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.
This book 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.
"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.Contents
More or Less
Fill It Up
Half Full, Half Empty Name that Coin
In the News
Look It Up
Newspaper Search Treasure Hunt
Get into Shapes Check Out
It's in the Bag Put It Away
How Long? How Far? Guess If You Can Appendices
1: Parents and the Schools
2: What Should I Expect from a Math Program?
3: What We Can Do To Help Our Children Learn 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 book 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 baby food, keep score or time at an athletic event, wallpaper a room, decide what type of shoe to buy, or wrap a present. Have you ever asked yourself, "Did I get the correct change?" or "Do I have enough petrol to drive 20 miles?" or "Do I have enough juice to fill all my children's flasks 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 computergenerated artwork.
Calculators and computers require us to be equally strong in math. Their 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. People are quick to admit that "I am not good at 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 realise 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 primary school. Now, children are starting right away to learn about the broad ideas associated with math, including problem solving, communicating mathematically, and reasoning.
Teachers are nursery schools are building bar graphs of birthday cakes to show which month has the most birthdays for the most children in the class. Pizzas or cakes can be used to learn fractions, and measurements can be taken using items other than rulers.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, and sections on activities you can do with your children. The activities take place in three locations: the home, the supermarket, and in transit.
The activities are arranged at increasingly harder levels of difficulty. The ones 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.
Each 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. To develop "transferable skills".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 cook, the doctor, the petrol station attendant, the solicitor, 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.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.More or Less Playing cards is a fun way for children to use numbers. What you'll need Coin 2 packs of cards 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 court 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 Pack 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 pack except ace to
6. Each player draws 8 cards from the pack. 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.Card Smarts Have your children sharpen their math skills even more. What you'll need Pack 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.
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 work out which coin you are thinking of. For example, "My coin has a face 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 dimes and quarters). 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 (25 cents or 50 cents is a good amount). 3. The first player rolls the die and gets the number of pennies shown on the die.