smiley face math – rising 1st · pdf filethe worksheets were field tested by the...

Prepared by the University of South Florida Saint Petersburg For a copy of these materials, go to www.cdnportfolio.net/smileyfacemath

Smiley Face Math – Rising 1st Graders

Acknowledgements

These materials were developed during a Problem Solving for Elementary

Teachers class at the University of South Florida Saint Petersburg (USFSP) during the

spring of 2009. The worksheets were field tested by the teachers in their own

classrooms.

The project was conceived and directed by Dr. Charles A. (Andy) Reeves. Dr.

Reeves previously developed the Superstars, Superstars II, and Sunshine Math packages

of supplementary materials for grades K-8. Dr. Reeves is particularly interested in

problem solving and in algebraic thinking.

The writers and field testers

Tierney D. Montooth is a 2nd

grade teacher at Campbell Park Elementary School

in Pinellas County, Florida. She is interested in using technology to enhance

mathematics learning as well as problem solving.

Rebecca (Becky) Walsh is a 1st grade teacher at Bay Haven Elementary School in

Sarasota County, Florida. Becky enjoys learning new ways to teach mathematics to her

students.

Christine Cherinka is a 3rd

grade teacher at Our Lady of Lourdes in Pinellas

County, Florida. Ms. Cherinka is particularly interested in teaching mathematics to all

students.

Technical Assistance

Final proofing and editing was provided by Dr. Vivian Fueyo, Professor and

Founding Dean of the USFSP College of Education. Dean Fueyo’s educational interests

include teacher education, teacher as researcher, teacher leadership, and strategies for

accommodating diverse learners. Dr. Zafer Unal, Assistant Professor of Early Childhood

Education, USFSP, prepared these materials for the internet. Dr. Unal’s interests include

technology in teacher education, institutional and program assessment, e-portfolios,

parental involvement and classroom management.

CONTENTS

SECTION 1: Introductory Materials

• Overview of the Next Generation Sunshine State Standards (NGSSS) for

First Grade students in Mathematics

• How to Use these Materials with Your Child

• Correlation of the Problems with the NGSSS

SECTION 2: Worksheets for Your Child

SECTION 3: Answers to the Worksheets, and suggestions on how to help your child solve

the problems.

Section 1

Overview of the Next Generation Sunshine State Standards in Mathematics, K-8,

adopted by the State Board of Education in September, 2007.

The Florida Board of Education adopted new mathematics standards in 2007.

The standards were developed by Florida teachers, supervisors, and university faculty.

The main goal was to reduce the number of standards listed each year so that teachers

could focus on fewer topics, but teach those topics in-depth. This emphasis reflects a

national trend and our work was based on the National Council of Teachers of

Mathematics’ publication Curriculum Focal Points for Prekindergarten through Grade 8

Mathematics. (NCTM 2006) The total number of math standards that a K-8 teacher is

responsible for covering has been reduced from an average of 87 per grade level, to 18.

So teachers will definitely have more time to teach in an in-depth fashion.

Each grade level has three Big Ideas and each Big Idea contains several

benchmarks under it, usually three or four. There are also Supporting Ideas for each

grade level that round out the curriculum and maintain two strands—algebraic thinking

and problem solving—over a several-year span. This strategy combines an in-depth look

at the Big Ideas in a given year, with topics that students should work on every year.

The Big Ideas for Grade 1 are:

BIG IDEA 1

Develop understandings of addition and subtraction strategies for basic

addition facts and related subtraction facts.

BIG IDEA 2

Develop an understanding of whole number relationships, including

grouping by tens and ones.

BIG IDEA 3

Compose and decompose two-dimensional and three-dimensional

geometric shapes.

This means that 1st graders are going to spend much of their math time (1) building a

foundation of understanding number relationships in regards to addition and subtraction,

(2) increasing their awareness of number relationships by grouping and counting by tens

and ones, and (3) taking apart and putting together two-dimensional and three-

dimensional geometric shapes.

The Supporting Ideas for Grade 1 come from the Algebraic Thinking strand, the

Geometry and Measurement strand, and the Number and Operations strand. From the

Algebraic Thinking strand, students will extend repeating and growing patterns, fill in

missing terms, and justify their reasoning. In Measurement, they will learn how to

measure the length of objects using nonstandard units of measurement and count the

units. In the Number and Operations strand, they will use mathematical reasoning and

begin to understand the tens and ones columns, including the use of invented strategies,

to solve two-digit addition and subtraction problems.

In short, your child will be learning a lot more about selected mathematics topics

than in the past. This shift in emphasis will produce a curriculum that is much more in-

depth about very basic ideas so that reteaching in future years will be unnecessary. What

is necessary, however, is that the ideas learned in one year be used and reinforced in later

years. Some have said that the math curriculum will go from a “mile-wide, inch-deep”

curriculum, to an “inch-wide, mile deep” curriculum. The truth lies somewhere between

those two extremes.

Reference

National Council of Teachers of Mathematics, Curriculum Focal Points for

Prekindergarten through Grade 8 Mathematics. Reston, VA: 2006.

How to Use these Materials with Your Child

The worksheets to follow are designed to be used during the summer prior to a

student entering first grade. The worksheets are similar to Florida’s popular Sunshine

Math program where students accumulate stars for doing extra problems. The answers

and how to help your child, without giving too much help, are in the back of this package.

The directions below are written for an individual parent, but can be adapted by schools,

churches, or other community groups sponsoring summer camps for youth groups. The

worksheets are each two pages in length so that, if copied front-to-back, they will each

use one sheet of paper.

Do not feel that you have to “teach” these problems to your child. That is

the job of the school system next year. But many times children learn things

incidentally, by talking with others. If you simply talk through the problems with

your child, perhaps he or she will remember that type of problem when it’s

encountered in first grade, and therefore be more successful with it.

Give out one worksheet a week during the summer. You might read all the

problems with your child the first night, being sure that each problem is well understood,

but not trying to solve the problems. As children about to enter first grade probably can’t

read very well, be sure your child can tell you what each problem means, before going

ahead. (You might do this activity two nights in a row, to be sure your child remembers

each problem.) You should ask the child for any ideas about how to solve the problems.

Then he or she can have all week to work on the problems.

When the week is up, have a “help session” in which your child explains to you

how the problems were solved. Help her or him understand the problems that were not

solved because similar problems will be seen later during the summer and all next year.

Each problem is worth 1-4 smileys, depending on how hard it is. You can award partial

credit for problems that are understood but a mistake was made, and you can give a

single smiley if a problem was completely missed, assuming the child now understands

how to proceed.

Your child’s reward for doing this extra work is accumulating smiley faces on a

chart—you’ll need to make one of those and keep up with it each week. The chart needs

to occupy a prominent place in your house, where the child and others will see it

regularly. You might consider adding some extra incentives for reaching certain levels.

For example, once 10 smileys are earned, he or she might get a book of their choice. For

reaching 25 smileys, a movie might be in order. For reaching 50 smileys, a trip to the

beach or a sleepover with their friends could be earned. The basic idea is that your child

can earn rewards by doing some extra math problems. And he or she will realize that

next year’s math class will be made much easier by knowing how to complete these

tasks.

SMILEY FACE MATH

Maria has this many smiley faces: ☻☻☻☺☺☺☺☺

Key: ☻ = 10☺

Note: You can make a chart by hand or do a computer version. The process of

making the smiley face chart on the computer is a math task in itself, one from which the

child can learn. You—or your child—can make a chart easily using a word processing

program by going to the “insert symbol” menu on a PC, and finding the smiley face

symbol. As the number of smileys on the chart becomes large, you can use a key such as

☻ = 10☺’s and your child will have learned something else about mathematics—how to

construct a useful chart to display data.

Materials:

Have common materials from around your house available for the child to use in

counting and representing sets of objects. Paper clips, beans, straws, and so forth, are

useful for this purpose. Materials that can be bundled into tens and ones—straws and

toothpicks, for example—are particularly useful at this grade level. A “hundreds chart”

like the one below is also useful in counting from one number to another.

Correlation of the Problems and the Next Generation Sunshine State

Standards in Mathematics for First Grade

Big Idea 1: Develop understandings of addition and subtraction strategies for basic addition facts and related subtraction facts. BENCHMARK CODE BENCHMARK

MA.1.A.1.1 Model addition and subtraction situations using the concepts of "part-whole," "adding to," "taking away from," "comparing," and missing addend."

[I 1, 2, 8; II 1; III 4, 5, 6, 7, 8; IV 1, 2, 3; V 1, 2, 3; VI 1, 2, 3; VII

1, 2, 3, 4, 7; VIII 1, 2, 3, 7; IX 4, 6, 7; X 3, 5, 7, 8] MA.1.A.1.2 Identify, describe, and apply addition and subtraction as inverse operations.

[V 9; VIII 4] MA.1.A.1.3 Create and use increasingly sophisticated strategies, and use properties such as

Commutative, Associative and Additive Identity, to add whole numbers.

[III 7; IV 7; II 8; VII 5] MA.1.A.1.4 Use counting strategies, number patterns, and models as a means for solving

basic addition and subtraction fact problems.

[I 1, 2, 8; II 1,4; IV, 7; V 1, 2, 3; VI 3; VII 1, 2, 3, 4, 7;VIII 1, 2, 3,

7; IX 6; VIII 1, 2, 3, 7; IX 4, 6, 7; X 3, 5, 7, 8]

Big Idea 2: Develop an understanding of whole number relationships, including grouping by tens and ones. BENCHMARK CODE BENCHMARK

MA.1.A.2.1 Compare and order whole numbers at least to 100.

[I 3, 5, 6, 7; III 1, 5; IV, 2; V 6; VI 4, 5, 6; VII 6; IX 8; X 4] MA.1.A.2.2 Represent two digit numbers in terms of tens and ones.

[II 2; V, 5; VI 5; VII, 6; IX, 8; X,1, 6] MA.1.A.2.3 Order counting numbers, compare their relative magnitudes, and represent

numbers on a number line.

[I 3, 6, 7; III, 1, 5; IV 2; V 6; VI 4, 5, 6; VII 6; IX, 8; X 4]

Big Idea 3: Compose and decompose two-dimensional and three-dimensional geometric shapes. BENCHMARK CODE BENCHMARK

MA.1.G.3.1 Use appropriate vocabulary to compare shapes according to attributes and properties such as number and lengths of sides and number of vertices.

[IV, 6; VII 7; VIII 6, IX 5] MA.1.G.3.2 Compose and decompose plane and solid figures, including making predictions

about them, to build an understanding of part-whole relationships and properties of shapes.

[III, 2; V 4; VII, 8; IX 5]

Supporting Idea: Algebra

BENCHMARK CODE BENCHMARK MA.1.A.4.1 Extend repeating and growing patterns, fill in missing terms, and justify

reasoning.

[I 4; II, 5; IV 4; IX 3]

Supporting Idea: Geometry and Measurement

BENCHMARK CODE BENCHMARK MA.1.G.5.1 Measure by using iterations of a unit, and count the unit measures by grouping

units.

[II 6, 7; IV, 8; X 2] MA.1.G.5.2 Compare and order objects according to descriptors of length, weight, and

capacity.

[III, 3; VI 7; IX 1]

Supporting Idea: Number and Operations

BENCHMARK CODE BENCHMARK MA.1.A.6.1 Use mathematical reasoning and beginning understanding of tens and ones,

including the use of invented strategies, to solve two-digit addition and subtraction problems.

[III 8; V 7, 8; VIII 5; X 6] MA.1.A.6.2 Solve routine and non-routine problems by acting them out, using manipulatives,

and drawing diagrams.

[I 1, 2, 8; III 4; IV 1, 3; V 1, 2, 3; VI 1, 2, 3; VII 1, 2, 7; VIII 1,

2, 3, 7; IX 4, 6, 7; X 3, 5, 7, 8]

Section 2

Smiley Face Math Name: _________________________________

Grade 1 Worksheet I

☺ ☺ 1. Tori found 4 pink shells and 5 gray shells. How many shells did she find? Show the

problem with counters.

Answer: Tori found ____ shells in all. 4 pink shells

☺ ☺ 2. James had 15 balloons. He let go of 9 and they floated away. How many balloons did

James have left? Draw a picture to show the problem.

Answer: James then had ____ balloons. 15 balloons

☺ ☺ 3. Name a number that comes between 23 and 38. Answer: _____

☺ ☺ ☺ 4. Draw the shape that comes next in this pattern. Explain your answer.

______

Explanation: ____________________________________________________________

____________________________________________________________

?

☺ ☺ 5. Which number is bigger, 86 or 68? Explain how you know.

Answer: _____ is bigger because ________________________________________

____________________________________________________________

☺ ☺ 6. Andy spun his top for 12 seconds on the first try, 9 seconds on the second try, and 13

seconds on the third try. Put Andy’s times in order from shortest to longest.

Shortest time: ________

________

Longest time: ________

☺ ☺ 7. Katie and John found between 80 and 85 empty water bottles at the park clean up.

Exactly how many bottles might they have found?

Answer: They might have found ____ , ____ , ____ ,

or ___ bottles

☺ ☺ ☺ 8. Spot ate 6 dog bones. Ruby ate 7 more than Spot. How many dog bones did Ruby

eat? Draw a picture to help you find the answer.

Answer: Ruby ate ______ bones.

Spot’s bones

Smiley Face Math Name: ____________________________

Grade 1 Worksheet II

☺ ☺ 1. Ringo has 7 toys for his cat. 4 of them are stuffed mice. How many of them are not

stuffed mice?

Answer: _____ toys are not stuffed mice.

☺ 2. Bob has fifty-six stamps in his collection. He has some strips of ten stamps, and some

loose stamps. Circle the group below that shows Bob’s fifty-six stamps.

group A group B group C

☺☺ 3. Tell how many stamps are in the groups above, that are not Bob’s stamps:

Answer: Group ____ is not Bob’s. This group has _____ stamps.

Group ____ is not Bob’s. This group has _____ stamps.

☺☺☺ 4. How many jellybeans should go in the box on the balance scale to make both sides

have the same number of jelly beans? _____ jelly beans

?

☺ ☺ ☺ 5. Write the missing numbers.

2, 4, 6, 8, 10, 12, _____, 16

5, 10, 15, 20, 25, 30, 35, _____, _____.

8, 7, 6, 5, ____, 3, 2, 1

☺ ☺ 6. Joey measured his toy car using paper clips. About how long was Joey’s toy car in

paperclips?

Answer: ______ paperclips long

☺ ☺ ☺ 7. Joey then measured his toy boat with the paperclip chain above. He had to use it four times

to measure how long the boat was. How long was the boat? ____ paperclips long

☺ ☺ ☺ 8. Kelly rolled two dice. The two numbers on the top faces equaled 6 when added

together. What two numbers might have come up on the top faces? (Get a pair of dice

and roll them and see what you find out.)

Answer: The two numbers may have been ____ and ____.

The two numbers may have been ____ and ____.

The two numbers may have been ____ and ____.


Grade 1 Worksheet III

☺ ☺ 1. Put numbers below each sea creature to show how many “legs” it has. Then circle the

creature with the smallest number of “legs”.

________ __________ _________ ____________

☺ ☺ ☺ 2. How many squares did it take to draw the dog picture?

Answer: ____ squares

☺ ☺☺☺ 3. Four girls are trying out for the talent show. Maria is shorter than Alice but taller

than Beth. Juanita is shorter than Beth. Circle Juanita. Draw a rectangle around Alice.

☺ ☺ 4. The first grade class went on a field trip to the zoo. They saw 1 lion and 2 giraffes.

How many legs did they see on those animals?

Answer: They saw ____ legs.

☺ ☺ ☺ 5. The Tigers scored 3 goals in a game. The Eagles scored 7 goals in the game. Which

team won, and by how many goals?

☺ ☺ 6. In April 2008, Joe Allison balanced 16 spoons on his face earning him a place in the

Guinness Book of World Records. If 9 spoons fell off Joe’s face, how many would he

still be balancing on his face?

Answer: ______ spoons would still be on his face.

☺ ☺ 7. Gracie has six tennis balls. Bailey has 14 tennis balls. How many more tennis balls

does Bailey have than Gracie?

Gracie’s tennis balls

☺ ☺ ☺ 8. Zaria read for 27 minutes on Saturday and 15 minutes on Sunday. How many minutes

did she read over the weekend?

Answer: Answer: The __________ won by ____ goals.

Answer: Bailey has _____ more

balls than Gracie.

Answer: She read _____ minutes

over the weekend.


Grade 1, Worksheet IV

☺☺☺ 1. Julie ate 5 chocolate chip cookies and Matt ate 7. How many cookies were eaten in all?

Answer: They ate _____ cookies together.

☺ 2. Which animal has 3 fewer than 5 legs—a duck, a dog, or a spider? Answer:_________

DUCK DOG SPIDER

☺☺☺ 3. Two ducks and a dog and a spider would have how many legs together?

Answer: _____ legs

☺ 4. Draw the missing picture in this pattern of beach toys.

_____________________

☺☺ 5. Mary made 7 photo albums. Neil made more albums than Mary. Which could be the

number of albums Neil made?

Circle your answer.

11 albums 6 albums 3 albums 7 albums

☺☺ 6. What shape will you make if you trace around the bottom of a cup with a crayon? Put

an X on the name of the shape.

☺☺☺ 7. Antonia had 15 pennies and got 3 more. Alice had 3 pennies and got 15 more. Who

had the most in the end, or did they have the same number of pennies?

Answer: ____________ had more, or they had the same amount.

Explain:

☺☺☺ 8. Measure how many of your feet it takes to go across your bedroom, to the nearest

whole foot. Then measure how far across your bedroom in the other direction. Write

your answers below.

Answer: My bedroom is about ______ of my feet across. It is about

_____ of my feet the other direction.

a. circle

b. square

c. rectangle

d. triangle


Grade 1, Worksheet V

☺☺ 1. Jason has 7 toy cars. James has the same number. How many do they have in all?

Answer: Together they have_____ toy cars. Jason’s cars

☺☺ 2. Tiffany saw 9 fish. Of those 9 fish, 2 swam away. How many fish does Tiffany see

now?

Answer: She sees ______ fish now.

☺☺☺☺ 3. a. How many students had goldfish for pets? _____ c. How many had cats for pets? _____

b. How many students had birds for pets? _____ d. How many more had dogs for pets,

than had hamsters for pets? _____

Class Pets

☺☺ 4. How many circles make up the polar bear face? _____

☺☺ 5. Write the two numbers shown by the tens and ones below:

☺☺ 6. Which number is bigger, 34 or 43? ______

Explain why you think _____ is bigger than _____:

☺☺ 7. Use the pictures in problem 5 to help you: 43 + 34 = _______

☺☺ 8. Use the pictures in problem 5 to help you: 43 – 34 = _______

☺☺☺ 9. a. Add 7 to how old you are. What is your answer? _____

b. Subtract 7 from your answer above. What is your new answer? ____________

c. What happens when you add 7 to a number, then subtract 7? What number do

you get?

_________________________________________________

______ ______

Smiley Face Math Name: _______________________

Grade 1, Worksheet VI

☺☺ 1. There are 8 slices of pizza in the box. Matt takes 1 slice and Emily takes 3 slices.

How many slices of pizza are left in the box?

☺☺☺ 2. Shayna had 9 balloons. Some floated away. Now she has 6 balloons. How many

balloons flew away?

☺☺☺ 3. What does the chart below show? ______________________________________________

Ann sees another ladybug. How many tally marks for ladybugs should there be now? _____

How many more ants did Ann see, than spiders? _______

Answer: _____ slices are left

Answer: _____ balloons flew away.

☺ 4. Draw below the number of tens and ones that would be between 33 and 35.

☺☺☺ 5. Fill in the 3 missing numbers in this part of a hundreds chart.

☺☺ 6. Mark’s baby sister weighed 6 pounds at birth. Julie’s baby brother weighed 8 pounds

at birth. What number between 6 and 8 could be the baby’s weight below? Write it in

the box.

☺☺ 7. A hot dog weighs 50 grams. A hamburger weighs 75 grams. Fries weigh 35 grams.

A milkshake weighs 80 grams. Circle the one that weighs the most. Put a square on the

one that weighs the least.

33 35

Make your drawing here:

0 5 1 2 3 4 6 9 10 8

Smiley Face Math Name:_____________________

Grade 1, Worksheet VII

☺☺ 1. Alice saw 4 pink flamingos at the zoo. Then she saw a penguin and her baby. Later

she saw a parrot. How many birds did she see in all?

☺☺ 2. The children below are playing jump rope. One of them had to go home. Then 2

more friends joined the fun. How many were playing jump rope then?

☺ 3. Start with 4 teddy bears. Add 6 more. How many teddy bears do you have?

☺ 4. Start with 6 teddy bears. Add 4 more. How many teddy bears do you have now?

☺☺ 5. Does 4 + 6 give the same answer as 6 + 4? _____ How do you know? Explain:

Answer: Alice saw ____ birds at the zoo.

Answer: There were _____ kids playing jump

rope at the end.

Answer: 4 + 6 = _____

Answer: 6 + 4 = _____

☺☺☺ 6. Below, write the numbers that come just before and just after 32, 43, and 61.

____, 32, ____ ____, 43, ____ ____, 61, ____

☺☺☺ 7. Nine frogs are in the pond. Three frogs hop away. How many frogs are left? ______

☺☺☺ 8. Draw a boy or a girl this way:

Draw a circle for the head:

Draw a triangle for the body:

Draw rectangles for the arms and legs:

How many shapes did you draw altogether? ______ shapes


Grade 1, Worksheet VIII

☺☺☺ 1. Two children were playing soccer. They needed nine to make a soccer team. How

many more children did they need to make a team?

☺☺☺ 2. A line of seven elephants was ready to enter the circus. Four jugglers were there also.

If each juggler rode in on an elephant, how many elephants would not have a rider?

☺☺ 3. Five ants were at a picnic. Then four new ants came along. Then four ants left after

eating so much food. How many ants were there then?

☺☺☺ 4. A number sentence for the ant problem above is 5 + 4 – 4 = ?

In this number sentence 4 is added and then subtracted. Explain what happens to the number you

start with, when a number is added and that same number subtracted.

Answer:

Answer: They needed ____ more players.

Answer: There were ____ more elephants.

Answer: There were ____ ants left at the picnic.

☺☺ 5. There were 100 leaves on the tree. In the fall they all blew away. How many leaves

were left on the tree?

☺☺☺ 6. Write the number of sides and the number of vertices for each figure below:

☺☺☺ 7. There were four children in a group. There was enough pizza for everyone to have

two slices. How many slices of pizza were there?

Answer: There were ____ leaves on the tree after they all

blew away.

___ sides and ___ vertices

triangle

___ sides and ___ vertices ___ sides and ___ vertices

square

pentagon

Answer: There were ____ slices of pizza.


Grade 1, Worksheet IX

☺☺ 1. Look at these containers in your kitchen. Write 1 for the container that would hold the

least water, 2 for the container that would hold the Middle amount, and 3 for the

container that would hold the most water.

a. a measuring cup ___ b. a milk carton ___ c. a tablespoon ____

☺ 2. Where is the dog in relation to the doghouse? Circle the correct word or words.

☺☺ 3. Draw what comes next in this repeating pattern.

_______ _______

☺☺☺ 4. The bunny had a basket with 6 eggs and another basket with 4 eggs. How many eggs

did the bunny have in all? _______ eggs

Inside Outside

Next to On top of

☺☺☺ 5. Find an example of a cube at home.

☺☺ 6. Joan baked 8 cupcakes for a birthday party. Miranda baked 5.

Who baked more cupcakes? __________ How many more? ________

Joan’s cupcakes:

Miranda’s cupcakes:

☺☺ 7. Amy had nine dolls. She gave 2 to her friend and lost one. How many dolls did Amy

have left? ___________

☺☺☺ 8. Circle the number that shows the largest number of blocks.

46 44 42

a. How many flat faces does a cube have? ____

b. How many edges does a cube have? ____

c. How many vertices (corners) does a cube have? ____


Grade 1, Worksheet X

☺☺☺ 1. Give the number of tens and ones for each group below:

___ tens and ___ ones ___ tens and ___ ones ___ tens and ___ ones

☺☺ 2. How many paperclips long is the pencil? _________ paper clips

How can you tell?

☺☺ 3. Karl scored 4 goals in a soccer game. He scored 1 goal in the next game and 2 goals

the game after that. How many goals did he score in the three games? _________

☺☺☺ 4. When you count, what number comes after 66? _____

When you count, what number comes before 32? _____

When you count, what number comes between 23 and 25? _______

☺☺ 5. Judy saw seven dolphins swimming. Then she saw four more. How many dolphins

did Judy see in all? ______ dolphins

☺☺☺ 6. Put the tens and ones together to show 25 + 31.

25 + 31 = ___ tens and ___ ones

☺☺ 7. There were 8 fire trucks at the truck show. Five left to go to a fire. How many trucks

were left at the truck show? _________

☺☺ 8. Jill wanted to make 10 sand castles. She has made 2 already. How many more does

Jill need to make?

Answer: Jill needs to make ___ more sand castles.

Section 3

Suggestions for Helping your Child Find the Answers

Grade 1, Worksheet I

1. Answer: 9 Encourage the child to represent the action of the problem with

counters—beans, coins, and so forth—or with a drawing. Your son or daughter will

likely show 4 counters first, and put 5 more with them, and count to find 9 altogether. Or

the child might show 4 fingers, and “count on” by saying “5, 6, 7, 8, 9. There are 9 in

all.”

2. Answer: 6. The natural way for children to follow the action in this problem is to

show 15 balloons, either with counters or by drawing them, and then 9 “go away” or are

marked out. They would then find how many were left.

3. Answer: Any reasonable number between 23 and 38. First have the child touch 23

with a left-hand finger, and then 38 with a right-hand finger. Tell the child that any

number between the left and right hands is a number between 23 and 38. Have the child

find several such numbers. A challenge would be to find all the numbers between 23 and

38. Be sure to mention that 23 itself, and 38, are not between 23 and 38.

4. Answer: Have the child verbally indicate the symbols as they are touched in

order, saying something like up, right, down as they move from left to right. This pattern

has a core of three things that repeat over-and-over again. Saying such words will

reinforce that, when the child gets to the question mark, up would come next.

5. Answer: 86 Some children might know to look in the “tens” column first to

determine bigger 2-digit numbers. Others might use a number line to help them decide

which is larger. If your child doesn’t know this already, then have the child bundle some

toothpicks or straws into tens and ones, and show that 86 is 8 tens and 6 ones, while 68 is

6 tens and 8 ones. The bundles can then be taken apart, if necessary, to see that 8 tens

and 6 ones is the bigger number.

6. Answer: 9, 12, 13 Your child might start from the smallest number and work up, or

start with the largest number they know.

7. Answer: 81, 82, 83, and 84 The child should choose a whole number or numbers

between the two numbers. If your child has difficulty, then point out 80 and 85 on a

hundreds chart—see “materials” in the introduction to this package.

8. Answer: 13 This problem involves the concept of how many more in one set than

another. The child might put out 6 counters to show Spot’s bones, and beside them put 6

more counter’s for Ruby’s as if she had eaten the same amount. But the child must add 7

more to Ruby’s pile now, as she ate 7 more than Spot. Then the child would count all of

Ruby’s bones and get 13. Some children will just draw seven more bones beside the 6

that are shown, and “count all” for the answer.


Grade 1, Worksheet II

1. Answer: 3. This problem is a “part-to-whole” subtraction problem. Suggest that the

student draw a picture or use counters to help. If the action of the problem is shown, the

child will show the set of 7 cat toys first, and then a subset of the toys (4 mice) will be

identified, and the remaining toys counted.

2. Answer: Group C. The problem shows groups of tens and ones. The tens have

purposely been mixed with the ones for the child to discriminate—this is atypical of

textbook presentations, where the tens always appear on the left and the ones on the right.

If your child isn’t familiar with tens and ones in this way, then have the child practice

bundling and unbundling toothpicks or straws to match various two-digit numbers.

3. Answer: Group A has 44 and Group B has 35. This is more counting of tens and

ones. As above, practice of this concept will be useful to the child in first grade.

4. Answer: 3 Encourage the child to draw the “missing” jellybeans to balance the two

sides. This problem is a precursor to solving equations and will later be represented

using a number sentence like “7 = 4 + ?” If the child is having trouble understanding the

concept of “balancing out”, have the child stand with 7 pennies in one hand and three

pennies in the other, like a balance scale, and ask “how many more do you need in one

hand, to have the same amount in both hands?” If still more help is needed, take the

pennies in one hand and line them up next to the pennies in the other hand, so that there

will be some “extras” in one hand. That’s how many need to be added to the other hand.

5. Answer: 14; then 40, 45; then 4 The first pattern is counting by two’s—have

the child say the numbers out loud to see if the pattern is recognized. If not, the child can

point with one finger and jump by 2s along a number line, or in the hundreds chart. The

child can practice counting by twos by counting the number of socks in a given number

of pairs, or the number of eyes for so many people, and so forth. The second pattern

involves counting by 5s—this can be practiced out loud also, as nickels are counted, or

minutes on a clock face are counted. The last pattern involves counting backward—if the

child has trouble, start on the right end and count toward the left. The child can practice

counting backward by “counting down” as a microwave oven counts, or a traffic signal

that shows how many seconds till the light turns red, or any number of things in the real

world.

6. Answer: 3 Some children might say 2½ paperclips, and that would be fine also. If

the child has trouble, have the child line up real paperclips to measure some items around

the house, such as a pencil or how far it is around his or her wrist.

7. Answer: 12 If the child answered “3” for the problem above, then he or she can put

together those 3 paperclips four times, getting 12. (If the answer was 2½ above, then the

answer to this problem would be 10.)

8. Answer: The numbers 1 and 5 make 6, as do 2 and 4, and also 3 and 3. The

importance of this problem is for students to recognize that these pairs (1,5), (2,4), and

(3,3) all belong to the same fact family. The pair (0,6) also belongs to this same fact

family, but zero is not a face on a die and so won’t come up in this context. If the student

has trouble understanding the idea of the problem, have them take a pair of dice and roll

them a number of times, counting the total number of pips that come “up” repeatedly.

Then the child should get the idea of the problem. (Note: at this point, don’t make a

distinction between 2 coming up on the first face and 4 on the second, and 4 coming up

on the first face and 2 on the second.)


Grade 1, Worksheet III

1. Answer: 4, 6, 5, and 0. Seahorse is circled. It will be interesting to see what your

child considers “legs”, and that’s why the word is in quotes for the problem. For

example, the child might think a crab has 8 legs, counting the two claws as legs. And the

child might think the seahorse has 1 leg, counting its tail as a leg. Any interpretation is

considered correct for this problem.

2. Answer: 13 Encourage the child to check off each square as it is counted, so that the

child can keep track. The dog’s nose might not be counted as a square, but it is a square

since the orientation of a figure is not considered in naming it..

3. Answer: The circle goes on the left-most girl, and the rectangle on the right-most.

The point of this problem is to have students engage in ordering lengths based on

descriptors that compare two lengths at a time. The first sentence says Maria is to the left

of Alice in the picture, and that Beth is to the left of Maria. The last sentence says that

Juanita is to the left of Beth.

4. Answer: 12 Encourage your child to use counters or draw a simple picture to solve

the problem. The problem is intentionally planned so that the numbers in the problem are

not the numbers to add, to teach the child to think critically.

5. Answer: The Eagles won by 4 goals Your child probably won’t have trouble

saying which team won, but “by how many goals” is a different question. Have the child

line up 3 counters next to 7 counters, pairing them up and seeing that there are 4 counters

under the eagles that are unmatched. Or the student can draw a quick sketch in a similar

manner.

6. Answer: 7 If the child follows the action of the problem with counters, he or she will

put out 16 counters to show those balanced on his face, then remove 9 of them to show

those that fell off. Then he or she will count what is left. The child might also draw a

simple picture in a similar manner. The child might even “count up” from 9 to 16 or

“count back” from 16 to 9.

7. Answer: 8 This problem is similar to #5 above in the way a child might solve it.

8. Answer: 42 minutes The child might use an invented strategy to solve the problem,

or simply count in an unusual way to put together 27 and 15. The child might use

counters, a number line or hundreds chart. This problem doesn’t lend itself to using

counters as much as it does to using a number line because the concept of time is not a

discrete category like the number of apples or bananas on a tree. Your child might prefer

to count the minutes on a clock face, which is a circular number line.


Grade 1, Worksheet IV

1. Answer: 12 If the child follows the action of the problem with counters or a

drawing, 5 items will be shown, 7 more, and then all will be counted find how

many together. Sophisticated counters might “count on” from 5 to 12, saying “5,

6, 7, 8, 9, 10, 11, 12”. If the child is very astute about counting, he or she will

start at the larger of the two numbers—7—and “count on” five more, getting 12

also, but in fewer steps.

2. Answer: duck To help a child understand this problem, have the child write

beneath each animal how many legs it has. Then have the child ask, for each one

in turn—is this number 3 fewer than 5? It is 3 fewer than 5 if 3 more can be put

with the number, and 5 results.

3. 16 The child can put down 2 counters for both ducks, then 4 counters for the

dog, then 8 counters for the spider, and “count all” to get 16. Or they might draw

a picture, or count in a more sophisticated way.

4. Answer: 4 beach balls This is a growing pattern in which the number of

beach balls increases by one each time through the pattern. If your child has

trouble seeing the pattern, have the child say the words out loud: ball, pail,

(pause) ball, ball, pail, (pause) ball, ball, ball, pail, (pause). Sometimes hearing

the words verbally will help children notice a pattern.

5. Answer: 11 For each possible number, ask “Is this more than 7?” How do you

know? If it’s more than 7, and you put out that many counters, part of the

counters, but not the whole set, would be 7. Be sure to notice how the child

handles the last number—7 counters. 7 is not more than 7.

6. Answer: Circle To find the answer to this problem, it might help to get a cup

from the kitchen so that the child can visually see what shape is made. The child

might struggle without having something visual in front of him or her.

7. Answer: They had the same amount. They both had 18. The purpose of the

problem is for the child to realize that it doesn’t matter the order in which one

adds two numbers. This is called the commutative property, and is quite useful in

computation because you can pick which number to add to the other one.

Usually, the smaller number is easier to add to the larger number because it’s

easier to “count on” in that manner.

8. Answer: will vary This activity should be fun to do with your child. The

child can put one foot in front of the other to measure in this fashion. The path

might have to be adjusted as it goes around furniture, but that’s the reality of

measuring in the real world. You might also measure in this fashion with your

own feet, and ask the child what will happen—Will your number of feet take

more or fewer steps to measure across the room? (This concept is a sophisticated

one which the child probably won’t understand—a longer unit gives a smaller

total number of units to span a distance—an inverse relationship.)


Grade 1, Worksheet V

1. Answer: 14 The child can represent the action of the problem by drawing or

placing 7 counters out, then 7 more counters, and “counting all.” He or she might

use a more sophisticated counting method such as “counting on” from 7 to 14—

saying “7, 8, 9, 10, 11, 12, 13, 14”.

2. Answer: 7 The child can represent the action of the problem by drawing or

placing 9 counters out, then removing 2 of them, and counting what’s left. Or the

child might use the drawing provided, which shows 9 fish but 2 of them are

swimming in the other direction from the first 7.

3. Answer: 4, 2, 6, and 4 The problem involves understanding graphical

representation of numerical data. Questions a, b, and c are simply reading data

from the graph, but problem d involves reading data and then comparing the two

numbers 7 and 3, and finding their difference. If the child has trouble with d,

have the child line up 7 counters next to 3 counters, matching up the 3 counters

for hamsters with 3 of the 7 counters for dogs, and then counting how many dog

counters are left without a matching hamster.

4. Answer: 6 To solve the problem, it might help to check off each circle as the

child counts it.

5. Answer: 43, 34 The child should be encouraged to count the tens first for

each group, then the ones. For the first group, for example, he might say ten,

twenty, thirty, forty; and then count the ones, saying 41, 42, 43, 44. Similarly for

the second group.

6. Answer: 43 Hopefully the child will refer to the pictures in problem 5 and say

something like ‘43 is bigger because 4 tens and 3 ones has more blocks than 3

tens and 4 ones. See, I can show you.’

7. Answer: 77 If you have toothpicks or straws that can be bundled into tens and

ones, the child can show both amounts, then push them together to show joining

the sets, and count all. Or the child can simply count the tens in both drawings

for problem 5, and then the ones in both drawings.

8. Answer: 9 As above, if you have counters that can be bundled, the child can

compare the two groups more easily to find their difference. In this case, one of

the groups of tens in 43 can be unbundled giving 13 ones, to compare to 4 ones in

34, and the difference in 13 and 4 is 9. The child might simply use the drawing

and mark out 3 tens in each group, and compare what’s left—13 squares and 4

squares.

An interesting site for comparing tens and ones electronically is:

http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html

The child will enjoy moving the red blocks up to match the blue blocks, and

watching them “zap away.”

9. Answer: will vary depending on the child’s age. The point of the problem is

for the child to add and then subtract the same number. Point out that when they

do so, the result gives the original number. Adding a number and then subtracting

that same number is called an inverse operation.


Grade 1, Worksheet VI

1. Answer: 4 Have the child draw a pizza and divide it into 8 slices, as equally as

possible. (You might want to demonstrate making a cross through the middle, and then

dividing the other sections evenly also.) Then the child can “remove” the eaten pieces,

and count what is left.

2. Answer: 3 The child might start with counters or the drawing provided, and show 9

balloons to start. Then the child might circle the 6 that are left, and ask—“How many are

not in the group that’s left? That’s how many flew away.”

3. Answer: The chart shows the number of bugs Ann saw in the garden, 3, 3 The

title of the chart always tells what it’s about; the tally marks for the ladybug go from 2 to

3, so there are now 3; She saw 7 ants and 3 spiders—if the child has difficulty

determining how many more, suggest showing 7 counters for the ants and 3 for the

spiders, matching up the counters as far as possible, and 4 “ant counters” will be left

unmatched.

4. Answer: 34 The child should draw 3 tens and 4 ones.

5. Answer: 34, 46, and 49 should be written in the circles. If the child can’t write the

numbers inside the circles, then the numbers can be written on the edge and a line drawn

to the circle. If the child has trouble, use the hundreds chart shown below and have the

child look for patterns in the numbers found.

6. Answer: 7 If the child has trouble, have them count from 5 to 10 and notice what

number is said after six, but before eight.

7. Answer: Milkshake is circled and fries have a square around them. If the child

has trouble comparing these 2-digit numbers that show weights, then have her or him

circle the four numbers on a hundreds chart. The numbers get bigger as you move from

left to right and from top to bottom.


Grade 1, Worksheet VII

1. Answer: 7 Encourage the child to use counters or use the given picture to show the

action of the problem. If counters are used, 4 counters are shown first, then 2 more for

the penguins, and then 1 more for the parrot. Sophisticated counters might “count on”

from 4 to find the answer. Other children might think of strategies like I know 4+2 is six,

and this is 4+ 2 + 1, so it’s going to be 1 more than 6. The answer is 7.

2. Answer: 4 If the child uses counters, he or she will start with 3 for the first three

kids, then remove 1, then put 2 more counters down, counting all to find 4. A drawing

might also be used, with the child making more marks for kids being added, and marking

out a symbol for the kid who goes home.

3, 4, 5. Answers: 10, 10, yes because 6+4 = 10 and 4+6 = 10 in problems 3 and 4

The child will likely solve problems 3 and 4 with counters or with a drawing. The

purpose of these three problems together is to show the commutative property of

addition—the order of the numbers being added doesn’t matter. (Don’t use

“commutative property” language with your child, but do encourage the child to think

about whether or not it matters which number is added to the other number—it doesn’t

matter.) The commutative property is useful in that it’s easier to add a smaller number to

a larger number, than the reverse.

6. Answer: 31, 33; 42, 44; 60, 62 If you have straws or toothpicks bundled into tens

and ones, you can show each of the three starting numbers, then remove 1 and add 1 to

get the numbers right before and right after the starting number. You might also circle

the starting numbers on a hundreds chart, and have the child locate the numbers before

and after the circled numbers.

7. Answer: 6 Again, the child can use counters or a drawing, or even the drawing that

goes with the problem. Notice that 3 frogs are already turned in a different direction than

the other 6.

8. Answer: 6 shapes The purpose of the problem is for the child to compose a

geometric figure from common shapes whose names they need to learn—circle, triangle,

and rectangle. The figure would look like this one:

If the child is interested, you might have them make other such figures from these shapes,

or add facial features, hands, etc., using common shapes.


Grade 1, Worksheet VIII

1. Answer: 7 Encourage the child to use counters, starting with 2 counters for the

original kids playing soccer. Then enough counters can be added to get a total of 9. This

may be difficult for your child because of having to keep up with the total number added,

and at the same time with the total number of kids. The child might use two colors of

counters, with the 2 original kids being one color, and the added kids another color.

2. Answer: 3 The child will probably use the drawing or make a group of 7 elephants,

and a group of 4 jugglers, and match them up, and then count the unmatched elephants.

A list of 7 “Es” and 4 “Js” is also an interesting way to proceed with the matching

process.

3. Answer: 5 Using counters, the child will likely start with 5, then add 4 more, then

remove 4. He or she could also count the ants on the page and add more of those, then

take away some.

4. Answer: The understanding you are looking for comes from the problem

above—adding and then subtracting the same number leaves you with what you

started with. The concept the child will eventually learn is that addition and subtraction

are “inverse operations.” I.E., subtraction undoes addition, and vice-versa.

5. Answer: 0 The concept to be understood here is what happens when you start with

a given number and remove that same amount. You get zero, the additive identity. Your

child may not have encountered the number 0 yet, but he or she will in first grade. You

might show where zero resides on a number line.

6. Answer: 3, 3; 4, 4; 5, 5 The point of the problem is for the child to meet the words

“sides” and “vertices”, which will be encountered in first grade. (Note: “vertices” is

plural for vertex.”) “Sides” refers to the straight line segments that make up a figure, and

“vertices” refers to the corners. Be sure the child knows what he or she is counting, and

suggest that each item be checked off when counted, to prevent recounting.

7. Answer: 8 The child might draw a picture for this problem, or might use counters to

show the 4 kids and 2 slices for each kid. Any simple list or drawing for this problem is a

good place to begin. This problem might lead into counting by 2s by the child, if he or

she is interested, saying “2, 4, 6, 8—there are 8 pieces of pizza.”


Grade 1, Worksheet IX

1. Answer: Measuring cup, 2; milk carton, 3; tablespoon, 1 Help your child find

these items. Ask if he or she were really thirsty and wanted some cold water, which of

the containers would he or she choose to drink from. Which container would be best at

satisfying their thirst?

2. Answer: Inside Have your child point to where the dog would be as you read the

word choices. Some children might say the dog is only partially inside the dog house

because its head is outside—give them an extra smiley face for that response!

3. Answer: Two starfish The core of this repeating pattern unit is 2 seashells and 1

starfish. The next picture would be 2 starfish. You might ask your child—What would

come after the 2 starfish? Hopefully he or she would say “a seashell.” If the child is

having difficulty understanding the repeating nature of the pattern, have her or him say

the words out loud for each object in turn, starting on the left.

4. Answer: 10 The child might use counters to show 6 eggs, then 4 counters for the

second basket of eggs, push the counters together, and count them all. Or the child might

draw a picture of the eggs, hopefully one with simple symbols for the eggs—Xs, boxes,

or ovals. (It gets in the way of mathematical problem solving, in the long run, if a child

draws detailed pictures of objects like painted eggs.) Your child might just “count on”

from 6 to 10 or use some other way of counting, without manipulatives or a drawing.

5. Answer: 6 faces, 12 edges, 8 vertices A die is a good model of a cube, and some

tissue boxes or other types of boxes might suffice as a model. The important thing is that

each face of a cube is a square, so all of the edges of the cube are the same length. To

help the child count, put a piece of tape on each face in turn, then on each edge in turn,

then on each vertex in turn.

6. Answer: Joan baked 3 more The child might use counters or use the picture of the

8 cupcakes, together with the picture of the 5 cupcakes. To find out how many more,

have the child match up the counters or cupcakes in the drawing, pairing them one-to-

one. There will be 3 left unmatched in the larger group—that’s how many more.

7. Answer: 6 Again, the child can use counters or a drawing and “act out” this

problem. Starting with 9, two would be taken away or marked out, then 1 taken away or

marked out, then what is left is counted. Some children might solve it by counting back

from 9 to 7, then counting back another time to 6. Or the child might use a different,

creative way of counting. Some children might just say “I know 9 minus 3 is 6.”

8. Answer: 46 If you have items that can be bundled into tens and ones, have the child

show each number that way. Then he or she can see that each number has the same

number of tens, so the largest bundle is the number with the largest number of ones.


Grade 1, Worksheet X

1. Answer: 5 tens and 3 ones; 5 tens and 4 ones; 6 tens and 2 ones If you have

counters that can be grouped into tens and ones, have the child make each set. If you

don’t have such counters, he or she can count the groups of tens and record, then the

individual ones and record that number. Notice on the middle and right-hand pictures,

the tens aren’t all on the left and ones on the right—this is so the child will have to

discriminate visually.

2. Answer: About 3 paperclips Use the paperclip in the picture and have your child

try to estimate about how many it would take to be the length of the pencil. Then take a

sheet of paper and mark the paperclip’s length as a line segment, and move the line

segment. The child may not realize that you have to align one end of the pencil, with the

end of the line segment.

3. Answer 7 goals The child might use counters or draw a picture to show starting

with 4 goals, then adding 2 more goals, then 1 more goal, counting all to find the total.

Be open to other ways the child may find the answer.

4. Answer 67, 31, 24 Discuss how numbers may come before, between, and after

another number. Give the child some simple examples before looking at the ones in this

problem. You may need to use a homemade hundreds-chart like the one at the top of the

next page.

5. Answer: 11 The child can use counters to show starting with 7, then adding another

group of 4, then counting to find the total. Or he or she may draw a simple diagram or

count in an unusual way.

6. Answer: 56 If you have counters that can be bundled into tens and ones, have the

child show each number in turn, then put the two piles of counters together and count the

total. Or the child might simply count the pictured piles as one pile.

7. Answer: 3 fire trucks were left Counters may again be used, starting with 8 and

removing 5 to follow the action of the problem. The child might simply use the diagram

provided, marking out the trucks that leave and counting the unmarked trucks. Or the

child might count back without using a model, saying “....8, 7, 6, 5, 4, 3. The answer is

3.”

8. Answer: 8 This problem is more difficult than previous subtraction problems

because the starting number and the end result are given—the child needs to find out how

many more are needed to get to that end result. The child will probably start with 2

counters (or the 2 sand castles shown in the picture) and add on enough till they have 10

altogether. This problem will later be solved by subtraction as a missing addend problem

(2 + ___ = 10), but don’t try to get the child to subtract at this point. It suffices for the

child to understand the meaning of the problem, and count to find the answer.

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