In this Warm-up, students compare the changes in output (temperature) over two intervals of input (time). The temperature in one interval changes by a greater amount than in the other interval, but in the latter, temperature changes more rapidly.
Thinking about what it means for temperature to drop “faster” activates the idea of rates of change and prepares for the work later in the lesson.
Display the task for all to see. Give students 2 minutes of quiet time to work the question, and then follow with a whole-class discussion.
Here are the recorded temperatures at three different times on a winter evening.
| time | 4 p.m. | 6 p.m. | 10 p.m. |
|---|---|---|---|
| temperature | 25∘F | 17∘F | 8∘F |
Who do you agree with? Explain your reasoning.
Sample responses:
Select 1–2 students from each group to explain their reasoning. As they explain, record and display their thinking for all to see. After both groups have had a chance to present, ask if anyone changed their mind because of the explanation they heard. If so, invite them to share their reasons.
It is not necessary to resolve the question at this point. Students will continue thinking about this question in the next activity.
Some students may ask for a clarification about what is meant by “faster” in this situation. Acknowledge that thinking about its meaning in context is a great way to approach the task. Encourage these students to interpret the word by using their understanding of the given information.
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In this Warm-up, students compare the changes in output (temperature) over two intervals of input (time). The temperature in one interval changes by a greater amount than in the other interval, but in the latter, temperature changes more rapidly.
Thinking about what it means for temperature to drop “faster” activates the idea of rates of change and prepares for the work later in the lesson.
Display the task for all to see. Give students 2 minutes of quiet time to work the question, and then follow with a whole-class discussion.
Here are the recorded temperatures at three different times on a winter evening.
| time | 4 p.m. | 6 p.m. | 10 p.m. |
|---|---|---|---|
| temperature | 25∘F | 17∘F | 8∘F |
Who do you agree with? Explain your reasoning.
Sample responses:
Select 1–2 students from each group to explain their reasoning. As they explain, record and display their thinking for all to see. After both groups have had a chance to present, ask if anyone changed their mind because of the explanation they heard. If so, invite them to share their reasons.
It is not necessary to resolve the question at this point. Students will continue thinking about this question in the next activity.
Some students may ask for a clarification about what is meant by “faster” in this situation. Acknowledge that thinking about its meaning in context is a great way to approach the task. Encourage these students to interpret the word by using their understanding of the given information.