## Reflection: Developing a Conceptual Understanding How Does It Grow? - Section 2: Whole Class Discussion

Having students reflect on why and how really helps them make sense of and understand the properties. Without this dual reflection, my students often notice the wrong things. They end up failing to conceptualize the math.

It is my experience that traditional textbook questions that ask students to identify the property in (7+4) + 6 = 7 + (4 + 6) are more likely to promote the misconception that the associative property is the one in which parentheses move and will often be mistaken for the distributive property. The idea of flexible regrouping is lost on students, and they never see the value in the property. Yet, this is important for fluency with mental mathematics.

In this lesson I listen for and invite multiple explanations and demonstrations of the same idea because it takes a while for my students to formulate, connect, and solidify ideas. In this case, I am asking my students to think about several different ideas. Making connections takes time, but it helps my students understand more completely.

Today, a student made a comment that initiated an unexpected, but necessary discussion with the class. While I was solving 66 + 7, by breaking down the 7 further (66+4+3) another student said it was easier for him to add 60 and 7 and then break the 6 into two threes (60+7+6=60+7+3+3). This inspired several other students to suggest other orders for the four addends (20+40+6+7, etc.) which in turn led a skeptical student asking if those expressions were really all equal. I turned the question back to the class and asked them to find some way to decide and to prove their conclusion. The most convincing were the ones that used an open number line.

Concept development
Developing a Conceptual Understanding: Concept development

# How Does It Grow?

Unit 2: Writing expressions
Lesson 7 of 7

## Big Idea: Students will verbally generalize the properties of addition as well as write a variable expression to describe a growth pattern.

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Standards:
Subject(s):
Properties (Number Sense), Math, Expressions (Algebra), growth patterns, variable expressions
54 minutes

### Erica Burnison

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