Emily and Mauricio reflect on the meaning of multiplication when finding the area of a rectangular room. They show multiplication as “groups of” in their drawing.
Episode Supports
Students’ Conceptual Challenges
The area formula utilizes a groups of interpretation of multiplication. The dimensions of a rectangle can be interpreted as some number of groups (one dimension), each comprised of a number (equal to the other dimension) of square units. For example, a rectangle with a width of 8 ft and length of 10 ft can be partitioned into 8 groups, each of which is made up of 10 square feet. This is readily seen in a grid by imagining the groups as vertical strips taking up the entire length of the rectangle and having a width of 1 foot. In other words, the groups can be seen as the columns of the array. However, in the previous lesson, as well as in this video, Mauricio and Emily create differently shaped groups (for example, by circling an array that is 2 ft wide and 5 ft long, [3:21]). This might mean that the pair haven’t yet fully understood why multiplication is used to measure two-dimensional objects.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 3:24] How would you indicate more groups of 10 in this drawing? How do you think Emily and Mauricio will show more groups of 10?
[Pause the video at 4:55] How would you show 10 groups of eight in this drawing?
Supporting Dialogue
[Pause the video at 1:36] Talk with a partner and explain why multiplication works to find the area of the rectangle? What does 10 times 8 (or 8 times 10) mean in this context? Can you use a groups of interpretation of multiplication in your explanation?
