Unit 6 Lesson 1

Expressions and Equations
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Unit 6
Expressions, Equations, and Inequalities

Lesson 1
Relationships between Quantities

Learning

Goal

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Let’s try to solve some new
kinds of problems.

Unit 6 ● Lesson 1

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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.

Pricing Theater Popcorn

Unit 6 ● Lesson 1 ● Activity 1

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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.

1.

How much do you think a bus containing 30 people would be
charged?

2.

If a bus is charged $122, how many people do you think it
contains?

3.

What rule do you think the state park uses to decide the
entrance fee for a vehicle?

Entrance Fees

Unit 6 ● Lesson 1 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

●

What are some ways that you can tell that this relationship is
not proportional?

●

What rule do you think the park uses to charge the entrance
fee for the vehicle and people?

Entrance Fees

Unit 6 ● Lesson 1 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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.

1.

How long do you think it will take to make 20 slices?

2.

If someone makes as many slices of toast as possible in 4
minutes and 40 seconds, how many slices do think they can
make?

Making Toast

Unit 6 ● Lesson 1 ● Activity 3

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

● Describe some rules we encountered in this lesson

for how one quantity was related to another
quantity.

● What made these situations more complicated than

relationships we have seen in the past?

● What were some tools or strategies we used that

were particularly helpful?

Relationships between Quantities

Unit 6 ● Lesson 1

Learning
Targets

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Unit 6 ● Lesson 1

I can think of ways to solve
some more complicated
word problems.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

A movie theater sells popcorn in bags of different sizes. The table shows
the volume of popcorn and the price of the bag.

If the theater wanted to offer a 60-ounce bag of popcorn, what would be a
good price? Explain your reasoning.

Movie Theater Popcorn, Revisited

Unit 6 ● Lesson 1 ● Activity 4

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative
Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0),
https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright
2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY
4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the
Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are
licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without
the prior and express written consent of Illustrative Mathematics.

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