Reflection: Staircase of Complexity Patterns in Addition - Section 3: Exploration

 

Here is an example of how "digging deeper" in the warm up section can help students notice patterns more readily here. This student claimed that the sum of one positive and one negative integer would be zero. While this is one correct posibility it was neglecting the relationship between the two integers. However, when I used the same questioning that I had in the warm up he quickly began exploring other posibilities. In this case all I had to ask was Is there another posibility?

Other questions that might help:

  • "will that be true for all positive and negative values?"
  • "are there any positive numbers that wouldn't give you zero?"
  • "Is there a way to get a positive sum when adding a positive to a negative number?"
  • "Is it possible to get a negative sum?"
  • "What has to be true for the sum to be positive, negative, or zero?"
  • "How can you tell by looking at the addends which it will be?" 
  • "What determines whether the sum will be positive, negative, or zero?"

The more experiences my students had with these types of questions the less and less time it took to have the discussions. After a while I wasn't even the one asking! Students began asking each other. When several groups are conducting these conversations independently it speeds up the process, because they don't have to wait for me. 

  Staircase of Complexity: Digging deeper
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Patterns in Addition

Unit 4: Operations with Integers
Lesson 9 of 24

Objective: SWBAT manipulate an integer sum to make it positive, negative, or zero in order discover the pattern in the number relationships.

Big Idea: Students will create integer addition problems that will be negative, positive, or zero.

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Subject(s):
Math, Number Sense and Operations, Operations and Expressions, Integer Addition, puzzle, questioning, conceptual development
  54 minutes
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