass, height, length, distance, capacity, time, temperature) and how they can be measured. They will also be making direct comparisons as they seek best fits. As they do so, they will engage in the language of comparison and discovering the dimensions that can be measured, thereby laying down the foundation for conservation of size and capacity.

Developmental sequence Conservation is a complex idea that children develop slowly over a long period of time. It cannot be taught but it can be encouraged through appropriate activities that allow children to: 1. make direct comparisons between two objects and use language such as small/big, full/empty 2. use objects and counting to assist in measuring 3. order objects by size or by estimated size 4. make direct or measured comparisons of three objects and use the language of comparison such as small/smaller/smallest, big/bigger/biggest 5. consider space and number together so that when a book is found to be the same length as a pencil, a visual image is made of the distance measured 6. realise that when we measure length or distance, we are measuring the length between two points.


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UNIT 7 Measuring Up


PREPARATION AND RESOURCES You will need to prepare: 1. dress-up clothes, finger puppets or soft toys suitable to use with “Goldilocks and the Three Bears” or “The Three Billy Goats Gruff” 2. junk modelling materials, glue, adhesive tape 3. collections of objects with characteristics such as small, large, heavy, light, long, short, big, small. 4. string, knitting wool, tape measures, crepe paper, coloured card, tape, glue, scissors, rice, sand and water 5. containers of different shapes and sizes with measuring cups and spoons of different sizes 6. bears each a different size 7. counters.

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) Tell Me What It’s Like to Be Big, Joyce Dunbar and Debi Gliori, Doubleday Books. Big Dog, Little Dog, P.D. Eastman, Random House Children’s Books. Blue Sea, Robert Kalan, HarperCollins Children’s Book Group.

Related stories Goldilocks and the Three Bears The Three Billy Goats Gruff The Enormous Turnip


Measuring Up 7 7 UNIT UNIT

FREE PLAY Target strategies ✒ Using the language of comparison ✒ Using size as the criteria for sequencing character and prop size ✒ Using size to create props to match characters

Resources Several materials for the children to create props with when dramatising the familiar stories Goldilocks and the Three Bears or The Three Billy Goats Gruff; these could include clothes for dress-ups, construction materials or junk materials, and simple finger puppets or soft toys to match the characters in the stories.

The activity First familiarise the children with the traditional stories and the repeating lines. Then tell them that you have put out a collection of things that they could use to act out the story or make up a similar “size” story of their own. Allow time for the children to create props with the materials or to create settings with the construction materials.

F R E E

As the children play, encourage them to use direct comparison through questions such as: “How do you know that the big bear will fit in that bed?” “Which is the baby bear? Why?” “How could you make a big bed out of these blocks/boxes?” “Will this bridge be strong enough for the Big Billy Boat Gruff to trip, trap over?”

Observation

P L A Y

As the children play and act out the stories, observe and note: ✒ the language of size and comparison that they are effectively using ✒ measurement strategies (direct comparison, estimation, using actual objects to measure with) ✒ which attributes of an object are used to make decisions about size ✒ whether more than one criteria is used when making comparisons.


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UNIT 7 Measuring Up

THE THREE BEARS Target strategies ✒ comparing size

Resource Card 17 The Three Bears

Resource card 17

✒ comparative language big/bigger/biggest ✒ small/smaller/smallest, middle-sized


Closed questions Which is daddy bear’s bed? Which is baby bear’s chair? Which porridge is the hottest/coolest? The bear I am thinking of is the smallest bear. Which one is it?

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The chair I am thinking of is the smallest. Which one is it? The bed I am thinking of is the middle-sized one. Which bed is it?

Open questions The porridge I am thinking of is not the hottest porridge. Which porridge might it be? The bear I am thinking of would be too big for baby bear’s bed. Which bear might it be? I am not thinking of the smallest bed. Which bed might I be thinking of? The bowl of porridge I am thinking of is not the emptiest. Which bowl of porridge might it be?

Flip questions I am thinking of one of the bears and your job is to find out which one. You can’t ask me questions about the bears but you can ask me questions about the bear’s belongings. Model the types of questions for the children: “Does your bear have the hottest porridge?” “Does your bear have the smallest bed?” “Does your bear have the middle-sized bed?”

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Measuring Up

7 UNIT

HEAVY AND LIGHT GRID Target strategies ✒ Using the language of comparison

Resource Card 18 Heavy and light grid

✒ Comparing objects by hefting

Resource card 18

heavy

✒ Comparing objects using 2 attributes (size and mass)

light

✒ Using a grid to locate objects small

Closed questions Try to match the pictures with real objects and allow time for the children to heft and compare objects prior to the routine.

bigger

biggest

Where on the grid are all the light (heavy, small, bigger, biggest) things?


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Where on the grid would I find something that is the biggest (smallest) and the heaviest (lightest)? I am thinking of something that is small and heavy and made of glass. What is it?

M e n t a l

Where on the grid would I find a middle-sized, light object?

Open questions I am thinking of a light object. What might it be? The object I am thinking of is not one of the biggest. What might it be? The object I am thinking of is bigger than a marble but smaller than a torch. What might it be? I am thinking of one of the heaviest objects. What might it be?

Flip questions I am thinking of one of the objects on the grid. You may ask me questions to find out what the object is. Model some questions and the elimination process for the children initially, for example: “Is the thing you are thinking of one of the light things?”

r o u t i n e s

“Is the thing you are thinking of round and made of glass?”


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UNIT 7 Measuring Up


TEDDY ACCESSORIES d a e h d n a s e v r a c s , s lt e b Tess has been makingd her three teddies. She bands for herself an too but we need to make says we should try it perly so the things we sure we measure prosize. make will be the right

Resources String or knitting wool, tape measure, paper strips, crepe paper, scraps of coloured card, adhesive tape, glue, scissors, teddies of different sizes.

The activity Tell the children what Tess is doing and ask them to explain how to measure a teddy (or a person) for a fitting so that outfits can be made to the right size. Tape measures have been listed in the resources not because the children are going to be taught how to use them but because in the real world this is what tape measures are used for and some children will want that touch of realism in their play. If necessary, prompt as follows: “I have some knitting wool here. How might that help us work out the correct sizes?” “Have you ever seen someone being measured? What do they do?” “This is a tape measure; do you know what this is for and why it has numbers on it?” Allow time for the children to experiment with measuring and with cutting and making the items for the bears. Let them try on the accessories and create any fix-ups that are needed before reflecting on the processes used.

Reflection After the children have made the teddy accessories to fit, discuss what has worked/not worked. Ask the children:

and M0.1 Using informal to comparative language s. as describe size and m

✒ how initial measurements were made ✒ how the string, knitting wool or tape measure proved useful or not useful ✒ whether they were surprised by the difference in the sizes of the belts, scarves and headbands and why? Compare the items made and involve the children in direct comparisons of length and fit on each bear. The children may now make some dress-up accessories for themselves. Do not rule out variations that the children might suggest such as Batman capes or Red Riding Hood capes.


Measuring Up 7 UNIT

THE RIGHT-SIZED CONTAINER cks ilo ld o G f o y r to s e th t u o Tess has been acting . She has three but she has a problemnot know how to work containers and does match which bear. She asks out which containers er work out a plan for can you please help h comparing them all?

Resources Three bears (each a different size), 3 containers each a different capacity but such that the tallest one has the smallest capacity, sand, rice or water, smaller containers and measuring cups and spoons.

The activity Tell the children about Tess’s problem. Show them the 3 bears and the containers but not the sand, rice or water and smaller containers that you have available for them. Ask the children to say which container is the biggest (holds the most) and to say why. Then ask them to order the containers from smallest (holds least) to largest (holds most). When the children are happy with the order, tell them that Tess got that far and then she suddenly thought: “But how do I really know they are in the right order?” Ask the children for suggestions, which might include filling each container. When appropriate, show the children the resources that are available and ask them to experiment with ways of checking which one holds the least and which holds the most. Allow time for the children to pour from one container to another and to use small containers to fill up big containers before asking questions to match the current situation, for example: “How many of these small cupfuls did it take to fill this container?” “Do you think it will take the same number to fill this container?” “You said this is the biggest container. What will happen if you pour all of the sand out of it and into this one? Will it be full too or will it overflow?”

Reflection Review what the children have done and what they have found, focusing in particular on aspects of conservation, such as:


“A tall container seems as if it should hold more but doesn’t actually.” Look for explanations about why that might be so. Remind the children that they will need to send their suggestions to Tess. Encourage them to contribute to a sequence of steps that will show her what they did to get their answers. Do this together as a class or allow time for the children to try and draw their own sequences. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5


UNIT 7 Measuring Up


SAME SIZE the same e r a t a th s g in th g in d in f n Tess has bee has e h s s y a s e h S . s ie d d te r e size as each of h le d id m r e h s a e iz s e m a s found more things theer bears. She wonders if size bear than the othe for us. that would be the sam

Resources Three teddies of different heights, string, wool or tape measure, assorted objects around the room or outside to compare with the bears.

The activity The term “same size” is deliberately open to interpretation here. When the children are carrying out their comparisons, it is likely that most of them will look only at the length or height of each teddy. There may be some children though who look at length and width or overall size. Some may even factor in the mass of each bear although this is unusual at this level of development. Explain to the children that there are not enough bears for everyone to carry them around, so ask for suggestions as to what to do. Remind them of the teddy accessory making activity they did earlier if you need to. Tell the children that they are going to send their comparisons to Tess, so they need to keep a record of which things are the same size as which bear. Do not tell them how to organise this as this is an important part of the problem solving. You may, however, say that you will give them three pieces of paper each in case they need them. Allow time for the children to begin making comparisons and recording. As you observe, ask questions to help them organise their thinking, for example: “Which of these things is the same size as the little bear?” “What could you do or add to the page that would help Tess know what is being compared to which bear.” If the children do not come up with a strategy, suggest direct questions such as: “Would it help it you drew a bear of each size?” “What could you do then to show which things match which bear?”

Reflection Share some of the examples and ask the children to comment on: ✒ the strategies used to show which things belong to which bear and their effectiveness


✒ how comparisons were made ✒ which teddy had more things the same size as it.

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Measuring Up 7 UNIT

THE BEAR’S HOUSE ears and b e e r th r e h r fo e s u o h a Tess has made same. She e th o d ld u o h s u yo t a th she thinks because s e s u o h r u yo f o s e r tu ic wants to see p r toy e th o e m o s r fo e s u o h a she wants to make me ideas. animals and needs so

Resources Construction materials or junk materials such as packaging, glue, adhesive tape, paints and assorted papers or decorations, digital camera (optional).

The activity Tell the children about Tess’s house and her request. Show them the range of materials that you have available for them to build with. Explain to the children that they may take their house home afterwards, providing they use junk materials. Ask the children to think back to their early experiences with 3-D construction and to talk about some of the problems that they encountered. Before they set about building their houses, you may need to make prompts about joining and fitting together and which shapes are the strongest. Encourage the children to compare materials by size and fit, and to keep in mind the sizes of the three bears that must fit inside. Ask the children to explain their thinking, the problems they encounter and their fix-up strategies as they work, so that you can use some of them at the reflection.

Reflection

cognising 2-D and 3-D

S0.1 Re For this reflection you many need to take a shapes by name. guided tour around the room to see and comment on the different houses that have been made and to test that the bears do actually fit inside them. Share some of the problems about the construction of each house and the fix-ups that were used. Talk about the sizes of the components and the overall house each time. Finally ask the children what they would do differently next time if they were asked to build something else. This will set up some useful hints for the investigation yet to come.



UNIT 7 Measuring Up

TESS SAYS A game for the whole class

Resources A space to move around in.

How to play This game is a variation on Simon Says. In the traditional version of the game, if the instruction is prefaced with “Simon says” then the children carry out the action. If however the instruction is given without those words at the beginning, the children do not carry out the actions. Obviously, in this version of the game, the words to use are “Tess says”. As this game is intended to focus on size, the instructions and actions should reflect size and could include instructions such as the following: ✒ stretch as tall as you can

g a m e s

✒ be a small as a cat ✒ stretch as wide as you can ✒ jump as high as you can ✒ make the longest/shortest steps possible ✒ stand on one leg for the longest time. Have fun and encourage the children to suggest actions and take turns being the caller too.

THE LONGEST LINE A game for 2 to 4 players

Resources A fixed number of counters such as tiles, bread tags or bottle tops; a die.

How to play The object of this game is to be the person with the longest line of counters. Players take turns to throw the die and take that many counters. They line their counters up in front of them. The players repeat the process until the counters are all used up. They then compare their lines by lining them up side by side or, if they can, by counting. Encourage the children to compare the lines each time and to talk about “more than”, “less than” and “how many” counters are needed to catch up or overtake other players.

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Measuring Measuring Up Up

7 UNIT

BUILD A BRIDGE ridge b s u o m r o n e n a ilt u b s a h Tess says she oat G y ill B t s e g ig b e th r fo h g that is strong enou . Gruff to walk across o. to e n o ild u b u yo n a c ks s She a

Resources Construction materials or junk materials such as packaging, adhesive tape, glue, scissors soft toy, digital camera (optional).

The investigation Remind the children of the story of The Three Billy Goats Gruff and the troll who lived under the bridge and then tell them about Tess’s bridge. Show the children how long Tess’s bridge is (to match the materials at hand and really introduce a challenge). Ask the students to brainstorm all of the things that they have learnt about building so far. Remind them of earlier activities with blocks and of the “Build a house for the bear” activity. Review some of the problems that they may have had with joining materials, finding the right materials in the first place, and so on. Show the children the materials available and the space to be bridged, and the soft toy that will be crossing the bridge. The children may begin selecting their materials and thinking about their designs straight away. Suggest that they might want to draw their bridge before they begin but only expect a few of them to have a go at drawing. Allow plenty of time for the children to investigate ways of spanning the distance and creating a strong structure before testing with their soft toy.

Reflection


Do a gallery tour and look at and test each bridge. Ask the children how they could find out how long the bridges are and which is the longest. Ask the children to explain what sorts of things needed to be considered when trying to make a long and strong bridge. Prepare some materials ready for testing some of their ideas.


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UNIT 7 Measuring Up

SNAKES AND LADDERS GAME A S S E S S M E N T A C T I V I T I E S

akes and n “S r e h ke a m to s ke a n s Tess drew awing r d d e h is in f e h S . d r a o b e Ladders” gam e th s a w ke a n s h ic h w d e r e d them and then won the is h ic h w t u o d in f e w ld u o longest. How c longest? Activity Sheet 31

Resources


Snakes and Ladders

Scissors, string or knitting wool, small counters or tiles.

Which snake is the longest? How could you find out?

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ direct comparison of objects ✒ using string to measure with ✒ ordering objects by length ✒ using the language of comparison

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Observer’s guide Show the children Tess’s Snakes and Ladders game board on the activity sheet and ask them how they could work out which snake is the longest, shortest or middle-sized. The children might think they know, so challenge them to prove to you that they have got them in the right order. Tell them that you have scissors, string, knitting wool and small objects that they could use to check the length of each snake. Observe and listen to the children think and begin to work. The children may: ✒ lay out the counters along the snakes and count or compare the number of counters required for the snakes ✒ cut out the snakes and try to use direct comparison ✒ use the string or wool to find the length of each snake and then compare the lengths of the strings. When the children are satisfied with their ordering of the snakes’ lengths, ask them to say which snake is the longest, shortest, shorter, longer and so on, to identify their confidence with comparative language.


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Measuring Up 7 UNIT

FILL THE GRID Prior experiences

Activity Sheet 32


Activity Sheet 32

Name

Fill the grid

✒ comparing objects by size and mass

long

short

✒ using grids to sort and show data ✒ using the language of comparison

small

Observer’s guide

bigger

Remind the children of the grid activity in the previous mental routine. Tell them that this is just like that grid except that biggest they need to find objects to draw in the different spaces on it. First read each heading on the grid and check that the children can find specific squares on the grid. Now ask them to think of (or find things in the room) that they could put in each space of the grid. Encourage the children to draw at least one object in each space and to explain why it goes in that space. Watch and question as the children make their decisions and note: © 2007 Blake Education – Natural Maths Strategies – Beginning Level

✒ whether they actually heft the objects or simply judge mass by size

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A S S E S S M E N T

✒ the range of comparative language that they bring to the task ✒ their effectiveness with deciding which cell in the grid to place objects into and the criteria used for those judgements.



A C T I V I T I E S

99

Unit 8 Shop ’til You Drop

Focus At this stage children will have had some experience of shopping. They may have noticed that money is used to buy things and that sometimes change is given. They may also be aware to some extent of environmental print displaying shop names and brands on carrier bags, packaging and advertising. This unit builds on these early ideas of money and shopping-related experiences. Through play activities the children will develop more formal ideas about money and paying for goods. Their attention will be drawn to the shape and colour of coins and notes, the handing over of money in exchange for goods, and the convention of giving goods a price, though not necessarily realistic prices for the children’s examples.

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Context The context for this unit is Shop ‘til You Drop. It is intended that the children will actually create not one but many shops which will become the shopping mall. They will also create shopping catalogues and posters. As they role-play being the shopper and then the shopkeeper, they will have opportunities to weigh goods, handle money, create shopping lists, pack and unpack shopping and transact in ways that replicate what real shoppers do.

Developmental sequence At this stage of their development children will move towards understanding the following meaning and purposes of money: 1. money is used to pay for goods 2. money includes coins and notes 3. change is sometimes given 4. goods have a sales price 5. goods are sorted and displayed 6. shopping catalogues tell what is for sale and highlight the prices of goods.


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UNIT 8 Shop ’til You Drop


PREPARATION AND RESOURCES You will need to prepare: 1. play items to put in a class shop 2. dress-up clothes, current shopping catalogues, play money and play till 3. a Father’s Day catalogue using cut-outs from a current catalogue or change the context to Easter, Mother’s Day or Christmas to suit 4. kitchen scales or pan balance 5. Pizza’s and toppings made from card and paper

Related picture books (some of the following books are no longer in print but may be available second-hand or from your library) Supermarket! Charlotte Doyle, Walker Books Ltd. Teddy Bears Go Shopping, Suzanna Gretz, A & C Black Children’s Books. The Shopping Trip, Arnold Shapiro, Troll Associates. Wilberforce Goes Shopping, Margaret Gordon, Puffin Books.

Related picture rhymes Five Currant Buns in a Bakers Shop Five currant buns in a baker’s shop, Round and shiny with sugar on the top. Along came (insert child’s name) with her (or his) money one day, Bought a currant bun and took it right away. (Repeat each verse until no currant buns remain.)



UNIT 88 UNIT

FREE PLAY Target strategies ✒ Knowing that money is used to pay for goods ✒ Recognising gold and silver coins ✒ Recognising and naming coins ✒ Knowing that change is sometimes given when shopping

The activity Create a class shop or series of shops where dress-ups are used for the clothes shop, toy foods for the fruit and veg shop, books for the book shop, and so on. Allow time for free play before beginning to formalise the shopping processes and protocols. Over a period of time, go shopping at the class shop with a list (use words and pictures) and encourage the children to make lists too. Show the children a specials shopping catalogue and ask for the specials at the counter. Give coins and ask for change. Provide some blank stickers and show the children how to write the values of the goods on the stickers so that the goods can be priced. Draw coins to show the values. At the end of play, encourage the children to close the till and sort the coins into bags. As the children play, ask questions such as:

F R E E

“How much is that?” “Which coin shall I give you?” “Do I get any change?” “Can you put it in the right-sized bag for me?”

Observation As the children play and transact with one another, note:

P L A Y

✒ whether they name coins correctly ✒ know that change can be given ✒ match coins to the coins shown on price labels ✒ observe the shopping protocols.


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SHOPPING CATALOGUES Target strategies ✒ Matching coins to pictures of them

Resource Card 19 Shopping Catalogue

Resource card 19

✒ Selecting a coin to pay for an item ✒ Knowing the difference between gold and silver coins

M e n t a l

Resources Play money, laminated copies of the resource card or a similar laminated sheet made up from current shopping catalogues with items of interest to the children.

Closed questions


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Which silver coin would you use to buy the chewy lolly? I paid for this item using the coin with the platypus on it. Which item did I buy? I bought the fish in the bag. Which coin did I use to pay for it?

r o u t i n e s

The coin I used did not have round sides. What did I buy? There was no animal on my coin. What did I buy?

Open questions I used a gold coin for this item. What might it have been? I used a silver coin to pay for this item. What might it have been? I used a coin with an animal on it to pay for this item. What might it have been?

Flip questions I bought something from the card/catalogue. You can ask me questions about the coins to find out what I might have bought. Questions could include: “Was your coin round?” “Was your coin silver?” “Was your coin the smallest in size?” In the early stages, help the children to match the actual coins to the coins on the card/catalogue and to remove or eliminate coins as each question is answered.

104



8 UNIT

FRUIT AND VEG Target strategies ✒ Applying number to shopping situations

Resource Card 20 Fruit and veg shop

Resource card 20

✒ Matching coins to purchases ✒ Knowing that sometimes more than one coin is needed to pay for things.

Resources Play money.

Closed questions


187

I bought 3 apples. Which coins did I use? I bought 2 oranges. How should I pay for them? I bought an apple and an orange. Which 2 coins do I need to pay for them?

M e n t a l

I bought the mushrooms and the bananas shown. Which 2 coins did I use to pay for them? I used the coin with straight sides. What did I buy?

Open questions I bought 3 things, all different. What might I have bought? I bought 2 items. Which coins might I have used? I gave the shopkeeper 2 different coins. What might I have bought? I used a gold coin and a silver coin to pay for some items. What might I have bought?

Flip questions I bought some things (less than three initially) from the fruit and veg shop. You may ask me questions to find out what I bought. Questions could include: “Were they all the same?”

r o u t i n e s

“Were they all vegetables?” “Was there a mix of fruit and veg?” Assist the children with the elimination of cards initially, by asking questions such as: “Now that we know they are all vegetables, which cards do we need to eliminate (take away)?”


105



TESS’S SHOPPING LIST when she t u b ls a im n a r e h d e fe to Tess wanted are. b s a w d r a o b p u c e th d r a od went to the cupbo fo ts n a w e h S t. a c a d n a She has a bear, a doguld she put on her shopfor 3 days. What sho ks how many of each food ping list? She also as will she need to buy.

Resources Soft toys to match those listed above (optional), number strips made from Resource Card 3.

The activity Read Tess’s problem to the class, review the three animals (matched to the soft toys if using them) and ask the children to help Tess decide what to put on her shopping list. Brainstorm ideas about personal pet experiences and known animal stories to help the children gather their thoughts on this. Remind the children that the animals will need food for 3 days before Tess goes shopping again, so they need to leave food for every day. Do not discuss the number of meals a day at this point; leave it for the children to consider. You might want to look at the class calendar, find what day it is today and plot when Tess goes shopping next. Some children will include the names of the days in their thinking. Explain to the children that they need to make a shopping list (drawing the things) for Tess so that she knows what to buy. As the children work, observe and ask questions about the quantity of items and how many altogether. Encourage the children to use their number strips to write the number of each item needed on their lists. Note the strategies for counting and whether the children are beginning to develop the concept of “altogether”. Some children will count each group of foods separately even after being asked how many altogether. At this stage in their development they are very probably still matching the number to the last item counted rather than to the number of objects in the group altogether.

Reflection Compare some of the lists in terms of foods selected, number of meals in a day, overall total, strategies used for representing and counting as well as their ease of use. Use some of the examples and focus on smart counting strategies, such as subitising and counting on.



Shop ’til You Drop 8 UNIT

ENOUGH MONEY? pping list: o h s r e h is e r e H . s in o c $1 Tess has six • 2 bones • 1 jar of honey • 4 little fish he s m e it h c a e r fo y a p to in She will use a $1 co e help her work out if she buys. She says pleas pay for them all. If she has enough coins to how many more coins will doesn’t have enough, she need?

Resources Play money.

The activity Read the problem to the children and make sure they know that she has to buy 2 bones and that they are $1 each so she will need two $1 coins. The children should be encouraged to find a way of solving the problem in their own way. They may, for instance: ✒ draw each item and then count to see how many there are altogether ✒ draw the items one at a time, matching coins to them as they go along ✒ draw the six coins and then draw the items with matching lines. Only prompt if necessary, suggesting that the children begin by drawing the correct number of each item first. They can then take six coins to match with the items, in which case they will see that they need one more coin to pay for them all.

Reflection

ey is derstanding that mon

N0.4 Un Share some of the work samples that use difused to buy things. ferent strategies and involve the children in explaining what each strategy is and how it works. This could include one-to one-matching, drawing and counting perhaps with numbers bedside the items, and fix-up strategies including crossing off where too many items were drawn in the first place.





THE FATHER’S DAY SHOPPING CATALOGUE gue lo ta a c y a D ’s r e th Fa is th s Tess has sent u hat you w w o n k to ts n a w e h S . e d that she ma at you th e u g lo ta a c y a D ’s r e th would put in a Fa make. der r o ill w e h s , e u g lo ta a c r u If you send her yo you to write an order for from it. She would like her too.

Resources A Father’s Day catalogue prepared beforehand, shopping brochures, scissors, glue, environmental print showing shop names or labels on items such as carrier bags and packaging or advertising materials.

The activity Show the children Tess’s catalogue and allow time for them to talk about what they think their dad would like for Father’s Day. Focus on the way items are grouped, for example tools at the top of the page and clothes at the bottom, just like going to different departments in a large store. Explain how Tess has drawn coins bedside the items so that the children will know how much to pay for them. Ask them what they would like to order from the catalogue and which coin they would use to pay for each item. Allow time for the children to write an order from Tess’s catalogue before they begin making their own catalogue. The children may draw items for their catalogue or select items from the shopping brochures that you have provided, cut and then paste them. Encourage the children to write a name for their shopping brochure and to write labels for the items for sale. Suggest that they decide what to include and how to sort those items before they paste them down or draw them in felt pen which will not rub off. Also encourage them to draw coins beside items so that Tess will know how much they cost.

Reflection Share the catalogues and focus questions and comments on:

that money is N0.4 Understanding used to buy things.

✒ the environmental print included ✒ how the items have been sorted ✒ what coins are needed to pay for the items ✒ what they think their dad would like most. Send the catalogues to Tess for a few days and when they come back with her order, the children can include them in their shopping play.

108



TESS’S PIZZA ppings – to e it r u o v fa 3 s a h e h S . Tess loves pizza extra. t s o c y e th t u b , to a m to d pineapple, salami an Salami is 10 cents. Pineapple is 5 cents. ents. Mushrooms are 20 c e h s s za iz p t n e r fe if d t a h w Tess wants to know he is only allowed 2 can order because s . Which coins will she need toppings on each pizzappings each time? to pay for the extra to

Resources Cut out some card to represent the pizza bases and use coloured papers for the salami, mushroom and pineapple pieces, coloured pencils.

The activity Read Tess’s problem to the children and show them the prepared materials. Make a pizza with 3 toppings and ask if Tess is allowed that many toppings, just to check that the children understand the problem. Ask the children to try making different pizzas that each have only 2 toppings. When they have made each pizza that follows the rule, tell them that they should draw it so they don’t forget what combination of toppings was used. Also ask them to draw the coins that would be needed to pay for the extra toppings each time. As the children make their pizzas, focus on how they are different from each other and look for combinations to make sure there are no repeats. You could ask the children to describe their toppings, for example, salami with mushrooms, salami with pineapple, so that they can begin to see that salami has been paired with the other 2 toppings and it is time to try a different combination. Encourage the children to draw the coins needed for the two toppings each time.

Reflection

oney is Understanding that m

N0.4 Use some of the children’s pizza drawings used to buy things. and identify the different toppings and how they are the same or different. Every time there is a different combination, draw it so that everyone can see it. At the end, discuss how they know that all the different topping combinations have been made and to say how many there were. The children might want to comment on their own favourite toppings, in which case other combination problems may emerge. They could send a list of their 3 favourite toppings as a combination problem for Tess to solve.




SHOPPING BINGO A game for 2 players

Resources

Resource Cards 21, 22, 23

Laminated game board (Resource Card 21) for each player, laminated shopping bingo reference card (Resource Card 22) for each group, 2 sets of laminated shopping cards (Resource Card 23), a set of play money coins to match the coins on the cards for each player.

Shopping Bingo cards

Shopping Bingo reference card Shopping Bingo game board

Resource card 23

Resource card 22

Resource card 21

How to play

g a m e s

To begin each player places two matching coins in each box of their board. On their turn each player turns over a shopping card and if they want to buy that item, they must pay for it with the matching coin from their board. They can refer to the reference card to see what other items are available for the same coin and so may decide instead to pass and wait for a different item, though this is risky. The first player to have spent their coins and filled their cards with bought items wins the game.

193


191



189

RACE TO A FULL SET A game for 2 or 3 players

Resources 3 sets of laminated cards made from Resource Card 23.

How to play Each player chooses two of the six coin denominations that they want to collect items to match. Players take turns to take one card from the pile, and if it belongs to the coin sets that they are collecting, they keep the card. Otherwise they put it on the discard pile. Play continues until either a player has two complete sets or until all of the cards in the pile have been played. At the end of play the player with the most cards on their game board is the winner.

110


Shop Shop ’til ’til You You Drop Drop

8 UNIT

FOR BOYS, GIRLS OR BOTH? gs than in th y o b e r o m e r a e r e th Tess says that t is a th if s r e d n o w d n a l o o h c girl things at her s ol. What do you think we the same at our scho should do to find out?

Resources Access to class toys, puzzles, books, construction materials and/or outdoor play equipment, book club catalogues (optional).

The investigation If you have a toy or book catalogue from one of the major chains, share it with the children. Focus on which things they think are for boys and which are for girls, and which would appeal to both. The colour in the images will influence this to a great extent, so focus on the actual objects rather than accept a general view. Ask the children what they think they can do to check out Tess’s statement. They will probably suggest sorting some books, puzzles or toys to find out if they agree with Tess. Encourage them to seek more than one response for each item before actually placing it in the “girls”, “boys” or “both” groups. When the children have finished sorting, ask them to comment on how many of each category there are in the collection that they sorted and to make a comparative statement about more than/less than/same as. Some children will be able to say how many more than or less than. The children may use one-to-one matching or counting for their comparisons, so use these as the basis of the reflection.

Reflection


Ask the children to comment on what they have found out and to explain their processes for deciding which category to put things in. It is possible that some overlaps and some contradictions between groupings will arise. Not all boys or all girls feel attracted to what has traditionally been considered boy’s or girl’s toys and books. Link overlaps to the fact that we need to ask several people for their views before we can make a decision about where to place things. Regroup the items if necessary and ask for suggestions for comparing group size.


111


THE TOY SHOP A S S E S S M E N T

Resources

Activity Sheet 33

Coins to match the toys in the shop.


Toy shop Which 3 things would you like to buy from the toy shop?

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ playing shop ✒ matching coins to pictures of them ✒ giving toy money for goods

Which 3 coins would you use to pay for them?

Observer’s guide

148


Begin by asking the children to cover the coins at the bottom of the page with matching coins. Then ask them to show which 3 things they would like to buy from the toy shop. Ask the children to give you the coins needed to pay for the items they have chosen. They may then cross off those coins at the bottom of the page so that they have a record. As the children match the coins, note the way they go about it, for example do they:

A C T I V I T I E S

112

✒ match by the number value or by the pictures on the coins ✒ know which coins are gold or silver and use this to help them make a match ✒ correctly match some or all of the coins. When the children decide which coins to pay with, note whether they: ✒ randomly offer coins ✒ randomly offer exactly 3 coins ✒ give 3 coins to match the coins on the tickets for each item.

that money is N0.4 Understanding used to buy things.



THE FRUIT AND VEG SHOP Resources

Activity Sheet 34

Play money

Activity Sheet 34

Name

The fruit and veg shop Which coins belong on each price ticket?

Prior experiences The children will be ready for this activity if they have had experiences with: ✒ drawing or copying coins ✒ playing shop ✒ giving play money to pay for goods Give both children the coins they need to pay for what they buy.

Observer’s guide


149

Show the children the page. Allow time for them to identify how many of each type of fruit and veg there are. Ask them which coins they think they should put onto each price tag and to say why. As the children match the coins, observe and question how they are deciding which coins go where. If necessary, ask why the illustrator has drawn some food items bigger than others and how that helps them to know which coins to use. The children can then remove the coins one at a time and write on the labels what they are. Read the speech bubbles and ask the children to draw the matching coins on the hands of the characters. Note whether the children actually look at the coins on the tickets and work from there or whether they simply draw random coins. You may find that some children demonstrate some equivalence as they select a 10-cent coin instead of two 5-cent coins to pay for the apples. You can make up other similar questions or add more challenge for some children, for example: “What if the customer wanted 2 cauliflowers?” “What if the customer wanted 5 oranges”?

unting N0.1 Subitising and co s using small groups of object number names. that money is N0.4 Understanding used to buy things.



113

Beginning level Index of Activity Sheets

114

Unit

Activity Sheet No

1

1

Tess’s mess

9

1

2

Tess’s list

11

1

3

Shape cards

12

1

4

Shape game board (1)

12

1

5

Shape game board (2)

12

1

6

Making groups

14

1

7

Fill the grid

15

2

8

Tess’s map

25

2

9

Making buildings from plans

28

2

10

Finding teddies

29

2

11

Hiding teddies

29

3

12

Tess’s paper plate fish

39

3

13

Fish number poster

41

3

14

Tess’s spotted fish

42

3

15

Fishy partners (1)

43

3

16

Fishy partners (2)

43

4

17

Patterns in our week

53

4

18

Fred’s quilt

56

4

19


57

5

20

Guess and check

64

5

21

Lift-the-flap-poster (2)

65

5

22

Lift-the-flap-poster (1)

65

5

23

Jumping frogs

66

5

24

Frogs

66

Title


Page1

Unit

Activity Sheet No

5

25

Finger Fun

67

5

26

Handfuls

70

5

27

Making snowmen

71

6

28

Tess’s Shape picture

79

6

29

Copy that truck

84

6

30

Favourite shapes

85

7

31

Snakes and Ladders

98

7

32

Fill the grid

99

8

33

Toy shop

112

8

34

Fruit and veg shop

113

Unit

Song Sheet No

2

1

Building Rhymes

18

3

2

Five Little Fishes

32

3

3

Fish Alive

32

3

4

Fish Eyes (teacher’s sheet)

32

3

5

Fish Eyes

32

Title

Title


Page1

Page1

115

Activity Sheet 1

Name

Tess’s mess

116


Activity Sheet 2

Name

Tess’s list

long short heavy light © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

117

Activity Sheet 3

Name

Shape cards

118


Activity Sheet 4

Name

Shape game boards (1) blue

yellow

green

red

yellow

green


119

Activity Sheet 5

Name


120

yellow

blue

red

blue

red

green


Name

Activity Sheet 6

Making groups Draw more things in each group.


121

Activity Sheet 7

Name

122

small

big

red

blue

small

Fill the grid


Activity Sheet 8

Name

Tess’s map TOY SHOP

BOUTIQUE

BUTCHER

BAKER

NEWSAGENT


123

Activity Sheet 9

Name

Making buildings from plans Find a block to match each of these blocks.

Use your blocks to make this building

124


Name

Activity Sheet 10

Finding teddies Where is the teddy hiding in this room?


125

Activity Sheet 11

Name

Hiding teddies Show where teddy could hide in this room.

126


Name

Activity Sheet 12

Tess’s paper plate fish You will need: 2 paper plates 2 fluffy eyes 2 google eyes Paper and scraps of paper Glue and a stapler

What to do: Make two fins and a tail. Staple the plates and the fins together. Decorate the fish. Give the fish a mouth. Stick on the fluffy eyes. Stick on the google eyes.


127


Fish number poster

128


Name

Activity Sheet 14

Tess’s spotted fish Add some spots to the fish and show how many spots each fish has.


129


Fishy partners (1) Find each fish a partner.

130


Name

Activity Sheet 16

Fishy partners (2) Give each fish a partner.


131


Patterns in our day

Monday puzzles

big books

dance

painting

puzzles

construction

singing

sport

storytelling

swimming

cooking

library

puzzles

big books

computers

sport

Tuesday

Wednesday

Thursday

Friday puzzles 132

construction storytelling


painting

Name

Activity Sheet 18

Fred’s quilt


133



134


Activity Sheet 20

Name

Guess and check

Guess

Look

Check

Guess

Look

Check

Guess

Look

Check

Guess

Look

Check

1

2

3

4 © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

135


Lift-the-flap 1oster (1)

136


Name

Activity Sheet 22

Lift-the-flap poster (2)

Cut around the black outlines of the previous activity sheet and paste the whole sheet onto this sheet to make a lift-the-flap poster. © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

137


Jumping frogs

138


Name

Activity Sheet 24

Frogs


139


Finger Fun Part 1 Fingers like to play,




Fingers like to give us all A great big surprise! (hands to front, all fingers showing) (hide hands behind back) Watch very carefully when fingers come out to play. (bend some fingers down and bring fingers out now) How many fingers? Can you say? (This part can be repeated until the children are subitising the number of fingers) Part 2 Fingers like to play,




Fingers like to give us all A great big surprise! (hands to front, all fingers showing) (hide hands behind back) Ready now to guess As fingers come back into sight. Show how many fingers! (bend some fingers down Were you right? and bring fingers out now)

140


Name

Activity Sheet 26

Handfuls

How many?

How many?


141


Making snowmen Each snowman needs: A hat

A cane

A bow tie

Two buttons

What extra items do the snowmen need?

142


Name

Activity Sheet 28

Tess’s shape picture


143


Copy that truck fold back

fold over

144


Activity Sheet 30

Name

Favourite shapes I like triangles and circles.

That’s why I like Ice-cream

Draw your own favourite shapes and objects.


145


Snakes and Ladders Which snake is the longest? How could you find out?

146


Activity Sheet 32

Name

Fill the grid

long

short

small

bigger

biggest


147


Toy shop Which 3 things would you like to buy from the toy shop?

Which 3 coins would you use to pay for them?

148


Name

Activity Sheet 34

The fruit and veg shop Which coins belong on each price ticket?

Give both children the coins they need to pay for what they buy.


149

song Sheet 1

Building Rhymes Build it Up Build it up, build it up, build it high, (use fists to model building high) Build it high, high, high into the sky. (involve the children in counting how many fists have been used)

Tower Block I am going to build a tower block (use blocks to model building) Very, very high. I am going to keep on building Until I reach the sky. (indicate how high you think it might grow) Can you count my building blocks To see how high it grows? (involve the children in chanting the count) Oh No, It’s getting wobbly . . . And over it goes. (nudge the tower over) Crash, crash, crash.

150


song Sheet 2

Five Little Fishes Under the ocean green and deep, Lie five little fishes fast asleep. (fingers on the left hand) Along came a bigger fish out of the blue. (the right hand) Swim little fish or he’ll catch you. (right hand moves around the left) Swim little fish, swim to the left, (wiggle left fingers, move to the left) Swim little fish, swim to the right, (wiggle left fingers, move to right) Swim little fish with all your might. (move all around)


151

song Sheet 3

Fish Alive One, two, three, four, five. (show the fingers of left hand) Once I saw a fish alive. Six, seven, eight, nine, ten. (show the fingers of the right hand) Then I let him go again. Why did you let him go? Because he bit my finger so.

(shake all fingers)

Which finger did he bite? This little finger on the right.

152

(show little finger)


song Sheet 4

Fish Eyes

(teacher’s sheet)

Fish eyes here, fish eyes there. Fish eyes looking everywhere.

(look all around)

Fish eyes, fish eyes looking left. (hands swimming left) How many fish eyes do you see? (count 1,2,3,4 eyes looking left) Fish eyes, fish eyes looking right. (hands swimming right) How many fish eyes do you see? (count 1,2,3,4 eyes looking right) Fish eyes, fish eyes looking straight at me. (hands swimming straight ahead) How many fish eyes do you see? (count 1,2,3,4 eyes looking straight at me) Fish eyes, fish eyes looking everywhere. (look all around) How many fish eyes do you see?

(count all the eyes)


153

song Sheet 5

Fish Eyes Fish eyes here, fish eyes there. Fish eyes looking everywhere. Fish eyes, fish eyes looking left. How many fish eyes do you see? Fish eyes, fish eyes looking right. How many fish eyes do you see? Fish eyes, fish eyes looking straight at me. How many fish eyes do you see? Fish eyes, fish eyes looking everywhere. How many fish eyes do you see?

154


Beginning level Index of Resource Cards Unit

Resource Card

1

1

Collections

6

1

2

Opposites poster

7

3

3

Number strips

33

3

4

Number cards

33

3

5

Magnetic fish

33

3

6

Fish cards

40

5

7

Number formation

60

5

8

Numbers and dice

62

5

9

Spot count

63

5

10


68

6

11


68

6

12

Shapes all around us

76

6

13

Shape pictures

77

6

14

Tile shapes

82

6

15

Shape game board

82

6

16


83

7

17

The Three Bears

90

7

18

Heavy and light grid

91

8

19

Shopping catalogue

104

8

20

Fruit and veg shop

105

8

21

Shopping Bingo game board

110

8

22

Shopping Bingo reference card

110

8

23


110

Title


Page

155

© Blake Education ISBN 978 1 92114 357 1

Natural Maths Strategies - Beginning Level - Ages 4-5

Collections

Resource card 1


157



Opposites poster

Resource card 2


159



Resource card 3

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

Number Strips


161

Resource card 4

Number cards

1 2 3 4 5 6 7 8 9 162


Magnetic Fish

Resource card 5


163

Natural Maths Strategies – Beginning Level © 2007 Blake Education Natural Maths Strategies – Beginning Level © 2007 Blake Education

Natural Maths Strategies – Beginning Level © 2007 Blake Education Natural Maths Strategies – Beginning Level © 2007 Blake Education

Natural Maths Strategies – Beginning Level © 2007 Blake Education







Fish cards

Resource card 6


165











Number formation

Resource card 7


167

6

7

seven six

1

one

2

3

three

8

eight

9

nine

Number and Dice

two

4

four

5

five

Resource card 8

168


Spot count

Resource card 9

1st spots

2nd spots

3rd spots

1

2

3

4

5

6

7


8

9 169




one

1

two

2

three

3

four

4

five

5

Resource card 10


171

Resource card 11

172


six

6

seven

7

eight

8

nine

9


Shapes all around us

11

12

Resource card 12

1

10

2

9

3 4

8 7

6

5


173



Shape pictures

Resource card 13


175



Tile shapes

Resource card 14


177

Resource card 15

178

Shapes game board



Resource card 16

Happy Birthday

fold line © 2007 Blake Education – Natural Maths Strategies – Beginning Level © Blake Education ISBN 978 1 92114 357 1 Natural Maths Strategies - Beginning Level - Ages 4-5

179



The Three Bears

Resource card 17


181



Heavy and light grid

heavy

Resource card 18

light

small

bigger

biggest


183



Shopping Catalogue

Resource card 19


185



Fruit and veg shop

Resource card 20


187



Shopping Bingo game board

Resource card 21


189



Shopping Bingo reference card

Resource card 22


191




Resource card 23


193


Natural Maths Strategies - Beginning Level - Ages 4-5 Natural Maths Strategies – Beginning Level © 2007 Blake Education












Based on world’s best practice! This series provides the core knowledge and understanding of the “big ideas” or concepts students require to become confident and enthusiastic maths users. This book is organised into eight units of work based on the current research into the developmental sequence in which young children generally acquire those concepts. Each unit is divided into five sections: Mental routines – 10-minute lesson starters with suggested closed and open questions designed to engage children and arouse their enthusiasm Problematised situations – challenges that encourage children to work mathematically with open-ended “real-life” situations and construct their own ideas. These lessons include a reflection session where mathematical language is used to describe successful strategies and more formal methods are introduced and demonstrated. Games – fun activities designed to reinforce the strategies developed in each unit. Investigations – open-ended investigations to encourage children to test and extend their skills. Assessment activities – consolidation activities that children should readily accomplish at the end of each unit. The series encourages the use of readily available concrete materials and is supported by colourful resource activity sheets and cards. The CD-ROM included with this book is designed to help teachers to plan and personalise their maths program and to record individual children’s progress. The Natural Maths Strategies series is a complete school program, which also encourages the use of supplemental resources to ensure a variety of maths teaching and learning experiences.

ISBN 978-1-92114-357-1

9

781921 143571