## Reflection: Grappling with Complexity Cooking with The Mathmaster Chef (Day 1 of 4) - Section 3: Powerpoint Exploration

In the past I have held off on teaching subtracting integers until my students had experienced addition first in an attempt to build up to the idea of adding the opposite. I have seen and used many "tricks" for helping students "remember rules" with limited success. I have since decided that these "shortcuts" are just attempts to hide the complexity, but instead it sends two dangerous messages about math:

• that math is too hard to understand
• that math doesn't have to make sense

Instead I decided to try to find a way to help students to understand the math, not just to be able to temporarily recall procedures. I think that if they understand the math my students can derive the shortcuts and explain the foundational math for why they work.

With this context of hot and cold cubes I decided to bring the idea of subtracting and it's equivalence to adding the opposite right up front. We learned all the different ways of changing the temperature at the same time and discussed the equivalence. The tough part is getting the kids to abandon their immediate jump to the numbers and to pause and think about the context. As long as they use the context they can begin to understand the relationships between positive and negative numbers and the effects the operation have on them.

The ideas that adding can make numbers smaller and that subtracting can make them bigger goes against everything they have learned about whole numbers. To have on top of that a situation in which a number itself can be associated with addition or subtraction makes it even more confusing. The need for comprehensible context is crucial, so the trick becomes how to get kids to use it.

Highlight the tough stuff
Grappling with Complexity: Highlight the tough stuff

# Cooking with The Mathmaster Chef (Day 1 of 4)

Unit 4: Operations with Integers
Lesson 1 of 24

## Big Idea: Students will begin to see that subtracting integers is equivalent to adding the opposite.

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Standards:
Subject(s):
Math, Integers, Number Sense and Operations, Operations and Expressions, negative number, temperature model, productive struggle, complexities
60 minutes

### Erica Burnison

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