Absolute Values of Numbers: IM 6.7.6
[url=https://im.kendallhunt.com/MS/teachers/1/7/6/preparation.html]“Absolute Values of Numbers”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.7.6
- IM 6.7.6 Lesson: Absolute Value of Numbers
- Practice 6.7.6
- IM 6.7.6 Practice: Absolute Value of Numbers
IM 6.7.6 Lesson: Absolute Value of Numbers
Decide mentally which one has a value that is closer to 0.
Decide mentally which one has a value that is closer to 0.
Decide mentally which one has a value that is closer to 0.
Decide mentally which one has a value that is closer to 0.
Move the bug to a starting point, choose a jump distance, and press the jump button. You may need to zoom in or out if your bug jumps off the screen.
A bug is jumping around on a number line.
If the bug starts at 1 and jumps 4 units to the right, where does it end up? How far away from 0 is this?
If the bug starts at 1 and jumps 4 units to the left, where does it end up? How far away from 0 is this?
If the bug starts at 0 and jumps 3 units away, where might it land?
The [b]absolute value[/b] of a number is the distance it is from 0. The bug is currently to the left of 0 and the absolute value of its location is 4. Where on the number line is it?
If the bug jumps 7 units and lands at 0, where could it have started?
If the bug is to the left of 0 and the absolute value of its location is 5, where on the number line is it?
If the bug is to the right of 0 and the absolute value of its location is 2.5, where on the number line is it?
A part of the city of New Orleans is 6 feet below sea level.
We can use “-6 feet” to describe its elevation, and “ [math]\text{\mid-}6\mid[/math] feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?[br][br]25 feet
We use the notation[math]\mid\text{-}2\mid[/math] to say “the absolute value of -2,” which means “the distance of -2 from 0 on the number line.”[br][br]What does [math]\mid\text{-}7\mid[/math] mean and what is its value?
[math]\mid25\mid[/math] feet
[math]\text{-}8[/math]
[math]\text{\mid-}8\mid[/math] feet
The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
We write “[math]\text{-}5^{\circ}C[/math]” to describe a temperature that is 5 degrees Celsius below freezing point and “[math]5^{\circ}C[/math]” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?[br][br][math]1^{\circ}C[/math]
[math]\text{-}4^{\circ}C[/math]
[math]\mid12\mid^\circ C[/math]
[math]\mid\text{-}7\mid^\circ C[/math]
Which temperature is colder: [math]\text{-}6^{\circ}C[/math] or [math]3^{\circ}C[/math]?
Which temperature is closer to freezing temperature: [math]\text{-}6^{\circ}C[/math] or [math]3^{\circ}C[/math]?
Which temperature has a smaller absolute value? Explain how you know.
At a certain time, the difference between the temperature in New York City and in Boston was 7 degrees Celsius. The difference between the temperature in Boston and in Chicago was also 7 degrees Celsius. Was the temperature in New York City the same as the temperature in Chicago? Explain your answer.
IM 6.7.6 Practice: Absolute Value of Numbers
On the number line, plot and label all numbers with an absolute value of 3/2.
The temperature at dawn is [math]6^{\circ}C[/math] away from 0. Select [b]all [/b]the temperatures that are possible.
Put these numbers in order, from least to greatest.
Lin’s family needs to travel 325 miles to reach her grandmother’s house.
At 26 miles, what percentage of the trip’s distance have they completed?
How far have they traveled when they have completed 72% of the trip’s distance?
At 377 miles, what percentage of the trip’s distance have they completed?
Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, d, she donates for different amounts of money, m, that she earns.
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[/img][br][br]What percent of her income does Elena donate to charity? Explain or show your work.
Which quantity, [math]m[/math] or [math]d[/math], would be the better choice for the dependent variable in an equation describing the relationship between [math]m[/math] and [math]d[/math]? Explain your reasoning.
Use your choice from the second question to write an equation that relates [math]m[/math] and [math]d[/math].