Negative Numbers 11-6-2023

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

Draw

Complete the Warm Up

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

LEARNING GOALS

• Use positive and negative numbers to describe quantities having opposite directions.

• Explain the meaning of 0 in contexts represented by positive and negative numbers.

• Identify and represent a number and its opposite on a number line.

• Represent, interpret, and order positive and negative integers and other rational numbers
using number lines and inequality statements.

KEY TERMS

• negative numbers
• infinity

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

Let’s use a number line to represent time.

Your teacher will assign students to participate in the activity.Be sure to
record what happens on the number line.

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

1.

For each student, plot and label the point where the student stands on
the number line. Also identify what time is represented by the point.

Student A: Stand at 0 to represent the time right now.
Student B: Stand at the point that represents 3 hours from now.
Student C: Stand at the point that represents 3 hours ago.
Student D: Stand at the point that represents 5 hours from now.
Student E: Stand at the point that represents 2 hours ago.
Student F: Stand at the point that represents 7 hours ago.

Labelling

For each student, plot and label the point where the student stands on the number line. Also identify what time is represented by the point.

Student A: Stand at 0 to represent the time right now.
Student B: Stand at the point that represents 3 hours from now.
Student C: Stand at the point that represents 3 hours ago.
Student D: Stand at the point that represents 5 hours from now.
Student E: Stand at the point that represents 2 hours ago.
Student F: Stand at the point that represents 7 hours ago.

Drag labels to their correct position on the image

F

E

D

C

A

B

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

A number line can be created by reflecting the positive numbers
across zero. The values to the left of zero on the number line are
called negative numbers and are labeled with a negative sign. The
positive values extend to positive infinity, and the negative numbers extend to negative infinity. Infinity, represented by the symbol ∞, means a quantity with no end or bound. The number line goes on forever in both directions!

Open Ended

2. 2. Describe the change in the values of the numbers as you move to the right on the number line.

3. The values change when going to the right of the number line ......

Open Ended

2. 3. Describe the change in the values of the numbers as you move to the left on the number line.

3. The values change when going to the left of the number line ......

Open Ended

4. 4.Describe the locations of the points that represent time in the future.

5. The points in the future represent.....

Open Ended

4. 5. Describe the locations of the points that represent time in the past.

5. The points in the future represent.....

Open Ended

4. 6. How would your number line be labeled differently from one created by a class that starts at a different time?

5. My number line would be different from another class because....

Open Ended

4. 7. What observations can you make about where a given number of hours before or after time 0 is plotted? The observation I made about the hours before 0 is..... and after 0 is.....

5. What do you notice about its distance from 0?

6. For example, what do you notice about 3 hours before and 3 hours after now? I noticed .......

7. Or 6 hours before and 6 hours after now? I noticed ....

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

Let’s think more about both sides of 0 on a number line.

Labelling

2. In the table, identify the value represented by the

3. location where the student is standing.
   
   Student A: Stand at 0.
   Student B: Stand at 4.5.
   Student C: Stand at the opposite of 4.5.
   Student D: Stand at –6.
   Student E: Stand at the opposite of –6.
   Student F: Stand at a location between 2 and 3.
   Student G: Stand at the location that is the opposite of Student F.

Drag labels to their correct position on the image

0

4.5

6

Draw

Plot and label the location where each student stands on the number line.

Student A: Stand at 0.
Student B: Stand at 4.5.
Student C: Stand at the opposite of 4.5.
Student D: Stand at –6.
Student E: Stand at the opposite of –6.
Student F: Stand at a location between 2 and 3.
Student G: Stand at the location that is the opposite of Student F.

Open Ended

3. 3. Describe the number line relationship of the students who were opposites of each other.

4. The relationship of the students who were opposite of each other on the number line ....

Lesson 1: Human Number Line

© Carnegie Learning, Inc.

Opposite numbers are reflections of each other across 0 on the number line.

• The opposite of a positive number is a corresponding negative number.

• The opposite of a negative number is a corresponding positive number.

Attaching a negative sign to a number means reflecting that number across 0 on the number line.

Open Ended

What is the opposite of 0?

The opposite of 0 is .....

Open Ended

What do you notice about the distance from 0 of corresponding opposite numbers?

I notice that the corresponding opposite numbers distance from 0 .....

Math Response

Use symbols to represent the opposite of 4.5 and the value it represents.

$$-\left(4.5\right)=$$

Type answer here

Correct Answer: -4.5

Deg^°

Rad

Math Response

Use symbols to represent the opposite of -6 and the value it represents.

$$-\left(-6\right)$$

Type answer here

Correct Answer: 6

Deg^°

Rad

Draw

Name the opposite of each number. Then, plot each number and its opposite on the number line.

Don't forget to label the number line!

Open Ended

c. Badwater Basin in Death Valley, California, is 86 meters below sea level.

This means that the Badwater Basin

Open Ended

Number lines can also be vertical, like a thermometer or a measure of elevation

Discuss and write a sentence to describe the meaning of each statement.

a. The weather forecaster predicts the temperature will be below zero.

This means that the weather will be...

Open Ended

b. A submarine travels at 3000 feet below sea level.

This means that the submarine travels...

Labelling

2. Mark each temperature on the thermometer shown.

a. The highest temperature on record in the United States is 134ºF. It occurred in 1913 in Death Valley, California.

b. The lowest temperature on record is -80ºF. It occurred at Prospect Creek Camp, Alaska.

c. The lowest temperature recorded in the contiguous 48 states is -70ºF. It occurred in Montana.

d. The highest winter average temperature in the United States is 78ºF, which occurs in Honolulu, Hawaii.

Drag labels to their correct position on the image

a

c

d

b

Open Ended

Montana= -70ºF.

Alaska= -80ºF.

Which is colder, the lowest temperature recorded in Alaska or the lowest temperature recorded in Montana? How do you know?

Poll

4. Yadi and Eric were comparing 25 degrees to -27 degrees.

• Yadi wrote 25 < -27 and justified her comparison by stating that the further a number is from zero, the greater the number.

• Eric wrote 25 > -27 and justified his comparison by stating that the greater temperature will be above the second temperature on a thermometer. Who is correct? Explain your choice.

• Yadi

• Eric

Dropdown

5. Plot each set of temperatures on the thermometer. Then insert a > or < symbol to make each number sentence true.​

a. -26ºF​ ​

Select answer

​ -31ºF

b. -6ºF​ ​

Select answer

-17ºF

c. -9ºF​

Select answer

8ºF ​ ​ ​

Reorder

Order the temperatures from least to greatest.

• -40°F

• -33°F
• 0°F
• 25°F

• 150°F

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Draw

Helen and Grace started a company called Top Notch. They check the company’s bank balance at the end of each week. The table shown represents the first 10 weeks of operation. Overdrafts, or weeks when they owe the bank money, are represented by amounts within parentheses. For example, ($25) denotes an overdraft of $25; they owe the bank $25. Amounts that are not in parentheses are when they made money.

Draw

a. Write each as a positive or negative number and then plot the number on the number line.

Open Ended

1. Use the table and number line to answer each question.

b. What does 0 represent in this situation?

In this situation 0 represents...

Dropdown

2. For each pair of weeks, write an inequality statement to

compare the positive and negative numbers.

a. Week 1 ​

Select answer

Week 5

b. Week 4 ​

Select answer

​ Week 6

Draw

You can compare different types of numbers by plotting the numbers on a number line.

3. Use the number line to answer each question.

a. Plot each value on the number line.

$$-7.98$$ $$-6\ \frac{2}{3}$$ $$12$$ $$-3$$ $$10.5$$ $$-13$$ $$-20$$ $$0$$ $$-17\ \frac{1}{2}$$

Open Ended

b. Which of the numbers has the least value? How do you know?

$$-7.98$$ $$-6\ \frac{2}{3}$$ $$12$$ $$-3$$ $$10.5$$ $$-13$$ $$-20$$ $$0$$ $$-17\ \frac{1}{2}$$

I know that ____ has the least value because...

Open Ended

c. Which of the numbers has the greatest value? How do you know?

$$-7.98$$ $$-6\ \frac{2}{3}$$ $$12$$ $$-3$$ $$10.5$$ $$-13$$ $$-20$$ $$0$$ $$-17\ \frac{1}{2}$$

I know that ____ has the least value because...

Open Ended

d. Order the numbers from least to greatest.

$$-7.98$$ $$-6\ \frac{2}{3}$$ $$12$$ $$-3$$ $$10.5$$ $$-13$$ $$-20$$ $$0$$ $$-17\ \frac{1}{2}$$