6.N.2.2 Illustrate addition and subtraction of integers using a variety of representations.
In a Nutshell
Manipulatives such as twocolor counters and number lines can be used to illustrate addition and subtraction of integers. The counters provide a physical and kinesthetic model where one side (color) of the counter represents positive integers and the opposite side represents negative integers. When modeling addition and subtraction of integers using counters, the magnitude and sign of the final result is determined by the number and color of remaining counters after performing the needed operation. Vertical and horizontal number lines provide another model in which students can visually see the addition and subtraction of integers.
Student Actions

Teacher Actions



Use and connect mathematical representations used to model integer addition and subtraction including twocolor counters and number lines.

Pose purposeful questions about the twocolor counter model used to illustrate integer addition and subtraction to assess students’ understanding of the topic such as “How do we represent subtracting a negative integer from a negative integer with counters, and how is this different from modeling the subtraction of a negative number from a positive number using counters?”
 Pose purposeful questions about the number line model used to illustrate integer addition and subtraction to assess students’ understanding of the topic, such as “What do you notice while subtracting negative integers using a number line?”

Key Understandings

Misconceptions


Understand that the magnitude and sign of the sum or difference of integers is determined by the number of counters and color of counters, respectively, when using the twocolor counter model.

Understand how to use zero pairs when modeling integer addition or subtraction using the twocolor counter model.

Understand that the direction you move on the number line model of integer addition and subtraction is determined by the operation and sign of the addend or subtrahend.


Think that the final result of an integer addition or subtraction problem modeled using counters is only determined by counting the number of counters disregarding the color of the counters.

Forget to use zero pairs (one color counter combined with the opposite color represents zero) in the counter model of integer addition and subtraction to determine the final result.

Think that subtracting a negative integer means that you move left (down) from the starting point on the horizontal (vertical) number line instead of moving right (up).

OKMath Framework Introduction
6th Grade Introduction
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