Reflection: Developing a Conceptual Understanding Secret Numbers - Section 2: Warm Up


I felt like the last part of this section was too teacher directed and wondered if there was a way to make it more student centered. I wanted students to come up with the idea of decomposing or splitting the -5 into -3+(-2) when faced with the problem 3 + (-5) in order to use the identity property and recognize the zero pair (3+ -3) + -2. This was actually relatively simple after doing Number Talks more regularly the next year.

Number Talks is a mental math routine that capitalizes on multiple strategies using place value, properties, and relationships between numbers and operations. After doing number talks my students became used to decomposing and recomposing numbers in different ways to make the problem simpler. 

Instead of telling students that the -3 was "hiding" in the -5 I asked them what -6 + 6 + 20 might look like with two addends. They came up with

  • 0 + 20
  • -6 + 26

Referring to the first expression I asked where the zero came from. Referring to the second expression I asked them where we find the zero in this problem.

Then I asked them how we might write 3 + (-5) with three addends that would contain a zero pair.

In another class I didn't even have to do that. I just asked "who sees a zero in 3 + (-5)?"

In yet another class I simply did a number talk with this problem and elicited multiple strategies from the students.

  Developing a Conceptual Understanding: Getting students to do more of the thinking
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Secret Numbers

Unit 4: Operations with Integers
Lesson 8 of 24

Objective: SWBAT solve integer addition puzzles by using patterns that determine whether the sum is positive, negative, or zero.

Big Idea: Students will develop greater negative number sense as they solve and create addition puzzles.

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Math, Patterns (Algebra), Number Sense and Operations, Operations and Expressions, Integer Addition, puzzle, student autonomy, cognitive demand
  54 minutes
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