IM 6.7.2 Lesson: Points on the Number Line
Which of the following numbers could be [math]B[/math]?[br][br][img]data:image/png;base64,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[/img]
Here are five thermometers. The first four thermometers show temperatures in Celsius. Write the temperatures in the blanks. The last thermometer is missing some numbers. Write them in the boxes.
Elena says that the thermometer shown here reads [math]-2.5°C[/math] because the line of the liquid is above [math]-2°C[/math]. Jada says that it is [math]-1.5°C[/math]. Do you agree with either one of them? Explain your reasoning.[br][br][img]data:image/png;base64,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[/img]
One morning, the temperature in Phoenix, Arizona, was [math]8°C[/math] and the temperature in Portland, Maine, was [math]12°C[/math] cooler. What was the temperature in Portland?
Use the applet below to draw a number line.
[list=1][*]Follow the steps to make your own number line.[br][list][*]Use the Line tool [icon]/images/ggb/toolbar/mode_join.png[/icon] to draw a horizontal line. Mark the middle point of the line with the Point tool [icon]/images/ggb/toolbar/mode_point.png[/icon] and label it 0.[/*][*]To the right of 0, continue using the Point tool to make marks that are 1 centimeter apart. Label the tick marks 1, 2, 3. . . 10. This represents the positive side of your number line.[/*][*]Use the Reflect Tool [icon]/images/ggb/toolbar/mode_mirroratpoint.png[/icon] to mark points on the other side of 0 so the two sides of the number line match up perfectly.[/*][*]Label the tick marks -1, -2, -3. . . -10. This represents the negative side of your number line.[/*][/list][/*][*]Then use your number line to answer the questions below. [/*][/list]
Use your number line to answer these questions:
Which number is the same distance away from zero as is the number 4?
Which number is the same distance away from zero as is the number -7?
Two numbers that are the same distance from zero on the number line are called [b]opposites[/b]. Find another pair of opposites on the number line.
Determine how far away the number 5 is from 0. Then, choose a positive number and a negative number that is each farther away from zero than is the number 5.
Determine how far away the number -2 is from 0. Then, choose a positive number and a negative number that is each farther away from zero than is the number -2.
Here is a number line with some points labeled with letters.
Determine the location of points [math]P[/math], [math]X[/math], and [math]Y[/math].[br][br]If you get stuck, you can check the box to reflect the number line to help you find the unknown values.
At noon, the temperatures in Portland, Maine, and Phoenix, Arizona, had opposite values. The temperature in Portland was [math]18°C[/math] lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
IM 6.7.2 Practice: Points on the Number Line
For each number, name its opposite.
[math]-5[/math]
[math]28[/math]
[math]-10.4[/math]
[math]0.875[/math]
[math]0[/math]
[math]-8,003[/math]
Plot the numbers on the number line by dragging the points.
Plot these points on a number line: -1.5, the opposite of -2, the opposite of 0.5, -2
Represent each of these temperatures in degrees Fahrenheit with a positive or negative number.
5 degrees above zero
3 degrees below zero
6 degrees above zero
[math]2\frac{3}{4}[/math] degrees below zero
Order the temperatures above from the coldest to the warmest.
Solve each equation.
[math]8x=\frac{2}{3}[/math]
[math]1\frac{1}{2}=2x[/math]
[math]5x=\frac{2}{7}[/math]
[math]\frac{1}{4}x=5[/math]
[math]\frac{1}{5}=\frac{2}{3}x[/math]
Write the solution to each equation as a fraction and as a decimal.
[math]2x=3[/math]
[math]5y=3[/math]
[math]0.3z=0.009[/math]
There are 15.24 centimeters in 6 inches.
How many centimeters are in 1 foot?
How many centimeters are in 1 yard?