Integer Operations

Topic: Number Sense: Integer Operations

Source: Multiple

Materials: Colored Counters (optional)

Objective(s): Develop models for addition, subtraction, multiplication of integers.

AZ Math Standards Performance Objectives (samples):

Strand 1: Number Sense and Operation

Concept 1: Numerical Operations

  • Grade 7PO1: Add integers.
  • Grade 7PO2: Subtract integers.
  • Grade 7PO5: Multiply integers.
  • Grade 3 PO12: Identify multiplication and division as inverse operations.

Directions:

Mailtime Situations: In this model, each integer operation can be translated into a “mailtime situation”. The mail carrier either brings or takes away checks or bills. A check represents a positive integer. A bill represents a negative integer. Bringing mail represents addition. Taking mail away represents subtraction.

Example Addition: The mail carrier brings a bill for $10 and a check for $15. Are you richer or poorer? By how much?

Thinking: -10 + 15 = 5

You are $5 richer.

Example Subtraction: The mail carrier brings a bill for $4 and takes away a check for $3. Are you richer or poorer? By how much?

Thinking: -4 – 3 = -7

You are $7 poorer.

Number-Line Model: In this model, a positive integer is represented by an arrow that points to the right. A negative integer is represented by an arrow that points to the left. For addition, arrows are “head-to-tail” and the sum is found at the point of the final arrow.

Example Addition: -4 + 6 = _____

For subtraction, arrows are “head-to-head” and the difference is found at the tail of the final arrow.

Example Subtraction: 3 – (-2) = _____

For multiplication, we use the repeated addition approach.

Example Multiplication: _____

The number-line shows 2 negative threes.

Adaptations – How could you adapt this activity for your grade level next year?

Assessment – How could you assess this activity?

Prior Knowledge – What type of knowledge should students have prior to completing this activity?

What Comes Next? – What would come next in an instructional sequence centered around this activity and/or related topics?

Integer Operations1

Integer Operations

Give a mailtime situation and a number-line model for each of the following integer operations.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

13. Suppose that the following number-line is used to model the addition 2 + 3. Do you think this representation is reasonable? Explain in detail.

14. Suppose that the following number-line is used to model the subtraction 3 – (-2). Do you think this representation is reasonable? Explain in detail.

Integer Operations1