 # The Opposite of a Number's Opposite

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Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades

### New York State Common Core Math Grade 6, Module 3, Lesson 5

Videos and solutions to help Grade 6 students know that the opposite of the opposite is the original number.

Lesson 5 Student Outcomes

• Students understand that, for instance, the opposite of is -5 denoted -(-5) and is equal to 5. In general, they know that the opposite of the opposite is the original number; e.g., -(-a) = a.
• Students locate and position opposite numbers on a number line.

Opening Exercises

1. Locate the number -2 and its opposite on the number line below.

2. Write an integer that represents each of the following:
a. 90 feet below sea level
b. \$100 of debt
c. 2 C above zero

3. Joe is at the ice cream shop and his house is 10 blocks north of the shop. The park is 10 blocks south of the ice cream shop. When he is at the ice cream shop, is Joe closer to the park or his house? How could the number zero be used in this situation? Explain.

Example 1: The Opposite of an Opposite of a Number

What is the opposite of the opposite of 8? How can we illustrate this number on a number line?
a. What number is 8 units to the right of 0?
b. How can you illustrate locating the opposite of on this number line? What is the opposite of 8?
c. Use the same process to locate the opposite of -8. What is the opposite of -8?
d. The opposite of an opposite of a number is __________

Exercise

Complete the table using the cards in your group.
1. Write the opposite of the opposite of -10 as an equation.

2. In general, the opposite of the opposite of a number is the ______

3. Provide a real-world example of this rule. Show your work.

Problem Set
1. Read each description carefully, and write an equation that represents the description.
a. The opposite of negative seven
b. The opposite of the opposite of twenty-five
c. The opposite of fifteen
d. The opposite of negative thirty-six

2. Jose graphed the opposite of the opposite of 3 on the number line. First, he graphed point P on the number line 3 units to the right of zero. Next, he graphed the opposite of P on the number line 3 units to the left of zero and labeled it K. Finally, he graphed the opposite of K and labeled it Q.

3. Is his diagram correct? Explain. If the diagram is not correct, explain his error, and correctly locate and label point Q. Write the relationship between the points:
a. P and K
b. K and Q
c. P and Q

a. A temperature rise of 15 degrees Fahrenheit
b. A gain of 55 yards
c. A loss of 10 pounds
d. A withdrawal of \$2,000

5. Write the integer that represents the statement. Locate and label each point on the number line below.
a. The opposite of a gain of 6
b. The opposite of a deposit of \$10
c. The opposite of the opposite of 0
d. The opposite of the opposite of 4
e. The opposite of the opposite of a loss of 5

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