Math Learning Activities

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.

Fun with newspaper ads

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.

Learning about graphing

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 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.

Learning about equivalencies

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.


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.

Learning basic facts

If your children elementary school and even middle school cannot answer basic fact problems in less than three seconds, some drill is in order. These facts, especially addition and multiplication, must be automatic for children in order for them to handle more advanced math easily. So this is your starting point for building math skills. Use a search engine to find "math drill activities."

Visit several websites with your children and bookmark the most appealing ones. Older children should work on drilling fraction, decimal and percentage equivalencies.

Drill, even on the computer, can be boring after a while. Both children with weak basic math skills and those who just need to keep their skills sharp should have fun playing math games. Search online for "math games" and bookmark the ones your children like best.

Math activities should not be confined to the computer. Games like Monopoly, Dominoes and Twenty-one are great for older children, while much younger children can enjoy Uno, Go Fish and Bingo for number recognition.

Understanding perimeter and area

The perimeter and area of objects can be very simple to find or require quite advanced math concepts. It is helpful for children at all levels to be able to see these problems.

Perimeter is the distance around an object as measured by some type of unit. Have your young children find the distance around a variety of things in your home: a door mat, a towel, the backyard or a tabletop. The question always is: How far is it around the object? Then depending on their ages, children can measure using blocks, paper clips, steps, a finger or a measuring tool.

Area is a more difficult concept to understand. It is the surface inside a shape. Young children can find the area of a newspaper or tabletop by finding out how many sponges, playing cards or 1-inch squares are needed to completely cover the tabletop. Older children should find the area of irregular figures by dividing them into squares and triangles and finding the area of each one, then adding the areas together.

Fun with Mental Math

Doing mental math is a fun way for children to show off their skill with numbers and is also a way to build their math skills. Easy Mental Math Multiplication: All children know how to multiply by 10. Teach them that it's also easy to multiply by 5. All they have to do is multiply by 10 and then divide by 2. Then, to multiply a number by 25, they need to multiply by 100, which is adding 2 zeros to the end of the number being multiplied. Then to get the answer, they can either divide by 4 once or by 2 twice.

More Challenging Mental Math: Here's how to multiply a two-digit number by 11, say: 11 x 24. Add the digits of 24 together and you get 6. Place the 6 between the 2 and 4 to get the answer 264. If the digits of the number to be multiplied by 11 add up to more than 9, there is another step you must take, say: 11 x 75. Add the digits of 75 together and you get 12. Put the 2 between the numbers after adding the 1 to the first digit (7 + 1). The answer is 825.

"Secrets of Mental Math" is a great book for older children wanting to learn amazing math tricks such as finding out the day for any date, from their birthday to the Declaration of Independence.

Geometry and vertices

It's never too early for children to be introduced to geometry and learn some of the terms. Vertex is one. It is a point or corner where two or more lines meet. The plural of vertex is vertices. A triangle has three vertices. Draw several polygons, and have your children tell you how many vertices each one has.

Children of all ages can have fun with vertices. Give them some chalk and have them draw shapes without retracing any line and without lifting the chalk. How many shapes can they invent? Then have them see how many letters of the alphabet can be drawn in this way.

A topologist (expert in this area) can look at a shape like an open envelope and tell whether it can be drawn without retracing any line and without lifting chalk, pen or pencil. The secret lies in looking at the points where the lines meet and counting how many in a shape have an odd number of lines meeting there. Have your children figure out how they can tell by the number of odd vertices in a shape whether it can be traced without lifting the tracing tool or going back over a line. It is a surprisingly low number (0, 1, 2 odd vertices). Even vertices don't matter. They may have to draw several figures to determine this answer.

More estimation

In mathematics, getting the exact answer is important, especially at school. Learning how to estimate can save your children from making mistakes in their calculations even if they are using calculators. Then there are other times when an estimate is good enough for a situation. Encourage them to practice the following tricks to become better estimators.

Estimation helps young children when they are adding or subtracting larger numbers such as 321 plus 874 or 932 minus 467. The trick is to round these numbers up or down to the nearest hundred (300 plus 900) (900 minus 500). Older children who work with larger numbers in the thousands will get more exact answers if they round to the nearest hundred. Millions should be rounded to the nearest hundred thousand.

Let your older children estimate what the tip should be in restaurants. For a 10 percent tip, all they have to do is move the decimal point one place to the left. If it's a 20 percent tip, they can simply double the amount of the 10 percent tip.

Handling fractions

Fractions are not used as much as they used to be. However, this is one math topic that is best understood by children when they have a lot of opportunities to explore the relationships between different fractions. The easiest way to do this is to have them make fraction pieces. Make two charts 7 inches wide by 10 inches long. Divide each into 10 equal horizontal rows. The first row will go the whole way across and be labeled "1." The next row will be divided in half and each half will be labeled "1/2." Continue in this way to the last row. Glue the charts onto cardboard for durability and cut one into pieces.

Younger children can use the fraction pieces to make fraction trains for 1/3, 2/3, 2/4, 3/4 and so on. Then have them make trains that are the same length as the 1 piece. For each train, ask them how many fraction pieces they used to make the 1 piece. Make sure they observe that the number of fraction pieces used to make the 1 piece is the same number as the bottom number of each fraction piece. Point out that this bottom number is called the denominator.

Older children can use the fraction pieces to learn about equivalent fractions. These are different fractions that represent the same number. Start with the 1/2 fraction piece. Show your children that a train of two 1/4 fraction pieces is the same as the 1/2 fraction piece. Then ask your children to build other trains that are the same length as the 1/2 fraction piece and the 1/3, 1/4 and 1/5 fraction pieces.

Measuring all kinds of things

Young children need to learn what measurement means. Begin with having them measure length, as it is the easiest to understand. A fun way to do this is to have them use nonstandard units of measure. Ask questions like "How many steps is it across your bedroom or the living room?" Then have them pace the steps, counting as they go. When your children get older, they can find out how many steps it is around the yard, house or block. They also can make paper-clip chains to measure items less than 1 foot long, such as a sock, a magazine, a pencil or a carrot. They can count the number of paper clips used to measure each item and then compare their length. Longer lengths can be measured with blocks, shoelaces or spaghetti pieces.

Once your children are comfortable using nonstandard units of measure, you can give them rulers and yardsticks. Begin by having them use the ruler to draw 2-inch and 6-inch lines. Then have them find objects that are approximately these lengths. Next, have them measure items in feet and inches such as table mats, game boards and desks. The next step is to introduce the yardstick. Ask them to use the ruler to determine how many feet a yardstick measures. Teach them how to use the yardstick to measure lengths longer than 3 feet, such as the size of rooms and the chairs in your home.

Older children should work with cups, pints, quarts and gallons. Have them fill containers to understand the relationship of these measures to each other.

Using calculators

Calculators aren't just for solving math problems; they also can be used to increase children's knowledge of mathematics as well as to reinforce what they have learned. Preschoolers and first-graders can enter the number 1 and then add 1 repeatedly. Or they can punch in a number and add 0 to it. You may want them to describe the results of what they are doing orally. This activity can be extended by having older school children repeatedly add or subtract such numbers as 2, 5 and 10. This helps them see number patterns and learn to count by these numbers.

Once children have learned to add, subtract, multiply and divide, they can use this knowledge to build numbers on the calculator. Have them use 4's as the digit and then add, subtract, multiply and divide the 4's to make as many numbers as they can. They also can go to to play a challenging division game using their calculators. Middle-school and high-school students can measure the circumference and diameter of several objects and use the calculator to calculate their ratio. This will help them understand the concept of pi.

Mastering multiplication

Multiplication presents problems for many children who have a hard time committing the basic facts (1 x 1 through 9 x 9) to memory. It is a very important skill that they will need in order to handle more advanced math, especially algebra. The task of learning the multiplication facts is much easier if your children build upon facts they have previously learned.

Here are some ways to help your children master multiplication. Use a set of multiplication cards (1 x 1 through 6 x 6) with the answers on the back. Have your children choose a card at random and use plates and counters to see the problem. For 2 x 3, they would use two plates with three counters on each one. They also can illustrate problems by using arrays of blocks.

Math and the Common Core

With the adoption of Common Core Standards (grades K-8), children are now expected to enter the next grade knowing everything that they learned in math in the previous grades. Parents are definitely going to have to see that their children do some math every summer so they are ready to start the next grade when new math material will be presented. It will take some effort for parents to help their children keep their math skills sharp, but it is not a formidable task.

Parents should go online to the PTA's website at and search for "parent guides for school success." This will let them find out what their children should have learned in math last year. There are several ways to keep these important skills sharp, including classes at schools, college, learning centers and math camps, as well as hiring a tutor.

Do not think that math work is just for younger students, there are summer math camps at many colleges. They give high-school students the opportunity to not only enhance their mathematical skills but also to see what college life is like. Plus, working as a math tutor can be a good summer job for teens.

There is also the option of finding games and drills online. One that can be a lot of fun and expands on the topics taught in class is Calculation Nation It is a free source where children in upper elementary and middle school can have fun playing strategy games with others throughout the world as they practice important math skills and the theories behind them.


Statistics is one part of math that is emphasized in the Common Core math curriculum. Have your children sit in a spot where a number of people will walk by. You will want to stay with younger children. Depending on their ages, they can observe the shoes of 10, 50 or 100 people. They can make a simple chart headed with "Velcro Fasteners and Shoelaces." For each person who walks by, they can indicate with a mark how his or her shoes are fastened. They can skip the people wearing flip-flops and sandals. When they have finished their observations, they can use statistics to describe their findings. For example, a young child might say: nine out of 10 people had shoelaces. An older child could say: 20 percent of the people had Velcro fasteners.

Popsicles and Toothpicks and Shapes

Children like to consume popsicles. Save these sticks so young children can use them in the following activity. Older children can use toothpicks in the activity.

Children should begin by building shapes with either the popsicle sticks or toothpicks. They will start by making flat shapes and naming them. Younger children can build figures using from three to five sticks. Older students should go on to see if they can build shapes with as many as 12 sides and name them.>

Once children have built flat shapes, they should move on to building and naming solids. The sticks and toothpicks can be held together with marshmallows, gumdrops or clay. Younger children can construct pyramids and cubes, while older ones can try to construct such challenging forms as dodecagons, tetrahedrons and icosahedrons. No matter what they build, it is important that children name each figure and count the number of its sides.

Use 24 sticks or toothpicks to form a square with nine squares inside it. Study the figure carefully. It doesn't just have nine squares. Challenge your children to find all 14 squares within the square. Search online "square with nine squares inside it" if this is too challenging.


Symmetry is used a lot in math and means that one shape becomes exactly like another when it is turned, flipped or slid. One basic type of symmetry is mirror symmetry. Look in the mirror. If you were to draw a line down the center of your face (called the line of symmetry), the right side would be a mirror image of your left side.

Mirror symmetry is all over the place. You'll find it inside in rugs and carpets. You'll find it outside in butterflies and buildings. And you'll find it in certain letters of the alphabet. Challenge everyone in the family to find as many examples of mirror symmetry that they can in 15 minutes. Everyone will find more examples of mirror symmetry if they look for lines of symmetry in any direction.

To tie symmetry to math, draw a variety of geometric shapes. Then draw a line through each one. Some, like circles and squares, can have many lines of symmetry. Others may have none. They are called asymmetric.

Dealing with decimals

We deal with decimals every day. Gasoline is measured in decimal gallons. Prices are listed in decimal dollars. An understanding of decimals is essential to live and cope in our world. Ask your young children to select priced items from a newspaper or other advertisement that they would like to buy. Have your children count out the exact amount of money needed to buy the items using only pennies, dimes and paper money.

For older children, choose some multiplication problems using decimals such as 34.7 x 12.38. Have them use a calculator to find the product (429,586) ignoring the decimal points. Next have the children learn the rule for placing a decimal point in this way: They should round each factor to the nearest one and multiply (35 x 12 = 420). Suggest that the decimal should be placed in 429586 as close as possible to 420. After working several problems, they should know the rule for locating the decimal point.

Learning how to us the abacus

The abacus is a great tool that has been used for thousands of years to make math problems easier to solve. It can teach children to count, is a great way for them to get an understanding of place value and can even be used to help children see how addition, subtraction, multiplication and division work. Plus, it is actually fun for children to use. You will easily find instructions for making different types of abacuses online. Abacuses also can be purchased.

For young children, use an abacus with four or five rows with one bead above the middle bar and four below. At first, the children can simply be taught to count the beads. Then the beads can be divided to show a number -- say, 7. Push two beads (2) beneath the bar to the center, and the top bead (5) down to the center bar to represent 2 + 5 = 7. As the children get older, they can begin to work with the second row (tens column) to show numbers between 10 and 20.

The abacus is also a great way to let children see how place value works. For this, they will need a traditional abacus with two beads above the dividing bar and five below. Each bead above the bar represents five units, and each one below represents one unit. And starting on the right, the first column of beads is the units/ones column, followed to the left by tens, hundreds, thousands and so on. To show the number 68 on the abacus, the children should click one bead down to the bar and three up in the ones row and one down and one up in the tens row. Have your children show a variety of numbers on the beads such as 55, 349, 6,436, 47, 852 and so on.

YouTube has videos showing children how to add, subtract and multiply on an abacus. And they can even find games to play on an abacus.

Graphing Information

Children need to know how to manage information. One way mathematics helps children interpret information is through graphing.

You can introduce young children to graphing with a small package of M&M candies. Make or have them make a list of the different colors of the candy on a piece of paper followed by a row of 10 or more small circles. Have your child sort out the candy by color and place the candies in the circles adjacent to their color names. They have made what is called a "concrete graph." Ask: What color is used most? What color is used least? This experiment can also be done with dry bean soup mix or colored marshmallows.

For one week, have your older children check early each day the television and newspaper or online predictions of the day's high temperature. They should make a graph with temperature on one axis and the days on the other. Then they should record each prediction with a different colored dot on the chart. At 4:00 p.m. (highest temperature time in the summer), they should check the actual temperature on an outdoor thermometer and record it on the chart with yet another colored dot. At the end of the week, they should connect each set of colored dots to see which temperature prediction was the most accurate.

Every day probability

We deal with probability every day -- the chance of rain, the chance of winning a coin toss and many other events. Probability is actually a branch of math dealing with the likelihood of a given event's occurrence that is a number between 0 (impossibility) and 1 (certainty).

Learning about probability can be a lot of fun for your children. If they want to have fun beyond the activities below, all you or they need to do is go online and search for probability games.

You can always start your young children's investigation of probability by having them toss a coin and recording the results. After 10 or so tosses, they will see that the probability of getting a head each time is one of two tosses.

Continue by giving the young children a bag containing five red, three green and two blue marbles. If they make a random draw, ask them what the probability is of their getting a non-blue marble. Then have them make and record the outcome of several draws to determine the probability. In math terms, there are 10 draw possibilities with eight possibilities of getting a non-blue marble. This can be shown as 8/10 and reduced to 3/4. In other words, in three out of four draws, they are likely to get a non-blue marble.

Here is an intriguing probability activity for older children that may take them awhile to do. Although it seems unlikely for this to be true, in every group of 30 people there is a better than 2 to 1 chance that two people will have the same birthday. Have them poll people to find out when their birthdays are. They can stop when they find two people with the same birthday.

Challenge your children to determine if they should switch doors in the game show "Let's Make a Deal" if the first door opened is a gag gift instead of a car. They'll find the answer if they play a simulated game many times.

Understanding what average means

One math term young children need to understand is "average" -- called "the mean" by mathematicians. The everyday definition is typical or common. The mean can be defined as the central value of a set of numbers. It is obtained by adding up all the numbers and then dividing by the number of numbers.

Since young children do not have an understanding of division, they are not ready to figure averages. However, the following activity will let them actually see what an average is. They should cut adding machine tape or toilet paper as long as each of four people (friends, family) is tall and write the person's name on the strip. A duplicate should be made of each strip and all strips taped together. This strip should be folded in half and then folded again. This divides the long strips into fourths. Next, they should cut along the fold lines. The length of one of these cut pieces of paper represents the average height of the four people. Have the children compare the length of each person's strip to the average length to determine whether the person is taller or shorter or just the same height as the average.

A challenging activity for older children is to have them select five stocks of companies that are important to them. Each day for a week, they will find the closing (last) price of each stock and then the average closing price for all five stocks and record this price in a table. Then each day they compare that day's average with the previous day's average to see if the average is higher or lower or unchanged from the previous day. To expand the activity, they can see if the New York Stock Exchange average is higher or lower than the previous day.

Fun with topology

Here is a math topic that many of you may not have heard of. However, it is increasingly being introduced in middle school and high school. It is called topology and is the study of surfaces. It is often called "rubber sheet geometry" and deals with the ways that surfaces can be twisted, bent, pulled or otherwise deformed from one shape to another.

Young children can begin to understand topology by drawing a figure such as a person or animal on a slightly inflated balloon. Then they can pull on the balloon from two sides to distort their original drawing. While the image will be different, it will still be a person or an animal.

The classic topological example is making a coffee cup and a doughnut equivalent to each other. It may sound impossible, but it isn't. Just make a coffee cup out of clay. Then you can twist, bend and shape the clay to form the shape of a doughnut. The equivalence is that they both have one hole.

Here is a math problem relating to topology: Find a blank map that shows a region of the United States and print it out. Then color it so no two bordering states have the same color. You should be able to do it using only four colors. Give it a try!

Prime and composite numbers

Your children will identify prime and composite numbers. A prime number is a whole number greater than 1 that can only be divided by itself and 1. A composite number is a whole number that can be divided evenly by numbers other than 1 or itself.

What your children will do in this activity is cut squares of paper (as many as 12), or they can use playing or index cards. Have your children use the squares or cards to make rectangles with numbers such as 5, 6, 7, 8, 9 and so on. If they make rectangles with 5, they will discover that it is only possible to make one rectangle, showing that 5 is a prime number. If they make rectangles with 6 squares or cards, they will have several choices, showing that 6 is not a prime but a composite number.

Your children should make rectangles with a variety of numbers to determine if a number is prime or composite. They can also make a grid with six rows of five numbers and number the squares from 1 to 30 and color the prime numbers.

A mathematician by the name of Goldbach made a conjecture that every even number is the sum of two prime numbers. Have young children test it with small numbers and older ones with much larger numbers.

Mental math

Before children go back to school or anytime to get them in the groove with numbers, do mental math activities at the dinner table.

Your preschoolers need to be familiar with the numbers up to 10. Begin by giving them any number between 0 and 10 and having them give the next number. Some young children may be ready to extend this activity to 20.

Kindergarten and first-graders can count by 2s (both even and odd numbers) and then have you say a number between 0 and 10 for them to add 2 to it. This can also be done with 5s and 10s and adding 5 to the number.

There are many tricks to adding numbers together using mental math. Here's one way to handle two-digit addition. Take the problem 64 + 79. You will break the numbers apart starting on the left side with the 10s column so you have 60 + 70 which equals 130. Next, you add the 1s column (4 + 9) to get 13. The last step is to add 130 + 13 to get the answer 143.

Another approach to mentally adding two-digit numbers is to break apart only one number. For the same problem 64 + 79, start on the left side so you have (60 + 4). Next add 60 + 79 to get 139. The final step is to add 139 + 4 to get the answer 143.

Next, have your children use a set of flashcards with the facts 2 x 7 through 6 x 9. They should show each problem with an array of blocks. For 2 x 7, the array would have seven blocks across in two horizontal rows. Then the array should be broken into two arrays as close to the middle as possible. The children would then write the multiplication fact for each array and add the two together for the answer. This will help them see that the product of 2 x 7 is equal to the sum of the arrays 2 x 3 + 2 x 4 -- facts that they should know. The next step is for children to use blocks or arrays to show that the product is the same for 2 x 7 and 7 x 2. Finally, the children should master one of the tricks used to multiply 9's.

Once you are sure that your children understand multiplication, have them drill, as practice will pay dividends. Search online for "one-minute multiplication drills."