During summer vacations, on rainy days, while waiting at the doctor's office or on a stroll through the neighborhood, learning never ends. Children can explore some fascinating mathematical possibilities in the world around them every day. For instance, math can be found outdoors in nature: Look for symmetry in leaves; count the number, sizes and kinds of trees on your street; and look at the various shapes and patterns of blooming flowers. Children will be learning math and enjoying it, too! The activities in this section can be done anytime and anywhere.

On This Page

A Tower of Numbers    Count It Out    Guess What I'm Thinking      Open for Business

What Coins Do I Have?    What Are My Chances?    Card Smarts    Calculated Answers

A Tower of Numbers
Preschool

		Young children can easily confuse letters and numbers. Throughout the day, have them notice and name both, or ask questions such as, "See the sign on that bus. Does it say 5 or E?"

Playing with blocks is fun, but it also can teach basic math skills such as number recognition, counting, identifying patterns, recognizing symmetry and sorting.

What You Need

• Sets of blocks that show both numbers (1-10) and letters (at least A through J)

What to Do

• Give your child the blocks and tell her to sort them so that one sets shows numbers and one set shows letters.

• Tell your child to look at the number blocks and choose the block with the number 1. Then have her build a tower by choosing and placing the remaining number blocks in the correct order. Have her say the name of each number as she places the block.

• Ask your child to build a second tower beside the first using only the letter blocks (beginning with "A") and placing them in order. Have her say the name of each letter as she places the block.

• Let her knock over the towers and scatter the blocks in front of her. Then tell her to use all the blocks to build a really big tower. When it's finished, have her find and point to numbers and letters as you say the names.

• Ask your child to use the blocks to make the following patterns:

  • one number, two letters
  • one letter, one number, two letters
  • A, 5, B, 4, C, 3
  • 1, 2, E, F

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Count It Out
Preschool-Kindergarten

		Be sure to use counters that are small enough for small hands to move but large enough not to pose a choking hazard.

Counting games make developing number sense easy and fun.

What You Need

• A group of 20-25 counters (beads, blocks, plastic eggs, coins), with three or four counters different from the others in some way (for example, red beads in a group of blue beads; dimes in a group of pennies)
• A die

What to Do

• Sit on the floor with your child and arrange the counters in a circle between you. Have her toss the die and say the number that comes up. Tell her to start at any point in the circle—except for one of the counters that is "different"—and count to that number, touching each counter as she goes.

• If she stops on a "regular" counter (a blue bead), she gets to take the counter and have another turn. If she stops on the different counter (the red bead), you get a turn. Leave the different counter in the circle.

• The winner is the player with the most counters when only the different counters remain. Involve the family and expand the game!

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Guess What I'm Thinking
Kindergarten-Grade 2

		It is important to help children develop an understanding of the characteristics of numbers—such as odd and even—and meanings of terms such as "more than" and "less than."

Games give children a chance to use math skills and math language in a non-threatening situation.

What to Do

• Let your child think of a number between a range of numbers. Try to guess the number by asking him questions. Here's a sample:

  (for kindergarten children)
  Child: I am thinking of a number between 1 and 10.
  Parent: Is it more than 6?
  Child: No.
  Parent: Is it less than 3?
  Child: No.
  (The child could be thinking of 4 or 5.)

  (for first and second graders)
  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 reach it by starting at 20 and counting by 5s?
  Child: Yes.
  (The child could be thinking of 25, 30, or 35.)

• After you've guessed your child's number, let him guess a number that you're thinking of by asking similar questions.

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Open for Business
Grades 1-5

		Learning to use calculators is important for children-they're part of everyday life. However, they are no replacement for strong arithmetic skills. Children should not be encouraged to rely too heavily on calculators.

Learning to use a calculator can help children understand and apply estimation and mathematical reasoning skills, as well as learn addition, subtraction, division and multiplication.

What You Need

• Empty containers (cartons or boxes)
• Old magazines, books, newspapers
• Calculator
• Pencil or crayon
• Paper

What to Do

• Help your child collect empty containers so that you can play as if you were shopping at the grocery store. Gather the items and put them on a table. Help think of a price for each item. Mark the prices on the containers. You can even mark some items on sale.

• Pretend to be the customer while your child is the cashier. Ask questions such as the following:

  • How much would it cost to buy three cartons of eggs?
  • If the price of soap is $5.00 for two bars, then how much does one bar of soap cost?
  • If I don't buy the cereal, how much is my bill?
  • How much more will it cost if I buy this magazine?

• Show your older child how math symbols (for example, +, -, ÷, x and =) are used on a calculator. Help her add the prices of each item on the calculator and total the amount using the (=) symbol. Have her write the total on a piece of paper, which will be your receipt.

• Have your child estimate the total cost of the items you are buying. Have her use a calculator to see if her estimate is correct.

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What Coins Do I Have?
Grades 2-5

		Games that involve math should be fun for children, so keep it light!

Using mathematical reasoning skills to figure out the unknown is good preparation for understanding algebra.

What You Need

• Coins of different denominations
• Paper
• Pen or pencil

What to Do

• Choose coins so that your child can't see, then hold out your closed hand and ask her questions such as the following:

  • I have three coins in my hand. They're worth 7 cents. What coins do I have? (a nickel and 2 pennies)
  • I have three coins in my hand. They're worth 16 cents. What coins do I have? (a dime, a nickel, a penny)
  • I have three coins in my hand. They're worth 11 cents. What coins do I have? (2 nickels and 1 penny)
  • I have three coins in my hand. They're worth 30 cents. What coins do I have? (3 dimes) Ask your child to tell you how she knows the answer.

• Make the game more challenging by asking questions that have more than one answer:

  • I have six coins in my hand. They're worth 30 cents. What coins could I have? (1 quarter and 5 pennies or 6 nickels).
  • I have coins in my hand that are worth 11 cents. How many coins could I have? (2—1 dime and 1 penny; 3—2 nickels and 1 penny; 6—1 nickel and 6 pennies; 11—all pennies) Again, ask your child to tell you how she knows the answer.

You get the idea! Give your child coins to figure out the answers.

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What Are My Chances?
Grades 2-5

		Call attention to the role that probability plays in everyday life by pointing how it is used in television weather forecasts or sports stories.

Playing games that involve chance is one way to introduce children to the meaning of probability.

What You Need

• Two coins
• Paper and pencil

What to Do

Play these coin games with your child:

• Flip one coin. Every time it comes up heads, your child gets 1 point. Every time it comes up tails, you get 1 point. Flip it 50 times. Tally by 5s to make it easier to keep track of scores. The player with the most points wins. If one player has 10 points more than the other person does, he scores an extra 10 points. Ask your child to notice how often this happens. (Not very often!)

• Flip two coins. If the coins come up two tails or two heads, your child scores 1 point. If it comes up heads and tails, you get 1 point. After 50 flips, see who has more points. Ask your child if he thinks this game is fair. What would happen if one player received 2 points for every double heads and the other player received 1 point for everything else. Would that be fair?

• Flip one coin. Then flip the other. If the second coin matches the first coin, your child scores 1 point. If the second coin doesn't match the first coin, you receive 1 point. Try this 50 times. Is the result the same as in the previous game?

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Card Smarts
Variations for All Grades

		Encourage children to use number cards to make up their own games for the family to play.

Games with number cards can help children develop strategies for using numbers in different combinations by adding, subtracting, multiplying and dividing.

What You Need

• Sets of number cards, 1-10 (you can make your own using heavy paper or index cards)
• Pencil and paper
• Coin

What to Do

Here are some games that you and your child can play with number cards:

• Number Sandwich With your younger child, review the numbers 1 through 10. Make sure that he knows the correct order of the numbers. Sit with him and shuffle and place two sets of number cards in a pile between you. Have him draw two cards from the pile and arrange them in order in front of him, for example 3 and 6, leaving a space between. Then have him draw a third card. Ask him where the card should be placed to be in the right order—in the middle? before the 3? after the 6?

• More or less? Sit with your younger child and place a shuffled set of number cards between you. Flip the coin and have your child call "heads" or "tails" to see if the winner of each round will be the person with a greater value card (heads) or a smaller value card (tails). Then each of you will draw a card. Compare the cards to see who wins that round. Continue through all the cards. When your child is comfortable with this game, change it just a bit. Divide the cards evenly between the two of you. Each of you places the cards face down and turns over one card at the same time. Have your child compare the cards to see if his card is more or less than yours. If his card is more than yours, ask him how much more. If it is less, ask how much less. The player with the greater or smaller value card (depending on whether heads or tails was tossed) takes both cards. The winner of the game is the player with more cards when the cards have all been used.

• Make a number This game is for your older child, and can be played with family and friends. Give each player a piece of paper and a pencil. Deal each player four number cards with the numbers showing. Explain that, using all four cards and a choice of any combination of addition, subtraction, multiplication and division, the player must make as many different numbers as possible in two minutes. The player gets one point for each answer.

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Calculated Answers
Variations for All Grades

		Asking children to explain in their own words how they arrive at a solution to a problem—including how they used a calculator—encourages them to get into the habit of thinking and reasoning mathematically.

Learning to use the special functions of calculators can expand children's knowledge of many arithmetic operations, help them to recognize number patterns and increase their ability to reason mathematically.

What You Need

• Calculator with counting function

What to Do

• Give your child a calculator that is appropriate for his age (one with large, easy-to-read keys is especially helpful). Show him how he can make the calculator "count" in sequence for him. (For most calculators, this is done by pushing a number button, then the + sign, then the button for the number to be added, then the = sign: for example: 1 + 1 =. To make the calculator count in sequence by adding 1, keep pushing the = button: 1 + 1 = 2 . . . 3. . . 4 . . . 5 and so on). Give the calculator to your child and have him try this, starting with 1 + 1.

• When your child is comfortable with this function, have him explore number patterns such as 2 + 2 =, 5 + 5 =, 50 + 50 = and so forth.

• Next, show your child that he can use the same procedure to subtract-by substituting the - sign for the + sign: 50 - 1 =, or 100 - 5 = . Encourage him to explore other patterns.

• Let your older child learn about negative numbers by seeing what the calculator when they count down from 0 (for example, 0 - 2 = ).

• Create number pattern puzzles for your child to solve. Try the following:

  • Write a sequence of numbers that follows a pattern, such as 3, 6, 9, 12. Ask your child what number comes next. Have him explain what the pattern is (counting by 3s).
  • Have your older child fill in missing numbers in patterns, such as 43, 38, ____, , ____, 23, ____, 13. Ask him what the pattern is. (subtracting by 5s)
  • Have your child create number patterns for you to identify.

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