Write equations for proportional relationships presented in tables.
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Lessons 4 and 5 focus on representing proportional relationships as equations. Equations are abstract and can be challenging for some students to grasp. Encourage students to return to the table to show the relationship between the two quantities, either adding a column to show the constant of proportionality or drawing an arrow across rows and indicating the multiplication. Ensure that students know what the variables in the equation represent to keep the context connected to the abstract form.
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion) and Anchor Problem 3 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.
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Felix worked at a music shop during the summer. The table below shows some of Felix’s hours and earnings. The amount of money he earned is proportional to the number of hours he worked.
# hours worked | Amount earned ($) |
1 | |
2 | 18 |
3 | |
5 | 45 |
10 | |
15 | 135 |
20 | 180 |
The table below shows measurement conversions between cups and ounces.
Cups | Ounces |
3 | 24 |
5 | 40 |
8 | 64 |
Let $$x$$ represent the number of cups and $$y$$ represent the number of ounces. Write an equation that represents this relationship.
The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio.
The table below shows the different mixtures of paint that the students made.
A | B | C | D | E | F | |
Yellow | 1 part | 2 parts | 3 parts | 4 parts | 5 parts | 6 parts |
Blue | 2 parts | 3 parts | 6 parts | 6 parts | 8 parts | 9 parts |
Art Class, Variation 2, accessed on Aug. 1, 2017, 3:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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A lemonade is made by mixing flavored powder, $$p$$, with water, $$w$$. The chart below shows some measurements that can be used to make different amounts of lemonade.
Amount of powder (tsp) | Amount of water (cups) |
$$\frac{1}{2}$$ | $$2$$ |
$$2$$ | $$8$$ |
$$3\frac{1}{2}$$ | $$14$$ |
$$4$$ | $$16$$ |
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