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Arrange students in groups of 2. Give them 2–3 minutes of quiet work time followed by a whole-class discussion.
The equation
Invite several students to share their situations and display their graphs for all to see. Ask:
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Elena babysits her neighbor’s children. Her earnings are given by the equation
Jada earns $7 per hour mowing her neighbors’ lawns.
Clare and Han have summer jobs stuffing envelopes for two different companies.
Han earns $15 for every 300 envelopes he finishes.
Clare’s earnings can be seen in the table.
| number of envelopes |
money earned in dollars |
|---|---|
| 400 | 40 |
| 900 | 90 |
Tyler plans to start a lemonade stand and is trying to perfect his recipe for lemonade. He wants to make sure the recipe doesn’t use too much lemonade mix (lemon juice and sugar) but still tastes good.
Recipe 1 is given by the equation
Recipe 2 is given in the table.
| lemonade mix (cups) | water (cups) |
|---|---|
| 10 | 50 |
| 13 | 65 |
| 21 | 105 |
If Tyler had 16 cups of lemonade mix, how many cups of water would he need for each recipe? Explain your reasoning by creating a graph or a table.
Some students may confuse the values for the rate of change of a situation. For example, Lemonade Recipe 1's equation,
Asking “How did you find the rate of change and what does it mean?”
Prompting students to list a few additional values or sketch a graph to see if it matches their interpretation of the rate of change.