Materials: bags of toothpicks for each pair of students
watch with second hand
paper and pencil
Grouping: Put students into pairs at random
Give each group a bag of toothpicks and have one of the students draw 4 columns on a piece of paper. The first column will have the heading NAME, the second NUMBER OF TOOTHPICKS, followed by, POINTS FOR EACH TOOTHPICK, and TOTAL POINTS. Under the first column put the first player's name followed by the second player's name. Have one student be the counter and timer, while the other picks up as many toothpicks as he or she can in 5 seconds. The pairs then record the data in the appropriate places in the chart. Pairs then switch roles and repeat the process.
This is the time to tell students that they are to assume that they are awarded 5 points for each toothpick they picked up. Discuss the fact that there is a value that varies for each turn (the number of toothpicks) and a value that remains the same (the number of points for each toothpick). The students then complete the chart for both of their turns. Discuss the differences between constants and variables.
Now discuss how the number of toothpicks collected each time varies form 1 turn to the next, and there needs to be a way to represent the value for everyone. So maybe "t" could be used for the number of toothpicks. Ask the students how they figured out how many points they earned. They should be able to tell you theat they multiplied the number of toothpicks by 5. Hence, you could write 5 x t, as your expression to show the number of points scored for "t" (any number of) toothpicks. At this point make sure students complete the rest of their chart.
Now have the students solve other problems such as; what if they earned 10 cents for each toothpick.