Laws & Guidance ELEMENTARY & SECONDARY EDUCATION
With activities for children in preschool through grade 5
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Mathematics in the Home — Activities

Your home is a great place for you to begin to explore and "talk" mathematics with your child. Incorporating math activities and language into familiar daily routines will show your child how math works in his everyday life and provide him with a safe environment in which to take risks by trying new things.

 Rhyme and Sing Number Hunt Walk and Count Find It Sort It Out Shape Up A-Weigh We Go
 Penny, Nickel, Dime Treasure Hunt In the News(paper) Fill It Up Tracking Time Fraction Action Simply Symmetrical

### Rhyme and Sing Preschool

 For titles of books that contain counting rhymes and songs, see the list of children's books in the Resources section at the end of this booklet.

Young children love to hear, sing and say nursery rhymes and songs. Counting rhymes and songs can be both enjoyable for them and introduce them to basic mathematics concepts, such as number names and number sequence.

What You Need

• Book of nursery rhymes or songs
• Feather

What to Do

• Teach your child to the following counting rhyme.

Four Little Ducks
Four little ducks that I once knew,
Fat ducks, skinny ducks, they were, too.
But one little duck with a feather on her back,
She ruled the others with a quack! quack! quack!
Down to the river they all would go,
1, 2, 3, 4, all in a row.
But one little duck with a feather on her back,
She ruled the others with a quack! quack! quack!

• Say the rhyme with your child several times. When she can say the rhyme all the way through, have other family members join you. Give your child a feather and have her lead everyone around the room as you all sing.

• For the following rhyme, show your child how to perform the actions.

Five Little Speckled Frogs
Five little speckled frogs
(hold up five fingers)
Sitting on a speckled log
Eating some most delicious bugs
(pretend to eat)
Yum! Yum!
One jumped into the pool
(jump)
Where it was nice and cool
(cross arms over chest and shiver)
Now there are four little speckled frogs.
(hold up four fingers)
Burr-ump!
(Continue until no frogs are left.)

• After saying the rhyme, ask your child to hold up the correct number of fingers to show how many frogs are in the rhyme at the beginning. Then have her hold up the correct number of fingers and count to five with you as you say each numeral.

• Teach your child any counting rhymes and songs that were your personal favorites when you were a child, or have your child ask her grandparents what rhymes they knew when they were children. Other counting rhymes, songs and games that you may want to teach your child include "One, Two, Buckle My Shoe," "This Old Man," "Ten in a Bed (Roll Over)" and "One for the Money."

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### Number Hunt Preschool

 Sometimes younger children don't understand that counting means naming numbers in a specific order. This simple point should be reinforced often.

By counting, using number names and learning to recognize differences in number values, children build a foundation for the development of number sense and mathematical reasoning.

• What You Need
• 3 plastic eggs that come apart (or similar containers)
• Buttons
• Plastic netting

What to Do

• In pieces of netting, loosely wrap different numbers of buttons and place one bag of buttons in each egg. With your child out of the room, hide the eggs.

• Call your child into the room and tell her that you've hidden three eggs and that you want her to find them. As she finds each egg, have her count aloud—"1," "2," "3."

• When she's found all the eggs, have her open each one and take out the bag of buttons (but not open it). Ask her to count how many buttons are in each bag.

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### Walk and Count Preschool-Kindergarten

 Throughout the day, find ways to let children practice using arithmetic skills. Ask, for example, "How many magazines came in the mail?" "How many more letters will we need to get to have 10 letters?" "Which are there more of, magazines or letters?"

Ordinary activities can be used to reinforce young children's number sense and introduce them to arithmetic operations such as addition and subtraction.

What to Do

• Take your child for a walk. You can walk around your neighborhood, through a park, or just around the rooms in your home. As you walk, say silly things for him to do, such as the following:

• Take two big steps and three little steps.
• Take three little steps, hop one time, take three big steps.
• Take one little step, turn around two times.
• Hop four times, turn around one time.
• Take three big steps forward and two big steps backward.

• Count aloud each kind of action that your child performs and compliment him for his efforts—"1, 2—1, 2, 3—1, 2. That's great!"

• Let your child turn the tables and say silly things for you to do as you walk.

• For your kindergarten child, expand the activity by asking him to "guess" (estimate) how many of his steps it will it take, for example, to get from the tree to the corner. After he makes his estimate, have him count steps to see how close the estimate is. Next ask him how many of your steps it will take. Will it take you more steps or fewer to go the same distance? Again, have him count to see if his answers are correct.

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### Find It Preschool-Kindergarten

 Calling attention to numbers that are all around them lets children know that numbers are important and that they are used for many different purposes.

Young children may not recognize that numbers are all around them. Pointing out numbers on everyday items increases their number sense.

What You Need

• Boxes, cans and bottles of food and other household supplies

What to Do

• Place several boxes, cans and bottles on the kitchen table. You might use a cereal box, a can of soup and a bottle of dishwashing soap. Sit with your child and point out one- or two numbers on each item. (Numbers can be found in the names of some products, as well as in the list of contents and in addresses. However, rather than point to a very large number, such as a ZIP code, point to one digit in that code—a 6 or 3 or 8.)

• Point to one of the items and say a number that is easy to see. Ask your child to find it. Then have him look for that number on the other items.

• Have your child choose a number for you to find on one of the containers.

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### Sort It Out Preschool-Kindergarten

 Children need to see that grown-ups also make math mistakes occasionally and that they identify their mistakes and find ways to correct them.

Sorting and matching activities introduce young children to many mathematical operations, including classification and measurement.

What You Need

• Pairs of socks of different sizes and colors
• Laundry

What to Do

• When you're sorting and folding clean laundry, have your child join you and do such things as the following:

• Hold up a pair of matching socks that belong to her and say, for example, "These socks go together because each sock is red and each one fits the same size foot—yours!"
• Pick up another sock and ask your child to look through the pile for the sock that matches it. When she chooses a sock, have her tell you how she knows that it's the right one.
• Continue holding up socks until your child has paired them all. If she mispairs any socks, gently correct her by asking her to tell the color of each sock and to put the socks together to see if they are the same size.
• After you've done this activity several times, let your child choose the socks for you to pair. (Occasionally choose a wrong sock to give her the chance to help you correct your mistake!)

• Have your child help you sort the laundry to be washed. Ask her, for example, to put all the blue things together, all the whites, all the towels and so forth. You might also have her count as she sorts. How many towels are there? How many shirts? Try saying, "I count five shirts. Is that right?" Then have your child count aloud the number of shirts. From time to time, give an incorrect number so that she can count the items one by one and show you that you've made a mistake.

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### Shape Up Preschool-Kindergarten

 Playing with children can provide many opportunities to engage in activities such as sorting, matching, comparing and arranging.

Using objects that are familiar to young children can be a good way to introduce them to differences in shapes and to classification.

What You Need

• Snack crackers in the shape of circles, squares, triangles
• Bread cut into different shapes

What to Do

Here are some simple things that you can do to focus your child's attention on different shapes:

• Fill a bowl with snack crackers in shapes such as circles, triangles and squares. Point to a cracker and say, for example, "Look, this one's round. This one has three sides. See, 1-2-3. This one has four sides. Let's count them—1-2-3-4." Place a circular cracker on the table and ask your child to find other crackers that have the same shape. Continue with the other shapes.

• As you make sandwiches, cut the bread into circles, squares and triangles so that you have two each of each shape. Ask your child to match the pairs of shapes to make Shape Sandwiches.

• Have your child search for and point out different shapes on his clothes or in the room.

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### A-Weigh We Go! Kindergarten-Grade 1

 Using simple bathroom and kitchen scales at home prepares children for using equipment in school to weigh and measure.

Observing, estimating, weighing and comparing are all essential mathematics skills.

What You Need

• Bathroom or kitchen scales
• Objects to weigh, such bags of sugar, flour, potatoes or onions; boxes of detergent and cookies; shoes of different sizes
• Paper and pencil
• A small plastic zipper bag filled with sugar and much larger zipper bag filled with cornflakes (or popped popcorn)
• Suitcase

What to Do

• Show your child two objects, such as a five-pound bag of sugar and a ten-pound bag of potatoes and ask him to guess which weighs the most. Show him how to use a scale to weigh the objects and see if his guess is right or wrong.

• Next show him several objects and ask him to guess how much each weighs. Have him write his estimates, then weigh the objects to see if they're correct.

• If you choose, have your child estimate his own weight, as well as that of other family members, and use the bathroom scale to check his guesses.

• Extend the activity or make it more challenging by doing the following:

• Show your child the small plastic bag filled with sugar and the larger bag filled with cornflakes or popped popcorn. Ask your child, which will weigh more, the smaller or the larger bag? Have him weigh the bags to check whether his guess is correct. Afterwards, point out that bigger does not always mean heavier.
• Ask your child how he can weigh a suitcase that is too large to fit on the bathroom scale. Listen carefully to his answers-try some of his suggestions, if possible-and praise him for learning to think through problems. If he doesn't come up with a solution, show him that one way to find the weight of the suitcase is for him to stand on the scales while holding it and noting the total weight. Then put the suitcase aside and weigh himself again and note his weight. If he subtracts his weight from the total weight, the answer is the weight of the suitcase.

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### Penny, Nickel, Dime Kindergarten-Grade 1

 Children can be confused by money. Some might think that the larger a coin is, the more valuable it is-so a penny or nickel would be more valuable than a dime.

Activities that involve money are a good way to develop mathematical reasoning and to reinforce what children are learning in school about numbers and arithmetic operations, such as addition and subtraction.

What You Need

• Die
• Pennies, nickels, dimes

What to Do

This is a good game to play with the family.

• Have each player roll the die and say the number. Then give the player that number of pennies. Explain that each penny is worth one cent.

• When a player gets five pennies, replace the pennies with a nickel. Explain that five pennies have the same value as one nickel—that is, five cents. When she gets five more pennies, replace the pennies and the nickel with a dime. Help her to see that the value of five pennies plus the value of a nickel (five cents) equals 10 cents, which is the value of a dime.

• The first player to reach a set amount—25 or 50 cents, for example—wins.

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 Keeping the tone of math activities light will increase the likelihood that children will want to do them and make the activities seem less like "homework."

Once children begin school, math-related activities at home can help to reinforce what they are learning about numbers and arithmetic operations such as addition and subtraction, as well as reinforce classification skills and mathematical reasoning.

What You Need

• Large container
• Buttons, bottle caps, old keys or any other small items that you can count

What to Do

• As a rainy day activity, place the items in the container and give it to your child. Have him sort and classify items into piles: keys, buttons and so forth. Then have him explain how the items in each pile are alike and how they are different. For example, some buttons may be big and some small; some keys may be silver-colored and some gold-colored.

• Have your child choose one of the piles and organize the items in it by one characteristic, such as length. Have him lay the items end to end then compare and contrast what he sees. For example, how many short keys? long keys?

• Next, ask your child to use the items in another pile of items to solve simple math problems. Try problems such as the following:

• If you have 10 bottle caps and give me two, how many bottle caps do you have left?
• If you have three big buttons and three small ones, how many buttons do you have altogether?

• Create activities that challenge your child to use mathematical reasoning. Ask him, for example, to look closely at items and answer questions such as the following:

• Is a gold-colored key always heavier than a silver-colored one?
• Do the big buttons always have more holes than the smaller ones?

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### In the News(paper) Kindergarten-Grade 1

 Newspapers also can be used to help young children learn to recognize numbers in different sizes and kinds of type and to understand that the way a number looks does not change its value.

Newspapers are good resources for building number sense and arithmetic skills and using mathematical reasoning.

What You Need

• Newspaper
• Scissors
• Pencil or crayon
• Glue
• Paper
• Hole puncher
• Yarn

What to Do

• Give your child a newspaper and a set of numbers to look for, for example from 1 to 25 (or 1 to 100 if she is familiar with the higher numbers). Have her cut out the numbers and glue them in numerical order onto a large piece of paper. Call her attention to any ways in which the numbers differ-for example, some will be a bigger size than others, some will be in bold or italic type. Have her read the numbers to you, then put the paper aside. Have her practice counting up to that number then counting down from it. Also try having her count to the number by 2s or 5s.

• Next, have your child make a counting book by using pictures she's cut from the newspaper. Have her write the page numbers at the bottom of each blank page and paste one item on page 1, two on page 2 and so forth. Explain that all of the things she puts on a page must be alike in some way—all animals, all basketball players, all cars and so on. Help her to write the name of the items on each page.

• Have your child read the book to you. Afterwards, ask her questions such as the following:

• How many pictures did you cut out altogether (1+2+...+10)?
• How many total pictures are on pages 1-3? on pages 1-6?
• We know that 6 = 2 x 3. Are there twice as many pictures on page 6 as on page 3?
• Are there twice as many pictures from page 1 to 6 as from pages 1 to 3?
• Which are there more of: pictures on pages 2, 3, and 4, or pictures on pages 5 and 6?

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### Fill It Up Grades 1-2

 As you use measuring cups, call attention to the different levels and use their names: "one-fourth," "one-half" and so on. This will begin to familiarize children with the language they will use when they begin to work with fractions.

Filling empty containers provides opportunities to explore geometric concepts such as "more or less" and volume, and to apply measurement skills.

What You Need

• Measuring cup
• Four large glasses of equal size and shape
• Water

What to Do

• On a table, put the glasses in a row and fill them with water as follows: one-third cup, one-half cup, three-fourths cup, 1 cup. Ask your child questions that encourage her to compare, estimate and think about measurement. Ask, for example, "Which glass has more water? Which has less?"

• Pour more water into one of the glasses to make it equal to the amount of water in another glass. Move the glasses around so that the glasses that have the same amount of water are not next to each other. Ask your child to find the glasses that have the same amount of water.

• Help your child to do math in her head. Ask questions such as, "If I have four cups of water and I need seven, how many more do I need to pour?"

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 A good way to show children how statistics are used in the "real world" is to call their attention to statistical charts in newspapers and magazines and talk with them about what the charts show and why this information is important.

Introducing children to statistics and data analysis can begin by having them collect information, analyze it and describe or present their findings in an organized way.

What You Need

• Stopwatch, watch or clock
• Newspaper
• Blank paper
• Graph paper
• Ruler
• Small round object to trace to make a pie chart

What to Do

• Show your child how to keep track of the time he spends on two activities, such as watching television and doing homework. Help him to make a chart with two columns, one labeled "Television" and one labeled "Homework." Down the left side of the chart, write the days of the week. Tell him that you want him to write the number of minutes he spends doing each activity on each day. At the end of the week, sit down with him and talk about what the table shows.

• Help your child to make a chart to use as he watches television. Give him a stop watch (or an easy-to-read clock or watch) and tell him to record how much time of each television show is used for commercials and how much time is used for the actual show. Have him keep the record for one night of viewing. On the graph paper, help him to make a bar graph that shows the different amounts of time devoted to the show and to commercials. Or, show him how to make a pie chart.

• Together with your child, keep track of how he spends time in one 24-hour period: time spent sleeping, eating, playing, reading and going to school. Help him to measure a strip of paper 24 inches long, with each inch representing one hour. Using a different color for each activity, have him color the number of hours he spends in each activity. You and other family members can make similar charts; then your child can compare the charts and see how everyone in the family spends time.

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 Children may reasonablywant to say, for example, that 1/4 cup plus 1/4 cup makes 2/4 cups. Letting them workwith measuring cups or other measuring devices can let them see that 2/4 is the same as 1/2.

In introducing children to the concept of fractions—numbers that aren't whole numbers (such as 1/2, 1/3 and 1/4)—it's often a good idea to use objects that they can see and touch.

What You Need

• Large clear container (holding at least 2 cups)
• Marker
• Measuring cups (1/2, 1/3 or 1/4 cup measure)
• Unpopped popcorn

What to Do

• Invite your child to help you make popcorn for the family. Begin by having her put a piece of masking tape from top to bottom on one side of the large container.

• For younger children, use a 1/2 cup measure. For older children, use a 1/3 or 1/4 cup measure. Choose the unit of measure and fill the measuring cup with popcorn. Give the cup to your child and ask her questions such as the following:

• How many whole cups do you think the container will hold?
• How many 1/2 cups (or 1/3 cups or 1/4 cups) do you think it will hold?

• Let your child pour the measured popcorn into the clear container. Have her continue to pour the same amount into the container until it is full. As she pours each equal amount, have her mark the level on the container by drawing a line on the tape. Then have her write the fraction, corresponding to the unit of measure on the line. After the container is full, have your child count up the total number of cup increments (1/2, 1/3 or 1/4) and compare it to her estimate from above.

• As you measure out the popcorn to pop, ask your child to answer questions such as the following:

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

• Pop the corn and enjoy!

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 For titles of books about shapes and patterns, see the list of children's books in the Resources section at the end of this booklet.

A shape is symmetrical if it can be cut along a straight line into two halves that are mirror images of each other. Learning about symmetry gives children a good sense of geometric principles and calls on their mathematical reasoning abilities.

What You Need

• Shapes such as a circle, a square and a rectangle, cut from heavy paper
• Sheets of paper (rectangular)
• Pencil, marker or crayon
• Magazine pictures of symmetrical objects
• Safety scissors
• Glue

What to Do

• As your child watches, show her the square that you've made. Fold it in half and show her that the two parts are exactly alike—or symmetrical. Do the same with the circle and the rectangle. Then give the shapes to your child and ask her to make the folds herself. Extend the activity by having her do the following:

• Find as many ways as she can to fold half of the square onto the other half. (There are four ways: two diagonals and two lines "down the middle").
• Do the same for the rectangle. (There are only two ways: down the middle of the long side, then down the middle of the short side. In going from a square to a rectangle, the diagonals are lost as lines of symmetry.)
• Do the same with the circle. (Circles can fold along any diameter. Use this discovery to introduce your child to the word "diameter"—the length of a straight line that passes through the center of a circle).
• Ask her to find the center of a circle by folding it in half twice. (She'll discover that any diameter-line of folding in half-passes through the center of the circle, an activity that will prepare her for understanding more complicated geometry later on.)

• Show your child a rectangular piece of paper. Ask her, "What shape will you get if you fold this piece of paper in half?" Have her fold the paper, then ask, "Did you get a square or another rectangle?" Using scissors to cut the paper, show her that a rectangle will fold to a square only if it is twice as long as it is wide.

• Fold a sheet of paper in half lengthwise. Have your child draw half of a circle, heart or butterfly from top to bottom along the fold on each side of the paper. Help her cut out the shapes that were drawn. Unfold the paper to see the symmetrical figure.

• Cut out a magazine picture of something that is symmetrical (try, for example, a basketball or a computer screen). Cut it down the center (the line of symmetry). Glue one half of the picture on the paper. Ask your child to draw the missing half.

• With your child, explore your house for symmetrical designs—things that have equal sides. Ask your child how many she can find. Tell her to look at wallpaper, floor tiles, pictures, bedspreads and appliances.

• Have your child print the alphabet. Then ask her to find a letter that has only one line of symmetry—only one way to be divided in half. (B has one—the line is across the middle.) Ask her to find a letter that has two lines of symmetry—two ways to be divided in half. (H has two—the lines are across the middle and down the center.) Ask which letters look the same when they're turned upside down? (H, I, N, O, S, X and Z.)

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