## Reflection: Intervention and Extension Breaking Down Barriers - Section 3: Re-Teach

Although I am a big fan of the area model, I found the definition of multiplication and its relationship to addition to be more useful for my students. Initially, I thought a visual model would be the most powerful, but I don't think their understanding of area was strong enough. The most useful information to bridge knowledge gaps is that which students comprehend fully.

I was surprised that the idea of repeated equal grouping was the spark that turned on the light bulb!

One of my students exclaimed that the expressions used to look like a confusing jumble of alien writing, but now he just sees groups of things. When I asked him what he meant he referred to the expression 5(2x+3) + 2(x+5) and said he saw two groups instead of a whole bunch of symbols he didn't understand. "there are 5 groups of 2x+3 and two groups of x+5." When I asked what that meant to him he replied that he had to add 2x+3 five times and x+5 two times. Then he wrote the repeated groups out in a stacked form (it reminded me of an array). Even though he said he had to add, when he calculated the value of the five groups, he multiplied. He counted the 3s and multiplied 3x5 and then he skip counted the variable terms.

I would have been interested to see what connections he saw between what he did and an array. I aslo really wanted to know if he saw 2x as two groups of x, but I didn't want to push it. I didn't want to interfere with his connection between the idea of groups and grouping symbols.

Intervention and Extension: Relying on student strengths

# Breaking Down Barriers

Unit 3: Equivalent Expressions
Lesson 10 of 23

## Big Idea: Using the physical model should help students see that the multiplication is distributed to all terms inside the parentheses.

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Standards:
Subject(s):
Math, Expressions (Algebra), area model, distributive property with variables
59 minutes

### Erica Burnison

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