In this Cyberchase activity, students look at different arrangements of desks. They discuss the number of factor pairs and relate this to the commutative property of multiplication. Based on commutativity, they learn why they must try factors up to the square root of a number.
Part I: Learning Activity
1. Read the following to your students: "Harry gets a job as a substitute teacher. After entertaining his students by juggling, he motivates them to explore multiplicative factors by looking at all the possible arrangements of the 24 student desks."
2. Ask students how they could arrange 24 desks into rows of equal length and discuss their answers. Some students will answer that there are 4 ways while others will probably answer that there are 8 ways.
3. Play the Harry the Substitute Teacher Video . Ask students to keep track of the various desk arrangements in the video clip.
4. Discuss the number of ways that the students in the video clip arranged the desks.
5. Distribute Handout 1: Commutative Operations .
6. Ask the students to complete the handout
7. Discuss the students' answers to the handout.
Part II: Assessment
Assessment: Level A (proficiency): Students are asked to generate all possible sizes for a rectangular candy box, and they will determine factor pairs for a set of numbers.
Assessment: Level B (above proficiency): Students are asked to generate all factor triples for the lengths of the sides of a rectangular prism.