 # Integers on the Number Line

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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 1, Lesson 2

Examples, solutions, videos and worksheets to help Grade 6 students learn about positive and negative numbers on the number line (opposite direction and value).

Lesson 1 Student Outcomes

• Students extend their understanding of the number line, which includes zero and numbers to the right, that are above zero, and numbers to the left, that are below zero.
• Students use positive integers to locate negative integers, moving in the opposite direction from zero.
• Students understand that the set of integers includes the set of positive whole numbers and their opposites, as well as zero. They also understand that zero is its own opposite.

What are Integers?

The set of whole numbers and their opposites, including zero, are called integers. Zero is its own opposite. The number line diagram shows integers listed in order from least to greatest using equal spaces.

Example 1: Negative Numbers on the Number Line

Starting at 0, as I move to the right on a horizontal number line, the values get larger. These numbers are called positive numbers because they are greater than zero.
Starting at 0, as I move further to the left of zero on a horizontal number line, the values get smaller. These numbers are called negative numbers because they are less than zero.

Opposites are the same distance from zero but on opposite sides. Zero is its own opposite.

Lesson 2 Student Outcomes

• Students use positive and negative numbers to indicate a change (gain or loss) in elevation with a fixed reference point, temperature, and the balance in a bank account.
• Students use vocabulary precisely when describing and representing situations involving integers; e.g., an elevation of -10 feet is the same as 10 feet below the fixed reference point.
• Students choose an appropriate scale for the number line when given a set of positive and negative numbers to graph.

Example 1: Take it to the Bank

For Tim’s 13th birthday, he received \$150 in cash from his mom. His dad took him to the bank to open a savings account. Tim gave the cash to the banker to deposit into the account. The banker credited Tim’s new account \$150 and gave Tim a receipt. One week later, Tim deposited another \$25 he had earned as allowance. The next month, Tim asked his dad for permission to withdraw \$35 to buy a new video game. Tim’s dad explained that the bank would charge \$5 for each withdrawal from the savings account and that each withdrawal and charge results in a debit to the account.

1. Number the events in the story problem. Write the number above each sentence to show the order of the events.

2. Write each individual description below as an integer. Model the integer on the number line using an appropriate scale.

Example 2: How Hot, How Cold?

Temperature is commonly measured using one of two scales, Celsius or Fahrenheit. In the United States the Fahrenheit system continues to be the accepted standard for non-scientific use. All other countries have adopted Celsius as the primary scale in use. The thermometer shows how both scales are related.
a. The boiling point of water is 100° C. Where is 100 degrees Celsius located on the thermometer to the right?
b. On a vertical number line, describe the position of the integer that represents 100 C.

Exercises 3–5

3. Write each word under the appropriate column, “Positive Number” or “Negative Number”.
Gain, Loss, Deposit, Credit, Debit, Charge, Below Zero, Withdraw, Owe, Receive

4. Write an integer to represent each of the following situations:
a. A company loses \$345,000 in 2011.
b. You earned for \$25 dog sitting
c. Jacob owes his dad \$5.
d. The temperature at the sun’s surface is about 5,600 ?
e. The temperature outside is 4 degrees below zero.
f. A football player lost 10 yards when he was tackled.

5. Describe a situation that can be modeled by the integer -15. Explain what zero represents in the situation. Lesson 1 Problem Set
1. Draw a number line, and create a scale for the number line in order to plot the points -2, 4, and 6.
a. Graph each point and its opposite on the number line.
b. Explain how you found the opposite of each point.

2. Carlos uses a vertical number line to graph the points -4, -2, 3, and 4. He notices that -4 is closer to zero than -2. He is not sure about his diagram. Use what you know about a vertical number line to determine if Carlos made a mistake or not. Support your explanation with a number line diagram.

3. Create a scale in order to graph the numbers -12 through 12 on a number line. What does each tick mark represent?

4. Choose an integer between -5 and -10. Label it R on the number line created in Problem 3, and complete the following tasks.
a. What is the opposite of R? Label it Q.
b. State a positive integer greater than Q. Label it T.
c. State a negative integer greater than R. Label it S.
d. State a negative integer less than R. Label it U.
e. State an integer between R and Q. Label it V.

5. Will the opposite of a positive number always, sometimes, or never be a positive number? Explain your reasoning.

6. Will the opposite of zero always, sometimes, or never be zero? Explain your reasoning.

7. Will the opposite of a number always, sometimes, or never be greater than the number itself? Explain your reasoning. Provide an example to support your reasoning. Lesson 2 Problem Set
1. Express each situation as an integer in the space provided.
a. A gain of 56 points in a game
b. A fee charged of \$2
c. A temperature of 32 degrees below zero
d. A 56-yard loss in a football game
e. The freezing point of water in degrees Celsius
f. A \$12,500 deposit

For Problems 2–5, use the thermometer to the right.
2. Each sentence is stated incorrectly. Rewrite the sentence to correctly describe each situation.
a. The temperature is -10 degrees Fahrenheit below zero.
b. The temperature is -22 degrees Celsius below zero.

3. Mark the integer on the thermometer that corresponds to the temperature given.
a. 70°F
b. 12°C
c. 110°F
d. -4°C

4. The boiling point of water is 212°F. Can this thermometer be used to record the temperature of a boiling pot of water? Explain.

5. Kaylon shaded the thermometer to represent a temperature of 20 degrees below zero Celsius as shown in the diagram. Is she correct? Why or why not? If necessary, describe how you would fix Kaylon’s shading.

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