Exponents use a power to tell how many times a number is multiplied by itself. If the number is six to the third power, for example, you multiply the number six three times -- 6 x 6 x 6 -- to get 216. Exponents are essential mathematical concepts that are the foundation for further study into scientific notation and other algebraic functions.

To introduce exponents to middle-schoolers, use activities that help them visualize the exponents. For the multiplication property, place an index card inscribed with the number seven on a table along with five jellybeans to represent the exponent. Place another card beside the first with the number seven and three jellybeans. Tell students that when the same number is multiplied, the exponents are added together. Count the number of jellybeans to yield seven to the eighth power. To show division, place a ruler on the desk to represent a division line. Place the index cards and jellybeans above and below the ruler with the five jellybeans on top and three on the bottom. Tell students that when the same numbers are on top of each other, the exponents are subtracted. Students will take away two jellybeans to yield seven to the second power. For a power to a power demonstration, use an index card with seven written on it, then represent an inner exponent with a group of five red candies and an outer exponent with a group of three green candies. Tell students to multiply the exponents to equal seven to the 15th power.

Take sixth- or seventh-graders on a scavenger hunt around the classroom to find a secret code using exponents. On an index card, write (3x to the third power) x (5y to the third power) / (3x to the second power) and post it on the wall. The second index card posted in another area of the room will have the answer to the first problem, 5x times y to the third power, the first letter of the secret code word in the corner of the card and the next problem on the back of the card. This answer to the second card leads to the third card, and so on, until the secret code word is discovered. Along with these correct cards, post decoy cards with commonly mistaken answers.

For grades five or six, place a “price” tag on objects around the room with sticky notes. These prices will be the answers to exponent questions marked on index cards. For example, a classroom poster may cost $128. This would cost the student an index card that has two to the fifth power times two to the second power written on it. Divide students into groups and give them a set of these index cards. The exponent question cards serve as the “money” students use to buy items. Have students walk around and make a list of things their group would be able to buy.

In upper middle school classes of algebra, have students make their own computer game using Microsoft PowerPoint software to create a game similar to a “Jeopardy” format. Create a game board by inserting a table into a slide with categories such as multiplying exponents, dividing exponents, and exponents with integers. Underneath each category, type point values 100, 200, 300 and 400 into the table. Create practice problems on separate slides, such as, “Simplify the expression: (7s to the second power) x (8s to the fourth power) x (2s to the sixth power).” Hyperlink the problem slides to a point value so that when the point value is clicked, the question will appear on the screen. Students will also create an answer key to go along with their game.