Math

Whenever your children are looking for some interesting math activities, let them choose some of these to do. The activities are especially helpful in the summer as children lose so much ground in math during that time. Select both age-appropriate and challenging activities. Many of the activities involve games and will be fun for your children to do. And be sure to have them try to solve some of the math riddles and puzzles.

Explain to your children that an unknown benefactor has given them \$1 million (lower the amount for younger children). The money, however, can only be spent by buying items advertised in the newspaper. Also, the following conditions must be met: (1) The exact amount must be spent whether it is \$1 or \$1 million. (2) No more than \$100,000 can be spent on an item. (3) Only one of each item can be bought.

In order to have older children employ their multiplication skills, allow them to purchase from two to nine of any item. Also, children can compete to see who is able to spend the money by purchasing the fewest items.

Using math on vacation trips

When your family goes on vacation, whether you are hitting the highway, skyway or the railroad tracks, math should always be part of the trip. Be sure to take along a calculator, as it will encourage your children to use math and work with larger numbers.

On the planning side, children can use maps to figure out trip mileage, which can then be broken down to miles that will be traveled each day. On the road, they can determine miles between gas stops, the average speed you are traveling and so on. For plane and train travel, children can also figure out the average speed. When they return to school, this type of math activity will lead to a better understanding of averages and rate-time-distance problems. Depending on their ages, children can also track how much is being spent on meals, lodging, souvenirs, and miscellaneous expenses.

During the trip, children can play math games. For example, you can make up a simple problem, such as 6 x 8 or 4 + 9, and see who finds the answer first on a license plate or billboard. For more math travel games, stop by a learning or teacher-supply store before taking off. Trips are also good times to teach simple mental math skills (see skill builders in resources) and practice them.

Math games with cards

In “Fraction Fun,” the cards from ace (1) through 10 in all suits are used. The deck is then divided between two players. Each player turns over two cards at a time and makes a fraction. The player with the larger fraction takes all the cards. Play continues until all the cards are played.

In “Make the Biggest Number,” the cards from ace (1) through 9 are used. Each player alternates drawing cards and puts a card down in the ten thousands, thousands, hundreds, tens or ones place on a piece of paper. The player with the largest number wins.

Using math at home

You use math at home every day and need to point this out to your children. Let them see you balancing the checkbook, paying bills, or determining how much paint is needed to cover the walls in a room. In the kitchen, let children do the measuring for recipes so they will see the difference between a 1/4 and 1/2 teaspoon or cup. Younger children can pour liquids from one container to another to learn about cups, pints, quarts and gallons. And children in elementary school and middle school should be turned loose with rulers, yardsticks and tape measures to measure all types of things around the house, from the height of every family member to the size of the TV screen.

Daily math practice times

In the busy world around your family, you can give your children considerable practice in using math. While moving around your community, have your young children keep their eyes open for numbers on streets and buildings so that they will be able to locate the address of where you are going. When you are walking with your elementary-school children, ask them to guess how many feet or yards it is from one point to another to give them a better idea of distances. You can actually check how accurate their guesses are by stepping off the distances. Count one child's step as a foot and three as a yard, or measure their stride for greater accuracy.

When you purchase items in stores, give your children the opportunity to pay for the goods or services. Young children can put coins in newspaper boxes, pay for ice-cream cones, learn how to make purchases from vending machines. And of course, as soon as it's age-appropriate, they can pay the bill at fast-food restaurants. Older children should be taught how to determine if they have received the correct change for \$5, \$10 or \$20 bills when making purchases.

Grocery stores are places where the use of math is essential. Older children can determine which item is cheaper by studying unit pricing labels. Younger children can weigh fruits and vegetables to learn about ounces and pounds.

Telling time and time zones

Telling time is a sophisticated task that is difficult for young children to learn. You can ease this task by putting stickers by every number on the face of the clock. For example, you would place a 5 by 1, a 10 by 2, and so on.

To help your young children get the idea of how long seconds and minutes are, use a timer to measure how long it takes them to do certain tasks. They can set the timer and find out how many times they can walk around a table in five seconds or how far they can walk in two minutes.

Your older children need to learn about time zones. If you have friends or relatives living in a different zone, discuss with your children what time it is in the other zone when you are making phone calls to them. Also, when you travel between time zones, be sure to point this out to your children.

Math riddles and puzzles

Some are silly, and some are very challenging. All will be fun to solve. The answers are at the end of this section.

1. What is the smallest number of ducks that can walk in this formation: two ducks in front of a duck, two ducks behind a duck, and a duck between two ducks?
2. If it takes ten people 10 days to plant a garden, how long will it take five people to plant half a garden?
3. Promise your parents that you will make your bed every day for 30 days if they will pay you 1 cent for the first day and for each day thereafter twice as much as the day before. If your parents agree, how much will they have to pay you for the thirtieth time that you make your bed?
4. If there are 25 students in your class and you shake every student's hand when you arrive, how many handshakes will you have to make?
5. If you reach into your sock drawer without looking, how many socks would you have to pull out to find a matching pair if you had 10 red socks 10 blue socks, and 10 green socks?
6. Choose your three favorite ice cream flavors. If you want a cone with two dips, how many different combinations of flavors could you have?
7. Draw a square on a piece of paper. Separate it into different regions by drawing 4 straight lines from one edge to another. What is the largest number of regions you can make?
8. Jane had 4 three-cent stamps and 3 four-cent stamps. How many different amounts of postage can be made from these stamps?
9. Farmer John was counting his cows and chickens and saw that together they had a total of 60 legs. If he had 22 cows and chickens, how many of each did he have?

Answers: If you have found another answer to any of the problems, e-mail us your answer. (1) 3 ducks, (2) 10 days, (3) \$536,870,912, (4) 24 handshakes, (5) 4 socks, (6) 6 combinations, (7) 11 regions, (8) 18 different amounts, (9) 8 cows and 14 chickens.

Graphing presents information in pictorial form. There are many types of graphs. Young children can be introduced to them by drawing the results of simple experiments. For example, open a small package of differently colored candies. Then have your children sort out the candies by color to form rows, and they will have made a graph. The same thing can be done with coins. Older children can graph the temperature by using strips of paper to represent the height of the mercury on a thermometer at noon every day for a week. They can glue the strips to a piece of paper forming a bar graph. The strips should be labeled by the day of the week.

Building geometric figures

Learn about solid geometry by making this very attractive display. It may take several days to build the completed models. Your children will use cardboard to build models of five regular solids: cube, tetrahedron, octahedron, icosahedron, and dodecahedron. They can find patterns for these figures online at www.mathisfun.com/geometry/model-construction-tips.html and other Web sites. When they are done, have them use the models to determine the number of faces, vertices, and edges for each solid. The vertices are the corners. The edge is where the two faces meet and connect the vertices.

Children need to know equivalencies to solve many measurement problems. They should have fun figuring out how old they are in days, weeks, and months. If they know the time they were born, they can also determine how many hours, minutes, and seconds old they are. And they can expand their knowledge by determining how many ounces they weigh.

Probability

Tossing two coins is a good way to introduce young children to the study of probability. Begin by talking about what happens if you and your child toss a coin simultaneously. Then write down the possible outcomes. Next, ask your child to make a prediction about how often two heads will turn up if the coins are tossed 20 times. Follow up by tossing the coins 20 times and tallying the outcomes as they occur. Did the outcomes agree with your predictions?

Here's a bit more difficult probability problem for older children using a pair of dice. Have your children roll the dice 20 times and find the difference between the number of dots on the top faces of the dice each time. Before beginning this experiment, they need to make a graph with the numbers 0 through 5 for the difference on one side and 1 through 20 on the other for the number of times a specific difference was rolled. After each roll, the results are entered on the graph. Have your children rank the differences from most often to least often. Do the experiment two more times. Then have your children answer the question: What difference is most likely to show up when you roll a pair of dice?

Learning to make estimates

Estimation is a useful skill for your children to have both in the real world and in doing math problems in school. Measurement estimation is a particularly practical skill. How far is it to the mailbox? How high is the counter top? It is especially helpful to use body units to get a rough idea of length. For example, if children know the length of their stride, they can easily walk off distances. Then for shorter measures, they can use their fingers and hands. Help your children acquire the measurement estimation skill by having them measure the length of their fingers, hands, feet, and stride. Then they can use their bodies to measure the length of their bedrooms, the distance from the couch to the refrigerator, the size of the TV screen, the width of a window, and the size of a book. They can check the accuracy of their measurements by using a tape measure or ruler.

Put mathematics into trips to the grocery store by teaching your children how to estimate what the total will be. Have them round prices to the nearest dollar and then to the nearest 50 cents. They will be amazed to discover that rounding to the nearest 50 cents usually brings their total to within a dollar of the cash register before the tax is added.

Mathematical palindromes

The more children play with numbers, the more intrigued they will be by math. They are probably familiar with word palindromes, such as dad, mom, and radar in which the letters in the word are the same whether you read them forward or backward. Numbers can be turned into palindromes, too. Here is how it works. Take 145 which is not a palindrome. Reverse it, and add. (145 plus 541). Your answer will be 686, a number palindrome. Have your children try this with easy numbers like 57, 48, and 86. They may have to reverse the sum several times to get a palindrome. Then give them the challenge of turning 89 into a palindrome. They'll need to fill a page with the calculations and get a lot of practice adding.

Learning the terms of statistics

Because so much computation is required, statistics is a very limited topic for young children. They can, however, become familiar with two basic concepts of statistics: the mode and the median. Be sure to use these words in doing the following activities with them.

Have your children toss a die twenty times and record the number on the top each time. The mode will be the outcome that occurs most often. Older children might enjoy observing how many times a phone rings in your home before it is answered for a couple of hours. This time the mode will give them an idea of whether your family is fast or slow in answering the phone.

Statisticians call the average, the mean. It is probably the most used statistic of all. Use a group of four people to introduce your children to this concept. Begin by cutting a strip of paper as long as each person is tall. Then tape the ends of the strips together. Fold the strip in half and in half again to find the average height of the group. Have the children compare their height to the average to discover who is taller and who is shorter. For more fun in determining averages, your children can use strips of paper to measure the distance of jumps.

Math riddles and puzzles

1. When does LEG + GET = PET?
2. Two hours from now, it will be half as long until noon as it will be an hour from now. What time is it now?
3. The ages of a mother and her daughter add up to 66. The digits of the mother's age are those of her daughter's reversed? What three possible ages could they be?
4. Leo has \$80 in his piggy bank and 20 bills. If he has four more \$1 bills than \$5 bills and 2 more \$5 bills than \$10 bills, how many bills of each denomination does he have?
5. If DESIGNER is worth 47231578, RING is worth 8351, and SEND is worth 2754. What is NERD worth?
6. How many addition signs should be put between the digits of the number 123456789 to equal 99? Where should they be placed?
7. Draw a blank tic-tac-toe game board. Can you arrange the numbers so that every row, column, and diagonal adds up to the same number?
8. Take six different books. How many ways can you arrange them from left to right in a bookcase?
9. Draw a clock face, including the numbers. Now, draw two lines across the face to divide it into 3 parts so that the sum of the numbers in each part is equal.

Answers: If you have found another answer to any of the problems, e-mail us your answer. (1) when LEG and GET are adjacent angles with E as the vertex. (2) 9:00 A.M. (3) Their ages could be 06 and 60, 24 and 42, 15 and 51. (4) He has four \$10 bills, six \$5 bills, and ten \$1 bills. (5) NERD is worth 5784. (6) The number should have seven addition signs and look like this: 1 plus 2 plus 3 plus 4 plus 5 plus 67 plus 8 plus 9. (7) The rows from left to right are: Row 1 – 2 9 4, Row 2 – 7 5 3, Row 3 – 6 1 8. (8) There are 720 ways to arrange the books. (9) One line should be drawn between 10 and 11 and 2 and 3. The other should be between 8 and 9 and 4.