Lesson 3-2: Opposites

Lesson 3-2: Opposites

And the Opposite of the Opposite

Student Outcomes:

• Understand that all integers (except 0) has an opposite

• Recognize that 0 is it's own opposite

• It is not necessary to put a positive sign on positive numbers

• The opposite of a negative number is shown as a double negative, -(-3). In general, know that they opposite of a opposite is just the original number. -(-3)=3

• Locate and position opposite numbers on a number line

In real life, what are some things that are opposite?

What about in math? What are some things that are opposite?

Each nonzero integer, a, has an opposite, written -a. How do we know they are opposites?

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Fill in the Blank

What is the opposite of -124?

Multiple Choice

Which point represents the opposite of zero on the number line?

• A

• B

• C

• D

• E

Fill in the Blank

What is the opposite of 0.49?

Fill in the Blank

What is the opposite of -⁵/₈?

Multiple Select

Which of the following are the opposite of A? (check ALL that apply)

• -A

• -B

• C

• D

• E

Multiple Select

Since we just figured out that A and E are opposites, which of the following equations are true? (check ALL that apply)

• A = E

• A = -E

• -A = -E

• -A = E

Multiple Choice

If a negative sign also means opposite, how can we write the opposite of negative six as an equation?

• -(-6) = 6

• -(-6) = -6

Multiple Choice

Which equation shows the opposite of the opposite of 10?

• -(-(10)) = -10

• -(-(10)) = 10

Open Ended

How would you write the opposite of the opposite of negative 12?

Fill in the Blank

B = 3

What does -(-B) equal?

Fill in the Blank

x = -7

What does -x equal?

Fill in the Blank

y = 13

What does -(-(y)) equal

Fill in the Blank

z = -6

What does -(-(z)) equal

Open Ended

Write a real world scenario that shows the opposite of the opposite. Here is an example:

Before Thanksgiving, Mr. Matlock weighed 175 pounds. He gained 9 pounds over the holidays. His wife put him on a diet and he lost 9 pounds. During February break, he gained 9 pounds again eating Valentine's candy.

Summarize

• How are opposite numbers related?

• What is the opposite of an opposite always going to be?

• What can a negative sign represent?