EasyK.com Free Reports

Helping your Child Learn Math

with activities for children

aged 5 through 13

By Patsy F. Kanter

Foreword

"Why?"

This is the question we parents are always trying to

answer. It's good that children ask questions: that's the best

way to learn. All children have two wonderful resources for

learning--imagination and curiosity. As a parent, you can

awaken your children to the joy of learning by encouraging

their imagination and curiosity.

Helping Your Child Learn Math is one in a series of books

on different education topics intended to help you make the

most of your child's natural curiosity. Teaching and learning

are not mysteries that can only happen in school. They also

happen when parents and children do simple things together.

For instance, you and your child can: sort socks on

laundry day--sorting is a major function in math and science;

cook a meal together--cooking involves not only math and

science but good health as well; tell and read each other

stories--storytelling is the basis for reading and writing (and

a story about the past is also history); or play a game of

hopscotch together--playing physical games will help your child

learn to count and start on a road to lifelong fitness.

By doing things together, you will show that learning is

fun and important. You will be encouraging your child to study,

learn, and stay in school.

All of the books in this series tie in with the National

Education Goals set by the President and the Governors. The

goals state that, by the year 2000: every child will start

school ready to learn; at least 90 percent of all students will

graduate from high school; each American student will leave the

4th, 8th, and 12th grades demonstrating competence in core

subjects; U.S. students will be first in the world in math and

science achievement; every American adult will be literate,

will have the skills necessary to compete in a global economy,

and will be able to exercise the rights and responsibilities of

citizenship; and American schools will be liberated from drugs

and violence so they can focus on learning.

This book is a way for you to help meet these goals. It

will give you a short rundown on facts, but the biggest part of

the book is made up of simple, fun activities for you and your

child to do together. Your child may even beg you to do them.

At the end of the book is a list of resources, so you can

continue the fun.

As U.S. Education Secretary Lamar Alexander has said:

The first teachers are the parents, both by example and

conversation. But don't think of it as teaching. Think of it as

fun.

So, let's get started. I invite you to find an activity in

this book and try it.

Diane Ravitch

Assistant Secretary and Counselor to the Secretary

Contents

Foreword

Introduction

The Basics

Important Things To Know

Math in the Home

Picture Puzzle

More or Less

Problem Solvers

Card Smarts

Fill It Up

Haft Full, Haft Empty

Name that Coin

Money Match

Money's Worth

In the News

Look It Up

Newspaper Search

Treasure Hunt

Family Portrait

Mathland: The Grocery Store

Get Ready

Scan It

Weighing In

Get into Shapes

Check Out

It's in the Bag

Put It Away

Math on the Go

Number Search

License Plates

Total It

How Long? How Far?

Guess If You Can

Appendices

Parents and the Schools

What Should I Expect from a Math Program?

Resources

Acknowledgments

Introduction

Most parents will agree that it is a wonderful experience

to cuddle up with their child and a good book. Few people will

say that about flash cards or pages of math problems. For that

reason, we have prepared this booklet to offer some math

activities that are meaningful as well as fun. You might want

to try doing some of them to help your child explore

relationships, solve problems, and see math in a positive

light. These activities use materials that are easy to find.

They have been planned so you and your child might see that

math is not just work we do at school but, rather, a part of

life.

It is important for-home and school to join hands. By

fostering a positive attitude about math at home, we can help

our children learn math at school.

It's Everywhere! It's Everywhere!

Math is everywhere and yet, we may not recognize it

because it doesn't look like the math we did in school. Math in

the world around us sometimes seems invisible. But math is

present in our world all the time--in the workplace, in our

homes, and in life in general.

You may be asking yourself, "How is math everywhere in my

life? I'm not an engineer or an accountant or a computer

expert!" Math is in your life from the time you wake until the

time you go to sleep. You are using math each time you set your

alarm, buy groceries, mix a baby's formula, keep score or time

at an athletic event, wallpaper a room, decide what type of

tennis shoe to buy, or wrap a present. Have you ever asked

yourself, "Did I get the correct change?" or "Do I have enough

gasoline to drive 20 miles?" or "Do I have enough juice to fill

all my children's thermoses for lunch?" or "Do I have enough

bread for the week?" Math is all this and much, much more.

How Do You Feel About Math?

How do you feel about math? Your feelings will have an

impact on how your children think about math and themselves as

mathematicians. Take a few minutes to answer these questions:

* Did you like math in school?

* Do you think anyone can learn math?

* Do you think of math as useful in everyday life?

* Do you believe that most jobs today require math skills?

If you answer "yes" to most of these questions, then you

are probably encouraging your child to think mathematically.

This book contains some ideas that will help reinforce these

positive attitudes about math.

You Can Do It!

If you feel uncomfortable about math, here are some ideas

to think about.

Math is a very important skill, one which we will all need

for the future in our technological world. It is important for

you to encourage your children to think of themselves as

mathematicians who can reason and solve problems.

Math is a subject for all people. Math is not a subject

that men can do better than women. Males and females have

equally strong potential in math.

People in the fine arts also need math. They need math not

only to survive in the world, but each of their areas of

specialty requires an in-depth understanding of some math, from

something as obvious as the size of a canvas, to the beats in

music, to the number of seats in an audience, to

computer-generated artwork.

Calculators and computers require us to be equally strong

in math. Theft presence does not mean there is less need for

knowing math. Calculators demand that people have strong mental

math skills--that they can do math in their heads. A calculator

is only as accurate as the person putting in the numbers. It

can compute; it cannot think! Therefore, we must be the

thinkers. We must know what answers are reasonable and what

answers are outrageously large or small.

Positive attitudes about math are important for our

country. The United States is the only advanced industrial

nation where people are quick to admit that "I am not good in

math." We need to change this attitude, because mathematicians

are a key to our future.

The workplace is rapidly changing. No longer do people

need only the computational skills they once needed in the

1940s. Now workers need to be able to estimate, to communicate

mathematically, and to reason within a mathematical context.

Because our world is so technologically oriented, employees

need to have quick reasoning and problem-solving skills and the

capability to solve problems together. The work force will need

to be confident in math.

Build Your Self-Confidence!

To be mathematically confident means to realize the

importance of mathematics and feel capable of learning to

* Use mathematics with ease;

* Solve problems and work with others to do so;

* Demonstrate strong reasoning ability;,

* See more than one way to approach a problem;

* Apply mathematical ideas to other situations; and

* Use technology.

The Basics

You may have noticed that we are talking about

"mathematics"--the subject that incorporates numbers, shapes,

patterns, estimation, and measurement, and the concepts that

relate to them. You probably remember studying

"arithmetic"--adding, subtracting, multiplying, and

dividing--when you were in elementary school. Now, children are

starting right away to learn about the broad ideas associated

with math, including problem solving, communicating

mathematically, and reasoning.

Kindergartners are building bar graphs of birthday cakes

to show which month has the most birthdays for the most

children in the class. Second graders are using pizzas to learn

fractions, and measurements are being taken using items other

than rulers (for example, the illustrator of this book used his

thumb to determine how large the pictures of the pizzas should

be in proportion to the size of the words on the activities

pages).

What Does It Mean To

* Be a Problem Solver,

* Communicate Mathematically, and

* Demonstrate Reasoning Ability?

A problem solver is someone who questions, investigates,

and explores solutions to problems; demonstrates the ability to

stick with a problem for days, if necessary, to find a workable

solution; uses different strategies to arrive at an answer;

considers many different answers as possibilities; and applies

math to everyday situations and uses it successfully.

To communicate mathematically means to use words or

mathematical symbols to explain real life; to talk about how

you arrived at an answer; to listen to others' ways of thinking

and perhaps alter their thinking; to use pictures to explain

something; to write about math, not just give an answer.

To demonstrate reasoning ability is to justify and explain

one's thinking about math; to think logically and be able to

explain similarities and differences about things and make

choices based on those differences; and to think about

relationships between things and talk about them.

How Do I Use this Book?

This book is divided into introductory material that

explains the basic principles behind the current approach to

math, sections on activities you can do with your children, and

lists of resources. The activities take place in three

locations: the home, the grocery store, and in transit.

The activities are arranged at increasingly harder levels of

difficulty. Look for the circles, squares, and triangles that

indicate the level of difficulty. The means that a child in

kindergarten through 1st grade could probably play the game,

the is for those in grades 2 and 3, and the signals an

activity for a child in grades 4 through 8.

The activities you choose and the level of difficulty

really depend on your child's ability if your child seems

ready, you might want to go straight to the most difficult

ones.

The shaded box on an activity page contains the answer

or a simple explanation of the mathematical concept behind the

activity so that you can explain when your child asks, "Why are

we doing this?"

With these few signs to follow along the way, your math

journey begins.

Important Things To Know

It is highly likely that when you studied math, you were

expected to complete lots of problems accurately and quickly.

There was only one way to arrive at your answers, and it was

believed that the best way to improve math ability was to do

more problems and to do them fast. Today, the focus is less on

the quantity of memorized problems, and more on understanding

the concepts and applying thinking skills to arrive at an

answer.

Wrong Answers Can Help!

While accuracy is always important, a wrong answer may

help you and your child discover what your child may not

understand. You might find some of these thoughts helpful when

thinking about wrong answers.

Above all be patient. All children want to succeed. They

don't want red marks or incorrect answers. They want to be

proud and to make you and the teacher proud. So, the wrong

answer tells you to look further, to ask questions, and to see

what the wrong answer is saying about the child's

understanding.

Sometimes, the wrong answer to a problem might be because

the child thinks the problem is asking another question. For

example, when children see the problem 4 + ___ = 9, they often

respond with an answer of 13. That is because they think the

problem is asking What is 4+9?", instead of "4 plus what

missing amount equals 9?"

Ask your child to explain how the problem was solved. The

response might help you discover if your child needs help with

the procedures, the number facts, or the concepts involved.

You may have learned something the teacher might find

helpful. A short note or call will alert the teacher to

possible ways of helping your child.

Help your children be risk takers: help them see the value

of examining a wrong answer; assure them that the right answers

will come with proper understanding.

Problems Can Be Solved Different Ways

Through the years, we have learned that while problems in

math may have only one solution, there may be many ways to get

the right answer. When working on math problems with your

child, ask, "Could you tell me how you got that answer?" Your

child's way might be different than yours. If the answer is

correct and the strategy or way of solving it has worked, it is

a great alternative. By encouraging children to talk about what

they are thinking, we help them to become stronger

mathematicians and independent thinkers.

Doing Math in Your Head Is Important

Have you ever noticed that today very few people take

their pencil and paper out to solve problems in the grocery,

fast food, or department store or in the office? Instead, most

people estimate in their heads.

Calculators and computers demand that people put in the

correct information and that they know if the answers are

reasonable. Usually people look at the answer to determine if

it makes sense, applying the math in their heads to the

problem. This, then, is the reason why doing math in their

heads is so important to our children as they enter the 21st

century.

You can help your child become a stronger mathematician by

trying some of these ideas to foster mental math skills:

1. Help children do mental math with lots of small numbers in

their heads until they develop quick and accurate

responses. Questions such as, "If I have 4 cups, and I

need 7, how many more do I need?" or "If I need 12 drinks

for the class, how many packages of 3 drinks will I need

to buy?"

2. Encourage your child to estimate the answer. When

estimating, try to use numbers to make it easy to solve

problems quickly in your head to determine a reasonable

answer. For example, when figuring 18 plus 29, an easy way

to get a "close" answer is to think about 20 + 30, or 50.

3. As explained earlier, allow your. children to use

strategies that make sense to them.

4. Ask often, "Is your answer reasonable?" Is it reasonable

that I added 17 and 35 and got 367? Why? Why not?

What Jobs Require Math?

All jobs need math in one way or another. From the

simplest thought of how long it will take to get to work to

determining how much weight a bridge can hold, all jobs require

math.

If you took a survey, you would find that everyone uses

math: the school teacher, the fast food worker, the doctor, the

gas station attendant, the lawyer, the housewife, the painter.

Math in the Home

This section provides the opportunity to use games and

activities at home to explore math with your child. The

activities are intended to be fun and inviting, using household

items. Please note that the activities for K-1st grade are

marked with a , the activities for grades 2 and 3 with a

, and activities for grades 4 through 8 with a .

Remember,

* This is an opportunity for you and your child to "talk

math," that is to communicate about math while

investigating relationships.

* If something is too difficult, choose an easier activity

or skip it until your child is older.

* Have fun!

Picture Puzzle

Using symbols to stand for numbers can help make math fun

and easier for young children to understand.

What you'll need

Paper

Pencil

Crayons

What to do

1. Choose some symbols that your child can easily draw to

stand for 1s and 10s (if your child is older, include 100s

and 1,000s).

A face could 10s, and a bow could be 1s.

2. List some numbers and have your child depict them.

For example:

More or Less

Playing cards is a fun way for children to use numbers.

What you'll need

Coin

2 decks of cards

Scratch paper to keep score

What to do

1. Flip a coin to tell if the winner of this game will be the

person with "more" (a greater value card) or "less" (a

smaller value card).

2. Remove all face cards (jacks, queens, and kings) and

divide the remaining cards in the stack between the two

players.

3. Place the cards face down. Each player turns over one card

and compares: Is mine more or less? How many more? How

many less?

This game for young children encourages number sense and

helps them learn about the relationships of numbers (more or

less) and about adding and subtracting. By counting the shapes

on the cards and looking at the printed numbers on the card,

they can learn to relate the number of objects to the numeral.

Problem Solvers

These games involve problem solving, computation,

understanding number values, and chance.

What you'll need

Deck of cards

Paper

Pencil

What to do

1. Super sums. Each player should write the numbers 1-12 on a

piece of paper. The object of the game is to be the first

one to cross off all the numbers on this list.

Use only the cards 1-6 in every suit (hearts, clubs,

spades, diamonds). Each player picks two cards and adds up

the numbers on them. The players can choose to mark off

the numbers on the list by using the total value or

crossing off two or three numbers that make that value.

For example, if the player picks a 5 and a 6, the player

can choose to cross out 11, or 5 and 6, or 7 and 4, or 8

and 3, or 9 and 2, or 10 and 1, or 1, 2, and 8.

2. Make 100. Take out all the cards from the deck except ace

through 6. Each player draws 8 cards from the deck. Each

player decides whether to use a card in the tens place or

the ones place so that the numbers total as close to 100

as possible without going over. For example, if a player

draws two 1s (aces), a 2, a 5, two 3s, a 4, and a 6, he

can choose to use the numerals in the following way:

30, 40, 10, 5, 6, 1, 3, 2. This adds up to 97.

These games help children develop different ways to see

and work with numbers by using them in different combinations

to achieve a goal.

Card Support

Have your children sharpen their math skills even more.

What you'll need

Deck of cards

Paper

Pencil

What to do

1. How many numbers can we make? Give each player a piece of

paper and a pencil. Using the cards from 1 (ace)-9, deal 4

cards out with the numbers showing. Using all four cards

and a choice of any combination of addition, subtraction,

multiplication, and division, have each player see how

many different answers a person can get in 5 minutes.

Players get one point for each answer. For example,

suppose the cards drawn are 4, 8, 9, and 2. What numbers

can be made?

4+9+8+2=23

4+9-(8+2)=3

(8-4)x(9-2)=28

(9-8)x(4-2)=2

2. Make the most of it. This game is played with cards from 1

(ace) to 9. Each player alternates drawing one card at a

time, trying to create the largest 5-digit number

possible. As the cards are drawn, each player puts the

cards down in their "place" (ten thousands, thousands,

hundreds, tens, ones) with the numbers showing. One round

goes until each player has 6 cards. At that point, each

player chooses one card to throw out to make the largest

5-digit number possible.

3. Fraction fun. This game is played with cards 1 (ace)-10,

and 2 players. Each player receives one-half of the cards.

Players turn over 2 cards each at the same time. Each

player tries to make the largest fraction by putting the 2

cards together. The players compare their fractions to see

whose is larger. For example, if you are given a 3 and a

5, the fraction 3/5 would be made; if the other person is

given a 2 and an 8, the fraction is 2/8. Which is larger?

The larger fraction takes all cards and play continues

until one player has all the cards.

Players can develop strategies for using their cards, and

this is where the math skills come in.

Fill It Up

Children enjoy exploring measurement and estimation. Empty

containers can provide opportunities to explore comparisons,

measurement, estimation, and geometry.

What you'll need

Empty containers in different shapes (yogurt cups, margarine

tubs, juice boxes with tops cut off, pie tins)

Rice, popcorn kernels, or

water

Marker

Masking tape

Paper

What to do

1. Have your child choose an empty container each day and

label it for the day by writing the day on a piece of

masking tape and sticking it on the container.

2. Discover which containers hold more than, less than, or

the same as the container chosen for that day by

filling the day's container with water, uncooked rice, or

popcorn kernels; and

pouring the substance from that container into another

one. Is the container full, not full, or overflowing? Ask

your child, "Does this mean the second container holds

more than the first, less, or the same?"

3. Ask your child questions to encourage comparison,

estimation, and thinking about measurement.

4. Put all the containers that hold more in one spot, those

that hold less in another, and those that hold the same in

yet another. Label the areas "more," "less," and "the

same?

5. After the containers have been sorted, ask, "Do we have

more containers that hold more, hold less, or hold the

same? How many containers are in each category?"

The process of predicting, filling the containers, and

comparing how much each will hold, gives your child the

opportunity to experiment with measurement without worrying

about exact answers.

Half Full, Half Empty

It is helpful to explore whole numbers and fractions

through measurement and estimation. Children can see

relationships and the usefulness of studying fractions.

What you'll need

Clear container with straight sides, that holds at least 4 cups

Masking tape

Marker

Measuring cup with 1, 1/2, 1/4, 1/8 cup measures on it

Uncooked rice, popcorn kernels, or water

Other containers with which to compare

What to do

1. Have your child run a piece of masking tape up the side of

the container so that it is straight from the bottom to

the top.

2. For younger children, use a 1-cup measure. For older

children, use a 1/2, 1/4, and 1/8 cup measure. Pour the

chosen amount of a substance listed above into the

container.

3. Mark the level of the jar on the masking tape by drawing a

line with a marker and writing 1 for one cup or 1/2, 1/4,

or 1/8 on the line.

4. Follow this procedure until the container is full, and the

tape is marked in increments to the top of the container.

Now, the jar is marked evenly to measure the capacity of

other containers.

5. While filling different containers, ask your child

"thinking" questions.

How many whole cups do you think this container will hold?

How many 1/2, 1/4, or 1/8 cups do you think the container

will hold?

How many 1/2 cups equal a cup?

How many 1/4 cups equal a 1/2 cup? A cup?

How many 1/8 cups equal a 1/4 cup? A 1/2 cup? A 1/8 cup?

This activity provides a "hands-on" opportunity for

children to experience fractions while making connections to

the real world.

Name that Coin

Children love to look at coins but sometimes cannot

identify the coins or determine their value.

What you'll need

Penny

Nickel

Dime

Quarter

What to do

1. Look at the coins and talk about what color they are, the

pictures on them, and what they are worth.

2. Put a penny, nickel, and dime on the floor or table.

3. Tell your child that you are thinking of a coin.

4. Give your child hints to figure out which coin you are

thinking of. For example, "My coin has a man on one side,

a building on the other."

5. Let your child think about what you have said by looking

at the coins.

6. Ask, "Can you make a guess?"

7. Add another clue: "My coin is silver."

8. Keep giving clues until your child guesses the coin.

9. Add the quarter to the coins on the table and continue the

game.

10. Have your child give you clues for you to guess the coin.

This guessing game helps young children learn to recognize

coins and develop problem-solving and higher level thinking

skills.

Money Match

This game helps children count change. Lots of repetition

will make it even more effective.

What you'll need

A die to roll

10 of each coin (penny, nickel, dime)

6 quarters

What to do

1. For young players (5- and 6-year-olds), use only 2

different coins (pennies and nickels or nickels and

dimes). Older children can use all coins.

2. Explain that the object of the game is to be the first

player to earn a set amount (10 or 20 cents is a good

amount).

3. The first player rolls the die and gets the number of

pennies shown on the die.

4. Players take turns rolling the die to collect additional

coins.

5. As each player accumulates 5 pennies or more, the 5

pennies are traded for a nickel.

6. The first player to reach the set amount wins.

7. Add the quarter to the game when the children are ready.

Counting money, which involves counting by 1s, 5s, 10s,

and 25s, is a challenging skill and usually does not come

easily to children until about the third grade.

Money's Worth

When children use coins to play games, it may help them

use coins in real life situations.

What you'll need

Coins

Coupons

What to do

1. Coin clues. Ask your child to gather some change in his or

her hand without showing what it is. Start with amounts of

25 cents or less. Ask your child to tell you how much

money and how many coins there are. Guess which coins are

being held. For example, "I have 17 cents and 5 coins.

What coins do I have?" (3 nickels and 2 pennies.)

2. Clip and save. Cut out coupons and tell how much money is

saved with coins. For example, if you save 20 cents on

detergent, say 2 dimes. Ask your child what could be

purchased using the savings from the coupon. A pack of

gum? A pencil? How much money could be saved with 3, 4, or

5 coupons? How could that money be counted out in coins

and bills? What could be purchased with that savings? A

pack of school paper? A magazine? How much money could be

saved with coupons for a week's worth of groceries? How

would that money be counted out? What could be purchased

with that savings? A book? A movie ticket?

Counting money involves thinking in patterns or groups of

amounts: 1s, 5s, 10s, 25s. Start these activities by having

your child first separate the coins or coupons by types: all

the pennies together, all the nickels, all the dimes, all the

quarters; the coupons for cereal, the coupons for cake and

brownie mixes, the coupons for soap.

In the News

Young children love to look at the newspaper. It is fun

for them to realize that there are things for them to see and

do with the paper.

What you'll need

Newspaper

Glue

Paper

Scissors

Pencil or crayon

What to do

1. Newspaper numbers. Help your child look for the numbers

1-100 in the paper. Cut the numbers out and glue them in

order onto a large piece of paper. For children who cannot

count to 100 or recognize numerals that large, only

collect up to the number they do know. Have your child say

the numbers to you and practice counting. Collect only

numbers within a certain range, like the numbers between

20 and 30. Arrange the numbers on a chart, grouping all

the numbers with 2s in them, all the numbers with 5s, and

so on.

2. Counting book. Cut out pictures from the newspaper and use

them to make a counting book. Page one will have one thing

on it, page 2 will have 2 things that are alike, page 3

will have 3 things that are alike, and so on. All the

things on the pages have to be the same. At the bottom of

each page, write the number of items on the page and the

word for the item. Have your child dictate a story to you

about what is on the page.

Being able to read and understand the newspaper involves

more than just the ability to read the words and understand

what they say. It also involves the ability to read and

understand numbers.

Look It Up

These activities help children understand how items can be

organized and grouped in logical ways.

What you'll need

Newspaper

Paper

Scissors

Glue

What to do

1. Section selection. Show your child that the paper is

divided into different sections and explain that each

section serves a purpose. Show him that each section is

lettered and how the pages are numbered.

2. Ad adventure. Provide your child with grocery store ads

from the newspaper. Help him see how many items are listed

and the prices. Compare the prices at different stores.

Ask which store has the best bargain and why. Talk about

the difference in prices between items bought at regular

price, items on sale, and items bought with coupons. What

happens when an item is bought on sale and bought with a

coupon?

3. Solid search. Look at the store ads or coupons for

pictures of all the cylinders, boxes, or cubes you can

find. What are their different uses? Paste the pictures on

paper and make a "book of geometric solids." Have one page

for each solid.

Understanding that there is a logical order to the way

things are arranged in the newspaper, and in the book of

solids, helps show that math skills can be used in organizing

written material. Comparing information, such as the sale

prices at stores, also helps children see logical relationships

that can be applied to writing.

Newspaper Search

Search through the newspaper for mathematical data.

What you'll need

Newspaper

What to do

1. Numbers in the news. Find the following things in the

paper:

a graph

a number less than 10

something that comes in 2s, 3s, 4s

a number more than 50 the days of the week

a number more than 100

a number that is more than 100 but less than 999

a symbol or word for inches, feet, or yards

a schedule of some kind

a triangle

a weather symbol

a percent sign

sports statistics

2. List it. Provide your child with the grocery section of

the newspaper in order to make up a list of food that will

feed the family for a week and meet a budget of a certain

amount of money. Have your child make a chart and use a

calculator to figure the cost of more than one item. If

the total for the groceries is too great, talk about which

items can be eliminated. Could the list be cut down by a

few items or by buying less of another item? What will

best serve the needs of the family?.

3. For a fraction of the cost. Give your child a few coupons

and grocery ads from the paper. Help your child match the

coupons to some of the grocery items in the ad. What

fraction of the cost is the coupon? For example, if an

item costs 79 cents and the coupon is for 10 cents off,

what fraction of the cost can be saved? (About 1/8.) What

percent are you saving on the item? (About 12 1/2

percent.)

One of the main ways people use numbers is for planning.

Knowing how to plan how much things will cost before going to

the store and how to read schedules and weather information

from the paper will help your child understand the world.

Treasure Hunt

Everyone's house has hidden treasures. There is a lot of

math you and your child can do with them.

What you'll need

Buttons

Screws

Washers

Bottle caps

Old keys

Sea shells

Rocks

or anything else you can count

What to do

1. Find a container to hold the treasures.

2. Sort and classify the treasures. For example, do you have

all the same sized screws or keys? How are they alike? How

are they different?

3. Use these treasures to tell addition, subtraction,

multiplication, and division stories. For example, if we

share 17 buttons among three friends, how many will we

each get? Will there be some left over? Or, if we have 3

shirts that need 6 buttons each, do we have enough

buttons?

4. Organize the treasures by one characteristic and lay them

end-to-end. Compare and contrast the different amounts of

that type of treasure. For example, there are 3 short

screws, 7 long screws, and 11 medium screws. There are 4

more medium screws than long ones. This may also provide

an opportunity to talk about fractions: 7/21 or 1/3 of the

screws are long.

Finding a container to hold the treasures gives your child

practice in spatial problem solving. The treasures may help you

to explain the concepts of addition, subtraction,

multiplication, and division because they can be moved around

and grouped together so your child can count the items.

Family Portrait

Have your child get to know members of your family by

collecting information and picturing it on a graph.

What you'll need

Paper

Pencil

Crayons

What to do

1. Choose an inherited family characteristic: hair colors,

for example.

2. Count how many people in the family have the different

hair colors.

3. Make a graph. For example, if 5 people have brown hair,

draw 5 heads side by side to show these five people. Do

the same for the other hair colors.

Graphs help everyone, including adults, understand

information at a glance. By looking at the lengths of the lines

of heads, your child can quickly see which hair color, for

example, is most common.

Mathland:

The Grocery Store

The grocery store is one of the best examples of a place

where math is real. Since trips to the grocery usually affect

everyone in the family, the following activities include

various levels of difficulty within the activity. Look for the

symbols to determine which parts of the activities are for

which ages:

for grades K-1

for grades 2 and 3

for grades 4 through 8.

All of these activities can take place over many visits to

the store.

Get Ready

Getting ready to go shopping can help parents and children

share their thinking strategies about math with one another.

What you'll need

Paper

Pencil

Coupons (if you use them)

What to do

1. Involve the family in making a list. List each item and

mark with checks or tallies to indicate the number needed.

2. Look at the price of an item you bought last week and

intend to buy this week. How much did it cost last week?

How much does it cost this week? Do you want to

Pay this week's price?

Wait until the price comes down?

Or, stock up if it is on sale?

3. Involve the group in deciding how much milk or juice will

be needed for a week. You might decide to estimate by

cups, explaining that 4 cups are equal to a quart and 4

quarts are a gallon.

4. If you collect coupons, organize them. Choose the coupons

that match the items on the grocery list. Discuss how much

money will be saved on various items by using coupons.

Practicing measurement and estimation will help improve

your children's ability to predict amounts with accuracy.

Scan It

Shopping is a part of life which really necessitates our

being mathematically informed to be good consumers.

What you'll need

Prices

What to do

1. Notice whether the grocery store has prices on the items

or whether the pricing is dependent on scanners.

2. If there are no prices on the items, notice the prices

listed on the shelves.

3. Assign each child the job of remembering the price of a

few items, particularly those listed on sale.

4. Being aware of the prices of items will help you verify

that the scanners are working properly and that the total

is accurate when you go to check out.

The ever increasing use of technology in the grocery store

puts the burden on you to beware. Your protection lies in

having strong mental math skills.

Weighing In

One fun place to try out estimation and measurement skills

in the grocery store is the produce section where everyone can

have the opportunity to participate.

What you'll need

The grocery scale

What to do

1. Help your child examine the scale. Explain that pounds are

divided into smaller parts called ounces and 16 ounces

equal a pound.

2. Gather the produce you are purchasing, and estimate the

weight of each item before weighing it.

3. Use sample questions to foster thinking about measurement

and estimation. You might Want to ask your child,

How much do you think 6 apples will weigh? More than a

pound, less than a pound, equal to a pound? How much do

the apples really weigh? Do they weigh more or less than

you predicted? How about the potatoes? Will 6 potatoes

weigh more or less than the apples? How much do potatoes

cost per pound? If they cost ___ cents per pound, what is

the total cost?

Some grocery stores have scales that tell all the answers

to these questions, so in that case, estimate using the

same procedure to make sure the machines are accurate.

Activities like this help children develop number sense

for weight and foster the ability to compare items when

measuring.

Get into Shapes

The grocery store is filled with geometric shapes.

What you'll need

Items at the store

What to do

1. Show your child the pictures of the shapes on this page

before going to the store. This will help to identify them

when you get to the store.

2. At the store, ask your child questions to generate

interest in the shapes.

Which items are solid? Which are fiat?

Which shapes have fiat sides?

Which have circles for faces? Rectangles?

Do any have points at the top?

3. Point out shapes and talk about their qualities and their

use in daily life.

Look to see what shapes stack easily. Why?.

Try to find some cones. How many can you find?

Look for pyramids.

Determine which solids take up a lot of space and which

ones stack well.

Discuss why space is important to the grocer and why the

grocer cares about what stacks well.

Boxes, cans, rolls of toilet paper or paper towels, ice

cream cones and cones that hold flowers, plus produce such as

oranges, grapes, and tomatoes are all geometric shapes.

Recognizing these shapes helps children connect math to the

real world.

Check Out

The check out counter is where we commonly think about

math in the grocery store. It's where the total is added up,

the money is exchanged, and the change is returned.

What you'll need

All the items you intend to buy

What to do

1. Have your child estimate the total.

2. Ask, if I have 10 one-dollar bills, how many will I have

to give the clerk? What if I have 20 one-dollar bills? 5?

How much change should I receive? What coins will I get?

3. Count the change with your child to make sure the change

is correct.

One way to make estimating totals easy is to assign an

average price to each item. If the average price for each item

is $2 and if you have 10 items, the estimate would be about

$20.

It's in the Bag

Here's some fun estimation to do with bags full of

groceries.

What you'll need

Bags of groceries

What to do

1. Have your child guess how many objects there are in a bag.

Ask: Is it full? Could it hold more? Could it tear if you

put more in it? Are there more things in another bag of

the same size? Why do some bags hold more or less than

others?

2. Estimate the weight of the bag of groceries. Does it weigh

5 pounds, 10 pounds, or more? How can you check your

estimate? Now, compare one bag to another. Which is

lighter or heavier? Why?

This activity exposes children to the experiences of

counting items and comparing qualities, as well as to judging

spatial relationships and capacity. It shows how to estimate

weight by feeling how much the bag weighs, comparing it to a

known weight (such as a 5-pound bag of sugar), or weighing it

on a scale.

Put It Away

Now, the sorting begins as you put away the groceries.

What you'll need

Your bags of groceries

Counter top or table to group items on

What to do

1. Find one characteristic that is the same for some of the

products. For example, some are boxes and some are cans.

2. Put all the items together that have the same

characteristic.

3. Find another way to group these items.

4. Continue sorting, finding as many different ways to group

the items as you can.

5. Play "Guess My Rule." In this game, you sort the items and

invite your child to guess your rule for sorting them.

Then, your child can sort the items, and you can guess the

rule.

Sorting helps children develop classifying and reasoning

skills and the ability to examine data and information.

Math on the Go

In this busy world, we spend a lot of time in transit.

These are some projects to try while you are going from place

to place.

While you're moving, have your children keep theft eyes

open for:

* street and building numbers;

* phone numbers on the sides of taxis and trucks;

* dates on buildings and monuments; and

* business names that have numbers in them.

Number Search

The object is to look for numbers around you: on cars,

buses, subways, and on foot.

What you'll need

Some type of transportation or

A place from which to observe

Paper

Pencil

Ruler

What to do

1. Create a chart that lists the numbers from 1-50.

2. Write down each number as family members locate that

number on a car, a sign, a building.

3. Write down words that have numbers in them such as

"one-stop shopping," "two-day service," or "Highway 20."

This is a great challenge for family members of all age,

because even young children can learn to recognize numbers.

License Plates

License plates have numbers and are fun to use to play

games while on the go.

What you'll need

License plates

Paper

Pencil

What to do

1. Copy down a license plate. Read it as a number (excluding

the letters). For example, if the license is 663M218, the

number would be six hundred sixty-three thousand, two

hundred eighteen.

2. Find other license plates and read their numbers. Is the

number less than, greater than, or equal to yours?

3. Estimate the difference between your number and another

license plate. Is it 10, 100, 1,000, or 10,000?

4. Record the names of the states of as many different

license plates as you see. From which state do you see the

most? Which has the fewest? Prepare a chart or graph to

show your findings.

These activities encourage reading, recognizing numbers,

noticing symbols, writing, counting, and graphing.

Total It

This is a good game for practicing quick mental

computation.

What you'll need

License plates

What to do

1. Call out the numbers on the license plate.

2. See who can add the numbers up correctly. What strategies

were used? (Were the numbers added by 10's like 2+8; were

doubles like 6+6 used?)

3. Try different problems using the numbers in a license

plate.

For example, if you use the plate number 663M218, ask,

"Using the numbers on the plate, can you:

make a 1 using two numbers? Yes, 3-2=1.

make a 1 using three numbers? Yes, 6-(3+2)=1

make a 1 using four numbers? Yes, (6+6)-8-3-1

make a 1 using five numbers? Yes, 3-[(6+6)-8-2]=1

make a 1 using six numbers? Yes, 8x2-(6+6)-3=1

make a 2 using 1 number? Yes, the 2.

The problem solving and computation going on in your

child's head is very important. It helps your child be creative

with numbers.

How Long? How Far?

Many times when you are on the go, you are headed

somewhere that requires you be there by a certain time.

What you'll need

Information about how far you're traveling and how long

it will take

What to do

1. Ask your children how far they think you are traveling.

Yards? Blocks? Miles?

2. Talk about how long it takes to get there. If it is 3:15

now, and it takes 45 minutes to get there, will we make it

for a 4:15 appointment? How much extra time will we have?

Will we be late?

These types of questions help children see the usefulness

of understanding distance and time.

Guess If You Can

When children practice asking questions about numbers,

they can develop an understanding of the characteristics and

meanings of numbers.

What you'll need

Questions about numbers

What to do

1. Let your child think of a number between a stated range of

numbers while you try to guess the number by asking

questions. Here is a sample conversation.

Child: I am thinking of a number between 1 and 100.

Parent: Is it more than 50?

Child: No.

Parent: Is it an even number?

Child: No.

Parent: Is it more than 20 but less than 40?

Child: Yes.

Parent: Can you divide this number up into 3 equal parts?

And so on ...

2. After you have guessed your child's number, let your child

guess a number from you by asking similar questions.

The questions asked demonstrate many different levels of

math. They can serve as learning tools for explaining concepts.

For example, you can take the opportunity to explain what an

even number is if your child does not know.

Parents and the Schools

Here are a few ideas that might help you support a

positive math environment in your child's school:

1. Visit the school and see if the children:

* Are actively engaged in math;

* Are talking about mathematics;

* Are working together to solve math problems;

* Have their math work on display;

* Use manipulatives (objects that children can touch and

move) in the classroom.

2. Explore the math program with your child's teacher,

curriculum coordinator, or principal. Here are some

questions you might ask:

* Are there manipulatives in the classroom?

* Are you familiar with the National Council of Teachers of

Mathematics standards (see next page)?

* How are the standards being used in this school?

* What can I do to help foster a strong math program where

children can explore math concepts before giving the right

answer?

3. If you would like to help out, here are some suggestions

for parent groups:

* Make games for teachers;

* Help seek out sponsors who believe in a strong math

program for the school and who might provide materials and

resources;

* Support math classes for families at your school.

4. Keep a positive attitude even if you don't like what you

see. Work to improve the math curriculum by doing some of

the things mentioned throughout this book.

5. Share this book with your child's teacher.

What Should I Expect from a Math Program?

The National Council of Teachers of Mathematics (NCTM) has

recently endorsed standards by which math should be taught in

the elementary and middle grade years. The powerful nature of

these standards is that they not only have the endorsement of

the academic community, but they are also heavily endorsed by

corporations. These endorsements, together with the

technological advances of our society and the lack of math

confidence in our work force, have combined to produce

tremendous support for the standards.

These standards make some assumptions about the way math

should be taught and what parents might see when visiting the

classroom. Here are some examples:

1. Children will be engaged in discovering mathematics, not

just doing many problems in a book.

2. Children will have the opportunity to explore,

investigate, estimate, question, predict, and test their

ideas about math.

3. Children will explore and develop understanding for math

concepts using materials they can touch and feel, either

natural or manufactured.

4. The teacher will guide the students' learning, not dictate

how it must be done.

5. Children will have many opportunities to look at math in

terms of daily life and to see the connections among math

topics such as between geometry and numbers.

6. Children will be actively involved in using technology

(calculators and computers) to solve math problems.

The complete list of standards is available from NCTM,

1906 Association Drive, Reston, Virginia 22091-1593

(1-800-235-7566).

Resources

1. Math for parents:

Burns, Marilyn. Math for Smarty Pants. Little, Brown and

Company.

Burns, Marilyn. The I Hate Mathematics Book. Little, Brown and

Company.

Curriculum and Evaluation Standards for School Mathematics.

National Council of Teachers of Mathematics. Reston, Virginia

Help Your Child Learn Number Skills. Usborne Parents' Guides,

EDC Publishing, 10302 East 55th Place, Tulsa, Oklahoma 74146.

The Learning With Series. Cuisenaire Company, P.O. Box 5026,

White Plains, New York 106025026, 1-800-237-3142.

Parker, Tom, (1984). In One Day. Houghton Mifflin Company.

Reys, Barbara. Elementary School Mathematics: What Parents

Should Know about Estimation. National Council of Teachers of

Mathematics. Reston, Virginia. 10 for $7.50.

Reys, Barbara. Elementary School Mathematics: What Parents

Should Know About Problem Solving. National Council of Teachers

of Mathematics. Reston, Virginia. 10 for $7.50.

Room, Adrian. The Guiness Book of Numbers. Sterling Publishing

Company, Inc., 387 Park Avenue South, New York, New York

10016-8810.

Stenmark, Virginia Thompson and Ruth Cossey. Family Math.

Lawrence Hall of Science, University of California at Berkeley,

Berkeley California 94720.

Thomas, David A., (1988). The Math-Computer Connection.

Franklin Watts.

Thomas, David A., (1988). Math Projects for Young Scientists.

Franklin Watts.

Math Matters. National PTA and Exxon Foundation. Video tape and

pamphlet useful for parent meetings.

The following pamphlets are available from the National Council

of Teachers of Mathematics, 1906 Association Drive, Reston,

Virginia 22091-1593 (1-800-235-7566). All are priced 20 for $5,

100 for $15.

"Family Math Awareness Activities"

"Help Your Child Learn Math"

"Using Calculators to Improve Your Child's Math Skills"

2. Books for children:

Almost every book you read with your child will offer the

opportunity to talk about math, because math is everywhere.

Some books lend themselves more to in-depth and specific math

discussion. Only a fraction of these books could be listed

here.

Anno, Mitsumasa. Anno's Counting Book. Thomas Y. Crowell.

Anno, Mitsumasa. Anno's Counting House. Philomel Books.

Anno, Mitsumasa. Anno's Hat Trick. Philomel Books.

Anno, Mitsumasa. Anno's Math Games. Philomel Books.

Anno, Mitsumasa. Anno's Mysterious Multiplying Jar. Philomel

Books.

Carle, Eric. The Grouchy Ladybug. Philomel Books.

Carle, Eric. 1,2,3 to the Zoo. Philomel Books.

Carle, Eric. The Very Hungry Caterpillar. Philomel Books.

Carter, David. How Many Bugs in a Box? Simon and Schuster.

Cobb, Vicki and Kathy Darling. Bet You Can. Avon.

Cobb, Vicki and Kathy Darling. Bet You Can't. Avon.

Conran, Sebastian. My First 123 Book. Aladdin Books.

Daly, Eileen. 1 Is Red. Western.

Dee, Ruby. Two Ways to Count to Ten. Holt.

Demi. Demi's Count the Animals 123. Grosset and Dunlap.

Feelings, Muriel. Moja Means One: Swahili Counting Book. Dial.

Grayson, Marion. Let's Count. Robert B. Luce, Inc.

Grayson, Marion. Count Out. Robert B. Luce, Inc.

Hoban, Tana. Circles, Triangles, and Squares. MacMillan

Publishing Company, Inc.

Hoban, Tana. Count and See. Macmillan Publishing Company, Inc.

Hoban, Tana. Is It Rough, Is It Smooth, Is It Bumpy? Macmillan

Publishing Company, Inc.

Hudson, Cheryl. Afro-Bets 123 Book. Just Us Productions.

Hutchins, Pat. The Doorbell Rang. Greenwillow Books.

Hutchins, Pat. One Hunter. Greenwillow Books.

Jones, Carol. This Old Man. Houghton Mifflin Company.

Keats, Ezra Jack. Over in the Meadow. Scholastic. Kitchen,

Bert. Animal Numbers. Dial.

Kredenser, Gaff. One Dancing Drum. Phillips.

Lionni, Leo. Numbers To Talk About. Pantheon Books.

Marley, Deborah. Animals One to Ten. Raintree.

McMillan, Bruce. Counting Wildflowers. Lothrop, Lee & Shepard

Books, Inc.

McMillan, Bruce. One, Two, One Pair. Scholastic. Nolan, Dennis.

Monster Bubbles. Prentice Hall.

Pluckrose, Henry. Know about Counting. Franklin Watts.

Pomerantz, Charlotte. The Half-Birthday Party. Clarion Books.

Ross, H.L. Not Counting Monsters. Platt and Munk.

Schwartz, David M. How Much Is a Million? Lothrop, Lee &

Shepard Books, Inc.

Schwartz, David M. If You Made a Million. Lothrop, Lee &

Shepard Books, Inc.

Tafuri, Nancy. Who's Counting? William Morrow & Co.

Testa, Fulvio. If You Take a Pencil. Dial.

Viorst, Judith. Alexander Who Used To Be Rich Last Sunday.

Atheneum.

Vogel, Ilse-Margret. 1 Is No Fun, But 20 Is Plenty.t Atheneum.

Ziefert, Harriet. A Dozen Dizzy Dogs. Random House.

3. Magazines and periodicals:

Dynamath. Scholastic. Available from the school division.

Filled with many different activities that involve all strands

of math. Children in grade 5 particularly like this. Nine

publications are sent each school year. $5.00 for the

subscription.

Games Magazine, P.O. Box 10147, Des Moines, Iowa 50347.

The adult version of Games Junior (see below). Older children

may prefer this to Games Junior.

Games Junior, P.O. Box 10147, Des Moines, Iowa 50347. A

challenging but fun magazine of all different kinds of games

that give children hours of "brain workouts." Appropriate for

ages 7 and up.

Math Power. Scholastic. Available from the school

division. Exciting and inviting, this magazine is filled with

many activities that involve all types of math. Good for grades

3 and 4. Nine publications are sent each school year for $5.00.

Puzzlemania. Highlights, P.O. Box 18201, Columbus, Ohio

43218-0201. Includes puzzles involving words, logical thinking,

hidden pictures, spatial reasoning, etc. The cost is about

$7.50 per month.

Zillions. Consumer Reports, P.O. Box 54861, Boulder,

Colorado 80322. Children's version of Consumer Reports. Shows

math in the real world and offers children the opportunity to

see how gathering data and information can lead to good

decision-making. The cost is approximately $2.75 per issue.

Acknowledgments

This book was made possible with help from the following

people: Phil Demartini, Headmaster, St. Francis School, Goshen,

Kentucky;, Janet G. Gillespie, Teacher, Woodlawn Elementary

School, Portland, Oregon; David Kanter; Sharon Nelson,

Principal, Lower School, Isidore Newman School, New Orleans,

Louisiana; Kathy Rabin, Teacher, Isidore Newman School; and

Annette Raphel, Curriculum Coordinator, Milton Academy, Milton,

Massachusetts.

Others who reviewed early drafts or provided information

and guidance include: Iris Carl, Past President, National

Council of Teachers of Mathematics; Mary Connolly, Marketing

Manager, Elementary Mathematics, DC Heath; Julie Fisher,

Visiting Mathematics Educator, National Council of Teachers of

Mathematics; Vera M. White, Principal, Jefferson Junior High

School, Washington, D.C.; and many people in the U.S.

Department of Education.

Special thanks go to Leo and Diane Dillon for their advice

on how to work with illustrators and to Alison Goldstein and

Emily Dorfman, two Maryland third graders who marked the

manuscript for color overlays. Appreciation is also expressed

to Nathan and Julie Kanter for testing many of the activities

contained in this book.

Patsy E. Kanter is Assistant Principal/Curriculum

Coordinator at the Isidore Newman Lower School in New Orleans,

Louisiana. She is also an instructor of family math and a

consultant for the Louisiana Children's Museum. She has been an

elementary school mathematics teacher, and she founded the

Newman Math Institute at Newman School. She is the author, with

Janet Gillespie, of Every Day Counts and Math Every Day and has

written articles on mathematics for professional magazines. She

has a B.A. from Newcomb College, and, in listing her academic

credentials, she credits her mother, Louise Hirsch Friedler, as

being her first teacher, "who always tried to make learning

interesting for me."

Jerry Guillot is the art teacher for Isidore Newman Lower

School in New Orleans, Louisiana, where he has taught for the

past 24 years. He has a B.A. from Lousiana State University and

received his teaching certification from Tulane University. He

has taught classes and workshops on elementary art for both

college students and private organizations. He is also a

graphic artist for a New Orleans company.

Brian A. Griffin (pages 10, 11, 30, 35, 45, 46) is a

designer for the San Jose Mercury News, San Jose, California.

He was formerly the Art Director of Kids Today, a weekly

children's newspaper published by Gannett Co., Inc. He has won

awards from the Society of Newspaper Design, PRINT Regional

Design Annual, and the Art Director's Club of Metropolitan

Washington.

What We Can Do

To Help Our Children Learn:

Listen to them and pay attention to their problems.

Read with them.

Tell family stories.

Limit their television watching.

Have books and other reading materials in the house.

Look up words in the dictionary with them.

Encourage them to use an encyclopedia.

Share favorite poems and songs with them.

Take them to the library--get them their own library cards.

Take them to museums and historical sites, when possible.

Discuss the daily news with them.

Go exploring with them and learn about plants, animals, and

local geography.

Find a quiet place for them to study.

Review their homework.

Meet with their teachers.

Do you have other ideas?

.