Unit 2

Using Equations to Solve Problems

Introducing Proportional Relationships

Lesson 6

Expressions and Equations

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Let’s use equations to solve problems involving proportional relationships.

Unit 2 ● Lesson 6

Learning

Goal

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Quotients with Decimal Points

Unit 2 ● Lesson 6 ● Activity 1

Without calculating, order the quotients of these expressions from least to greatest.

42.6 ÷ 0.07

42.6 ÷ 70

42.6 ÷ 0.7

426 ÷ 70

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Place the decimal point in the appropriate location in the quotient: 42.6 ÷ 7 = 608571

Use this answer to find the quotient of one of the previous expressions.

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Warm-up: Number Talk

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

Concert Ticket Sales

Unit 2 ● Lesson 6 ● Activity 2

A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of $311,000 in sales from these tickets.

1. Assuming that all tickets have the same price, what is the price for one ticket?
2. How much will they make if they sell 7,000 tickets?
3. How much will they make if they sell 10,000 tickets? 50,000? 120,000? a million? x tickets?
4. If they make $404,300, how many tickets have they sold?
5. How many tickets will they have to sell to make $5,000,000?

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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.

Recycling

Unit 2 ● Lesson 6 ● Activity 3

Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of $0.14.

1. If a family threw away 2.4 kg of aluminum in a month, how many cans did they throw away? Explain or show your reasoning.
2. What would be the recycled value of those same cans? Explain or show your reasoning.
3. Write an equation to represent the number of cans c given their �weight w.
4. Write an equation to represent the recycled value r of c cans.
5. Write an equation to represent the recycled value r of w kilograms of aluminum.

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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.

Using Equations to Solve Problems

Unit 2 ● Lesson 6

• What were some helpful ways we organized information?
• What were some equations we found in this lesson?
• In each equation, what did the letters represent? What did the number mean?
• y = 62.2x
• c = 62.5w
• r = 0.014c
• r = 0.875w

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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.

Unit 2 ● Lesson 6

• I can find missing information in a proportional relationship using the constant of proportionality.
• I can relate all parts of an equation like to the situation it represents.

Learning

Targets

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Granola

Unit 2 ● Lesson 6 ● Activity 4

Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories.

1. If she eats 2 servings of granola, how many calories does she eat?
2. If she wants to eat 175 calories of granola, how many servings should she eat?
3. Write an equation to represent the relationship between the number of calories and the number of servings of granola.

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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.

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).

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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).

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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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