Helping your Child Learn Math
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?
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