## Reflection: Developing a Conceptual Understanding Common Factor the Great! - Section 1: Warm up

Finding the greatest common factor (GCF) of two numbers is a process of identifying how the numbers are related to each other. This is a different way of thinking for my students. They are not often more comfortable reasoning by rote, than looking for patterns relating math facts.

I find that many of my students have learned their multiplication facts by rote memorization alone. In my view they have missed out on the opportunity to develop good mathematical practices. For instance, rote memorization may involve perseverance, but it does not encourage reasoning concretely and abstractly or developing an understanding of the structure of a number.

My students often measure their proficiency with math facts in terms of the speed of their recall. In order to slow them down to engage their reasoning I ask them to compare two numbers (18 & 12) in a Venn Diagram and include every way the two numbers differed or were the same. When they take the time to consider these numbers they come up with facts like:

• factors of 1, 2, 3, 6
• even numbers
• both have a 1 in them

These are all interesting observations and they can be discussed meaningfully.

• We can discuss the meaning of the GCF in terms of all of the factors
• We can consider the importance of the designation even and odd in terms of factors
• We can discuss place value and the idea that they both numbers have a 10, not a one, which is also a helpful idea with respect to flexible multiplicative reasoning

When students learn their math facts through number sense routines that teach them how to decompose and recompose the numbers flexibly, they learn to look for and use the relationships between the numbers to solve problems.

Developing a Conceptual Understanding: Thinking about Factoring

# Common Factor the Great!

Unit 3: Equivalent Expressions
Lesson 16 of 23

## Big Idea: Students will relate factoring a variable expression to a real world situation.

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Standards:
Subject(s):
Math, factoring polynomial expressions, Expressions (Algebra), area model, white boards, real world
54 minutes

### Erica Burnison

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