Relationships between Quantities: IM 7.6.1
[url=https://im.kendallhunt.com/MS/teachers/2/6/1/preparation.html]“Relationships between Quantities”[/url] from IM Grade 7 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 7.6.1
- IM 7.6.1 Lesson: Relationships between Quantities
- Practice 7.6.1
- IM 7.6.1 Practice: Relationships between Quantities
IM 7.6.1 Lesson: Relationships between Quantities
A movie theater sells popcorn in bags of different sizes. The table shows the volume of popcorn and the price of the bag.
Complete one column of the table with prices where popcorn is priced at a constant rate. That is, the amount of popcorn is proportional to the price of the bag. Then complete the other column with realistic example prices where the amount of popcorn and price of the bag are not in proportion.
A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32.
How much do you think a bus containing 30 people would be charged?
If a bus is charged $122, how many people do you think it contains?
What rule do you think the state park uses to decide the entrance fee for a vehicle?
A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 12 slices.
How long do you think it will take to make 20 slices?
If someone makes as many slices of toast as possible in 4 minutes and 40 seconds, how many slices do think they can make?
What is the smallest number that has a remainder of 1, 2, and 3 when divided by 2, 3, and 4, respectively? Are there more numbers that have this property?
IM 7.6.1 Practice: Relationships between Quantities
Lin and Tyler are drawing circles. Tyler's circle has twice the diameter of Lin’s circle. Tyler thinks that his circle will have twice the area of Lin’s circle as well. Do you agree with Tyler?
Jada and Priya are trying to solve the equation [math]\frac{2}{3}+x=4[/math].[br][list][*]Jada says, “I think we should multiply each side by [math]\frac{3}{2}[/math] because that is the reciprocal of [math]\frac{2}{3}[/math].”[/*][*]Priya says, “I think we should add [math]-\frac{2}{3}[/math] to each side because that is the opposite of [math]\frac{2}{3}[/math].”[br][/*][/list][br]Which person’s strategy should they use? Why?
Write an equation that can be solved using the other person’s strategy.
What are the missing operations?
In football, the team that has the ball has four chances to gain at least ten yards. If they don't gain at least ten yards, the other team gets the ball. Positive numbers represent a gain and negative numbers represent a loss. Select [b]all [/b]of the sequences of four plays that result in the team getting to keep the ball.
A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered.
Is the relationship between number of turkey subs delivered and amount charged proportional? [i]Explain [/i]how you know.[br]
How much does the store charge for 1 additional turkey sub?
Describe a rule for determining how much the store charges based on the number of turkey subs delivered.
Which question cannot be answered by the solution to the equation [math]3x=27[/math]?