Reflection: Developing a Conceptual Understanding The Three Little Bears - Section 2: Warm Up


I have purposely chosen larger numbers than the students are used to because I want them to reason about the operations and generalize about patterns rather than jump immediately to calculations. I have found that when they jump to calculations too soon they never engage in any reasoning and don't notice when their result makes no sense. It is important to constantly ask them "why does that make sense?" and encourage them to refer back to the context of what is happening with the hot and cold cubes. 

I have changed my mind on the best way to support them when they are stuck. When deciding how to scaffold the math I was afraid that I might end up doing their thinking for them. I have found that focusing on helping them make sense of the context allows them to figure out how that relates to the math. For example:

If Mama Bear likes her cocoa frozen what are some of the ways you could make that using hot and cold cubes?

  • What temperature would each bear like?
  • Do you think we would add cubes or subtract cubes to get that temperature? Explain.
  • What would that look like mathematically?
  • What might that look like on a number line? (rather than setting it up for them)
  • Where is that (taking away cold cubes) represented in the expression?

 Students are confronting misconceptions here like "subtraction always makes the numbers smaller" and this can take some extra time as well as explicit attention to the misconception. I would raise the questions "When might subtracting make a number bigger?", "when would negative 50 make a number bigger?", etc. 

  Promoting reasoning over rushing to calculations
  Developing a Conceptual Understanding: Promoting reasoning over rushing to calculations
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The Three Little Bears

Unit 4: Operations with Integers
Lesson 7 of 24

Objective: SWBAT recognize and explain patterns in integer addition and subtraction to help determine whether the outcome is positive, negative, or zero.

Big Idea: Students begin to make sense of how adding and subtracting with negative numbers relates to prior experience and knowledge of adding and subtracting with positive numbers.

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Math, Number Sense and Operations, Operations and Expressions, integer addition and subtraction, negative number, sorting, reasoning, questioning
  54 minutes
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