SO WHY IS 243x5 FOUR HUNDRED EIGHTY MORE THAN 245x3? GUIDED EXPLORATION

GR 5-9: UNDERSTANDING HOW PLACE VALUE AFFECTS MULTIPLICATION

OVERVIEW

The problem in the title is certainly NOT where we would start when introducing these ideas. Most middle school math educators would start with a simpler problem and use scaffolding to generalize to a 3-digit multiplier.

Students will begin with an example like 17 × 6 vs. 16 × 7, which differ by 10. This helps focus on interchanging the units digits that differ by 1 while keeping tens digit unchanged. If the tens digit is 1, the difference is seen to be 10 × 1. Then move on to a tens digit of 2, like 25 × 4 vs. 24 × 5, which differ by 10 × 2 = 20. Move on to more complicated examples which allow difference of units digits to be greater than 1 and a tens digit greater than 1. E.g., 35 × 7 = 245 vs. 37 × 5 = 185. The units digits now differ by 2, and 30 × 2 = 60, which is the difference of 245 and 185. Expect students to guess where the 30 came from!