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IM: 7.5.5: Representing Subtraction (Lesson)

By Newsela Staff
Last updated 3 months ago
23 Questions
5.1: Equivalent Equations
Consider the equation 2 + 3 = 5. Here are some more equations, using the same numbers, that express the same relationship in a different way:

  • 3 + 2 = 5
  • 5 - 3 = 2
  • 5 - 2 = 3

For each equation, write two more equations, using the same numbers, that express the same relationship in a different way.

9 + (-1) = 8

-11 + x = 7

5.2: Subtraction with Number Lines
Here is an unfinished number line diagram that represents a sum of 8.

How long should the other arrow be?

For an equation that goes with this diagram, Mai writes 3 + ? = 8. Tyler writes 8 - 3 = ?. Do you agree with either of them?

What is the unknown number? How do you know?

Here is another unfinished diagram that represents sums.

What equation would Mai write if she used the same reasoning as before?

What equation would Tyler write if he used the same reasoning as before?

How long should the other arrow be?

What number would complete this equation? Be prepared to explain your reasoning.

Here is another unfinished diagram that represents sums.

What equation would Mai write if she used the same reasoning as before?

What equation would Tyler write if he used the same reasoning as before?

How long should the other arrow be?

What number would complete this equation? Be prepared to explain your reasoning.

Draw a number line diagram for (-8) - (-3) = ? What is the unknown number? How do you know?

5.3: We Can Add Instead

Match each diagram to one of these expressions:

Which expressions have the same value? What do you notice?
  • 3+7
  • 3-7
  • 3+(-7)
  • 3-(-7)

Complete each of these tables. What do you notice?

Are you ready for more?

It is possible to make a new number system using only the numbers 0, 1, 2, and 3. We will write the symbols for adding and subtracting in this system like this: 2 \bigoplus 1 - 3 and 2 \circleddash 1 = 1. The table shows some of the sums.


In this system, 1 \bigoplus 2 = 3 and 2 \bigoplus 3 = 1. How can you see that in the table?

What do you think 3 \bigoplus 1 should be?

What about 3 \bigoplus 3?

What do you think 3 \circleddash 1 should be?

What about 2 \circleddash 3?

Can you think of any uses for this number system?