Students generate two sets of values: one set could be values in a proportional relationship, and the other set could not. The purpose of this Warm-up is to remind students of some characteristics that make a relationship proportional or not proportional, so that later in the lesson, they are better equipped to recognize that a relationship is not proportional and explain why.
Look for students who have a reasonable way to explain why their set of numbers is not proportional, such as “The unit price is different for each size,” or “Each size costs a different amount per ounce.”
Invite students to share experiences going to the movies. What do they know about the popcorn for sale? What sizes does it come in? About how much does it cost?
Tell students that in this activity, they will come up with prices for different sizes of popcorn—one set of prices in which the price is in proportion to the size, and another set of prices in which the price is not in proportion to the size, but is still reasonable. Ask students to be ready to explain the reasons they chose the numbers they did. If needed, review what it means for a relationship to be proportional: the values for one quantity are each multiplied by the same number to get the values for the other quantity.
Arrange students in groups of 2. Give 2 minutes of quiet work time and then invite students to share their response with their partner, followed by whole-class discussion.
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 prices where the amount of popcorn and price of the bag are not in proportion.
| volume of popcorn (ounces) |
price of bag, proportional ($) |
price of bag, not proportional ($) |
|---|---|---|
| 10 | 6 | 6 |
| 20 | ||
| 35 | ||
| 48 |
Answers vary for the rightmost column. Sample response:
| volume of popcorn (ounces) |
price of bag, proportional ($) |
price of bag, not proportional ($) |
|---|---|---|
| 10 | 6 | 6 |
| 20 | 12 | 11 |
| 35 | 21 | 20 |
| 48 | 28.8 | 25 |
The purpose of this discussion is to elicit different ways of viewing a proportional relationship. For example, for 20 ounces and 35 ounces, students might move from row to row and think in terms of scale factors. This approach is less straightforward for 48 ounces, and some students may shift to thinking in terms of unit rates.
Invite a student to share their prices for the proportional relationship and how they decided on those numbers. Ask if any students thought of it in a different way.
Then invite a student to share their prices for the relationship that is not proportional and record these for all to see. Ask students to explain ways you can tell that the relationship is not proportional.
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Students generate two sets of values: one set could be values in a proportional relationship, and the other set could not. The purpose of this Warm-up is to remind students of some characteristics that make a relationship proportional or not proportional, so that later in the lesson, they are better equipped to recognize that a relationship is not proportional and explain why.
Look for students who have a reasonable way to explain why their set of numbers is not proportional, such as “The unit price is different for each size,” or “Each size costs a different amount per ounce.”
Invite students to share experiences going to the movies. What do they know about the popcorn for sale? What sizes does it come in? About how much does it cost?
Tell students that in this activity, they will come up with prices for different sizes of popcorn—one set of prices in which the price is in proportion to the size, and another set of prices in which the price is not in proportion to the size, but is still reasonable. Ask students to be ready to explain the reasons they chose the numbers they did. If needed, review what it means for a relationship to be proportional: the values for one quantity are each multiplied by the same number to get the values for the other quantity.
Arrange students in groups of 2. Give 2 minutes of quiet work time and then invite students to share their response with their partner, followed by whole-class discussion.
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 prices where the amount of popcorn and price of the bag are not in proportion.
| volume of popcorn (ounces) |
price of bag, proportional ($) |
price of bag, not proportional ($) |
|---|---|---|
| 10 | 6 | 6 |
| 20 | ||
| 35 | ||
| 48 |
Answers vary for the rightmost column. Sample response:
| volume of popcorn (ounces) |
price of bag, proportional ($) |
price of bag, not proportional ($) |
|---|---|---|
| 10 | 6 | 6 |
| 20 | 12 | 11 |
| 35 | 21 | 20 |
| 48 | 28.8 | 25 |
The purpose of this discussion is to elicit different ways of viewing a proportional relationship. For example, for 20 ounces and 35 ounces, students might move from row to row and think in terms of scale factors. This approach is less straightforward for 48 ounces, and some students may shift to thinking in terms of unit rates.
Invite a student to share their prices for the proportional relationship and how they decided on those numbers. Ask if any students thought of it in a different way.
Then invite a student to share their prices for the relationship that is not proportional and record these for all to see. Ask students to explain ways you can tell that the relationship is not proportional.