Helping Your Child Learn Maths
Helping Your Child Learn Maths 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 Helping Your Child Learn Math is one in a series of books on different For instance, you and your child can: sort socks on laundry By doing things together, you will show that learning is fun and All of the books in this series tie in with the National Education This book is a way for you to help meet these goals. It will give you a As U.S. Education Secretary Lamar Alexander has said: The first teachers are the parents, both by example and conversation. So, let's get started. I invite you to find an activity in this book Diane Ravitch Assistant Secretary and Counsellor to the Secretary Contents Foreword Introduction The Basics Important Things To Know Maths in the Home Picture Puzzle Mathland: The Grocery Store Get Ready Number Search Appendices Parents and the Schools Acknowledgments Introduction Most parents will agree that it is a wonderful experience to cuddle up It is important for-home and school to join hands. By fostering a It's Everywhere! It's Everywhere! Math is everywhere and yet, we may not recognize it because it doesn't You may be asking yourself, "How is math everywhere in my life? How Do You Feel About Math? How do you feel about math? Your feelings will have an impact on how * 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 You Can Do It! If you feel uncomfortable about math, here are some ideas to think Math is a very important skill, one which we will all need for the Math is a subject for all people. Math is not a subject that men can do Calculators and computers require us to be equally strong in math. Positive attitudes about math are important for our country. The United The workplace is rapidly changing. No longer do people need only the Build Your Self-Confidence! To be mathematically confident means to realize the importance of * 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. You may have noticed that we are talking about Kindergartners are building bar graphs of birthday cakes to show which 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 To communicate mathematically means to use words or mathematical To demonstrate reasoning ability is to justify and explain one's This book is divided into introductory material that explains the basic The activities are arranged at increasingly harder levels of The activities you choose and the level of difficulty really depend on The shaded box on an activity page contains the answer or a simple 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 Wrong Answers Can Help! Above all be patient. All children want to succeed. They don't want red Sometimes, the wrong answer to a problem might be because the child Ask your child to explain how the problem was solved. The response You may have learned something the teacher might find helpful. A short Help your children be risk takers: help them see the value of examining Doing Math in Your Head Is Important Have you ever noticed that today very few people take their pencil and Calculators and computers demand that people put in the correct You can help your child become a stronger mathematician by trying some 1. Help children do mental math with lots of small numbers in their 2. Encourage your child to estimate the answer. When estimating, try to 3. As explained earlier, allow your. children to use strategies that 4. Ask often, "Is your answer reasonable?" Is it reasonable All jobs need math in one way or another. From the simplest thought of If you took a survey, you would find that everyone uses math: the This section provides the opportunity to use games and activities at Remember, * This is an opportunity for you and your child to "talk * If something is too difficult, choose an easier activity or skip it * Have fun! Picture Puzzle Using symbols to stand for numbers can help make math fun and easier What you'll need Paper What to do 1. Choose some symbols that your child can easily draw to stand for 1s 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 What to do 1. Flip a coin to tell if the winner of this game will be the person 2. Remove all face cards (jacks, queens, and kings) and divide the 3. Place the cards face down. Each player turns over one card and This game for young children encourages number sense and helps them These games involve problem solving, computation, understanding number What you'll need Deck of cards What to do 1. Super sums. Each player should write the numbers 1-12 on a piece of Use only the cards 1-6 in every suit (hearts, clubs, spades, diamonds). 2. Make 100. Take out all the cards from the deck except ace through 6. 30, 40, 10, 5, 6, 1, 3, 2. This adds up to 97. Card Support Have your children sharpen their math skills even more. What you'll need Deck of cards What to do 1. How many numbers can we make? Give each player a piece of paper and 4+9+8+2=23 2. Make the most of it. This game is played with cards from 1 (ace) to 3. Fraction fun. This game is played with cards 1 (ace)-10, and 2 Fill It Up Children enjoy exploring measurement and estimation. Empty containers What you'll need Empty containers in different shapes (yogurt cups, margarine tubs, water What to do 1. Have your child choose an empty container each day and label it for 2. Discover which containers hold more than, less than, or the same as filling the day's container with water, uncooked rice, or popcorn pouring the substance from that container into another one. Is the 3. Ask your child questions to encourage comparison, estimation, and 4. Put all the containers that hold more in one spot, those that hold 5. After the containers have been sorted, ask, "Do we have more Half Full, Half Empty It is helpful to explore whole numbers and fractions through What you'll need Clear container with straight sides, that holds at least 4 cups What to do 1. Have your child run a piece of masking tape up the side of the 2. For younger children, use a 1-cup measure. For older children, use a 3. Mark the level of the jar on the masking tape by drawing a line with 4. Follow this procedure until the container is full, and the tape is 5. While filling different containers, ask your child 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? Name that Coin What you'll need Penny What to do 1. Look at the coins and talk about what color they are, the pictures 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. 5. Let your child think about what you have said by looking at the 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. Money Match This game helps children count change. Lots of repetition will make What you'll need A die/dice to roll What to do 1. For young players (5- and 6-year-olds), use only 2 different coins 2. Explain that the object of the game is to be the first player to 3. The first player rolls the die and gets the number of pennies shown 4. Players take turns rolling the die to collect additional coins. 5. As each player accumulates 5 pennies or more, the 5 pennies are 6. The first player to reach the set amount wins. 7. Add the quarter to the game when the children are ready. Money's Worth When children use coins to play games, it may help them use coins in What you'll need Coins What to do 1. Coin clues. Ask your child to gather some change in his or her hand 2. Clip and save. Cut out coupons and tell how much money is saved with What could be purchased with that savings? A pack of school paper? A Counting money involves thinking in patterns or groups of amounts: 1s, In the News Young children love to look at the newspaper. It is fun for them to What you'll need Newspaper What to do 1. Newspaper numbers. Help your child look for the numbers 1-100 in the 2. Counting book. Cut out pictures from the newspaper and use them to Being able to read and understand the newspaper involves more than just Look It Up These activities help children understand how items can be organized What you'll need Newspaper What to do 1. Section selection. Show your child that the paper is divided into 2. Ad adventure. Provide your child with grocery store ads from the 3. Solid search. Look at the store ads or coupons for pictures of all Understanding that there is a logical order to the way things are 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 2. List it. Provide your child with the grocery section of the 3. For a fraction of the cost. Give your child a few coupons and Treasure Hunt Everyone's house has hidden treasures. There is a lot of math you What you'll need Buttons What to do 1. Find a container to hold the treasures. 2. Sort and classify the treasures. For example, do you have all the 3. Use these treasures to tell addition, subtraction, multiplication, 4. Organize the treasures by one characteristic and lay them Family Portrait Have your child get to know members of your family by collecting What you'll need Paper 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 Graphs help everyone, including adults, understand information at a Mathland: The grocery store is one of the best examples of a place where math is 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 What you'll need Paper What to do 1. Involve the family in making a list. List each item and mark with 2. Look at the price of an item you bought last week and intend to buy 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 4. If you collect coupons, organize them. Choose the coupons that match Scan It Shopping is a part of life which really necessitates our being What you'll need Prices What to do 1. Notice whether the grocery store has prices on the items or whether 2. If there are no prices on the items, notice the prices listed on the 3. Assign each child the job of remembering the price of a few items, 4. Being aware of the prices of items will help you verify that the The ever increasing use of technology in the grocery store puts the Weighing In One fun place to try out estimation and measurement skills in the What you'll need The grocery scale What to do 1. Help your child examine the scale. Explain that pounds are divided 2. Gather the produce you are purchasing, and estimate the weight of each 3. Use sample questions to foster thinking about measurement and How much do you think 6 apples will weigh? More than a pound, less than Some grocery stores have scales that tell all the answers to these 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 2. At the store, ask your child questions to generate interest in the 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 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 Discuss why space is important to the grocer and why the grocer cares Check Out The check out counter is where we commonly think about math in the 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 3. Count the change with your child to make sure the change is correct. 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 2. Estimate the weight of the bag of groceries. Does it weigh 5 pounds, Put It Away Now, the sorting begins as you put away the groceries. What you'll need Your bags of groceries What to do 1. Find one characteristic that is the same for some of the products. 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 5. Play "Guess My Rule." In this game, you sort the items and Math on the Go In this busy world, we spend a lot of time in transit. These are some 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. The object is to look for numbers around you: on cars, buses, subways, What you'll need Some type of transportation or 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 3. Write down words that have numbers in them such as This is a great challenge for family members of all age, License Plates License plates have numbers and are fun to use to play games while on What you'll need License plates What to do 1. Copy down a license plate. Read it as a number (excluding the 2. Find other license plates and read their numbers. Is the number less 3. Estimate the difference between your number and another 4. Record the names of the states of as many different license plates 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? 3. Try different problems using the numbers in a license plate. For example, if you use the plate number 663M218, ask, "Using the make a 1 using two numbers? Yes, 3-2=1. How Long? How Far? Many times when you are on the go, you are headed somewhere that 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? 2. Talk about how long it takes to get there. If it is 3:15 now, and it Guess If You Can When children practice asking questions about numbers, they can develop What you'll need Questions about numbers What to do 1. Let your child think of a number between a stated range of numbers 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 The questions asked demonstrate many different levels of math. They can Here are a few ideas that might help you support a positive math 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 2. Explore the math program with your child's teacher, curriculum * Are there manipulatives in the classroom? * Are you familiar with the National Council of Teachers of Mathematics * How are the standards being used in this school? * What can I do to help foster a strong math program where children can 3. If you would like to help out, here are some suggestions for parent * Make games for teachers; * Help seek out sponsors who believe in a strong math program for the * Support math classes for families at your school. 4. Keep a positive attitude even if you don't like what you see. Work 5. Share this book with your child's teacher. The National Council of Teachers of Mathematics (NCTM) has recently These standards make some assumptions about the way math should be 1. Children will be engaged in discovering mathematics, not just doing 2. Children will have the opportunity to explore, investigate, 3. Children will explore and develop understanding for math concepts 4. The teacher will guide the students' learning, not dictate how it 5. Children will have many opportunities to look at math in terms of 6. Children will be actively involved in using technology (calculators The complete list of standards is available from NCTM, 1906 Association 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. Help Your Child Learn Number Skills. Usborne Parents' Guides, The Learning With Series. Cuisenaire Company, P.O. Box 5026, Parker, Tom, (1984). In One Day. Houghton Mifflin Company. Reys, Barbara. Elementary School Mathematics: What Parents Should Know Reys, Barbara. Elementary School Mathematics: What Parents Should Know Room, Adrian. The Guiness Book of Numbers. Sterling Publishing Company, Stenmark, Virginia Thompson and Ruth Cossey. Family Math. Lawrence Hall Thomas, David A., (1988). The Math-Computer Connection. Franklin Watts. Thomas, David A., (1988). Math Projects for Young Scientists. Franklin Math Matters. National PTA and Exxon Foundation. Video tape and The following pamphlets are available from the National Council of "Family Math Awareness Activities" "Help Your Child Learn Math" "Using Calculators to Improve Your Child's Math Skills" Almost every book you read with your child will offer the opportunity 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 Hoban, Tana. Count and See. Macmillan Publishing Company, Inc. Hoban, Tana. Is It Rough, Is It Smooth, Is It Bumpy? Macmillan 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 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 McMillan, Bruce. One, Two, One Pair. Scholastic. Nolan, Dennis. Monster 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 Schwartz, David M. If You Made a Million. Lothrop, Lee & Shepard 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 Games Magazine, P.O. Box 10147, Des Moines, Iowa 50347. The adult Games Junior, P.O. Box 10147, Des Moines, Iowa 50347. A challenging but Math Power. Scholastic. Available from the school division. Exciting Puzzlemania. Highlights, P.O. Box 18201, Columbus, Ohio 43218-0201. Zillions. Consumer Reports, P.O. Box 54861, Boulder, Colorado 80322. This book was made possible with help from the following people: Phil Others who reviewed early drafts or provided information and guidance Special thanks go to Leo and Diane Dillon for their advice on how to Patsy E. Kanter is Assistant Principal/Curriculum Coordinator at the Jerry Guillot is the art teacher for Isidore Newman Lower School in New Brian A. Griffin (pages 10, 11, 30, 35, 45, 46) is a designer for the 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 Find a quiet place for them to study. Review their homework. Meet with their teachers. Do you have other ideas? ----------- END -----------
Welcome! You Are Here Articles/Parenting/Helping Your Child Learn Maths.
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.
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.
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.
important. You will be encouraging your child to study, learn, and stay in
school.
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.
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.
But don't think of it as teaching. Think of it as fun.
and try it.
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
Scan It
Weighing In
Get into Shapes
Check Out
It's in the Bag
Put It Away
Math on the Go
License Plates
Total It
How Long? How Far?
Guess If You Can
What Should I Expect from a Math Program?
Resources
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.
positive attitude about math at home, we can help our children learn math at
school.
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.
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.
your children think about math and themselves as mathematicians. Take a few
minutes to answer these questions:
probably encouraging your child to think mathematically. This book contains
some ideas that will help reinforce these positive attitudes about math.
about.
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.
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.
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.
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.
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.
mathematics and feel capable of learning to
The Basics
"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.
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).
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.
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.
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?
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.
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.
your child's ability if your child seems ready, you might want to go straight
to the most difficult ones.
explanation of the mathematical concept behind the activity so that you can
explain when your child asks, "Why are we doing this?"
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.
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.
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.
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?"
might help you discover if your child needs help with the procedures, the
number facts, or the concepts involved.
note or call will alert the teacher to possible ways of helping your child.
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.
paper out to solve problems in the grocery, fast food, or department store or
in the office? Instead, most people estimate in their heads.
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.
of these ideas to foster mental math skills:
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?"
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.
make sense to them.
that I added 17 and 35 and got 367? Why? Why not?
What Jobs Require Math?
how long it will take to get to work to determining how much weight a bridge
can hold, all jobs require math.
school teacher, the fast food worker, the doctor, the gas station attendant,
the lawyer, the housewife, the painter.
Math in the Home
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 .
math," that is to communicate about math while investigating
relationships.
until your child is older.
for young children to understand.
Pencil
Crayons
and 10s (if your child is older, include 100s and 1,000s).
2 decks of cards
Scratch paper to keep score
with "more" (a greater value card) or "less" (a smaller
value card).
remaining cards in the stack between the two players.
compares: Is mine more or less? How many more? How many less?
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
values, and chance.
Paper
Pencil
paper. The object of the game is to be the first one to cross off all the
numbers on this list.
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.
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:
These games help children develop different ways to see and work with
numbers by using them in different combinations to achieve a goal.
Paper
Pencil
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)=3
(8-4)x(9-2)=28
(9-8)x(4-2)=2
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.
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.
can provide opportunities to explore comparisons, measurement, estimation,
and geometry.
juice boxes with tops cut off, pie tins) Rice, popcorn kernels, or similar.
Marker
Masking tape
Paper
the day by writing the day on a piece of masking tape and sticking it on the
container.
the container chosen for that day by
kernels; and
container full, not full, or overflowing? Ask your child, "Does this
mean the second container holds more than the first, less, or the same?"
thinking about measurement.
less in another, and those that hold the same in yet another. Label the areas
"more," "less," and "the same?
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.
measurement and estimation. Children can see relationships and the usefulness
of studying fractions.
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
container so that it is straight from the bottom to the top.
1/2, 1/4, and 1/8 cup measure. Pour the chosen amount of a substance listed
above into the container.
a marker and writing 1 for one cup or 1/2, 1/4, or 1/8 on the line.
marked in increments to the top of the container. Now, the jar is marked
evenly to measure the capacity of other containers.
"thinking" questions.
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.
Children love to look at coins but sometimes cannot identify the coins or
determine their value.
Nickel
Dime
Quarter
on them, and what they are worth.
For example, "My coin has a man on one side, a building on the
other."
coins.
This guessing game helps young children learn to recognize coins and
develop problem-solving and higher level thinking skills.
it even more effective.
10 of each coin (penny, nickel, dime)
6 quarters
(pennies and nickels or nickels and dimes). Older children can use all coins.
earn a set amount (10 or 20 cents is a good amount).
on the die.
traded for a nickel.
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.
real life situations.
Coupons
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.)
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?
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?
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.
realize that there are things for them to see and do with the paper.
Glue
Paper
Scissors
Pencil or crayon
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.
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.
the ability to read the words and understand what they say. It also involves
the ability to read and understand numbers.
and grouped in logical ways.
Paper
Scissors
Glue
different sections and explain that each section serves a purpose. Show him
that each section is lettered and how the pages are numbered.
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?
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.
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
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
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?.
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.
and your child can do with them.
Screws
Washers
Bottle caps
Old keys
Sea shells
Rocks
or anything else you can count
same sized screws or keys? How are they alike? How are they different?
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?
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.
information and picturing it on a graph.
Pencil
Crayons
side by side to show these five people. Do the same for the other hair
colors.
glance. By looking at the lengths of the lines of heads, your child can
quickly see which hair color, for example, is most common.
The Grocery Store
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:
their thinking strategies about math with one another.
Pencil
Coupons (if you use them)
checks or tallies to indicate the number needed.
this week. How much did it cost last week? How much does it cost this week?
Do you want to
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.
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.
mathematically informed to be good consumers.
the pricing is dependent on scanners.
shelves.
particularly those listed on sale.
scanners are working properly and that the total is accurate when you go to
check out.
burden on you to beware. Your protection lies in having strong mental math
skills.
grocery store is the produce section where everyone can have the opportunity
to participate.
into smaller parts called ounces and 16 ounces equal a pound.
item before weighing it.
estimation. You might Want to ask your child,
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?
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.
to the store. This will help to identify them when you get to the store.
shapes.
daily life.
well.
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.
grocery store. It's where the total is added up, the money is exchanged, and
the change is returned.
clerk? What if I have 20 one-dollar bills? 5? How much change should I
receive? What coins will I get?
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 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?
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.
Counter top or table to group items on
For example, some are boxes and some are cans.
as you can.
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.
projects to try while you are going from place to place.
Number Search
and on foot.
A place from which to observe
Paper
Pencil
Ruler
car, a sign, a building.
"one-stop shopping," "two-day service," or "Highway
20."
because even young children can learn to recognize numbers.
the go.
Paper
Pencil
letters). For example, if the license is 663M218, the number would be six
hundred sixty-three thousand, two hundred eighteen.
than, greater than, or equal to yours?
license plate. Is it 10, 100, 1,000, or 10,000?
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.
(Were the numbers added by 10's like 2+8; were doubles like 6+6 used?)
numbers on the plate, can you:
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.
requires you be there by a certain time.
Blocks? Miles?
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.
an understanding of the characteristics and meanings of numbers.
while you try to guess the number by asking questions. Here is a sample
conversation.
number from you by asking similar questions.
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
environment in your child's school:
classroom.
coordinator, or principal. Here are some questions you might ask:
standards (see next page)?
explore math concepts before giving the right answer?
groups:
school and who might provide materials and resources;
to improve the math curriculum by doing some of the things mentioned
throughout this book.
What Should I Expect from a Math Program?
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.
taught and what parents might see when visiting the classroom. Here are some
examples:
many problems in a book.
estimate, question, predict, and test their ideas about math.
using materials they can touch and feel, either natural or manufactured.
must be done.
daily life and to see the connections among math topics such as between
geometry and numbers.
and computers) to solve math problems.
Drive, Reston, Virginia 22091-1593 (1-800-235-7566).
Resources
National Council of Teachers of Mathematics. Reston, Virginia
EDC Publishing, 10302 East 55th Place, Tulsa, Oklahoma 74146.
White Plains, New York 106025026, 1-800-237-3142.
about Estimation. National Council of Teachers of Mathematics. Reston,
Virginia. 10 for $7.50.
About Problem Solving. National Council of Teachers of Mathematics. Reston,
Virginia. 10 for $7.50.
Inc., 387 Park Avenue South, New York, New York 10016-8810.
of Science, University of California at Berkeley, Berkeley California 94720.
Watts.
pamphlet useful for parent meetings.
Teachers of Mathematics, 1906 Association Drive, Reston, Virginia 22091-1593
(1-800-235-7566). All are priced 20 for $5, 100 for $15.
2. Books for children:
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.
Company, Inc.
Publishing Company, Inc.
Numbers. Dial.
Books, Inc.
Bubbles. Prentice Hall.
Books, Inc.
Books, Inc.
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.
version of Games Junior (see below). Older children may prefer this to Games
Junior.
fun magazine of all different kinds of games that give children hours of
"brain workouts." Appropriate for ages 7 and up.
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.
Includes puzzles involving words, logical thinking, hidden pictures, spatial
reasoning, etc. The cost is about $7.50 per month.
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
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.
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.
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.
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."
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.
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:
geography.
.
