Using Negative Numbers to Make Sense of Contexts: IM 6.7.5
[url=https://im.kendallhunt.com/MS/teachers/1/7/5/preparation.html]“Using Negative Numbers to Make Sense of Contexts”[/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 6.7.5
- IM 6.7.5 Lesson: Using Negative Numbers to Make Sense of Contexts
- Practice 6.7.5
- IM 6.7.5 Practice: Using Negative Numbers to Make Sense of Contexts
IM 6.7.5 Lesson: Using Negative Numbers to Make Sense of Contexts
What do you notice? What do you wonder?
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[/img]
The manager of the concession stand keeps records of all of the supplies she buys and all of the items she sells. The table shows some of her records for Tuesday.
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[/img][br][br]Which items did she sell? Explain your reasoning.
How can we interpret -58 in this situation?
How can we interpret -10.35 in this situation?
On which item did she spend the most amount of money? Explain your reasoning.
A vending machine in an office building sells bottled beverages.
The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.[br][img]data:image/png;base64,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[/img][br][br]What might a positive number mean in this context?
What about a negative number?
What would a “0” in the second column mean in this context?
Which numbers—positive or negative—result in fewer bottles in the machine?
At what time was there the greatest change to the number of bottles in the machine?
How did that change affect the number of remaining bottles in the machine?
At which time period, 8:05–8:09 or 8:25–8:29, was there a greater change to the number of bottles in the machine? Explain your reasoning.
The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?
[size=150][size=100]Priya, Mai, and Lin went to a cafe on a weekend. Their shared bill came to $25. Each student gave the server a $10 bill. The server took this $30 and brought back five $1 bills in change. Each student took $1 back, leaving the rest, $2, as a tip for the server.[br][br]As she walked away from the cafe, Lin thought, “Wait—this doesn’t make sense. Since I put in $10 and got $1 back, I wound up paying $9. So did Mai and Priya. Together, we paid $27. Then we left a $2 tip. That makes $29 total. And yet we originally gave the waiter $30. Where did the extra dollar go?”[/size][/size][br][br][size=100]Think about the situation and about Lin’s question. Do you agree that the numbers didn’t add up properly? Explain your reasoning.[/size]
IM 6.7.5 Practice: Using Negative Numbers to Make Sense of Contexts
Write a positive or negative number to represent each change in the high temperature.
Tuesday’s high temperature was 4 degrees less than Monday’s high temperature.
Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature.
Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
Friday’s high temperature was 2 degrees less than Thursday’s high temperature.
Decide which of the following quantities can be represented by a positive number and which can be represented by a negative number. Give an example of a quantity with the opposite sign in the same situation.
Tyler’s puppy gained 5 pounds.
The aquarium leaked 2 gallons of water.
Andre received a gift of $10.
Kiran gave a gift of $10.
A climber descended 550 feet.
Make up a situation where a quantity is changing.
Explain what it means to have a negative change.
Explain what it means to have a positive change.
Give an example of each.
On the number line, label the points that are 4 units away from 0.
If you fold the number line so that a vertical crease goes through 0, the points you label would match up. Explain why this happens.
On the number line, label the points that are [math]\frac{5}{2}[/math] units from 0. What is the distance between these points?
Evaluate each expression.
[math]2^3\cdot3[/math]
[math]\frac{4^2}{2}[/math]
[math]3^1[/math]
[math]6^2\div4[/math]
[math]2^3-2[/math]
[math]10^2+5^2[/math]