## Reflection: Staircase of Complexity What if There is No Common Factor? - Section 4: Close

Today's ticket out worked well to set the stage for future thinking about factoring completely. Eventually, I will give students a "rule" that they should always look for the greatest common factor first.  However, the concept is that when you are done factoring (however you start) all of your factors should be prime.  This ticket out allows students to see that even after they factored once, their factors were still not prime and so one part of the expression could be factored again.

See What if...Student Work 1: This student realized that the expression was not factored completely but did not say to factor using the greatest common factor.  For now, this is okay, if students realize that the resulting factors (2(2x-4)) still have a common factor.  They will eventually get to the correct factorization of 4(x-2).

See What if...Student Work 2: This student was able to determine the greatest common factor and also showed a good understanding of how to find the original expression.

Staircase of Complexity: Setting the Stage

# What if There is No Common Factor?

Unit 4: Polynomial Expressions
Lesson 12 of 18

## Big Idea: The factoring by grouping strategy is used to get students thinking about factoring an expression into two binomials.

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40 minutes

### James Bialasik

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