developing numeration skills for numbers 0 - 50 with your students. ... Illustration and design by Janice Bowles .... Draw sweat shirts on each of the people.
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Bev Dunbar Activities, blackline masters & assessment pages that are fun and easy to use N U M B E R
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Introduction Exploring 0 - 50 Numeration At last! Here are more than 60 carefully sequenced teaching ideas for developing numeration skills for numbers 0 - 50 with your students. Making your life easier has been a major aim in this series. With the suggested activities, the 40 blackline masters, the sample programs and the outcome indicators, you’ll find planning your numeration program for the year is now so manageable. A summary at the start of each unit identifies the key mathematical ideas. There are enough suggestions in each unit to have up to a whole class studying that topic for at least a week! The Sample Weekly Program shows you one way to do this. Every activity is fun, easy-to-implement and easy-to-understand. Each one is carefully designed to maximise the way in which your students build up their knowledge of our Base 10 counting system. Students are encouraged to think and work mathematically with an emphasis on mental recall and practical manipulation of objects. A second book, Exploring 0 - 50 (Operations), covers simple addition, subtraction, multiplication and division with whole numbers to 50. The third resource in this set are discussion cards, the Numbers to 50 Picture Pack which support the ideas in both books with 23 large colour pictures. Together they provide you with the practical number resources you need to keep both your young students and you keen and motivated. Look forward to sharing the joys of exploring numbers to 50 with your students.
Copyright Bev Dunbar MATHS Matters 2000 Reprinted 2003, 2007 Exploring 0 – 50 (Numeration) ISBN-13: 978 186509 143 3 ISBN-10: 186509 143 X Published by Blake Education Locked bag 2022 Glebe NSW 2037 www.blake.com.au Illustration and design by Janice Bowles
Additional illustrations pages 49 - 57 by Jane Schneider Illustration on page 75 suppplied by: IMSI’s MasterClips Collection, 1875 Francisco Blvd, San Rafael CA 94901-5506, USA.
Printed by Printing Creations 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
2
Revisiting 0 - 9
3
Exploring 10 - 90
21
Exploring 11 - 19
47
Exploring 1 - 50
79
Outcome Indicators
92
Sample Yearly Program
93
Sample Weekly Program
94
How to use the activities
Over 60 easy-to-use activities exploring numeration to 50 have been placed into four separate units to enable you to readily plan and implement activities for the whole class, groups and individuals. You’ll never run out of ideas for what to teach your students again!
Grouping strategies
Start by revisiting the numbers 0 - 9 then look at groups of 10 from 10 - 90 from as many perspectives as possible. Next, explore 11-19 where you’ll now be able to see each number as a group of 10 and extras. Build on these place value understandings in the final unit by exploring numbers from 21 - 50 and beyond.
= small group = whole class
C P M O R PV
= = = = = =
EX PL OR
IN G NU M BE RS 0- 50
Counting
Each activity includes coded Outcome Indicators to help your planning, programming and unit assessment. This shows how easy it is to implement each activity in your classroom.
How to use the sample programs
NU M ER
AT IO
E SAMPL
YEARLY
Term 2 g 11-19 Explorin ce 3D Spa Length g +/ Explorin Money Volume gx Explorin Mass Fractions Revision
Topics
PROGR
AM
) Term 3 (revision g 0-20 Explorin ce a 2D Sp Area g +/ Explorin Position
Time gx Explorin ature Temper Fractions Revision
mber: t: 10 Nu ks suremen r of wee 8 Mea Numbe Space: /Data:1 Chance
NAME
N C1 Counts forwards C2 Co /backw unts for ards by wards/ba 1s to ... C3 Co ckward unts for s by wards/ba 2s to ... C4 Co ckward unts for s by 5s wards, to ... C5 Co backward unts on s by 10s from on C6 Ide to ... e specifi ntifies 1 ed numb more, 1 C7 Ide er to an less tha other ntifies 2 n a given more, 2 C8 Ide number less tha to 10 ntifies 1 n a given more, 1 C9 Ide number less tha ntifies 2 to 10 n a given more, 2 C10 Ide number less tha to ntifies 1 20 n a given more, 1 C11 Ide number less tha Patternin ntifies 2 to n a given 20 g P1 more, 2 number less tha Recognis to 50 n a given es, descr P2 number ibes, cre Predicts, to 50 ates nu continu mber pa P3 es the nex Identifies tter ns t few item missing P4 s in item a Ide nu s in a nu Matching mber pa ntifies a mber pa ttern group of M1 Est ttern objects imates, as odd models, M2 Ma or even counts 0-9 tches nu objects merals, M3 Est number imates, words 0-9 models, M4 Ma to counts gro sets of ob tches nu ups of 10jects merals, M5 Est 90 objec number imates, ts words 10models, M6 Ma 90 to set counts 0-2 tches nu s of 10 ob 0 objec merals, jects M7 Est ts number imates, words 0-2 models, M8 Ma 0 to set counts 0-5 Orderin tches nu s of objec 0 objec g O1 merals, ts ts number Places nu words 0-5 merals, O2 Us 0 to set objects, es, reads, s of objec words 0-9 orders "1s ts O3 Pla into cou t" to "10 nting ord ces nume th", "first" er rals, ob O4 Pla to "tenth jects, wo ces nume " rds 10-90 rals, ob O5 Us into cou jects, wo es "1st" nting ord rds to 0-2 "20th" to er O6 Pla 0 into cou identify Recording ces nume nting ord position er rals, ob R1 s jects, wo Uses tall rds 0-50 y marks R2 to record into cou Writes nu nting ord countin merals g from 0-9 er R3 0-9 Writes nu mb er words R4 Writes nu "zero" to merals "nine" R5 10-90 Writes nu mber wo R6 rds "ten" Uses tall to "ninety y marks R7 " to record Writes nu countin merals g from 0-2 R8 0-20 Writes nu 0 mber wo R9 rds "zero" Uses tall to "twent y marks R10 Wr y" to record ites nume countin rals 0-5 g from 0-5 R11 Wr 0 Place 0 ites numb er words PV1 Mo Value "zero" to dels gro "fifty" ups of 10 PV2 Mo ones as dels nu 1 ten mbers to PV3 Exp 20 as on lains the e group value of PV4 Mo of 10 an ea ch digit d extras dels nu in numb mbers to PV5 Exp ers 0-20 50 as bund lains the 92 les of 10 value of Explori ng 0 - 50 and ext each dig ras Numerati it in numb on ers 0-50
atics Mathem
Term 1 Week g 0-9 Week Revisitin ce 1 3D Spa 2 Length g +/ 3 Explorin ce 4 2D Spa 5 Volume g 10-90 6 Explorin 7 Mass 8 Time 9 Revision 10
Counting Patterning Matching Ordering Recording Place Value
Outcom Record e Indicators Sheet
A complete list of Outcome Indicators is provided on p. 92 to help you see how and when this outcome has been reached.
Exploring 0 - 50 Numeration
= pair
Coded Outcome Indicators (see p.92)
The overall outcome for each unit is to estimate, count, compare, order and represent whole numbers up to 50, with a special emphasis on the development of place value and mental recall.
2
PAIR
CLASS
The objective is to develop knowledge, skills and understanding for the numbers 0 - 50 in a variety of fun, child-centred ways.
A second feature is the Sample Weekly Program for Mathematics (see p.94 for complete details). You can see one way to organise a selection of activities from the “Exploring 10 - 90” unit (see p.21-46) as a five day unit.
= individual
GROUP
Each unit includes blackline masters for activity cards, games and practical worksheets as well as an end-of-unit check-up. The activities within each unit can generally be adapted to the study of any number. Remember to revisit a favourite activity later in the year using higher numbers.
A special feature of this book is the Sample Yearly Program for Mathematics (see p.93). It is one way to organise a 40 week teaching year for 6 year olds, exploring a unit in Number, Space, Measurement, Chance and Data for a week at a time.
ONE
Term 4 g 0-50 Explorin ce 3D Spa Data Chance/ g +/ Explorin ce 2D Spa Position g÷ Explorin Revision rement Measu on si vi Re Number vision Space Re
Total: 40 ion: 6 15 Revis
Using Dot Cards What to do ◆
◆
Make an A3 copy of the “twos pattern” (BLM p.6) and the “random pattern” (BLM p.7) 0-9 dot cards. Laminate, then cut out as sets of ten cards for whole class demonstrations. Make an A4 copy of the “twos pattern” and the “random pattern” 0 - 9 dot cards for each group (e.g. yellow paper for “twos”, and green for “random”). Cut out along the dotted lines as sets of ten separate cards.
Whole class ideas ◆
Use a mixture of random and pattern cards. Shuffle the large cards. Hold up one card for four seconds then hide it again. Guess how many dots you saw (e.g. whisper your answer to the person sitting next to you). How do you know? Discuss strategies. Check guesses by counting. CLASS
Repeat this activity, gradually making the viewing time shorter and shorter. Do the guesses get closer? What’s the shortest viewing time you need? Are some cards more difficult to guess closely? ◆
◆
Shuffle the cards. Ask individual students to sort them into counting order forwards or backwards, according to the number of dots. Hold up three cards at random. Ask students to identify which one has the most dots. Reinforce spatial language. e.g. “the one on the right”, “the one in the middle”, “the one on the left”.
◆
Hold up a card at random. Everyone races to form a group with the matching number of students in it.
◆
Hold up a random card. Ask students to hold up fingers to match the number of dots. Repeat, but this time individuals race to collect a matching number of objects.
◆
Hold up a card at random. In pairs, create a story using that number to tell to another pair (e.g. 7 “My mum paid seven dollars for my lunch yesterday”).
Small group variations ◆ ◆
Model the whole class actions using the smaller cards.
GROUP
Give each student nine counters. Rearrange the counters to match the twos pattern dot cards. How many other patterns can they discover using the counters?
Exploring 0 - 50 Numeration
5
How Far Can You Go?
ONE
C4 P2 R4
Resources A calculator, scrap paper/pencil for each student. Activity Press on . Press 10 . Press + + . Press = . Write 10 at the top of your paper. Press = again. What number is showing now? Write this new number under the first. Guess what will happen when you press = again? Check your guess by pressing = . Repeat. Continue until you can’t guess anymore. What number did you reach? Compare your answers with a friend. Are the numbers the same? Why?
Paper People Chain
ONE
C4 O3 R4
Resources Coloured paper and scissors for each student. Activity Demonstrate how to make paper people by concertina folding then cutting out the outline of a person, with hands and feet attached. Experiment with how many folds you can make and how many people you end up with. Draw sweat shirts on each of the people. Write in multiples of 10 in order forwards or backwards. How many groups of ten can you make?
Sort the Lion’s Mane
PAIR
C4 O3
Resources 10 coloured plastic pegs (each with a number from 0 - 90), a paper plate (with a lion’s face in the centre), storage container. Activity Make the lion’s mane by placing pegs around the edge of the paper plate in counting order from 0 - 90. Ask your partner to close their eyes while you rearrange two pegs. Can your partner spot the mistake and correct it quickly? Variation Sort 10 different “zero” to “ninety” pegs in the same way.
Which Path?
ONE
C4 P2 O3
Resources Rabbit/Frog (BLM p.42), cut into two. Activity Help the rabbit munch up all the carrots by drawing a line from each carrot to the next, counting by 10s from 0 to 90.
Help the frog jump from lilypad to lilypad by drawing a line from one lilypad to the next, counting by 10s from “ninety” to “zero”.
Exploring 0 - 50 Numeration
41
Help this rabbit eat all the carrots
90
0 10
80 70
20 40
30
60 50
Which way will the frog jump? fifty ninety
ten
seventy
sixty eighty
zero twenty
42
Exploring 0 - 50 Numeration
thirty
forty
Please Sit Down
CLASS
M5
Activity Everyone stands up. Call out a number from 1 - 20. The class has to cooperate to finish with the matching number of students standing and the rest sitting down.
Frog Jumps
CLASS
C1,2,3,4 O4
Resources 20 beanbags (or 20 chalk dots on the ground) 50 cm apart. Activity In the playground, tell the story of how frogs love to jump from lily pad to lily pad. Pretend each beanbag is a lily pad. Discuss the starting point, where your feet are together before you jump to the first lily pad. Call this “Start”. Can you jump like a frog from the start to the last lily pad counting each jump aloud? Variations ◆ Invent stories about a jumping frog. Select individual students to model each story as you tell it (e.g. This frog jumped along 12 lily pads then had a rest. She then jumped along 3 more lily pads. How many jumps altogether?) ◆ Create stories that involve jumping backwards as well as forwards. Start at any number. ◆ Label each “lily pad” by writing “Start” in chalk, then a chalk number from 1 to 20 beside each beanbag. This activity will prepare you for working with number lines later in the year. ◆ Jump over two lily pads at a time and count by 2s from 2 to 20 forwards or backwards. ◆ Place the lily pads closer together. Jump by 5s to 20 forwards and backwards. ◆ Use just 9 lily pads. Revise counting by 10s from 10 to 90 by writing 10, 20 ... 90 in chalk beside each lily pad. Start at any lily pad. Jump forwards or backwards.
Join Them Up
ONE
O4
Resources “Join them up” (BLM p.68), cut up as two separate activities. Activity Guess what each picture will look like when completed. Join the dots in counting order forwards or backwards. Was your guess close? Variation Invent your own 1 - 20 dot picture clues for a friend to use. Exploring 0 - 50 Numeration
67
Join Them Up 8 6
10
4
2
12
9
7 5
11 13
15
3 1
14
17 16 18 20
19
Join Them Up seven six
eight
ten
eleven
nine five
twelve
four three thirteen two one
fourteen en
te gh
ei
nineteen twenty teen seven 68
Exploring 0 - 50 Numeration
fifteen sixteen
Check-up 0 - 50
C3 M7,8 06 PV4,5 GROUP
CLASS
Resource 0 - 50 Check-up (BLM p.91). Activity Use this worksheet with small groups or with the whole class as a written form of assessment. Record students’ responses on the Outcomes Indicators Checklist (p.92). The following are suggested instructions and sample teacher’s comments used when developing student profiles: Place Value Look at the packets of crayons. Write the number that tells you how many crayons altogether. Can you write this as a word too? Sample Profile Comments “Models numbers to 50 as bundles of 10 and extras.” Place Value Look at the next boxes. How do we write this as a number? Write it in the spaces on the right. What about the next number - 46. Write how many tens and ones as words in the space on the left.” Sample Profile Comments “Writes numerals to 50 as words and numerals.” Counting Look at the number pattern on the caterpillar’s body. Can you guess the pattern? Finish it by writing in the missing numbers. Sample Profile Comments “Counts by 5s to 50 and records this as a pattern.” Ordering Look at the box with the numbers starting at 25. The naughty cat has hidden some of the numbers. Write in all the missing numbers yourself. Sample Profile Comments “Places numerals 0-50 into counting order.” Place Value Look at the long sausage dog. Guess how many spots altogether. Write your guess on the left. Now put a circle around all the groups of 10 spots. Write the actual number of spots you discover at the right. Sample Profile Comments “Models and counts numbers to 50 as groups of tens and ones.” Matching The fish have jumped out of their tanks and they’re all mixed up. Draw a line from each fish to its matching tank. Sample Profile Comments “Matches numerals 0-50 to sets of objects.” 90
Exploring 0 - 50 Numeration
0 - 50 Check-up
three tens and two ones
4
25
28
6
32
35
43
39
38 30 23
35
42 47
26
39 41
21
twenty to twenty-nine
thirty to thirty-nine
forty to forty-nine
91
EXPLORING 0 - 50
NUMBER
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 life-time 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 0 - 50 Numeration includes: • Number outcomes and indicators • A sample weekly maths program • A yearly maths overview In fact, there is everything you need to bring the numbers 0 - 50 alive in your classroom.
• More than 60 carefully sequenced maths activities • 40 blackline masters • 18 photocopiable reference posters for class displays • Assessment tasks and ideas
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 ISBN 978-1-86509-143-3
NUMBER Exploring 1 - 5 Exploring 6 - 10 Games and Activities for 0 - 10
Numbers to 50 Picture Pack Exploring 0 - 100 Numeration Exploring 0 - 100 Operations Exploring Fractions Exploring Money Exploring Calculators
Exploring 0 - 50 Numeration Exploring 0 - 50 Operations
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