Unit 7, Lesson 2
Points on the Number Line
Grade 6
2.1
Warm-up
Which of the following numbers could be represented by point ?
2.45
2.11
-2.5
2.2
Activity
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Here are five thermometers. The first four thermometers show temperatures in degrees Celsius . Write the temperatures in the blanks.
Five vertical thermometers, a through e. Thermometer a is shaded up to 1. Thermometer b is shaded up to 2. Thermometer c is shaded up to the halfway point between 3 and 4. Thermometer d is shaded to the halway point between negative 1 and 0. Thermometer has tick marks labeled negative 20, blank, blank, negative 5, blank, blank, ten, blank, blank, 25. - The last thermometer is missing some numbers. Write them in the boxes.
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Elena says that the thermometer shown here reads because the line is above . Jada says that it is . Do you agree with either of them? Explain your reasoning.
2.3
Activity
Your teacher will give you a sheet of tracing paper. Follow the steps to make your own number line.
- Use a straightedge or a ruler to draw a horizontal line. Mark the middle point of the line, and label it 0.
- To the right of 0, draw tick marks that are 1 centimeter apart. Label the tick marks 1, 2, 3, . . . , 10. This represents the positive side of your number line.
- Fold your paper so that a vertical crease goes through 0 and the two sides of the number line match up perfectly.
- Use the fold to help you trace the tick marks that you already drew onto the opposite side of the number line. Unfold and label the tick marks -1, -2, -3. . . -10. This represents the negative side of your number line.
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Use your number line to answer these questions:
- Which number is the same distance away from 0 as is the number 4?
- Which number is the same distance away from 0 as is the number -7?
- Two numbers that are the same distance from 0 on the number line are called opposites. Find another pair of opposites on the number line.
- Choose a positive number and a negative number that is each farther away from 0 than is the number 5.
- Choose a positive number and a negative number that is each farther away from 0 than is the number -2.
Pause here so your teacher can review your work.
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Here is a number line with some points labeled with letters. What are the locations of points , , and ? Be prepared to explain or show your reasoning.
Student Lesson Summary
Two numbers that are the same distance from 0 and on different sides of the number line are opposites. For example, points A and B are opposites because they are both 2.5 units away from 0 and on opposite sides of 0.
We can also say that the opposite of 8.3 is -8.3, and the opposite of is . The opposite of 0 is itself.
Here is another labeled number line with some rational numbers. A rational number is a number that can be written as a positive or negative fraction.
The number 4 is positive, and its location is 4 units to the right of 0 on the number line. The number 4 can be written as or or any other equivalent fraction.
The number is negative, and its location is units to the left of 0 on the number line. To locate on the number line, we can divide the distance between 0 and -1 into thirds and then count 2 thirds to the left of 0.
All fractions and their opposites are rational numbers.
Two numbers are opposites if they are the same distance from 0 on the number line, but on different sides. One is negative, and the other is positive.
A rational number is a number that can be written as a positive fraction, a negative fraction, or zero.
- 8 and -8 are rational numbers because they can be written as and .
- 0.75 and -0.75 are rational numbers because they can be written as and .