Students are given bags, one at a time, with a certain number of linker cubes with the number marked on the bag. This student received bags with 8, 9, 10, 15 and 25 cubes. The student then creates all of the arrays (rectangles) possible with the linker cubes. For 15, this student made 5 rows of 3 and 15 rows of 1. The students draw their arrays on the grid paper. Students then write down all of the facts in the fact family. For 5 rows of 3, the student wrote:
5 x 3 = 15 because there are 5 rows with 3 in each
3 x 5 = 15 because there are 3 columns with 5 in each
15 ÷ 5 = 3 because there were 15 cubes split into 5 rows
15 ÷ 3 = 15 because there were 15 cubes split into 3 columns
Relating multiplication and division to arrays
encourages students to make connections between multiplication and division as inverse operations. This activity also prepares students for the study of factors in fourth grade. It also prepares students for the study of squared numbers (like 5 x 5 = 25).
The work below is from second grade classes introduced to multiplication/division fact families in the spring.
Indicators:
6.3.6.2 explain and apply the concept of inverse operation as it relates to multiplication and division.
6.3.4.1 develop, use, and explain strategies to multiply and divide multiplication and division fact families.
6.2.4.2 use concrete objects to model multiplication and division facts.
