also by dr. nicki newton · 2016. 7. 18. · -ii- story problems can be great! story problems are...

Also by Dr. Nicki Newton

Guided Math in Action: Building Math Proficiency

Problem Solving With Math Models: Grade 1





Gigglenook Publications

P.O. Box 110134

Trumbull CT 06611

Email: [email protected]

Website: www.drnicki123.com

Produced by the Gigglenook Production Team

Copyright © 2012 Gigglenook Publications

All rights reserved. No part of the book may be reproduced in any form,

stored in a retrieval system, by any mechanical, photocopying, recording,

scanning, electronic means, or otherwise under Section 107 or 108 of the

1976 United States Copyright Act, without prior written permission in

writing from the publisher, except by a reviewer, who may quote brief

passages in a review.

Permission is given to individual classroom teachers to reproduce the

pages for classroom instruction use only. Reproduction of these materials

for an entire school or district is strictly forbidden.

For additional copies of this publication or permission to reproduce this

work, please contact Gigglenook.

Chief Operating Officer: Dr. Nicki Newton

Publisher: Gigglenook Publication

Cover Design: This Way Up Productions

Text Design and Composition: Bonnie Harrison-Jones

Printed in the United States of America

ISBN-13: 9781491253526

ISBN-10: 1491253525

Volume 1: September, 2013

Dedicated to Mom and Pops, Always

-ii-

Story problems can be great! Story problems are the stuff life is made of. If

we can make connections for children between their daily lives and the

problems we pose and solve in school, we will have much more success.

We need to provide scaffolds into the process.

The New Math Common Core (2010) places a big emphasis on problem

solving. The first mathematical practice mentioned states that students

should “Make sense of problems and persevere in solving them (CCSSM).

” It goes on to describe this by stating that mathematically proficient

students should be able to explain a problem and find ways to enter into it.

According to the New Math Common Core students should be able to

solve problems with objects, drawings and equations. Let’s take a closer

look at kindergarten. Kindergarten students should work with 4 of the 12

types of problems with numbers within 10.

The new national math standards – known as the Math Common Core,

actually adopted the framework for story problems, created by Carpenter,

Fennema, Franke, Levi & Empson, (1999); Peterson, Fennema & Carpenter

(1989). The research says that the more teachers understand these types of

problems and teach them to their students, the better students understand

the problems and are able to solve them. Furthermore, the research makes

the case that the KEY WORD METHOD should be avoided!

Students should learn to understand the problem types and what they are

actually discussing rather than key word tricks. Key words only work with

really simplistic problems and so as students do more sophisticated work

with word problems, the key words do not serve them well. Using a key

word strategy can actually lead students in the wrong direction, often

encouraging the wrong operation. For example, Susie has 10 marbles. John

has 4 more than she does. How many do they have altogether? Sometimes,

students using a key word method, incorrectly add 10 and 4 instead of

adding 10 and 14. Another example, Carol has 18 marbles. She has 3 times as

many as John does. How many does John have? Sometimes, students using a

-iii-

key word method, incorrectly multiply 3 times 18 instead of dividing 18 by

3.

This book is about giving students a repertoire of tools, models and

strategies to help students think about, understand and solve word

problems. We want to scaffold reasoning opportunities from the concrete

(using objects) to the pictorial (pictures and drawings) and finally to the

abstract (writing equations).

-iv-

I would like to thank many people for their support, expertise, guidance,

and encouragement during this project. First of all I would like to thank

God, without him this would not be possible. Second, I would like to thank

my mom, pa, big mom, and granddaddy. Third, I would like to thank my

family for all their love and support, especially my Tia that calls me every

day and ask me “What have you accomplished today?” I would like to

thank all of my friends that support me all the time. Finally, this book

series would not have been possible without the continual support of The

Gigglenook Book Production Team. Thank you to everyone that has

helped with this series along the way.

Problem Solving with Math Models© 2012 1

Adding to Problems

“Adding to” problems are addition problems that involve action.

There are 3 types. Kindergarteners have to know the first type of problem

according to the CCSS (2010). The first type is adding to problems where the

result is unknown. For example: Jenny had 5 marbles. John gave her 3 more.

How many marbles does Jenny have altogether now? In this problem type the

result is unknown. Teachers tend to tell these types of problems. They are

basic and straightforward.

Taking From Problems

“Taking From” problems are all about subtracting. There are three

types. Kindergarteners have to know the first type of problem according to

the CCSS (2010). The first type is taking from problems where the result is

unknown. For example: Jenny had 5 marbles. She gave John 3. How many

marbles does Jenny have left? In this problem the result is unknown. Teachers

tend to tell these types of problems. They are basic and straightforward.

Put Together/Take Apart Problems

“A Put Together/Take Apart” problem discusses the parts and the

whole. There are three types of Put Together/Take Apart Problems.

Kindergarteners are expected to know 2 types of these problems. The first

is a problem where the Whole is Unknown. For example: Susie has some

marbles. Five are red and five are blue. How many marbles does she have

altogether? We know both parts and the task is to figure out the whole.

Kindergarteners are also expected to know the third type of problem

which is a Part Whole with Both Parts Unknown. For example, John has 10

vehicles. Some are trucks and some are cars. How many of each could he have?

There are many possible combinations to the answer. Students must learn

to think about and solve these types of problems with pictures, diagrams

and tables.

2 Problem Solving with Math Models© 2012

There are several great tools to use for solving number stories. In this

book students will use three different tools to think about the word

problems. They will use Number Frames, Pictures and The Number Line.

Number Frames

Number frames provide a visual scaffold for children to understand

word problems. There are 3 different types of number frames- The Five

Frame, the Ten Frame and the Double Ten Frame. Five is the first anchor

number so we should always start with Five Frames, although few math

programs do. Ten is foundational and many math programs do use this

frame. Finally, the Double Ten Frame helps to increase the range of

number in word problems. Number frames are visual scaffolds that help

students to see what they are doing and think about the numbers in

different ways. Kindergarteners focus on the Five Frame and the Ten

frame.

FIVE FRAME

TEN FRAME


Drawings/Pictures

Drawings are a great strategy. Drawings allow students to think

about the problem, visualize it and then draw it out as a “pathway” instead

of just “jumping straight to a solution (CCSS, 2010).” It is important to

teach children to read the problem, stop, and think about what is

happening in the problem and then to draw what they pictured.

+

The Number Line

Number Lines help to scaffold children’s work. Number lines are

more abstract and so you want to scaffold student thinking from concrete

through pictorial to abstract. When working with the number line students

are working at an abstract level. You can most certainly use them with

facts through 10 for kindergarteners.

1 2 3 4 5 6 7 8 9 10


When you have the students solve problems with the number frames,

actually give them something to put on the frames. When students draw a

picture it has to match the story. Finally, when they are using the number

line, make sure they know where to start and how to jump across the

number line. You also want to show students what the equation to match

the story looks like. In kindergarten, students should be exposed to

expressions and equations but they don’t have to be able to write the

equations.


:

When you introduce the problem, be sure to tell the students what

type of problem it is.

Remember that you can take the same problem and rework it in

different ways throughout the week.

Work on a problem type until the students are proficient at

recognizing and solving that problem type. Also give them

opportunities to write and tell that specific problem type.

Be sure to contextualize the problems in the students’ everyday lives.

Using the problems in the book as models, substitute the students’

names and their everyday things.

Be sure to provide tons of guided practice. Solve problems together

as a class, with partners and in groups. Individual practice should

come after the students have had plenty of opportunities to work

together and comprehend and understand what they are doing.

Emphasize that there is no one correct way to solve a problem but

that there is usually only one correct answer.

Encourage students to always show their work.


hese types of problems are the easiest types of addition problems.

In these problems students are looking for what happened at the

end of the story. We know what we started with and what we added to

that part. We are trying to find out how many we have altogether now.

PROBLEM John had 4 marbles. Henry gave him 3 more.

How many does he have now?

MODEL

EQUATION 4 + 3 = ? 4 + 3 = 7

T

Unit 1 – Add to Result Unknown


Way#2: Draw pictures.

+

Way#3: Solve on the number line.

1 2 3 4 5 6 7 8 9 10

Way#1: Put some counters on your number frame.



1. Zack had 1 airplane. His friend Kenny gave him 4

more airplanes. How many airplanes does Zack have now?

Way#1: Solve on the five frame

Way#2: Draw pictures

Way#3: Solve on the number line

1 2 3 4 5 6 7 8 9 10



2. Tiffany had 2 dolls. Amber gave her 2 more dolls. How

many dolls does Tiffany have now?




1 2 3 4 5 6 7 8 9 10



3. Kristin had 1 chocolate chip cookie. She bought 1

more from Ashley. How many cookies does Kristin have now?




1 2 3 4 5 6 7 8 9 10



4. Alex had 2 toy trucks. He got 1 more toy truck for his

birthday. How many toy trucks does he have now?




1 2 3 4 5 6 7 8 9 10



5. Andrea has 1 dog. She wants to buy 2 more. How

many dogs will Andrea have then?




1 2 3 4 5 6 7 8 9 10



6. Sabrina had 3 dolls. Tara gave her 1 more doll. How

many dolls does Sabrina have now?




1 2 3 4 5 6 7 8 9 10



7. Ariel had 3 stickers. Riley gave her 2 more stickers.

How many stickers does Ariel have now?




1 2 3 4 5 6 7 8 9 10



8. Kendall finished reading 6 books for Mr. Smith’s class.

She has 4 more books left to read. How many books will Kendall read altogether for Mr. Smith’s class?

Way#1: Solve on the ten frame



1 2 3 4 5 6 7 8 9 10



9. Erica had 5 pieces of candy. Timothy gave her 2 pieces

more. How many pieces of candy does Erica have now?




1 2 3 4 5 6 7 8 9 10



10. Kevin had 8 toy elephants. He got 2 more elephants for

his birthday. How many toy elephants does Kevin have now?




1 2 3 4 5 6 7 8 9 10



11. Tom had 8 marbles. He got 1 more marble for his

birthday. How many marbles does he have now?




1 2 3 4 5 6 7 8 9 10



12. Denise did not have any dolls. Her Aunt Sue bought

her 3 dolls. How many dolls does Denise have now?




1 2 3 4 5 6 7 8 9 10



13. David has 5 baseball cards. He needs 1 more baseball

card to complete his collection. How many baseball cards will David have once his collection is complete




1 2 3 4 5 6 7 8 9 10



14. Quinn had 4 books. Calvin gave him 4 more books.

How many books does Quinn have now?




1 2 3 4 5 6 7 8 9 10



15. Summer had 3 dresses. Her older sister April gave her

4 more dresses. How many dresses does Summer have now?




1 2 3 4 5 6 7 8 9 10



Solve with a model: Use a ten-frame, draw a picture or

make a number line.

1. Sue had 5 apples. Her brother gave her 2 more. How many does she have now?

2. David had 4 toy trucks. He got 6 more for his

birthday. How many does he have now?



3. Jamal had 7 marbles. He got 2 more from his friend

John. How many does he have altogether now?

4. Maria had 5 rings. Her mother gave her 2 more. How

many does she have now?

5. Carlos had 5 action figures. He got 5 more for his birthday. How many does he have now?


n these problems students are looking for what happened in the

end of the story. In this type of story we know what happened at

the beginning and also what change occurred. We are trying to find out

how many things remained after some things were taken away.

PROBLEM John had 3 apples. He gave 2 away. How many

does he have left?

MODEL

EQUATION 3 – 2 = ? 3 - 2 = 1

I

Unit 2 – Take From Result Unknown


Way#1: Put counters on the number frame and then

take some off.

Way#2: Draw a picture and cross out things!

Way#3: Make jumps on the number line and then jump BACK.

1 2 3 4 5 6 7 8 9 10



1. Chuck had 4 gummy bears. He gave 2 to Mickey. How

many gummy bears did Chuck have left?




1 2 3 4 5 6 7 8 9 10



2. Ethan had 5 pieces of gum. He gave 3 pieces of gum to

Emily. How many pieces of gum did Ethan have left?




1 2 3 4 5 6 7 8 9 10



3. Kayla had 5 puppies. She gave 4 away. How many

puppies did Kayla have left?




1 2 3 4 5 6 7 8 9 10



4. Denver had 3 blocks. He gave Allison 2 blocks. How

many blocks did Denver have left?




1 2 3 4 5 6 7 8 9 10



5. Charlie had 5 brownies. He gave 5 brownies away.

How many brownies did Charlie have left?




1 2 3 4 5 6 7 8 9 10



6. Dawn had 5 dolls. She gave Maria 2 dolls. How many

dolls did Dawn have left?




1 2 3 4 5 6 7 8 9 10



7. Trevor had 2 slices of pizza. He ate 1 slice. How many

slices of pizza did Trevor have left?




1 2 3 4 5 6 7 8 9 10



8. Maria had 9 lollipops. She gave Jean 3 lollipops. How

many lollipops did Maria have left?




1 2 3 4 5 6 7 8 9 10



9. Claudette had 10 pencils. She gave Wendy 1 pencil.

How many pencils did Claudette have left?




1 2 3 4 5 6 7 8 9 10



10. Anna had 7 peaches. She ate 2 peaches. How many

peaches did Anna have left?




1 2 3 4 5 6 7 8 9 10



11. Danny had 8 cupcakes. He gave Kelly 1 cupcake. How

many cupcakes did Danny have left?




1 2 3 4 5 6 7 8 9 10



12. Katie had 6 carrot sticks. She gave Aaron 3 carrot

sticks. How many carrot sticks did Katie have left?




1 2 3 4 5 6 7 8 9 10



13. Maggie had 10 posters. She gave Carla 2 posters. How

many posters did Maggie have left?




1 2 3 4 5 6 7 8 9 10



14. Chris had 10 pieces of bubble gum. He gave Ricky 5 of

them. How many did Chris have left?




1 2 3 4 5 6 7 8 9 10



15. Wayne had 7 jellybeans. He ate 1 of them. How many

did Wayne have left?




1 2 3 4 5 6 7 8 9 10




make a number line.

1. Sue had 5 apples. She gave 1 away. How many did she have left?

2. Lucas had 7 trucks. He gave 2 to his brother. How many did he have left?



3. Maria had 10 rings. She gave 5 to her sister. How

many does she have left?

4. Maya had 8 marbles. She gave 4 to her brother. How many did she have left?

5. Darrel had 5 candies. He gave 3 to his friends. How many did he have left?


hese types of problems are about sets of things. In them we

know both parts and we are looking for the whole. What

distinguishes a Put Together/Take Apart Problem from an Add to Result

Unknown problem is action. In a Put Together/Take Apart Problem there

is no action only a set of something.

PROBLEM John had five red apples and five green ones.

How many apples did he have altogether?

MODEL

EQUATION 5 + 5 = ? 5 + 5 = 10

T

Unit 3 – Put Together/Take Apart - Whole Unknown


Way#1: Use the number frame to show one part and

then the other part.

Way#2: Try drawing pictures to help!

+

Way#3: Put together the 2 numbers on the number line. Start at the first number and then hop to the next.

1 2 3 4 5 6 7 8 9 10



1. Miguel has 3 cats and 1 dog. How many pets does

Miguel have?




1 2 3 4 5 6 7 8 9 10



2. Audrey has 2 chocolate cookies and 3 peanut butter

cookies. How many cookies does Audrey have?




1 2 3 4 5 6 7 8 9 10



3. Nicole has 2 yellow hats and 2 pink hats. How many

hats does Nicole have?




1 2 3 4 5 6 7 8 9 10



4. There are 2 orange butterflies and 1 yellow butterfly.

How many butterflies are there?




1 2 3 4 5 6 7 8 9 10



5. Bridget has 4 brown teddy bears and 1 white teddy

bear. How many teddy bears does Bridget have altogether?




1 2 3 4 5 6 7 8 9 10



6. Marta has 1 green shirt and 1 pink shirt. How many

shirts does Marta have?




1 2 3 4 5 6 7 8 9 10



7. Hong has 2 brothers and 1 sister. How many siblings

does Hong have?




1 2 3 4 5 6 7 8 9 10



8. Maddie 5 brown hamsters and 1 white one. How many

hamsters does Maddie have altogether?




1 2 3 4 5 6 7 8 9 10



9. Will has 5 green trucks and 5 blue ones. How many

trucks does Will have altogether?




1 2 3 4 5 6 7 8 9 10



10. Parker has 7 pieces of lemon candy and 2 pieces of

cherry candy. How many pieces of candy does Parker have altogether?




1 2 3 4 5 6 7 8 9 10



11. Edgar has 3 cupcakes with pink frosting and five

cupcakes with vanilla frosting. How many cupcakes does Edgar have altogether?




1 2 3 4 5 6 7 8 9 10



12. There are 8 boys and 2 girls on the playground. How

many children are there altogether?




1 2 3 4 5 6 7 8 9 10



13. Ari has 3 orange circles and 3 yellow ones. How many

circles does Ari have altogether?




1 2 3 4 5 6 7 8 9 10



14. There are 2 men acrobats and 3 women acrobats at

the circus. How many acrobats are there altogether?




1 2 3 4 5 6 7 8 9 10



15. Brian has 5 red marbles and 2 blue ones. How many

marbles does Brian have altogether?




1 2 3 4 5 6 7 8 9 10




make a number line.

1. John has 5 orange marbles and 5 purple ones. How many marbles does he have altogether?

2. Elena has 7 green candies and 1 blue one. How many candies does she have altogether?



3. Trevor has 3 dinosaur books and 4 space books. How

many books does he have altogether?

4. Grace has 5 green rings and 1 pink one. How many rings did she have altogether?

5. Treshawn had 3 toy trucks and 2 toy cars. How many toy vehicles did he have altogether?


hese types of problems are Put Together/Take Apart problems

with both addends unknown. In these problems we are talking

about sets of something. In this particular type of problem we are talking

about all the ways a set can be put together. For example, We have 4

markers. Some are green and some are yellow. How many could be green and how

many could be yellow, if there are some of each? We could have 3 green and 1

yellow, 2 green and 2 yellow or 1 green and 3 yellow. Students have to find

all the ways to do that problem.

With this type of problem we could model our thinking by using real

objects, pictures, diagrams, or tables. When you have your students use

concrete materials, they can see what is happening. When you have the

students solve it with pictures they learn how to organize information and

draw it out. Then, when they use a table, they are working at an abstract

level. It is important to emphasize that information should be neat and

organized.

T

Unit 4 – Put Together/Take Apart


Green Markers Yellow Markers

Way# 2: Using the Table technique.

MARKER COMBINATION

Green Yellow 3 1

2 2

1 3

0 5

Way#1: Try drawing pictures to help!



1. Betty has 4 hats. Some hats are yellow and some hats

are pink. How many hats could be yellow? How many hats could be pink? What are all the possible

combinations, if there are some of each?


Way#2: Solve with a table

HATS

Yellow Pink

3

2

1

0 5



2. Byron has 5 pets. Some of his pets are dogs and some

of his pets are cats. How many of his pets could be dogs? How many of his pets could be cats? What are

all the possible combinations, if there are some of each?



PETS

Dogs Cats 4

3

2

1

0 5



3. Audrey saw 6 butterflies on a tree. Some of the

butterflies were yellow and some of the butterflies were red. How many butterflies could be yellow? How many

butterflies could be red? What are all the combinations, if there are some of each?



BUTTERFLIES

Yellow Red 5

4

3

2

1

0 5



4. Courtney has 8 teddy bears. Some teddy bears are

brown and some teddy bears are white. How many teddy bears could be brown? How many teddy bears

are could be white? What are all the combinations, if there are some of each?



TEDDY BEARS

Brown White 7

6

5

4

3

2

1

0 5



5. Samantha has 9 shirts. Some of her shirts are green

and some of her shirts are pink. How many shirts could be green? How many shirts could be pink? What

are all the possible combinations, if there are some of each?



SHIRTS

Green Pink 8

0 5



6. Samuel has 5 marbles. Some marbles are red and

some marbles are green. How many marbles could be red? How many marbles could be green? What are all

the possible combinations, if there are some of each?



MARBLES

Red Green 5

0 5



7. There are 7 kids on the playground. Some are girls and

some are boys. How many could be girls on the playground? How many could be boys on the

playground? What are all the possible combinations, if there are some of each?





8. Kimi has 5 pairs of socks. Some are green and some

are blue. How many pairs of socks could be green? How many pairs of socks could be blue? What are all

the possible combinations, if there are some of each?



0 5



9. Carolyn has 9 shapes. Some are squares and some are

circles. How many shapes could be squares? How many shapes could be circles? What are all the

possible combinations, if there are some of each?



0 5



10. Francis has 5 hamsters. Some hamsters are brown

and some hamsters are white. How many hamsters could be brown? How many hamsters could be white?

What are all the possible combinations, if there are some of each?



0 5



11. Parker has 7 toy trucks. Some toy trucks are green

and some toy trucks are blue. How many toy trucks could be green? How many toy trucks could be blue?

What are all the possible combinations, if there are some of each?



0 5



12. Beverly has 4 books. Some books are about bunnies

and some books are about turtles. How many books could be about bunnies? And how many books could

be about turtles? What are all the possible combinations, if there are some of each?





13. Martha has 4 cupcakes. Some cupcakes are vanilla

and some cupcakes are chocolate. How many cupcakes could be vanilla? How many cupcakes could

be chocolate? What are all the possible combinations, if there are some of each?



0 5



14. Mr. Ted has 5 new students in his class. Some of the

students are girls and some of the students are boys. How many of each could there be? What are all the

possible combinations, if there are some of each?



0 5



15. Mia has 10 skirts. Some of the skirts have polka dots

and some of the skirts have bows. How many of each could she have? What are all the possible

combinations, if there are some of each?



0 5



Solve with a model: Draw a picture or make a table.

1. Sue had 5 rings. Some were purple and some were pink. How many of each could she have had?

2. Tom had 7 toy trucks. Some were black and some were green. How many of each could he have had?



3. Raul had 4 marbles. Some were blue and some were

brown. How many of each could he have had?

4. Lucy had 8 cupcakes. Some were vanilla and some were chocolate. How many of each could she have had?

Final Word Problems


NAME:

DATE:

Solve the Problems. Show your thinking. Draw a picture, use a number line or make a table

1. Tom had 5 apples. Sue gave him 2 more. How many does he have altogether now?

2. Lee had 7 trucks. He got 3 more for his birthday. How many does he have altogether now?


3. Raul had 10 pieces of gum. He gave 9 away. How

many does he have left?

4. Lucy had 7 dolls. She gave 3 away. How many does she have left?

5. Marvin had 1 blue marble and 1 green one. How many marbles did he have altogether?

Final Word Problems


6. Carlos has 2 blue balls and 6 purple ones. How many does he have altogether?

7. Lynn saw 5 butterflies. Some were pink and some were orange. How many of each could she have seen?

What are all the possible combinations?

8. Marcus had 6 marbles. Some were blue and some were yellow. How many of each could he have had?

What are all the possible combinations?


9. Larry had 5 books about tigers and 4 books about

lions. How many books did he have altogether?

10. Maria brought 3 lemon cupcakes and 3 strawberry

ones to the school party. How many cupcakes did she bring altogether to the party?


Answer Key

Add to Result Unknown Practice

Problems

1. 5 airplanes

2. 4 dolls

3. 2 chocolate chip cookies

4. 3 toy trucks

5. 3 dogs

6. 4 dollhouses

7. 5 stickers

8. 10 books

9. 7 pieces of candy

10. 10 toy elephants

11. 9 marbles

12. 3 dolls

13. 6 baseball cards

14. 8 books

15. 7 dresses

Unit 1 Test

1. 7 apples

2. 10 toy trucks

3. 9 marbles

4. 7 rings

5. 10 action figures

Take From Result Unknown

Practice Problems

1. 2 gummy bears

2. 2 pieces of gum

3. 1 puppy

4. 1 block

5. 0 brownies

6. 3 dolls

7. 1 slice

8. 6 lollipops

9. 9 pencils

10. 5 peaches

11. 7 cupcakes

12. 3 carrot sticks

13. 8 posters

14. 5 pieces of gum

15. 6 jelly beans

Unit 2 Test

1. 4 apples

2. 5 trucks

3. 5 rings

4. 4 marbles

5. 2 candies


Put Together/Take Apart—Whole

Unknown Practice Problems

1. 4 pets

2. 5 cookies

3. 4 hats

4. 3 butterflies

5. 5 teddy bears

6. 2 shirts

7. 3 siblings

8. 6 hamsters

9. 10 trucks

10. 9 pieces of candy

11. 8 cupcakes

12. 10 children

13. 6 circles

14. 5 acrobats

15. 7 marbles

Unit 3 Test

1. 10 marbles

2. 8 candies

3. 7 books

4. 6 rings

5. 5 toy vehicles

Put Together/Take Apart—Both

Addends Unknown Practice Problems

1. Hats

Yellow Pink

3 1

2 2

1 3

2. Pets

Dogs Cats

4 1

3 2

2 3

1 4

3. Butterflies

Yellow Red

5 1

4 2

3 3

2 4

1 5

4. Teddy Bears

Brown White

7 1

6 2

5 3

4 4

3 5

2 6

1 7


5. Shirts

Green Pink

8 1

7 2

6 3

5 4

4 5

3 6

2 7

1 8

6. Marbles

Red Green

4 1

3 2

2 3

1 4

7. Kids

Boys Girls

6 1

5 2

4 3

3 4

2 5

1 6

8. Socks

Green Blue

4 1

3 2

2 3

1 4

9. Shapes

Circles Squares

8 1

7 2

9. Shapes

6 3

5 4

4 5

3 6

2 7

1 8

10. Hamsters

Brown White

4 1

3 2

2 3

1 4

11. Trucks

Green Blue

6 1

5 2

4 3

3 4

2 5

1 6

12. Books

Bunnies Turtles

3 1

2 2

1 3

13. Cupcakes

Vanilla Chocolate

3 1

2 2

1 3


14. Students

Girls Boys

4 1

3 2

2 3

1 4

15. Skirts

Polka

Dots

Bows

9 1

8 2

7 3

6 4

5 5

4 6

3 7

2 8

1 9

Unit 4 Test

1. Rings

Purple Pink

4 1

3 2

2 3

1 4

2. Trucks

Black Green

6 1

5 2

4 3

3 4

2 5

1 6

3. Marbles

Blue Brown

3 1

2 2

1 3

4. Cupcakes

Vanilla Chocolate

7 1

6 2

5 3

4 4

3 5

2 6

1 7


1. 7 apples

2. 10 toy trucks

3. 1 piece of gum

4. 4 dolls

5. 2 marbles

6. 8 balls

7. Butterflies

Pink Orange

4 1

3 2

2 3

1 4

8. Marbles

Blue Yellow

5 1

4 2

3 3

2 4

1 5

9. 9 books

10. 6 cupcakes


REFERENCES

Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999).

Children’s Mathematics: Cognitively Guided Instruction. Portsmouth,

NH: Heinemann.

Common Core Standards Writing Team (Bill McCullum, lead author).

(2011, May 29). Progressions for the common core state standards in

mathematics: K, Counting and cardinality; K-5, operations and algebraic

thinking (draft). Retrieved from:

www.commoncoretools.wordpress.com.

Peterson, P. L., Carpenter, T. P., & Loef, M. (1989). Teachers' Pedagogical

Content Beliefs in Mathematics. Cognition and Instruction, Vol. 6, No. 1,

pp. 1-40.

http://www.commoncoretools.wordpress.com/

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