Reflection: Rigor Matching Equivalent Expressions - Section 2: Warm up


This seems like a really simple task, but the complexity lies in the fact that we are purposely uncovering the tricky part and not trying to hide it with tricks. I have never taught the reason why we don't change addition problems before.

Some questions that I found really helpful in surfacing the conflict were:

  • "How are the last two problems different from the rest?"
  • "Why are they harder to think about?"
  • "Will we ever have this problem with addition?" (no) "Why not?"

When thinking about these questions it is helpful to consider context or use symbols (plus and minus) to represent the expressions. 

What they notice is that the last two are asking us to remove something (positives or negatives/hot cubes or cold cubes) that isn't there. That is really difficult to represent visually or concretely without using the abstract idea of adding 'neutral pairs' of positives and negatives. 

The last question is really important in helping my students see that the difficulty only occurs with subtraction. When adding you don't ever have to worry about not having enough to remove. This is why we generally change only subtraction, to solve a simpler problem.

  Putting the tricky part center stage
  Rigor: Putting the tricky part center stage
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Matching Equivalent Expressions

Unit 4: Operations with Integers
Lesson 16 of 24

Objective: SWBAT solve subtraction problems by solving the easier equivalent addition problem instead.

Big Idea: Students will understand the equivalence as a tool for them to use.

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Math, Number Sense and Operations, Operations and Expressions, subtracting integers, white boards
  54 minutes
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