Lesson 5Representing Subtraction
Learning Goal
Let’s subtract signed numbers.
Learning Targets
I can explain the relationship between addition and subtraction of rational numbers.
I can use a number line to subtract positive and negative numbers.
Lesson Terms
- deposit
- withdrawal
Warm Up: Equivalent Equations
Problem 1
Consider the equation
For each equation, write two more equations, using the same numbers, that express the same relationship in a different way.
Activity 1: Subtraction with Number Lines
Problem 1
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
.
Tyler writes. Do you agree with either of them? What is the unknown number? How do you know?
Problem 2
Here is one unfinished diagram that represents a sum.
Here is another unfinished diagram that represents a sum.
For the first image, what equation would Mai write if she used the same reasoning as before? What about the second image?
For the first image, what equation would Tyler write if he used the same reasoning as before? What about the second image?
Problem 3
Draw a number line diagram for
Activity 2: We Can Add Instead
Problem 1
Match each diagram to one of the expressions
Diagram 1
Diagram 2
Diagram 3
Diagram 4
Diagram 1
Diagram 2
Diagram 3
Diagram 4
Problem 2
Which expressions in the first question have the same value? What do you notice?
Problem 3
Complete each of these tables. What do you notice?
expression | value |
---|---|
expression | value |
---|---|
Are you ready for more?
Problem 1
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:
In this system,
and . How can you see that in the table? What do you think
should be? What about
? What do you think
should be? What about
? Can you think of any uses for this number system?
Lesson Summary
The equation
Notice that the value of
We can solve the equation
Likewise,
Notice that the value of
We can solve the equation
In general:
If