Answer:
hope this helps
Explanation:
A context is described, and students generate two sets of values. 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.
The numbers were deliberately chosen to encourage different ways of viewing a proportional relationship. 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.
There are many possible rationales for choosing numbers so that size is not proportional to price. As long as the numbers are different from those in the “proportional” column, the relationship between size and price is guaranteed to be not proportional. Look for students who have a reasonable way to explain why their set of numbers is not proportional, like “the unit price is different for each size,” or “each size costs a different amount per ounce.”
Ask students to remember the last time they went 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.
Arrange students in groups of 2. Give 2 minutes of quiet work time and then invite students to share their sentences 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 example 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