Illuminations: Combinations

# Combinations

This unit focuses on combinations, a subject related to the probability-and-statistics strand of mathematics. Students are encouraged to discover all the combinations for the given situation using problem-solving skills (including elimination and collection of organized data). This unit was adapted from "Ideas:  Combinations" by  Marcy Cook, which appeared in The Arithmetic Teacher, Vol. 36, No. 1 (September, 1988) pp. 31 - 36.

### Math Content

In Activity 1, "Shorts and Shirts," students:

• estimate the number of possibilities that can be made from a given number of factors,
• compute the number of possibilities, and
• generalize the number of possible combinations that can be made.

In Activity 2, "Ice-Cream Cones," students:

• predict the number of  two-color combinations that can be made from eight colors,
• determine the number of combinations that can be made, and
• generalize the number of possible combinations that can be made.

### Individual Lessons

Lesson 1 - Shorts and Shirts

Students are encouraged to discover all of the possible combinations for outfits consisting of shirts and shorts. Students apply problem-solving skills (including elimination and collection of organized data) to draw their conclusions.

Lesson 2 - Ice Cream Cones

Students are encouraged to discover all the combinations for ice cream cones. They use problem-solving skills (including elimination and collection of organized data) to draw their conclusions. Students also discuss whether or not order matters mathematically for the given problem.

### NCTM Resources

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