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IM: 7.5.5: Representing Subtraction (Lesson)

Last updated 9 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.
1

9 + (-1) = 8

1

-11 + x = 7

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

1

How long should the other arrow be?

1

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

1

What is the unknown number? How do you know?

Here is another unfinished diagram that represents sums.

1

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

1

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

1

How long should the other arrow be?

1

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

Here is another unfinished diagram that represents sums.

1

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

1

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

1

How long should the other arrow be?

1

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

1

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

5.3: We Can Add Instead
1

Match each diagram to one of these expressions:

Draggable itemCorresponding Item
3+7
3-7
3+(-7)
3-(-7)
1

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

1

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.


1

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

1

What do you think 3 \bigoplus 1 should be?

1

What about 3 \bigoplus 3?

1

What do you think 3 \circleddash 1 should be?

1

What about 2 \circleddash 3?

1

Can you think of any uses for this number system?