Students use their own hops and skips to develop a conceptual understanding of the role of variables in expressions and equations.

Materials:

• At least 3 students. Note: For suggestions to do this activity with large groups or classes, see Hopping, Bouncing, and Jumping for Variables Lesson Plans.
• Small white board for each student
• Dry erase markers
• Jump ropes
• Balls to bounce (such as tennis balls, racket balls, or basketballs)
• Stop watch or timer

Directions:

You and your group will be given three tasks: (1) hopping on one foot, (2) jumping rope, and (3) bouncing and catching a ball. For each task, you will be given 30 seconds (or one minute for an older group) to repeat the activity as many times as possible. Between when the timer begins and when it ends, you will need to silently count how many times you complete the activity. It is important that you are the only one in your group to know your own task count.

Note: These are just recommended activities. Feel free to use your imagination and substitute or add any activities that can be timed and counted. Some other ideas for activities are: jumping jacks, push ups, sit-ups, shooting free throws, running laps, "kicking" paper football field goals, etc.

When you are done, whisper to the teacher the number of times you performed the task. The teacher will hand you a white board with a special variable expression on it that describes your task count, and how it compares to your group members.

Note: The simplest way to generate these variable expressions is to represent the first student's task count as a letter. For each following group member, describe their task count as being some amount more or fewer than the first student's. For example:

Marry hopped 21 times	Board says m
Latonia hopped 25 times	Board says m+4
Brett hopped 18 times	Board says m-3

Once everyone has a board, show each other your variable expressions. Without sharing your task numbers, can you put the boards in order from least to greatest? How? Can you figure out what the variable represents? Remember: variables always represent a number. What number does your group's variable stand for? (Hint: use your secret task count.) Once you've figured out the variable, can you use it to find out your group member's secret task counts just by looking at their boards?

Repeat this with each activity. Note: The variable expressions should get gradually more complex as students display greater understanding. One way to do this is to make the variable a number of your choosing, rather than a particular student's task count. As a teacher, don't be afraid to take time to come up with variable expressions using multiple operations including multiplication, division, parentheses, fractions, exponents, square roots, absolute values, etc.

Extension Activity: For older students, consider writing expressions with two or more variables and having the students work together to solve them.

This work placed into the public domain by the Riverbend Community Math Center.