COVER, 3D Space & Position - Blake Education

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3D Space E x p lo r i n g

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Position Bev Dunbar Activities, blackline masters & assessment pages that are fun and easy to use

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Exploring 3D Space and Position with Lower Primary

Bev Dunbar

Introduction Exploring 3D Space and Position Space is one of the least appreciated mathematical substrands. Teachers often feel the concepts are less clearly sequenced than those in Number or Measurement and the need for practical manipulation of resources can be a stumbling block. To help inspire you, here are over 35 action-packed lesson themes for manipulating 3D Space and Position ideas in fun, practical ways. All the resources required are easy-to-find, everyday objects. And the flexible activities range from simple to challenging, to help you cater for different ability groups. Making your teaching life easier is a major aim. The book is divided into sequenced units, each packed with enough photocopiable playing cards, activity cards and worksheets for small groups or a whole class to explore, for at least a week at a time. You'll find easy-to-follow instructions, with assessment help in the form of clearly stated outcomes linked to outcome indicators (see p.91). Each activity is designed to maximise the way in which your students construct their own understandings about 3D Space or Position. Activities are open-ended and encourage students to think and work mathematically. The emphasis is on practical manipulation of materials and the development of language and recording skills. This book is a companion to two other Space books in the ‘Exploring Maths’ series, Exploring 2D Space and Exploring Chance, Data and Graphs. Look forward to exploring these concepts with your students.

Copyright © Bev Dunbar Maths Matters 2002 Reprinted 2005 Exploring 3D Space and Position ISBN 978 1 86509 226 6 226 3 1 86509 Published by Blake Education Locked Bag 2022 Glebe NSW 2037 Series editor: Garda Turner Illustration and design by Janice Bowles Printed by Green Giant Press The blackline masters in this book may be reproduced by the original purchaser for use with their class(es) only.

Contents How to Use this Book

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Sorting and Classifying

3

Investigating 3D Properties

21

Constructing and Modelling

33

Exploring Position Language

55

Identifying Positions

67

Exploring Paths and Grids

77

Outcome Indicators Record

91

Sample Yearly Topics

92

Sample Weekly Programs

93

© Blake Education 978 1 86509 226 3

Exploring Maths - Space - Exploring 3D Space and Position

How to use this Book Over 35 Teaching Ideas More than 35 exciting teaching ideas have been placed into 6 units to assist your lesson planning for the whole class or small groups. Each activity has clearly coded learning outcomes and easy-to-follow instructions. Activities are open-ended and encourage your students to think for themselves.

Over 45 Blackline Masters There are 4 types of blackline masters. 1. Activity Resources e.g. p.11 Sort me These support your free exploration as well as structured activities. Laminate them for reuse with small groups. 2. Playing Cards e.g. p.49 Slice it up Cut these out, shuffle and use over and over again for small group games. Photocopy each set in different colours to assist class management. 3. Activity Cards e.g. p.69 Dinosaur bones Use these as an additional stimulus in group work. The language is simple and easy to follow. Encourage your students to invent their own tasks too. You can laminate them for years of reuse.

d Area

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th an Leng ring

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How amazing

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4. Reusable Worksheets e.g. p. 81 How amazing Unlike normal worksheets, these allow for different solutions and can be used by the same students again with different results. The structured tasks support your learning outcomes.

Outcome Indicators Record The complete list of learning outcomes is available on page 91. Use this to record individual student progress. Try to assess a few students each day.

Sample Weekly Program On pages 93 and 94, you’ll find two examples of how to organise a selection of activities as a 5-day unit for your class.

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Exploring 3D Space and Position



81

Sorting and Classifying

In this unit, your students will: • • • •

Sort, compare, describe 3D objects (3D1-1) Recognise, name simple 3D objects (3D1-2) Match 3D objects with 2D drawings, photographs (3D1-3) Make, describe, copy, extend patterns using 3D objects (3D1-4)

(The complete outcomes can be seen in the Outcome Indicators Record Sheet on page 91) Exploring 3D Space and Position



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Describe it What are you trying to do?

★ Sort, compare, describe 3D objects (3D1-1)

How many can play? ★ Whole class, pairs

What do you need?

★ Random classroom objects, e.g. blocks, toys, empty shopping packets, home corner objects ★ Pencils ★ What did I buy? worksheet (BLM p.5)

What do you do?

★ Pass a variety of objects around the class. Ask everyone to look at, feel and talk about these with the students near them. ★ What sort of things do you describe? e.g. colours, shapes, textures, size, uses, heaviness ★ Give everyone a minute to stand up, walk around and find an interesting small object. Now sit down in pairs with a partner and tell them everything about your object. e.g. A chalkboard duster: It’s hard, made of wood but soft on the top. It’s a creamy colour. It’s about as long as my foot. ★ Go out into the playground. Give everyone a minute to find an interesting large object. With a partner, describe each object in as many different ways as you can. What’s the largest thing someone describes? Are there even more ways you could talk about it? ★ Play a guessing game back in the classroom. Ask someone to describe a familiar object to the class. Can they guess the object in fewer than 10 guesses?

Variations

★ Describe objects around your home to your family. Can they guess each object in less than one minute? ★ Use the worksheet. Play What did I buy? in a small group. Fold the worksheet in half. Open it up and draw a secret shopping item on the inside, e.g a large red car, a spiky hairdo. Close your worksheet. Your group asks you to describe your secret object. e.g. What shape is it? What colour? How many questions before someone guesses your object?

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What did I buy?

What did I buy?

5 © Blake Education 978 1 86509 226 3


Where does it belong? What are you trying to do? ★ Sort, compare, describe 3D objects (3D1-1)

How many can play?

★ Small groups, whole class

What do you need? ★ A collection of mixed objects for each group, e.g. blocks, toys, cartons, shells ★ Where does it belong? worksheet (BLM p.7)

What do you do?

★ (Reveal a collection of mixed objects). Someone threw everything together instead of packing them away tidily. Look at each object carefully. Do any of the objects belong together? e.g. All the blocks. Discuss different sorting possibilities. ★ Imagine you secretly sort these objects into 2 piles. You sort them in a way you think no one else has thought of. How would you do this? ★ Whisper your secret sorting idea to the person next to you. e.g. Put all large objects here. Put small objects there. Did anyone else think of your idea? Think of another way to sort these objects. ★ Discuss some class sorting suggestions, e.g. objects with holes/without holes, red/not red objects. ★ Form small groups. Give each group a collection of mixed objects. Secretly discuss how you will sort your objects into 2 piles. Sort, then count the number of objects in each group. Which pile has more objects? Ask another team to guess your sorting idea. ★ Record your secret sort on the worksheet. Draw a picture of one or more of the objects from your first pile in the box on the left. Draw pictures of objects from your second pile in the box on the right.

Variation ★ Think of a secret sorting idea, e.g. has metal on it/doesn’t have metal; solid/hollow. Sort some objects into your 2 groups. Hold up a new object. Where does this belong? Ask different students to guess your sort and predict which group it belongs in.

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7 © Blake Education 978 1 86509 226 3


Tell me about it What are you trying to do?

★ Sort, compare, describe 3D objects (3D1-1)


What do you need?

★ A mystery bag, e.g. drawstring cloth bag or a paper shopping bag ★ Variety of random 3D objects ★ Pencils, paper ★ Tell me about it worksheet (BLM p.9)

What do you do?

★ Place an object on your hand, e.g. an alphabet cube. Tell me all you can about this object. e.g. It’s large, red, made from wood and has blue writing on it. ★ Place a different object in your other hand, e.g. a pencil sharpener. What’s the same about this object? e.g. That’s also red. What’s different? e.g. That one’s made from plastic and it’s little. ★ Imagine you can’t see an object but you can touch it with your hands. What features could you describe? e.g texture, size, shape What features could you not describe? e.g. colour ★ Secretly place an object in a mystery bag. Ask someone to feel inside and describe what they find. (e.g. A hairbrush: It’s prickly at one end and has a smooth handle at the other.) Can you guess the object from the description? Encourage everyone to ask more questions. e.g. Does it have any holes in it? ★ Place some objects at the front of the class. Ask everyone to look at them then close their eyes. Select one of the objects to describe to the class. Can they guess your object just by listening to your description, without opening their eyes? ★ Work in pairs. Think of an object to describe to your partner. Can they guess your object just by listening to your description? Swap roles.

Variation

★ Work with a partner, using the worksheet. Describe an object for them to draw on the left hand. e.g. Draw a large blue box with a lid. Describe a different object for them to draw in the right hand. e.g. Draw a small yellow ball with pink stripes.

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Exploring Length and Area



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Sort me What are you trying to do? ★ Sort, compare, describe 3D objects (3D1-1)

How many can play? ★ Whole class

What do you need? ★ ★ ★ ★

Wooden blocks A metal fork, a book and an apple Workbooks, scissors, paste Sort me pictures (BLM p.11)

What do you do?

★ Look at the blocks. Talk about different ways to sort them, e.g. curved/straight shapes. ★ Play a sorting game. Hold up a metal fork. What could belong with this? e.g. another fork, a knife and spoon, other objects from the kitchen, other things made from metal. Encourage creative responses. ★ Hold up a book. What could belong with this? e.g. another book, something else from the window shelf, something else from Tom’s bag ★ Hold up an apple. What could belong with this? e.g. another apple, something else to eat for lunch ★ Look at the Sort me pictures. How might you sort them? Cut out the pictures then find your own way to sort them, then paste them into your workbook. ★ Discuss different sorting criteria.

Variations

★ Look through magazines for pictures to cut out and sort. ★ Everyone draws 3 objects and cuts them out. Form small groups. Put all the pictures together in a pile. Find a way to sort them into different groups.

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Is this a box? What are you trying to do? ★ Recognise, name simple 3D objects (3D1-2)

How many can play?

★ Whole class, small groups

What do you need?

★ Real-life examples of cubes, spheres, cylinders and cones ★ Workbooks, pencils ★ Ball, box, can worksheet (BLM p.13)

What do you do?

★ Throw and catch a ball at random around the class. What’s so special about this shape? e.g. There are no straight edges; there’s no up or down or sides; it can bounce. What else do you know that is like this shape? e.g. a tennis ball, a beach ball What’s the smallest ball shape you know? e.g. a hundreds and thousands sprinkle What are other names for this shape? e.g. a sphere ★ Throw and catch a box of breakfast cereal around the class. What’s so special about this shape? e.g. There are straight edges with corners that are sharp; there are no curved bits; it doesn’t bounce. What else do you know that is like this shape? e.g. a gift box, a suitcase. What’s the largest box shape you know? e.g. a room, a house. What are other names for this shape? e.g. a cube, a rectangular prism ★ Pass a can of soup around the class. What’s so special about this shape? e.g. There are some curved bits; it looks like a circle on the top and bottom of the can. What else do you know that is like this shape? e.g. a gutter downpipe, a finger. What’s the widest shape like this you know? e.g. an above ground swimming pool. What are other names for this shape? e.g. a cylinder ★ Walk with a partner around your classroom. How many shapes can you discover that are like a ball, like a box or like a can? ★ Discuss the idea that shapes that look alike may not be exactly the same in all ways. e.g. A crayon is like a cylinder but it has a small pointy end.

Variation

★ Record some of your discoveries on the worksheet.

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Spin-a-shape What are you trying to do?

★ Recognise, name simple 3D objects (3D1-2) ★ Match 3D objects with 2D drawings, photographs (3D1-3)

How many can play? ★ Small groups

What do you need?

★ A mixed collection of spheres, boxes, blocks, cylinders and other shapes ★ One-minute timer ★ Paper, pencils ★ Magazines, scissors, paste, paper ★ Shape spinners (BLM p.15) (cut out, laminated, with a toothpick through the centre)

What do you do? ★ You need a mixed collection of objects and a timer. Spin the spinner. Start the timer. Race to collect as many shapes that match the spinner as you can before the timer stops. Who collected the most examples? Who collected the tiniest example? Who collected the largest example? NB: Where ? appears on the spinner, think of a shape that is not a sphere, not a box and not a cylinder. e.g. It could be a cone, a triangular prism, a pyramid. ★ You need paper and a pencil. Spin the spinner. This time draw a picture of a shape you can see in your classroom that matches the shape on the spinner. ★ Spin the spinner. This time name a real-life object that is not in your classroom that matches the shape on the spinner.

Variations

★ Spin the spinner. Race to look through magazines for a matching shape to cut out. Decide as a group how you will make a group display from your cut-outs. ★ Construct your own spinner with pictures of other simple shapes you know, e.g. a pyramid, a cone, a triangular prism.

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Shape snap What are you trying to do? ★ Recognise, name simple 3D objects (3D1-2) ★ Match 3D objects with 2D drawings, photographs (3D1-3)


What do you need?

★ Shape snap cards (BLM p.17,18)

What do you do?

★ Discuss the objects shown on the cards. What common shape is each one most like? e.g. The television is like a large box. The balloons are like balls. The pipe is like a can, open at either end. Some of the shapes are not like a box, a ball or a can. ★ Shuffle the cards and deal them face down to each player. ★ Decide who will start the game. In turn, reveal your top card. Look for a match with someone else. e.g. The alphabet cube is a box shape like the backpack. Call out ‘Snap!’ when you see a shape match. If you are the first to see the match you win all the cards in the matching pile. There could be more than one matching card. ★ Decide who will start the game. Everyone secretly looks at their top card. The person who starts the game describes their card to the other players. Each player then decides whether their top card is a match or not. If so, they reveal it. If not they place it face down in the middle. The person who described their card wins all the matching cards.

Variations

★ With a partner, invent your own games using these shape cards. ★ Make a large shape book or wall frieze. Decide on specific 3D shapes to look for in magazines, e.g. boxes, balls, cans and cones. Work in small groups. Each group could cut out just one type of picture.

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17 © Blake Education 978 1 86509 226 3


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What’s my pattern? What are you trying to do? ★ Make, describe, copy, extend patterns using 3D objects (3D1-4)



‘Magic’ cloth, e.g. a tea towel Groups of 3D objects, e.g. buttons, shells, blocks, crayons Construction toys, e.g. DUPLO, stickle bricks, multilinks What’s my pattern? cards (BLM p.20)

What do you do?

★ Reveal the cloth. Imagine this is a special cloth that puts things under it into a pattern. What is a pattern? What is not a pattern? How do you know? ★ Secretly make a pattern with several objects under the cloth, e.g. button, shell, block, button, shell, block. Reveal your pattern and talk about it. ★ Challenge someone else to make a different pattern under the cloth, e.g. red, red, yellow, blue blocks. Ask another person to continue this pattern. ★ What are different ways you can make a pattern? change colours, shapes, sizes put some things upside down use different quantities ★ Decide on a pattern to make with a partner. When you have about 6 or more objects, challenge another team to continue your pattern.

Variation ★ This is suitable for parent helpers or if you have a strong reader in the group. Work in pairs as part of a small group. Shuffle the cards and place them face down in the centre. Everyone makes a pattern with at least 6 objects in it. Turn over the top card. Read out the instruction. Try to follow the instructions with your pattern and your partner. e.g. Hide 2 objects - your partner has to tell you the hidden objects by looking at the other objects left in your pattern.

?

means you make up your own pattern challenge.




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Copy my pattern.

Continue my pattern.

Make a new pattern.

Change my pattern.

Talk about my pattern.

Hide one object.

Hide two objects.

?




Investigating 3D Properties

In this unit, your students will: • Predict and test which objects stack or pack (3D2-1) • Predict and test which objects roll or slide (3D2-2) • Identify, count, and describe faces, edges and corners of 3D objects (3D2-3)




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Stack and pack it What are you trying to do? ★ Predict, test which objects stack, pack (3D2-1)

How many can play?


What do you need?

★ Large and small empty boxes ★ Variety of toys, balls, blocks, containers, cans, books ★ Scissors, coloured pencils, workbooks ★ Mr Stack and Mrs Pack cut-outs (BLM p.23)

What do you do?

★ Tell the story of Mr Stack and Mrs Pack. They love to find things which stack or pack well. They don’t like things which don’t stack or pack well. Why do you think they feel this way? ★ Hold up an object, e.g. an empty milk carton. What do you mean by ‘stack’? How can you discover whether this stacks well? Guess first, then find a way to check. e.g. Get more cartons and try to put them on top of each other as high as they can go. Name some other things you think will stack easily. Name some things you think won’t stack easily. Explain your reasons. ★ Hold up another object, e.g. a ball. What do you mean by ‘pack’? How can you discover whether this packs well? Guess first, then find a way to check. e.g. Find other balls the same size and try to fit them into a box. Name some other things you think will pack easily. Name some things you think won’t pack easily. Explain your reasons. ★ Each team colours and cuts out a copy of Mr Stack and Mrs Pack. ★ Give each team a box of mixed objects to sort into two piles for Mr Stack (objects which stack/don’t stack easily) and two piles for Mrs Pack (objects which pack/don’t pack easily). ★ What will you do if an object belongs to both Mr Stack and Mrs Pack? ★ Record some of your discoveries in your workbook.

Variation

★ Challenge someone to find an object which can pack well but would be difficult to stack. Is it possible to discover an object which can stack easily but not pack?

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Mrs Pack Mr Stack

23 © Blake Education 978 1 86509 226 3


Roll or slide it What are you trying to do? ★ Predict, test which objects roll or slide (3D2-2)

How many can play?



Boxes of mixed 3D objects Wooden planks or ramps Workbooks, coloured pencils Mr Roll, Mrs Slide cut outs (BLM p.25)

What do you do?

★ Tell the story of Mr Stack and Mrs Pack’s neighbours. Mr Roll loves experimenting to see which objects roll. Mrs Slide loves experimenting to see which objects slide. ★ What can you do to your body to make it roll? What can you do to make it slide? Demonstrate if possible. ★ How can you discover whether an object can roll or slide? Discuss suggestions. e.g. Release objects from the top of a ramp. Check and discuss your results. ★ Each team colours and cuts out a copy of Mr Roll and Mrs Slide. ★ Give each team a ramp and a box of mixed objects to sort into two piles for Mr Roll (objects which roll/don’t roll) and two piles for Mrs Slide (objects which slide/don’t slide). ★ What will you do if an object belongs to both Mr Roll and Mrs Slide? ★ Record some of your discoveries in your workbook.

Variation

★ Which object rolls the furthest? Which object slides the furthest? How can you find out? Does changing the slope of your ramp make a difference?

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Mrs Slide Mr Roll

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What shape is my face? What are you trying to do? ★ Identify, count, describe faces, edges, corners of 3D objects (3D2-3)



Close-up pictures of wild animals (optional) A collection of interesting 3D objects Geometric blocks, paint, paper, dot stickers What shape is my face? worksheet (BLM p.27)

What do you do?

★ Close your eyes. Imagine the face of a wild animal. What does it look like? Open your eyes and tell the person sitting next to you what you saw. ★ What is a face? Do all people have faces? Do all animals? ★ Pass around some 3D objects. Do objects have faces? How can you tell? Discuss different reactions. ★ Explain that a face on an object is not like a face on a person or an animal. It is a flat surface. Not all objects will have faces. Objects can also have many faces, unlike people and animals. The faces will also feel different. e.g. Some may be smooth, some may feel rough. ★ Find an object with a flat face, e.g. a box. What shape is this face? e.g. Some faces are square, some are rectangular. Can you find a different object which also has a face the same shape as this one? e.g. a book ★ Find a partner. Walk around the room together. Find faces that are the shape of a square, a circle, a triangle or a rectangle. Are there any other face shapes you can discover? ★ Record your favourite discoveries on the worksheet.

Variations

★ Count the number of faces on an object. Put a dot sticker on each face to show it has been counted. Which object has the most faces? ★ Identify different faces on blocks. Paint the faces in different colours and print face patterns on paper. e.g. ★ Play games with logic blocks. Make shape trains by varying one attribute at a time. e.g.

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Where’s my edge? What are you trying to do? ★ Identify, count, describe faces, edges, corners of 3D objects (3D2-3)


What do you need?

★ A collection of 3D objects ★ One-minute timer ★ Where’s my edge? cards (BLM p.29)

What do you do?

★ Close your eyes. Imagine you are at a swimming pool. You are standing right on the edge. Open your eyes and tell the person next to you where you are. ★ What is an edge? Where do you see edges? e.g. the edge of a cliff, the edge of a forest, the edge of the playground ★ Explain that the edge of an object is where two faces meet. Pass around some objects to explore with your hands. Do all objects have an edge? Can an object have more than one edge? Discuss your discoveries together. e.g. An edge can be very long. An edge can be sharp or soft. ★ Consider safety issues. Explain that some edges are so sharp they can cut you. Take care when exploring edges with your fingers. ★ With a partner, walk around inside and outside your classroom investigating edges. ★ Discuss your discoveries together after a suitable time limit.

Variation

★ Work in small groups. Shuffle the cards and give one to each player. Start a one-minute timer. Try to find a matching shape to bring back to your group within the time limit.

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the shortest edge

the longest edge

the most edges

the fewest edges

a soft edge

a sharp edge

a wiggly edge

the most interesting edge

all curved edges

all straight edges 29



Corners What are you trying to do? ★ Identify, count, describe faces, edges, corners of 3D objects (3D2-2)


What do you need? ★ ★ ★ ★ ★

One-minute timer A very large cardboard box Coloured pencils, scissors, paste Little Jack Horner cut-outs (BLMs p. 31, 32) Prepared example of Little Jack Horner

What do you do?

★ Recite the rhyme Little Jack Horner. Ask everyone to stand up and move to a corner of the room like Jack. How do you know where this is? What is a corner? Discuss everyone’s suggestions. ★ A corner is the point or place where three or more faces on an object meet. It can be sharp to touch. You can have corners on the inside of objects (e.g. a room) or the outside of objects. The corner of the room is the spot where the two walls and the floor (or ceiling) meet. It is only a tiny place, just large enough to put your finger tip into, but you ususally refer to the whole area near this as the corner. ★ Discuss the inside and outside corners of the box. ★ Start the timer. How many different corners can you spot by the time the minute is up? What is the highest corner you can see? ... the lowest corner? ... the tiniest corner? ... the sharpest corner? Are there any other inside corners you can discover? Which object has the most corners? ★ Reveal your Little Jack Horner cut-outs. Demonstrate where the corner of his room is. Explain how to fold along the dotted lines then cut out the room along the bottom centre line to the dot, fold under and paste to create his corner. Show how to colour and cut out Jack, cut along his arms and fold to create a 3D effect. Cut out and paste the pie into one hand and fold the other to make him eating it.

Variations

★ Draw your own picture of Little Jack Horner to colour, cut out and place in a corner of your home. ★ Look for other poems, rhymes, and stories about corners or write your own. ★ The special name for the corner of an object is a vertex.

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Cut along thick, solid lines, fold along dotted lines.



Cut along thick, solid lines, fold along dotted lines.

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Constructing and Modelling

In this unit, your students will: • • • • •

Construct and model 3D objects using a variety of materials (3D3-1) Represent 3D objects through drawings and artwork (3D3-2) Create and identify cross-sections of 3D objects (3D3-3) Change the shape of 3D objects by bending, stretching, flattening (3D3-4) Construct a 3D object from a 2D net (3D3-5)

Exploring 3D Space and Position © Blake Education 978 1 86509 226 3


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Build it What are you trying to do? ★ Construct, model 3D objects using a variety of materials (3D3-1)


What do you need?

★ Building materials, e.g. DUPLO, multilinks, sticklebricks, large wooden blocks, empty cardboard cartons/containers ★ Timer, e.g. 3 minutes ★ Build it cards (BLM p.35)

What do you do?

★ Discuss different building materials used around the world, e.g. stone, bricks, wood, plaster sheets, metal, glass, concrete, ice. People use these to build in three dimensions - they can build along the ground (wide and deep) and they can build up (high). You can build solid objects, e.g. a sculpture, and you can build hollow objects, e.g. a house. ★ Discuss the building material available in your classroom. What sort of things can you build in three dimensions with each type? ★ Form small groups with one type of material for each group. ★ Set the timer. Each group tries to use as much of the material as possible to build a 3D structure. ★ Discuss the type of structures built by each group, e.g. height, width, colours, shapes, spread out/compact. ★ Rotate groups. ★ Which is your favourite material to use? Why?

Variations

★ Set the timer. Each person in the group builds a separate, smaller object. Compare and discuss your objects at the end of the time limit. ★ Shuffle the Build it cards. Turn over the top card. Build your model to match the statement on the card. For a greater challenge, combine two or more cards.

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as tall as your knee

as wide as the door

as long as a desk

as high as your shoulders

at least 20 pieces

red, green and yellow pieces

more blue than yellow pieces

between 30 and 40 pieces

smaller at the top than the bottom

with at least 2 holes in it 35



What shape is it? What are you trying to do? ★ Construct, model 3D objects using a variety of materials (3D3-1)

How many can play? ★ Up to 4 small groups

What do you need?

★ A packet of geometric biscuits, tray ★ Parent helpers ★ Playdough, plaster, water, moulds, plasticine, packet cake mix, a variety of cake trays, cooking utensils, bubble mix and bubble blowers, soft wire, workbooks ★ What shape is it? activity cards (BLM p.37,38)

What do you do?

★ Tip out the biscuits onto a tray. How can you make a 3D shape from these? e.g. Try stacking them to create a tall shape. Is there any other way? Can you make a cylinder or a box shape? Is your shape solid or hollow? What other biscuit shape challenges can you think of? After your discussion, eat them! ★ Blow some bubbles. Talk about the shapes you see. Can you make a bubble like a box? A ball? A cylinder? Why? Why not? Is a bubble solid or hollow? Can a bubble have a hole in it? What other bubble challenges can you think of? ★ Explain the group tasks. Give each group the following materials: Squish it: playdough Mould it: plaster, water, plastic moulds, plasticine Cook it: cake mix, cooking equipment Blow it: bubble mix, bubble blowers, soft wire Try to create as many different 3D shapes as you can with your materials. ★ Form rotating groups with a parent helper and an activity card for each group. ★ Discuss the results of your explorations together. Record your best discoveries in a workbook.

Variation

★ Try making different shapes with wet sand in a sand tray. Use plastic moulds, home made plasticine moulds or just your bare hands.

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Squish it Secretly make an object. Swap it with a friend then talk about your new shape. Guess what it is. If you are correct, squish it and start again. If not, ask your partner to keep adding bits until you guess correctly.

Mould it What’s the largest shape you can make? What’s the smallest? Use different mould shapes. Create your own moulds from plasticine. Does your shape have faces, edges or corners? Can you make a shape with a hole in it?



37

Cook it What type of cake shapes can you make? Predict how much mix you will need and how high each cake will rise. When baked, investigate different ways to slice them up. Look at the inside shapes you make.

Blow it How many different bubble shapes can you make? Make your own blowers. Change your bubble mix. What’s the largest bubble you can make? Which bubble shape lasts the longest?

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I spy What are you trying to do? ★ Construct, model 3D objects using a variety of materials (3D3-1)



Picture of a sea-captain or pirate with a telescope (optional) A telescope (optional) or a rolled up sheet of newspaper Paper, paste or sticky tape I spy fold-ups (BLMs p.40, 41)

What do you do?

★ Some 3D shapes are very useful for humans. Which ones can you think of? ★ Pass around the telescope (or newspaper roll). What shape is it? e.g. It’s a cylinder with a circle at the end. Who uses an object like this in real life? e.g. an astronomer, a sea-captain, a stargazer. Why? e.g. It helps you see objects that are far away. ★ Imagine you can only see the world through a telescope. How can you make your own pretend telescope? e.g. Use an old cardboard cylinder from the kitchen, or roll a piece of paper lengthways then paste the ends together. Discuss suggestions. ★ Make your own telescope. Find a partner. Explore what the world looks like from the end of your telescope. Walk around the classroom carefully, with your friend to guide you. Is there any difference if you look through your left or your right eye? ★ Explore what the outside world looks like through a telescope. Walk around with your partner to guide you. ★ Discuss other uses for a cylinder, e.g. to store rolled up pictures, to put pencils in, as a vase.

Variations

★ Make a telescope in a different shape. The net on p.40 folds to make a rectangular shape with a square at each end. The net on p.41 folds to make a rectangular shape with a triangle at each end. Can you think of a way to make any other shapes? ★ How can you make a cone from a sheet of paper? It can be used to hold some sweets for a party, or as a party hat.




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Fold along the dotted lines. Paste this tab to the other edge.

Rectangular prism telescope 40 © Blake Education 978 1 86509 226 3


Fold along the dotted lines. Paste this tab to the other edge.

Triangular prism telescope 41



Draw it What are you trying to do? ★ Represent 3D objects through drawings and artwork (3D3-2)


What do you need?

★ Photographs, pictures of 3D objects ★ Coloured pencils, paper ★ Draw it worksheets (BLMs p.43,44)

What do you do?

★ Discuss how you recognise features in a photograph or picture. ★ Imagine that you can’t talk. Your birthday is soon. You can’t find any photograph or picture of what you would like for your birthday present. You want to draw a picture to show your grandma what to buy. What are the essential features to put in your drawing? e.g. shape, size, colour, small details ★ Secretly decide on a birthday present to draw. Think about which features to include. Draw your picture then swap pictures with a friend. Can you guess what their secret present is without them talking about it? ★ Discuss what you found easy about this task, what you found difficult. Do other students feel the same way?

Variations

★ Work with a partner. Find an object that you both think is interesting to draw. Place the object in front of you both and draw it. Compare drawings. Which features are the same? Which are different? ★ Find another object. One person draws with the object in front of them. The other person looks at the object for up to one minute, then draws the object from memory, with their back to the object. Compare drawings. Which features are the same? Which are different? ★ Use only the top section of the Draw it worksheet on p.43. Look at the outlines. Can you guess which 3D object each represents? Think of at least 2 different possibilities. Draw in your own details to create a 3D picture. The bottom section shows you one solution. It is the original picture. You can cut and paste these to match later. ★ Use the Draw it worksheet on p.44 for a greater challenge.

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43 © Blake Education 978 1 86509 226 3


44 © Blake Education 978 1 86509 226 3


Copy me What are you trying to do? ★ Represent 3D objects through drawings and artwork (3D3-2)

How many can play? ★ Small groups, pairs

What do you need?

★ Giant envelope with sample drawing of a 3D model made from blocks ★ Building blocks, e.g. DUPLO, sticklebricks, multilinks, foam blocks ★ Pencils, paper, craft paper, paint, paintbrushes, scissors, paste, playdough, plasticine ★ Copy me activity cards (BLMs p.46, 47)

What do you do?

★ Reveal the picture hidden in the envelope. How do you know what this is? Could you make an identical model from blocks just by looking at the drawing? Ask someone to try. ★ Discuss the results. How can you show height? ... width? ... depth? Is colour important? How do you know how many blocks to use? ★ Form small groups. Explain each group task. Use only a few blocks, e.g. 4-6, to start with. Build with more blocks as you gain confidence. ★ Give each group an activity card. Collect the equipment you need. ★ Rotate groups after a suitable time limit. ★ Discuss your results as a whole class. Was it easier to copy from a drawing than a painting? ... from cut paper rather than a tracing? Was there more than one solution each time?

Variations

★ Follow building instructions with commercial 3D building blocks, e.g. DUPLO, LEGO. ★ Draw your own picture of a model made from playdough or plasticine for a friend to use as a modelling instruction.




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Trace it Build a flat model from blocks. Trace around this on paper. Hide your model. Ask a friend to make a copy of your model by looking at your tracing. Compare models.

Draw it Build a model from blocks. Draw a picture showing all the details. Hide your model. Ask a friend to make a copy of your model by looking at your drawing. Compare models.

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Paint it Build a model from blocks. Paint a picture showing all the details. Hide your model. Ask a friend to make a copy of your model by looking at your painting. Compare models.

Cut or tear it Build a model from blocks. Make a copy by cutting, tearing and pasting coloured paper to make a picture. Hide your model. Ask a friend to make a copy of your model by looking at your picture. Compare models.



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Slice it up What are you trying to do? ★ Create, identify cross-sections of 3D objects (3D3-3)


What do you need? ★ ★ ★ ★ ★

Two unsliced loaves of bread (round, square), a bread knife Playdough, plasticine, clay, wet sand Plastic knives, plastic covers for each desk Timer Slice it up challenge cards (BLM p.49)

What do you do?

★ Talk about the different shapes of a loaf of bread. Do you buy your bread sliced or unsliced? Talk about the shapes you see on the outer sides of a loaf. Talk about the shape you see inside when you slice a loaf into two. ★ What happens if you cut the bread in a different way? e.g. slice it at an angle Predict then check. Is the inside shape the same as before? Does this always happen? ★ What if you slice up other objects? Form small groups with playdough or plasticine, a desk cover and some plastic knives for each group. Make an object from playdough and predict then check which inside shape will be revealed when you slice it up. ★ Report some of your discoveries back to the whole class. ★ What other objects can you slice up? e.g. meat, vegetables, fruit for dinner Why do you do this? e.g.to make smaller portions, for decoration, to make food look interesting

Variations

★ Slice up vegetables or fruit and investigate the inside shapes that are revealed. Predict first, then check. ★ Cut a long piece of wood at different angles and join the pieces together to make a frame. ★ Work in small groups with the challenge cards. Use playdough and a plastic knife to explore different solutions. Shuffle the cards and turn over the top card. Set a time limit. How many different objects can you make that have the shape shown when you slice each object in two? Does cutting the object at different angles change the shape formed? ★ Draw your own Slice it up challenge cards for another team to try.

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49



Change my shape What are you trying to do?

★ Change the shape of 3D objects by bending, stretching, flattening (3D3-4)

How many can play?


What do you need?

★ Balloons ★ Variety of rubber, plastic, foam, wooden 3D shapes, playdough ★ Variety of cardboard boxes ★ Scissors ★ Change my shape activity cards (BLMs p.51, 52)

What do you do?

★ How many different shapes can you make from one balloon? Inflate a balloon and discuss the shape formed. What can you do to change this shape? Discuss suggestions, e.g. pull it, stretch it, step on it. ★ Why can you change the shape of some objects and not others? e.g. Some are soft and easy to squash, others are hard and solid – you’d have to cut them to change the shape. Some aren’t rigid and can be pushed. ★ Which of these changes are permanent? Why? Why not? ★ Discuss the 4 activities. Each team will focus on one aspect to investigate. Form small groups with an activity card each. Collect the equipment you need. Encourage each group to be creative in their investigations. ★ Report back to the whole class. What were your most interesting discoveries? What did you find the most difficult to do?

Variation

★ Investigate ways to change the shape of fruit and vegetables. e.g. Can you flatten a banana? ...bend a carrot? ....twist a zucchini?

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Bend it Which objects can be bent? Predict first, then check. Do the bends stay in shape? Which object can be bent the most? ... the least? How does the object change shape? Can you undo your bend?

Stretch it Which objects can be stretched? Predict first, then check. Do the stretches stay? Which object can be stretched the most? ... the least? How does the object change shape? Can you undo your stretch?



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Flatten it Which objects can be squashed flat? Predict first, then check. Which type of object can be flattened the most? How does the object change shape? Can you undo the flattening?

Twist it Which objects can be twisted? Predict first, then check. Which type of object can be twisted the most? How does the object change shape? Can you untwist your object?

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Open it out What are you trying to do? ★ Construct a 3D object from a 2D net (3D3-5)

How many can play?


What do you need?

★ Variety of large and small cardboard boxes, plastic containers ★ Net for triangular prism (BLM p.54)

What do you do?

★ What things do you store in boxes in your home? Discuss. ★ Sometimes a box is empty but you still want to keep it. How can you store it so it doesn’t take up as much space? e.g. You can try to squash it flat. Demonstrate. Discuss the shapes you now see. ★ Can all boxes be opened out to make a flat shape? Predict first, then check. Can your object be closed up again? Are small objects easier to flatten than large objects? ★ A net is a flattened object that can be folded to make a 3D shape. A net is when you squash a box flat then open it out so that there are no faces overlapping. It sometimes has extra tabs to allow you to paste one face next to another. ★ Form small groups. Look at different ways to flatten a box to make a net, then refold it. Encourage each group to be creative in their investigations. ★ Report back to the whole class. What were your most interesting discoveries? What did you find the most difficult to do?

Variations

★ Make a triangular box using the net on p.54. Decorate the 5 faces. Cut along the outside edges, fold and paste the tabs to create your 3D object. ★ Other nets can be found in Book 1: Exploring 1-5 (p.70 - triangular pyramid) and Book 2: Exploring 6-10 (p.16 - cube) of the Exploring Maths series.

Exploring Length and Area © Blake Education 978 1 86509 226 3


53

TA B

TA B

B TA

TAB

B TA

54




Exploring Position Language

In this unit, your students will: • • • •

Use informal position language (P1-1) Describe the position of an object from different points of view (P1-2) Use the terms left and right (P1-3) Describe and follow simple directions (P1-4)




55

Where am I? What are you trying to do? ★ Use informal position language (P1-1) ★ Describe the position of an object from different points of view (P1-2)


What do you need?

★ Toy collections, e.g. farm animals, wild animals, dinosaurs, matchbox cars, DUPLO people ★ A teddy bear ★ Where is baby? cards (BLM p.57)

What do you do? ★ Describe your position in the room, e.g. beside the table, near the window. Repeat with someone else in the room. ★ Select 5 or more students to stand at random. Secretly imagine you are one of these students. Ask everyone to guess who you are without mentioning your name. e.g. They can’t ask ‘Are you Phil?’ Instead they ask you position questions. e.g. ‘Are you in front of Lucy?’ ‘Are you beside the cupboard?’ Only when they have worked out all your clues can they then say your name. e.g. ‘Are you Lee?’ How many questions before the rest of the class guess who you are? ★ Make a list showing all the position terms you used, e.g. on the chalkboard or wall display. Discuss. ★ Form pairs. Give each pair 5 or more objects, e.g. farm animals. Rearrange these objects in front of you. Secretly imagine you are one of the objects. Your partner asks you position questions to guess who you are. Keep a record of how many questions they ask. What’s the fewest number of questions you need?

Variations ★ Play Select someone to hide a teddy somewhere in the room, while everyone else shuts their eyes. Ask position questions to discover teddy’s secret hiding place. e.g. Is teddy inside the cupboard? ...under the table? ★ Play Baby loves to play games with her father. Shuffle the cards. Take turns to look at the top card. Describe Baby’s position by inventing a small story. e.g. Baby is hiding behind Dad because she is frightened of the rhino at the Zoo.

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57 © Blake Education 978 1 86509 226 3


Line them up What are you trying to do? ★ Use informal position language (P1-1) ★ Describe the position of an object from different points of view (P1-2)


What do you need?

★ A4 paper, cut into 2 long strips ★ Pencils, crayons, scissors, paste ★ Line them up worksheet (BLM p.59)

What do you do?

★ Ask 5 students to stand in a line at the front of the class. Who is first? Who is last? Who is next to Sam? ★ Who am I? Give position clues related to the students at the front. How quickly can someone guess which person you are thinking of? ★ Discuss the objects on the worksheet. Colour and cut them out. Work in pairs. Tell a partner how to paste objects in a line by giving position clues. e.g. The emu is first. The apple is next to the emu. ★ Swap strips with another pair. Play Who am I? Can you quickly guess which object your partner is thinking of by asking position questions? ★ Review different ways to describe a position.

Variations

★ Paste your objects anywhere on a whole page. Play Who am I ? with a partner. ★ Play Where are you? as a partner or whole class game. In the playground, call out instructions for everyone to follow. e.g. Go around the large tree and under the monkey bars. Call out ‘Where are you now?’ Elect someone to call out their position. e.g. I’m beside the wall. I’m next to the fence.

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59

Left or right? What are you trying to do?

★ Describe the position of an object from different points of view (P1-2) ★ Use the terms left, right (P1-3)


What do you need?

★ Paper, crayons, scissors, paste ★ Ribbons ★ Foot cut-outs (BLM p.61)

What do you do?

★ Look at your hands. Talk about the similarities and differences. e.g. Older hands are more wrinkled. Some might have freckles. Look at the shape of your hands. e.g. fingers held together, fingers spread apart ★ Trace the outline of your hands onto paper. Whose hand is the largest? How can you tell? e.g. Compare by overlapping hands onto the outline. ★ Discuss the fact that some people use their left hand more than their right. Find out who is left-handed in your class. Tie a ribbon around everyone’s left hand. Investigate what your left hand looks like when it is face down on the desk or face up. Where is the thumb each time? ★ Write the word left on your left-hand outline. ★ Explore what you can do with your left hand. e.g. Can you write your name? ... throw a ball? ... undo a shirt button? ★ Make a list of things that are easy to do with your left hand and things that are difficult to do.

Variations

★ Have a left day. e.g. Walk starting with your left foot. Try to do everything you can with your left hand. Eat your lunch chewing everything from the left side. ★ Make multiple copies of the foot outlines. Colour, e.g. left foot red, right foot green, laminate (optional) and cut out. Shuffle the cutouts. Place these in a long line all around your room. Ask someone to walk along it following the left or right instructions. e.g. Left, left, left means hop 3 times on your left foot.

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Robots What are you trying to do? ★ Use the terms left, right (P1-3) ★ Describe and follow simple directions (P1-4)


What do you need?

★ Balls, beanbags, hoops ★ Direction spinner, activity cards (BLM p.63)

What do you do?

★ What is a robot? Why did humans invent them? What would you ask a robot to do if you had one for a day? ★ Imagine you are a robot. What directions will you need to follow to move about? e.g. Go forwards 4 steps. Turn right. Go backwards 2 steps. ★ Form pairs. One person is a robot. The other person gives directions to follow. Swap roles after a suitable time limit, e.g. 3 minutes. ★ Discuss any problems or difficulties. e.g. Left and right relate to the person moving. If you and your robot are both facing forwards, then left and right will mean the same. If your robot is facing towards you, then their left and right will be opposite to yours. You can solve this problem by always facing in the same direction as your robot. Or your robot can wear a ribbon on their left hand as a reminder.

Variation

★ Form small groups with a spinner, cards placed face down, a beanbag, a ball and a hoop. Take turns to spin the spinner, turn over the top card and follow the instructions. e.g. Jump to the left. Catch a beanbag with your left hand. Bowl a hoop backwards. Are some instructions easier to carry out than others?

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Direction spinner t h g

b a c

ri

kw

fo

rw

ft

le

ar ds

a r d s Colour, laminate, cutout. Place a small stick through the centre and check for bias.

kick a ball

bowl a hoop

catch a beanbag

throw a ball

hop

jump 63



Arrows What are you trying to do? ★ Use the terms left, right (P1-3) ★ Describe and follow simple directions (P1-4)


What do you need?

★ Crayons, scissors, chalk ★ Plenty of arrow cutouts (BLM p.65) ★ Wild animal worksheet (BLM p.66)

What do you do?

★ Imagine you are not able to talk. Your friend is afraid of bees and you can see one coming near them. You want to show them where it is. What can you do? e.g. Point to the bee with your hand. ★ Everyone stand up. Using your right hand, point to the ceiling, to the left, backwards, to the corner of the room. How else can you communicate a direction without talking? ★ Sometimes people use arrows to show directions. Where do you see arrows used in your daily life? e.g. In a large carpark to show where the shops start. ★ Explain how to use the arrow cutouts to lay out a path for someone to follow. e.g. Each arrow can represent one step. ★ Explore making and following arrow paths with a partner or in a small group. Try leading someone with a blindfold, giving position clues as you go. e.g. Take 4 steps forwards, then turn left. Take 3 steps forwards then stop. Go under the table.

Variations

★ Use chalk arrows instead of arrow cutouts on the playground. Make a path for someone else to follow. ★ Devise an outdoor obstacle course using tables, chairs, boxes and PE equipment. Use the arrows to show which direction to go in. Can you make a map of your course by recording the information as a diagram? ★ Work with a partner. Use the Wild animal worksheet. Imagine your partner is a small bird that can fly or walk about everywhere at the waterhole. Ask your partner to draw their path as arrows on the worksheet as you describe where they go. e.g. Start at the big tree. Go to the top of the elephant’s trunk.

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65 © Blake Education 978 1 86509 226 3


66



Identifying Positions

In this unit, your students will: • Describe the position of an object in models, pictures, sketches (P2-1) • Construct a model from memory, verbal instructions or diagrams (P2-2) • Draw an object from different points of view (P2-3)




67

Dinosaur bones What are you trying to do? ★ Describe the position of an object in models, pictures, sketches (P2-1) ★ Construct a model from memory, verbal instructions or diagrams (P2-2)

How many can play?

★ Whole class, pairs within 4 small groups


Model dinosaurs Construction materials, e.g. wooden blocks, DUPLO A cloth, e.g. a tea towel Dinosaur bones activity cards (BLMs p.69, 70)

What do you do?

★ What do you know about dinosaurs? ★ Imagine you are a palaeontologist hunting for dinosaur bones. You discover a complete set, but the bones are jumbled up. How will you put them back together? Discuss with another palaeontologist. ★ Imagine the construction materials are dinosaur bones. Demonstrate how to build part of a dinosaur with 4 pieces. What could this be? e.g. Part of a dinosaur head or a leg. ★ Explain the group activities. Form 4 groups with an activity card per group. Find a partner within your group. Collect two identical sets of about 4-6 blocks, where the colour, shape and size match. Suggest that each pair start by using 3-4 blocks for each activity. ★ Increase the difficulty later by adding one block at a time.

Variations ★ Try using more pieces. What’s the largest number of pieces you can copy from memory? Is it easier to remember if all the pieces are the same colour? ★ Play as a group game with identical pieces for each player. The leader sits in the centre with a model. The other players sit in a circle facing out. Each player asks the leader a question about the model. What’s the smallest number of questions needed to copy it? ★ Hide your model. Your partner now feels under the cloth but this time tells you how to put their pieces together to make a copy of your model. ★ Take turns to tell each other one block to place at a time.

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Yes/No Sit back to back. Secretly build a dinosaur. Your partner tries to build an identical copy by asking you questions. You can only answer ‘Yes’ or ‘No’. Don’t let your partner see your model until the end. Compare models.

Look alikes Secretly build a dinosaur. Show it to a partner for a short time then hide it. Ask your partner to make an identical copy from memory. What’s the shortest time they need? Compare models.

69 © Blake Education 978 1 86509 226 3


Under the cloth Secretly build a dinosaur. Hide it under a cloth. Your partner can now feel your model with their hands under the cloth. They can’t peek under! Can they use these clues to build an identical model? Compare models.

Talk to me Sit back to back. Secretly build a dinosaur. Tell your partner how to build an identical copy. e.g. Put the large red piece next to the long blue one. Don’t let them see your model until the end. Compare models.

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Draw me What are you trying to do? ★ Draw an object from different points of view (P2-3)

How many can play?


What do you need?

★ Paper, pencils, blocks ★ Draw me cards (BLM p.72)

What do you do?

★ Stand up. Face a partner. Talk about the different body parts you can see, e.g. 2 arms, 2 hands, a neck. ★ Discuss how to draw a picture of your partner. Where will you start your drawing? e.g At the head? At the feet? From one arm? ★ Discuss the position of each body part. e.g. Your head is on top of your neck. What would you look like if the parts were in a different order? ★ Discuss the meaning of each instruction on the Body parts cards. e.g. Draw 2 legs means without the feet. Draw a head means without any facial features. ★ Play a drawing game as a whole class or in small groups. Try to draw a complete body by drawing each part in isolation as instructed. Shuffle the cards. The leader calls out the instructions shown on the top card. Everyone draws that body part on their paper. Keep drawing one body part at a time until your person is complete. Compare drawings. Are all the parts in the correct position? Are they all in proportion?

Variations

★ Investigate famous artworks that mix body parts, e.g. Picasso’s Weeping Woman. ★ Use 2 identical sets of blocks. Build a model dinosaur with one set. Draw a picture of your model. Hide your model. Ask a partner to use the second set of blocks to recreate an exact copy based on your drawing. Compare models.




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Draw a head.

Draw a body.

Draw 2 legs.

Draw 2 arms.

Draw 2 hands.

Draw 2 feet.

Draw some hair.

Draw 2 eyes.

Draw a mouth and a nose.

Draw a hat.

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Which view? What are you trying to do? ★ Draw an object from different points of view (P2-3)



Interesting objects to draw, e.g. a teapot, a shoe A chalkboard, chalk Paper, pencils Which view? worksheet (BLM p.74)

What do you do?

★ Think of objects which look the same from any viewpoint, e.g. a beach ball. The shape is always a sphere, no matter how you hold it. ★ Think of objects which look different from different viewpoints, e.g. a pet cat seen from in front, behind, from the side. ★ Hold up an interesting object, e.g. a teapot. Try to show just the front view, e.g. place it in an open box. Challenge someone to draw on the chalkboard what this object will look like when seen from above. Compare the drawing with the actual view. Discuss similarities and differences. ★ Discuss the worksheet. What is meant by the different viewpoints? e.g. Looking from above means to imagine you are flying like a bird and can look down directly on the top of your object. ★ Work with a partner. Find an object to draw from different views on your worksheet. Compare drawings. Discuss.

Variations

★ Look at an object from the front only. Imagine what it will look like from different viewpoints. Draw these imagined views on your worksheet. Compare the actual view with your drawing. Is your imagination close? ★ Look at objects from a second storey window, e.g. cars in the teachers’ carpark. Discuss ways in which objects look different from above.




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Looking from the front

Looking from the left side

Looking from above

Looking from below

74 © Blake Education 978 1 86509 226 3


Feed the animals What are you trying to do? ★ Describe the position of an object in models, pictures, sketches (P2-1) ★ Solve problems related to position ★ Work cooperatively as a team

How many can play? ★ Small group

What do you need?

★ Scissors ★ Five plastic farm animals, e.g. DUPLO cow, horse, pig, chicken and sheep, a farmer and a trough ★ Feed the animals clue cards (BLM p.76)

What do you do?

★ When do you stand in a queue? e.g. To buy a movie ticket at the cinema. Why do you do this? e.g. To prevent arguments as to who was there first. ★ Maria lives on a small farm. Each night her animals queue up to be fed. If they are not in the exact order she has worked out, then they squabble and fuss. Your challenge is to put the animals into order. It is not an easy challenge! ★ Look at the Feed the animals clues. Each of the five cards tells you about part of the queue. Discuss the problem in your own words. How can you work out your solution? ★ Work together to find a solution. What strategies do you use? ★ Check your solution against each statement. Which animal is first in line? Which animal is last? ★ When you are convinced your solution is correct, see if you can discover a different one.

Variation

★ Invent your own position problem like this, e.g. cars lining up at traffic lights, people standing in a bus queue. Write your clues onto cards for another team to solve. Find or draw objects to use as props to solve your problem. Solutions to Feed the animals:

S Co P

Ch P Co

H S S

Co Ch Ch

P H H




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Maria’s animals are standing in a line.

The cow is not last.

The sheep is next to the chicken. The pig is near the cow. The horse is behind the chicken. 76 © Blake Education 978 1 86509 226 3


Exploring Paths and Grids

In this unit, your students will: • Describe, follow and draw a path on a simple map or maze (P3-1) • Describe positions on a simple grid (P3-2) • Use coordinates to describe positions on a simple grid (P3-3)




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Lead the way What are you trying to do? ★ Describe, follow, draw a path on a simple map or maze (P3-1)



Hansel and Gretel storybook String, wool, coloured chalk Pencils, paper Lead the way worksheet (BLM p.79)

What do you do?

★ Discuss animals that leave scent trails as they walk, e.g. ants. ★ When are your footsteps visible when you walk? e.g. After walking in a puddle of water, wet sand or mud. ★ Discuss the story of Hansel and Gretel, who left a breadcrumb trail into the forest. ★ Imagine that everywhere you walk you leave a trail. How could you do this? e.g. Tie string to your starting place or draw a chalk line behind you on the playground. ★ Work with a partner. Decide on a way to mark a short trail in the room or playground. Ask another team to follow your trail. Were there any problems? ★ Draw your trail on paper. Write about it too!

Variations

★ Draw a map showing the way from your house to a friend’s house. Show key things you see along the way. Write instructions for someone else to follow. ★ Use the Lead the way worksheet. Select two students’ houses. Mark the path you would take to get from one to the other. Then write instructions for someone who is driving you from one house to the other.

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How amazing What are you trying to do? ★ Describe, follow, draw a path on a simple map or maze (P3-1)

How many can play? ★ Pairs, individuals

What do you need?

★ Examples of commercial maze worksheets ★ How amazing worksheet (BLM p.81)

What do you do?

★ What is a maze? e.g. It is a set of possible paths, most of which lead to deadends. Where do you see mazes? e.g. Giant hedge mazes in an amusement park. ★ How do you find your way out of a maze? Discuss suggestions. ★ Look at the sample mazes. Usually there is a problem to solve. e.g. There is a lost child and you have to find the path that leads to his parents. The paths often cross over, or turn corners. There is usually only one correct path that leads you from one end of the maze to the other. ★ Demonstrate how to find a path through one of the sample mazes. ★ Explain the worksheet. The rabbit wants to get to her yummy carrot dinner. At present there are many paths to take. Which way would you go? ★ Work with a partner. Block off some of the paths to create your own maze. Ask another team to discover your path in the shortest time possible. Is there more than one way to do it? ★ Discuss any problems as they arise.

Variations

★ Look at picture books about mazes. e.g. Madgwick, W. (1992) Animaze. Australia: Koala Book Company. ★ Make up your own How amazing worksheet problem for another team to solve. e.g. Find the best way for a car to get to a garage.

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How amazing

81 © Blake Education 978 1 86509 226 3


Tic tac toe What are you trying to do? ★ Describe positions on a simple grid (P3-2)


What do you need?

★ Chalkboard, chalk ★ Small tiles or counters in 2 colours ★ Tic tac toe grids (BLM p.83)

What do you do?

★ Draw a 3 x 3 grid on the chalkboard. Discuss names to describe each of the 9 positions, e.g. the middle, the top left corner. ★ Describe a normal Os and Xs game where you try to get 3 of your markers in a row, column or diagonal. Ask 2 players to compete at Os and Xs on the board. ★ Explain the rules for your new Tic tac toe game. This time you can’t touch your own counters, e.g. red. When it is your turn to play, you tell the other player where to place your counter. You are still trying to get 3 of your counters in a row, column or diagonal. ★ Is there a winning strategy? Discuss after several games have been completed.

Variations

★ Add more rules. e.g. You can’t use the middle space until your third go. ★ Play on a larger grid, e.g. 4 x 4 spaces. ★ Play with blindfolds. Tell a third player how to place your counters. Remember your goes by seeing a mental picture of your board!

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Tic tac toe

Tic tac toe

83 © Blake Education 978 1 86509 226 3


Dino-jig-saur What are you trying to do? ★ Describe positions on a simple grid (P3-2)


What do you need?

★ Coloured pencils, paper, scissors, paste ★ Dino-jig-saur pieces (BLM p.85) ★ Dino-jig-saur grid (BLM p.86)

What do you do?

★ Imagine you are a palaeontologist trying to unjumble pieces of a dinosaur. There are usually not many clues to help you. ★ Talk about jigsaw puzzles. How do you know where to place each piece? What’s the largest number of pieces you can put together? 50? 100? 500? What clues do you look for? e.g. corners, edges ★ Look at the worksheet with the 9 dinosaur pieces. Your challenge is to cut these out then arrange them to make the body of a dinosaur. Each one is marked with a clue to help you, e.g. middle 2. What does this mean? ★ Look at the 3 x 3 grid. Discuss the different labels for the columns and rows. Explain how to cut out each dinosaur piece one by one and paste it onto the matching space on the grid. ★ When the last piece has been placed, your dinosaur should be complete. Colour it in, although no-one knows exactly what colour dinosaurs were!

Variations

★ Draw your own 3 x 3 grid. Draw an interesting picture on this grid, e.g. your favourite pet. Cut up this grid, one square at a time. Write your clue on the back of each square, e.g. right 3. Ask a friend to put your picture back together by following your clues. ★ As a super challenge, design even larger grid puzzles, e.g. 3 x 6, 4 x 4.

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Middle 2 Left 2 Right 1

Left 3 Middle 1

Right 3

Left 1 Right 2

Middle 3

Dino-jig-saur pieces




85

Right Exploring 3D Space and Position



1

2

3

Left

Middle

Dino-jig-saur 86

Take me there What are you trying to do? ★ Describe positions on a simple grid (P3-2)

How many can play? ★ Small groups, pairs

What do you need?

★ Pencils, paper ★ Take me there grid (BLM p.88)

What do you do?

★ What are special features of the area where you live? e.g. shops, a river, wheat farms. What other features would you need to record if you were drawing a map? e.g. roads, railways, bridges ★ Tell the person next to you how to get from your house to somewhere else in your neighbourhood. e.g. Go to the end of the street then turn right at the roundabout. ★ Discuss the Take me there grid. What do the symbols stand for? e.g. The car might represent a carpark. The boat might be on a lake or a river. The hot air balloon may be a base for early morning flights. ★ Imagine you are the person in the bottom left corner. Where would you like to visit on your map? e.g. the duck pond. If you can only move to the left or right and up or down, how could you get there? ★ Discuss directions together. e.g. Move 2 spaces to the right. Go up 2 spaces. Go one space to the right again. Where are you? Is there another way? ★ Play with a partner and a grid each. Start in the bottom left corner. Give instructions for your partner to follow. ★ Swap roles.

Variations

★ Colour in your path as you go for a permanent record of your wanderings. ★ Create your own grid map of your area.




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88 © Blake Education 978 1 86509 226 3


Find the treasure What are you trying to do? ★ Use coordinates to describe positions on a simple grid (P3-3)

How many can play? ★ Pairs, small groups

What do you need?

★ Counters in 2 colours, e.g. red, black ★ Paper, pencil ★ Find the treasure grid (BLM p.90)

What do you do?

★ Long ago, cargo ships carried silver, gold and precious objects around the world. Shipwrecks were common. Some people believe treasure can still be found on a deserted island, hidden there by a pirate or a shipwreck survivor. ★ Look at the island map. Describe what you can see, e.g. a volcano. Where would you hide treasure on this island? ★ Look at the grid. Discuss the labels for each column and each row. Explain how to name each space by reference to these labels. e.g C4 is the space where column C and row 4 intersect. These are its coordinates. Practise pointing to and naming grid spaces using coordinate labels. ★ Play a partner game. Take a grid map each and some coloured counters. Sit so that your map can’t be seen by your partner, e.g. back to back. The leader hides some treasure at random on their island, e.g. 4 black counters. The other player tries to find this treasure by calling out coordinate clues. e.g. Is it on D5? If incorrect, mark this spot with a counter, so you remember that you have asked it. Continue marking spaces on the map until all the treasure is discovered. ★ Swap roles.

Variations

★ Play a small group version with the leader in the centre and the other players facing out in a circle. ★ Play a more challenging game by hiding only one piece of treasure. ★ Play an easier game by drawing up a smaller grid, e.g. 3 x 4, labelling the columns and rows and drawing your own island. ★ Work with a partner. Draw a 5 x 5 grid. Label the columns A to E and the rows 1 to 5. Write in all the letters of the alphabet at random in the 25 spaces. Write z (the 26th letter) in the same space as q. You now have your own alphabet code. Write secret messages to each other in code. Only you will be able to decipher them!




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Find the treasure

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B

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D

90 © Blake Education 978 1 86509 226 3


E

EXPLORING 3D SPACE AND POSITION

NAME

Outcome Indicators Record Sheet Exploring 3D Space 3D1-1 Sort, compare, describe 3D objects 3D1-2 Recognise, name simple 3D objects 3D1-3 Match 3D objects with 2D drawings, photographs 3D1-4 Make, describe, copy, extend patterns using 3D objects 3D2-1 Predict, test which objects stack or pack 3D2-2 Predict, test which objects roll or slide 3D2-3 Identify, count, describe faces, edges, corners of 3D objects 3D3-1 Construct, model 3D objects using a variety of materials 3D3-2 Represent 3D objects through drawings and artwork 3D3-3 Create, identify cross-sections of 3D objects 3D3-4 Change the shape of 3D objects by bending, stretching, flattening 3D3-5 Construct a 3D object from a 2D net Exploring Position P1-1 P1-2

Use informal position language Describe the position of an object from different points of view

P1-3

Use the terms left, right

P1-4 P2-1

Describe and follow simple directions Describe the position of an object in models, pictures, sketches Construct a model from memory, verbal instructions or diagrams

P2-2 P2-3

Draw an object from different points of view

P3-1

Describe, follow, draw a path on a simple map or maze

P3-2

Describe positions on a simple grid

P3-3

Use coordinates to describe positions on a simple grid




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Sample Yearly Mathematics Topics Mathematics Topics for 5 year olds Week 1 2 3 4 5 6 7 8 9 10

Term 1 Prenumber Prenumber Space: 3D Number Space: 3D Number Space: 2D Number Space: 2D Number

Term 2 Number Length Number Time Number Mass Temperature Number Money Revision

Term 3 Chance/Data Number Space: Position Number Space: 3D Space: 2D Time Number Volume Revision

Term 4 Chance/Data Early Fractions Length Early +/Area Time Mass/Volume Space: Position Number Revision Measurement Revision

Mathematics Topics for 6 year olds Week 1 2 3 4 5 6 7 8 9 10

Term 2 Numeration 3D Space Length Exploring +/Money Volume Exploring x Mass Fractions Revision

Term 1 Numeration 3D Space Length Exploring +/2D Space Volume Numeration Mass Time Revision

Term 3 Numeration 2D Space Area Exploring +/Position Time Exploring x Temperature Fractions Revision

Term 4 Numeration 3D Space Chance/Data Exploring +/2D Space Position Exploring ÷ Measurement Revision Number Revision Space Revision

Mathematics Topics for 7 year olds Week 1 2 3 4 5 6 7 8 9 10 92

Term 1 Numeration 3D Space Exploring +/Length 2D Space Volume Numeration Time Exploring x Revision

Term 2 Numeration 3D Space Exploring +/Area Fractions Mass Exploring x Money Position Revision

Term 3 Numeration 2D Space Exploring +/Length Exploring x Temperature Exploring ÷ Chance/Data Fractions Revision




Term 4 Numeration Time Exploring +/2D Space Exploring x Volume/Mass Exploring ÷ Measurement Revision Number Revision Space Revision




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• Whole class sharing, discussion.

• Group activities: A: Is this a box? (p.12) B: What shape is my face? (p.26) C: Slice it up (p.48).

• Review activities.

• Group activities: A: Spin-a-shape (p.14), Game 3/magazine match. B: Where’s my edge? (p.28) C: Change my shape (p.50). • Who am I? (3D shape clues).

• Whole class: Explore 3D shapes in playground walk. Discuss edges. Explore how to bend, stretch, flatten shapes.

• Whole class: Pass around random 3D shapes. Discuss and sort.

• Whole class: Discuss random shapes. Emphasise boxes, balls, cans. Discuss what is/is not a face on an object.

• Group activities: A: Spin-a-shape (p.14), Games 1/2. B: What shape is my face? (p.26), variations. C: Slice it up (p.48) + challenge cards.

WEDNESDAY

TUESDAY

• Group activities: A: Shape snap (p.16) B: Where’s my edge? (p.28) + variation C: Change my shape (p.50).

• Fast workers: Make your own triangular box. Decorate. Hang as class mobile.

• Mixed group circle activity: Say everything you can about a shape when it is your turn.

• Whole class: Who am I? (3D shape clues game). Revise balls, boxes, cans faces, edges, corners.

• Whole class: Who am I? (3D shape clues game). Discuss 3D pictures. Find matching shapes in the room. Discuss Shape snap pictures.

FRIDAY

3D shapes for each group Scissors, paste Triangular prism net (BLM p.54)

THURSDAY

Pictures of 3D shapes Shape snap cards (BLMs p.17,18) Cards (BLM p.29)

like a box, cone, ball, can face, edge, corner slice, like a circle, triangle, square pull, stretch, flatten, squash net

Magazines Rubber, foam, plastic, wood 3D shapes

• • • • •

LANGUAGE

SUBSTRAND 3 Dimensions TERM 2 WEEK 3

MONDAY

Balls, boxes,cans Playdough, plastic knives Worksheets (BLMs p.13, 27)

1-minute timer Paint, paper, dot stickers Shape spinners (BLM p.15) Challenge cards (BLM p.49)

Sort, compare, describe 3D objects (3D1-1) Recognise, name simple 3D objects (3D1-2) Match 3D objects with 2D drawings or photos (3D1-3) Count,describe faces, edges, corners of 3D objects (3D2-3) Create, identify cross-sections (3D3-3) Bend, stretch, flatten to change shape of an object (3D3-4)

RESOURCES

• • • • • •

OUTCOMES

STRAND Space GRADE K/1/2

Sample Weekly Program

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• Whole class: Revise position vocab. e.g. left, right, front, back. When do you use this language? • Outdoor group activities: A: Beanbags B: Balls C: Hoops (In pairs call out instructions to your partner, e.g. use your left hand, roll the ball under your legs.) • What’s my direction? whole class game. e.g. Everyone runs to the left, crawls around the tree.

MONDAY

Balls Beanbags Hoops

• Small group activity: Robot spinner game. Spinner/cards, ball/ beanbag/hoop for each group.

• Partner activities: Robots (p.62) (Instruct your partner how to move around an area, e.g. 3 steps to the left, turn right.)

• Whole class: Revise position vocab, e.g. left, right, front, back.

TUESDAY

Balls, beanbags, hoops Spinners (BLM p.63) Scissors

5

• Dinosaur challenge: Which team can construct the largest dinosaur in 3 minutes?

• Repeat activities with 4-5 blocks.

• Group activities using 4 blocks each: A: Yes/no B: Look alikes C: Under the cloth D: Talk to me

• Whole class: Dinosaur bones (p.68).

WEDNESDAY

• Revise position language. Repeat partner Robots game.

• Partner activity using 4-5 blocks each: Draw me (p.71) variation. Discuss, compare models then swap roles.

• Group activities using 4-5 blocks each: A: Yes/no B: Look alikes C: Under the cloth D: Talk to me. • Repeat activities with 4-5 blocks.

• Whole class: Discuss model dinosaurs. How could you recognise one in a drawing? What are the key features?

FRIDAY

Model dinosaurs Construction materials Pencils, paper

• Whole class: Dinosaur bones (p.68). Line up model dinosaurs. Discuss positions e.g left, right, middle, first, last.

THURSDAY

Model dinosaurs Construction materials Activity cards (BLMs p.69,70) Tea towels

to the left of, to the right of in the middle, on the top, on the bottom next to, beside, near from above, from below, from the front, from the side first, second ... last

Model dinosaurs Construction materials Activity cards (BLMs p.69,70) Tea towels

• • • • •

LANGUAGE

SUBSTRAND Position TERM 3 WEEK

Describe and follow simple directions (P1-4) Describe position of object in model, picture, sketch (P2-1) Construct model from memory, verbal instructions, diagrams (P2-2) Draw object from different points of view (P2-3)

RESOURCES

• • • •

OUTCOMES

STRAND Space GRADE 1

Sample Weekly Program

EXPLORING LENGTH AND AREA

SPACE

LOWER PRIMARY

The Exploring Maths series is designed to provide busy teachers with practical resources that are mathematically up-to-date, fun and easy to use. Each book contains a wealth of activities, blackline masters and assessment tasks for a whole lifetime of teaching. These activities encourage your children to think mathematically by exploring, experimenting, being creative and taking risks. By asking questions and active discovery, children learn to enjoy using mathematics as part of their everyday lives.

Exploring 3D Space and Position includes: • A sample yearly maths overview for 3 grades • A sample weekly program.

• Six carefully sequenced units • Over 30 activity-based, easy-to-use teaching plans • 46 blackline masters • Useful activity cards for independent small group work • An outcome indicators checklist to record individual progress

In fact, plenty to ensure you enjoy teaching 3D Space and Position to your 5 - 7 year olds.

About the author Originally a primary school teacher, Bev Dunbar is now actively involved in teacher education as a Mathematics Consultant and University Lecturer in Mathematics Education working in both the State and Catholic Education systems. Bev is a passionate believer in fun, practical resources which help teachers make maths lessons a highlight of the day.

Titles in the Exploring Maths series NUMBER Exploring 1-5 Exploring 6-10 Games and Activities for 0-10 Exploring 0-50 Numeration Exploring 0-50 Operations Numbers to 50 Picture Pack Exploring 0-100 Numeration

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Exploring 0-100 Operations Exploring Calculators Exploring Fractions Exploring Money

SPACE Exploring 3D Space & Position Exploring 2D Space Exploring Graphs, Chance & Data

MEASUREMENT Exploring Length/Area Exploring Volume/Mass Exploring Temperature/Time

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ISBN 1-86509-226-6

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