math learning wheels - primary

Turn-to-Learn

MATHMATHLEARNING WHEELSLEARNING WHEELS

20 Ready-to-Reproduce Patterns That Put a New Spin on Math Skill-Building!

S C H O L A S T I C

BPROFESSIONAL OOKS

NNeeww YYoorrkk •• TToorroonnttoo •• LLoonnddoonn •• AAuucckkllaanndd •• SSyyddnneeyy

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Acknowledgment Page

To my children Rick, Tony, Steve and Betsy. And to all of my students

who have enjoyed learning math with math wheels.

Scholastic Inc. grants teachers permission to photocopy the patterns from this book for classroom use. No other

part of this publication may be reproduced in whole or in part, or stored in a retrieval system, or transmitted in

any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without permission of the

publisher. For information regarding permission, write to Scholastic Professional Books, 555 Broadway, New York,

NY 10012-3999.

Cover design by Vincent Ceci and Jaime Lucero

Cover and interior illustrations by Bob Alley

Interior design by Robert Dominguez and Jaime Lucero for Grafica

Copyright 1998 © by Jacquelyn Johnson Howes. All rights reserved.

ISBN: 0-590-11757-2

Printed in the U.S.A

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Table of Contents

Welcome to Math Wheels! . . . . . . . . . . . . . . . . . . . . . . 4

Putting Math Wheels Together . . . . . . . . . . . . . . . . . . . 5

Introducing Math Wheels . . . . . . . . . . . . . . . . . . . . . . . 6

The Wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Counting Bear . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Numeration

Two-ie the Toucan . . . . . . . . . . . . . . . . . . . . . . . . 16Skip Counting

Plus the Cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Addition

Minus the Dog . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Subtraction

Penny the Pig . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Money

Hickory Dickory Clock . . . . . . . . . . . . . . . . . . . . 30Time

George the Giraffe . . . . . . . . . . . . . . . . . . . . . . . 34Patterns

Sam the Shape Clown . . . . . . . . . . . . . . . . . . . . . 37Geometric Shapes and Math Symbols

Times the Dinosaur . . . . . . . . . . . . . . . . . . . . . . . 40Simple Multiplication

Piece-O-Pizza . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Simple Fractions

Blank Problem Wheels . . . . . . . . . . . . . . . . . . . . . . . . 47

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5:00

Welcome to Math Wheels! Math Wheels are a fun-filled interactive alternative to flash cards andworksheets that present math facts in a game format that children love.Because they invite children to take skill-building into their own hands,Math Wheels are a powerful learning tool you and your students willenjoy using again and again. Each engaging shape is designed to comple-ment popular classroom themes. What’s more, because the wheels areself-correcting (all students have to do is flip the moving answer-hider toreveal the solution), they offer children instant feedback. And, if a childdoes miss a problem, a turn of the wheel provides a fresh opportunity totry again. Some of the wheels are interchangeable (Plus, Minus andTimes) so if, for example, you are doing a dinosaur unit, you can enhancethe unit by pairing the dinosaur shape with the problem wheel thataddresses the math skill of your choice.

Math Wheels are perfect for use with the whole class, in small group set-tings, and for individual one-on-one practice. They can be used as the focusof a teacher-directed activity, or placed in a learning center for children touse independently or in pairs. And best of all, Math Wheels are easy tomake and simple to store.

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Putting Math Wheels TogetherWhenever possible, involve children in making the wheels themselves.

1. To make the wheels you’ll need:• paper • markers or crayons • scissors• brass fasteners • glue • oaktag

You can make the wheels in the following ways:

• Simply photocopy the patterns, cut, and color;• Photocopy the patterns and paste them to oaktag (or manila folders) for

added durability, cut and color;• Photocopy the patterns onto colored paper, paste them to oaktag, and cut

them out;• Photocopy the patterns directly onto oaktag if your copier allows, and cut

them out.

2. Next, cut open the windows. While older students may be able to do thison their own, younger ones may need some help. In either case it helps touse small pointed scissors.3. Once you’ve created the character, use a brass fastener to attach theproblem wheel through the x checking to be sure that the problems and theanswers appear in the windows. Use a second brass fastener to attach themoveable answer-hider through the circle .

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CONSTRUCTION TIPS

11.. Color contrasts: You can copy each problem wheel onto colored paper thatcontrasts with the color of the character. This contrast makes it easier forchildren to focus on the information that appears in the character’s windows.

22.. Laminated wheels: If you would like to make sturdier wheels, try laminatingthem.

33.. Textured wheels: You can give your Math Wheels added texture by cover-ing them with colored felt or yarn, cotton balls, or glitter. You can also addgooglie eyes.

44.. Oversized wheels: While students will love having their own Math Wheels,you may want to make an enlarged version to display in a learning centeror to use while working with the whole class. To make these oversized ver-sions, simply enlarge the patterns on your copy machine and follow theassembly steps outlined above.

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Introducing Math WheelsMath Wheels are a wonderful tool forpracticing or reinforcing math facts.Prior to using the Math Wheels in yourclass, children may need many opportu-nities to come to an understanding of theconcepts that lie beneath the skills andfacts. Concrete activities using manipu-latives, coupled with real-life math expe-riences (measuring, counting, sorting,graphing, estimating, etc.), provide chil-dren with the rich background they willneed to get the most from Math Wheels.

It is best to introduce the wheels in asmall group setting. After demonstrat-ing how to use each wheel, call atten-tion to the operation or skill it features.Show children how one part of eachcharacter can be used to hide theanswer so they can check their work. Becertain to allow each child a chance touse the wheel with you.

Personifying Math Wheel CharactersMath Wheels come to life when theyare treated as class mascots who livein your math corner. Begin by talkingto a Math Wheel character as youwould talk to a puppet. Here are somesimple scenarios to try:

• Pretend that your Math Wheel char-

acter doesn’t understand the very

skill he or she is displaying. Ask chil-

dren to explain in their own words

how to do the math.

6

TIPS FOR SENSITIVEEVALUATIONS WITH

MATH WHEELS

• Children are often sensitive to

their own progress without

adult intervention or formal

yardsticks. Encourage chil-

dren to play down their com-

petitive spirit and to respond

positively to each other’s

progress as they use the

math wheels.

• You might keep some manipu-

latives—connecting cubes or

counters—on hand. Then, as

you work through problems

with the Math Wheels, invite

children to use the manipula-

tives to demonstrate how they

arrived at each answer.

• Notice if any children are

repeatedly stumped by par-

ticular problems or skills. It’s

possible that these children

need additional concrete

experiences in order to

understand the underlying

math concepts.

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• Have Math Wheel characters await your children at the classroom door.

Invite students to solve a Math Wheel problem as they enter the room or

leave for recess.

• When you have a few moments to spare (lining up to go somewhere, wait-

ing for dismissal, etc.) use your character to dialogue with children about

the math they learned that day.

Customizing Math WheelsYou and your students can create your own Math Wheel characters like thebaseball wheel shown here using the blank problem wheel templates on page47. Once you’ve created the characters and are ready to attach the problemwheel, check to be sure that the problems and answers show through thewindows properly.

More Math Wheel Ideas

• String a length of clothesline or yarn across a bulletin board; hang the line

low enough so children can reach it. Place each character and one or more

of the problem wheels you’ve already introduced to the group into a self-clos-

ing plastic bag. Use a paint marker (available from art supply stores) to label

each bag. Use a clothespin to clip each bag to the line and invite children to

access them throughout the day.

• Create a Math Wheel display to enliven the classroom and to help you

keep track of which wheels each student has used. Cover a bulletin board

with colorful paper. Tack the Math Wheels across the top of the display. Use

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a marker to draw vertical lines between the wheels and then draw horizontal

lines across the board creating enough boxes under each Math Wheel for

your students. Write their names to the left of the chart. As students are

introduced to a particular Math Wheel, invite them to place an X or a sticker

in the box below the character that corresponds with their name.

This will help you and your students keep track of the work they are doing.

• You can use completed wheels to make a class book of math story prob-

lems. Have students pick their favorite characters to include. Review some of

the common language used in story problems—how many altogether? How

many left? Then, have each student write a story problem about the charac-

ter of their choice using the math skill it addresses. Students should write

and illustrate their problem on one page and paste their math wheel to the

opposite page. Children will enjoy presenting their story problems and solv-

ing their classmates’.

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5:00

ABCD

E 7¢

Jaime

Ingrid

Robert

Liza

Tony

Carmen

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Home School Connection

• Math Wheels are a perfect addition to a take-home thematic

backpack program. Be certain to include a letter explaining the

importance of using Math Wheels with children, copies of blank

problem wheels (page 47) for families to customize, as well as

some tips for use at home. Don’t forget to invite family feedback!

We’ve included a sample letter you may adapt to fit your own

needs on page 10.

• You might even ask parents to volunteer to make Math Wheels

at home. Working parents who find it almost impossible to vol-

unteer during the school day may welcome this chance to help

out—and children will beam with pride when characters created

in their homes are used in class.

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3+4

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Plus ate 4

treats. I

gave him 7

more. How

many did

he eat

altogether?

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3+4

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Dear Families,

It’s your child’s turn to bringhome one of our Math Wheels!

In class we use theseMath Wheels to helpstrengthen and reinforcethe math facts we havelearned. Your child canshow you how thesewheels work. Try holdingand turning the wheel asyour child answers theproblems featured there. Then, work with yourchild to make up some new problems of yourown using the blank wheel included here. Letyour child lead the way and you should have agreat time practicing math facts together.

Thank you for your participation.

Sincerely,

__________________________Your Child’s Teacher

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3+4

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TheWheels

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Counting BearHere’s a bear you can count on to strengthen counting skillsagain and again!

Ask students to turn their wheels so that the lowest number appears in the

window. Invite children to add numbers (Add 2; add 3; add 1, etc. . . ) totaling

any number up to 10. Children should turn their wheels to keep a running

count. When the series of directions is complete, check to see if each child

has arrived at the same number.

EXTENDING THE LEARNING

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COUNTING BEAR

Pattern

Cutout

Cutout

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COUNTING BEAR

Problem Wheel

4

8

37

5

2

4

3

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Two-ie the ToucanYou bet your beak this bird will double your skip counting fun!You might want to give Two-ie a whole new look by pasting oncolorful feathers.

Use the blank problem wheel template on page 47 to make additional skip-

counting wheels. Two-ie can help children count by three’s, five’s, ten’s, or by

odd and even numbers.


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Cutout

Cutout

x

TWO-IE THE TOUCAN

Pattern

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18

246

3388

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20

8 82 2

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2222

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TWO-IE THE TOUCAN

Problem Wheel

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Plus the CatThis kitty cat provides the purrfect way to learn addition familyfacts!

Invite students to create a collection of cat things. Ask how many students

have cats at home. Then brainstorm a list of things their cats love to do, play

with, or eat that Plus might like too. Once your list is complete, have students

create these items using paper, clay, yarn or whatever supplies you have

available. Then, encourage students to use these handmade manipulatives to

help them solve problems on Plus’s addition wheels.


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x

Cutout

Cutout

PLUS THE CAT

Pattern

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0-5

5-10

1+2

3

2+3

5

4 + 1

5

2 + 2 4

1 + 3

4

0+

2

2

1+1

2

3+1

4

2+1

3

0+55

3+2

5 1+

4

5

x

2+3

5

6+3

9

2 + 5

7

4 + 2 6

5 + 4

9

7+

3

10

2+6

8

6+4

10

3+4

7

5+38

2+810

2+

4

6

x

PLUS THE CAT

Problem Wheels

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9+9

18

7+4

11

8 + 7

15

7 + 9 16

5 + 7

129+

8

17

8+8

16

6+8

14

8+9

17

8+5

13

9+615

5+

9

14

x

4+6

10

6+7

13

3 + 8

11

8 + 7 15

5 + 7

126+

8

14

4+9

13

8+4

12

9+5

14

7+4

11

5+813

9+

6

15

x

22

10-15

up to 18

PLUS THE CAT

Problem Wheels

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Minus the DogTake this subtraction pooch for a walk and your students’ mathskills will really add up!

Invite students to write stories describing how minus the take-away dog

got his name.


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1–

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Cutout

Cutout

x

MINUS THE DOG

Pattern

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25

5

1–

4

11–

0

42–

2

2 1– 1

53

–

241–

3

3

2–

1

43–

1

52

–

3

31–2

50

–

5 54–

1

10

8–

2

94–

5

53–

2

10 6– 4

83–

597–

2

6

4 –

2

86 –

2

107

–

3

75–2

96

–

3 105–

5

5-10

1-5

x

x

MINUS THE DOG

Problem Wheels

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18

9–

9

117–

4

15 8–

7

16 7– 9

127

–

5

179 –

8

16

8 –

8

148 –

6

135

–

8

178–9

159

–

6 149–

5

15

8–

7

106–

4

13 6–

7

14 5– 9

118

–

3

156 –

9

12

5 –

7

134 –

9

148

–

6

157–8

114

–

7 138

–

5

up to 18

10-15

x

x

MINUS THE DOG

Problem Wheels

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Penny the PigPenny is a priceless addition to any money unit.

After children have arrived at the correct sum for each answer, offer them an

array of coins and challenge them to arrive at the same sum using as many

different coin combinations as they can.


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7¢

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Cut

out

Cut

outx

PENNY THE PIG

Pattern

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10¢

11¢

20¢

25¢40¢

35¢50¢

7¢ 28¢

30¢

x

x

25¢

10¢

20¢

25¢20¢

30¢30¢

50¢ 5¢

5¢

PENNY THE PIG

Problem Wheels

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Hickory Dickory ClockThere’s no such thing as a bad time to learn how to tell time withHickory Dickory Clock.

Ask students to think about how they spend their time. Turn the wheel to

reveal a time of your choice. Invite children to share what they do at that time

whether it be a.m. or p.m. You might even take the activity one step further by

recording students’ responses and graphing the results.


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55::0000

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Cut out

Cutout

31

x

HICKORY DICKORY CLOCK

Pattern

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Hour and Half Hour Wheel

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1122

1111

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6655

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11221111

1100

99

88776655

44

33

2211

1122

1111

1100

99887766

55

44

3322 11

11221111

1100998877

6655

4433 22 11

1122

1111

11009988

7766

55

44 3322

11

11221111110099

88

7766 55 44

33

22

11

11221111

1100998877

6655

44 33 2211

33

44::4455

66::2200

99::0 05 5

1111::33

55

1122::115522::440077::1100

1100::445555::5 50 0

33::5555

88::1155

11221111

1100

99

8877 66 55

44

33

2211

11::2255

x


5 Minute Intervals Wheel

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34

George the GiraffePatterning skills won’t be such a stretch when George the Giraffecomes to play.

Invite students to create their own patterns for George using one of the blank

wheels on page 47. Once their patterns are complete, have students exchange

their wheels with a friend to see if they can identify each other’s patterns.


ABCD

E

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Cutout

Cutout

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GEORGE THE GIRAFFE

Pattern

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24

62

46

2

4

l ww

l w

w

sssnsssn

snsn

sn

s

ABCDE

F

XXOOXX

O

l

l

ll

ll

l

1 2 3 1 2 3

XO

XO

X

O

AEIOUA

E

X Y Z X Y Z X

Y

ll

lll

lll

l

x

GEORGE THE GIRAFFE

Pattern & Problem Wheel

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x

66

66

66

66

66

66

x

5

66

37

Sam the Shape ClownIdentifying geometric shapes and operation symbols is simplewhen Sam shows you how.

Have children look around the classroom to locate the shapes that appear in

Sam’s shape window. Ask them to think of other places they see these

shapes—on the street, in the store, or in their homes.


Note: Some students may find it easier to locate and count the shapes and symbols presented

here if they are color-coded. While some students may choose to create their own codes, you

can suggest they color the images in the following way: square–orange; triangle–green; hexa-

gon–yellow; trapezoid–red; rhombus–blue; parallelogram–tan; circle–pink; rectangle–gray;

plus–brown; minus–black; times–purple; equals–light blue.

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66

66

66

66

66

66

x

Cutout

Cutout

SAM THE SHAPE CLOWN

Pattern

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66

66

1 5

69

58

7810

46

5

x

SAM THE SHAPE CLOWN

Pattern & Problem Wheel

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40

Times the DinosaurFun won’t become extinct when you use this friendly dino toteach the times tables!

While you’re at recess, invite children to gather natural materials (stones,

sticks, pieces of grass) to demonstrate a problem Times poses to them.


6x4

24

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x Cut

out

Cut

out

TIMES THE DINOSAUR

Pattern

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2s & 5s

3s & 4s

1x3

3

2x4

8

3 x 3

9

4 x 4 16

5 x 3

156x

4

24

2x3

6

3x4

12

4x3

12

5x4

20

6x318

1x

4

4

x

1x2

2

2x2

4

3 x 5

15

4 x 2 8

5 x 5

256x

2

12

2x5

10

3x2

6

4x5

20

5x2

10

6x530

1x

5

5

x

TIMES THE DINOSAUR

Problem Wheels

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43

Piece-O-PizzaYou and your students can help yourselves to a tasty slice of fractions!

Have a real pizza party. Order some pizzas to be delivered unsliced (or bake

some of your own from scratch). Then, have children take turns cutting the

pizza into halves, fourths, eighths, and sixteenths. Consider duplicating many

copies of the Piece-0-Pizza Math Wheel for each student so that they can

compile individual fraction books in which each page features a different frac-

tional amount of pizza.


11––88

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Cut

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Cut

out x

PIECE-0-PIZZA

Pattern

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11 11––22

11––2211––44

11––44

33––44

11 –– 8 8

33––88

45

x

PIECE-0-PIZZA

Problem WheelFraction Remaining

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11 11––22

11––2233––44

33––44

11––44

77 –– 8 8

55––88

x

PIECE-0-PIZZA

Problem WheelFraction Missing

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x

x

BLANK WHEELS

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48

NOTES

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math learning wheels - primary

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