The purpose of this Warm-up is to bring up two main methods for figuring out missing numbers in a table that represents a proportional relationship. The two methods students might use for this activity are:
This activity is to get students thinking about the second method as a more efficient method, since it works for every row. This lays the groundwork for solving problems using proportional relationships and for the activities in this lesson.
Introduce the context of this activity by asking students, “When it is hot outside, what do you like to drink to refresh yourself?” Then, explain that people in Mexico make a drink called agua fresca (AH-gwah FREH-skah) by blending fresh fruit with water and ice.
Arrange students in groups of 2. Give 1 minute of quiet work time followed by time to compare their table with a partner. Then hold a whole-class discussion.
A recipe for watermelon agua fresca calls for 21 cup of cubed, seeded watermelon and 1 cup of ice. Complete the table to show how much watermelon and ice to use in different numbers of batches of the recipe.
| watermelon (cups) | ice (cups) |
|---|---|
| 21 | 1 |
| 43 | |
| 143 | |
| 1 | |
| 221 |
| watermelon (cups) | ice (cups) |
|---|---|
| 21 | 1 |
| 43 | 121 |
| 87 | 143 |
| 1 | 2 |
| 141 | 221 |
The purpose of this discussion is to contrast two different methods for completing the table: using scale factors between rows and using the constant of proportionality between columns.
Display the table for all to see, and invite students to share their answers and reasoning for each missing entry. Record their ideas directly on the table if possible. Ask students if they agree or disagree with the values in the table.
To help students compare, contrast, and connect the different approaches, consider asking:
If not mentioned by students, highlight that the constant of proportionality is the same for every row in the table, while the scale factor may differ for each pair of rows.
Some students may assume the watermelon column will continue to increase by the same amount if they do not pay close attention to the values in the ice column. Ask these students what they notice about the values in the ice column and if it makes sense for the watermelon amount to increase by the same amount each time.
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The purpose of this Warm-up is to bring up two main methods for figuring out missing numbers in a table that represents a proportional relationship. The two methods students might use for this activity are:
This activity is to get students thinking about the second method as a more efficient method, since it works for every row. This lays the groundwork for solving problems using proportional relationships and for the activities in this lesson.
Introduce the context of this activity by asking students, “When it is hot outside, what do you like to drink to refresh yourself?” Then, explain that people in Mexico make a drink called agua fresca (AH-gwah FREH-skah) by blending fresh fruit with water and ice.
Arrange students in groups of 2. Give 1 minute of quiet work time followed by time to compare their table with a partner. Then hold a whole-class discussion.
A recipe for watermelon agua fresca calls for 21 cup of cubed, seeded watermelon and 1 cup of ice. Complete the table to show how much watermelon and ice to use in different numbers of batches of the recipe.
| watermelon (cups) | ice (cups) |
|---|---|
| 21 | 1 |
| 43 | |
| 143 | |
| 1 | |
| 221 |
| watermelon (cups) | ice (cups) |
|---|---|
| 21 | 1 |
| 43 | 121 |
| 87 | 143 |
| 1 | 2 |
| 141 | 221 |
The purpose of this discussion is to contrast two different methods for completing the table: using scale factors between rows and using the constant of proportionality between columns.
Display the table for all to see, and invite students to share their answers and reasoning for each missing entry. Record their ideas directly on the table if possible. Ask students if they agree or disagree with the values in the table.
To help students compare, contrast, and connect the different approaches, consider asking:
If not mentioned by students, highlight that the constant of proportionality is the same for every row in the table, while the scale factor may differ for each pair of rows.
Some students may assume the watermelon column will continue to increase by the same amount if they do not pay close attention to the values in the ice column. Ask these students what they notice about the values in the ice column and if it makes sense for the watermelon amount to increase by the same amount each time.