Binomials Lesson 3 Episode 4 (Teachers)

Repeating Your Reasoning

Emily and Mauricio apply what they learned in Episodes 1-3 (drawing a picture, finding the area of the new garden in different ways, and writing arithmetic equations) when the length of the original garden is increased by 2.5 feet.

Episode Supports

Students’ Conceptual Challenges

The instructor asks the pair where they see 10 of something in the drawing, which would correspond to the equation 2.5 × 4 = 10, and if they can think about it as groups of [7:20]. Mauricio circles four groups of 2.5 square units, each of which corresponds to a column of the array. This is different from past episodes, in which groups didn’t necessarily correspond to rows or columns of the array. Consider checking in with your students to see if they’ve made this transition to seeing the groups as rows or columns in the array.

Focus Questions

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 1:05] What is the area of Jamal’s new garden when the length is increased by 2.5 ft?
2. [Pause the video at 3:58] Why did Mauricio write 7.5 × 4? Where did the 7.5 come from?

Supporting Dialogue

[Pause the video at 5:27] Emily has written 4 × 5 + 2.5 × 4 = 30. Talk with a partner to identify where in the drawing you see each number. Discuss why multiplication is appropriate for 4 × 5 and 2.5 × 4, and why addition is appropriate for combining those two products.