Comparing Situations by Examining Ratios
5 min
Teacher Prep
Setup
Narrative
This Warm-up familiarizes students with the context of running on a treadmill and the quantitative data it displays before they solve problems about running speed in the next activity.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 3. Ask students what they know about treadmills. If not already mentioned in their responses, explain that a treadmill is an exercise machine for walking or running. Point out that while the runner does not actually go anywhere on a treadmill, a computer inside the treadmill keeps track of the distance traveled as if the runner were running outside.
This (optional) video shows a person starting a treadmill and walking at a constant speed for a few seconds.
A guy is walking on the treadmill.
Give students a minute of quiet time to observe the images. Ask students to be prepared to share at least one thing that they notice and one thing that they wonder about the picture. Ask them to give a signal when they have noticed or wondered about something.
Student Task
What do you notice? What do you wonder?
Mai's Treadmill Display
Jada’s Treadmill Display
Sample Response
Students may notice:
- The displays show Mai’s and Jada’s workouts.
- A bunch of different measurements are shown: incline, distance, level, calories, pulse, heart rate, and pace.
- Both displays show 10 for incline, 3.0 for distance, 12 for level, 125 for pulse, and 80% for heart rate.
- Mai’s display shows 24:00 for time, 8:00 for pace, and 481 for calories. Jada’s display shows 30:00 for time, 10:00 for pace, and 411 for calories.
Students may wonder:
- In what units are incline, distance, and time measured?
- What does pace mean? Is it different from speed?
- Who is running faster?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If no students mention the speed of each runner, ask them what they can tell about it from the displays. Point out that Mai’s display shows 24 minutes as the running time and 3 miles as the distance run, and Jada’s display shows 30 minutes as the running time and 3 miles as the distance run. Tell students that they’ll think more about what these quantities tell us about the runners’ speed in the next activity.
Anticipated Misconceptions
Because a person running on a treadmill does not actually go anywhere, it may be challenging to think about a distance covered. If this comes up, suggest that students think about running the given distances outside on a straight, flat road at a constant speed.
Standards
- 6.RP.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <em>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</em>
- 6.RP.A.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <span>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</span>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Comparing Situations by Examining Ratios
5 min
Teacher Prep
Setup
Narrative
This Warm-up familiarizes students with the context of running on a treadmill and the quantitative data it displays before they solve problems about running speed in the next activity.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 3. Ask students what they know about treadmills. If not already mentioned in their responses, explain that a treadmill is an exercise machine for walking or running. Point out that while the runner does not actually go anywhere on a treadmill, a computer inside the treadmill keeps track of the distance traveled as if the runner were running outside.
This (optional) video shows a person starting a treadmill and walking at a constant speed for a few seconds.
A guy is walking on the treadmill.
Give students a minute of quiet time to observe the images. Ask students to be prepared to share at least one thing that they notice and one thing that they wonder about the picture. Ask them to give a signal when they have noticed or wondered about something.
Student Task
What do you notice? What do you wonder?
Mai's Treadmill Display
Jada’s Treadmill Display
Sample Response
Students may notice:
- The displays show Mai’s and Jada’s workouts.
- A bunch of different measurements are shown: incline, distance, level, calories, pulse, heart rate, and pace.
- Both displays show 10 for incline, 3.0 for distance, 12 for level, 125 for pulse, and 80% for heart rate.
- Mai’s display shows 24:00 for time, 8:00 for pace, and 481 for calories. Jada’s display shows 30:00 for time, 10:00 for pace, and 411 for calories.
Students may wonder:
- In what units are incline, distance, and time measured?
- What does pace mean? Is it different from speed?
- Who is running faster?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If no students mention the speed of each runner, ask them what they can tell about it from the displays. Point out that Mai’s display shows 24 minutes as the running time and 3 miles as the distance run, and Jada’s display shows 30 minutes as the running time and 3 miles as the distance run. Tell students that they’ll think more about what these quantities tell us about the runners’ speed in the next activity.
Anticipated Misconceptions
Because a person running on a treadmill does not actually go anywhere, it may be challenging to think about a distance covered. If this comes up, suggest that students think about running the given distances outside on a straight, flat road at a constant speed.
Standards
- 6.RP.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <em>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</em>
- 6.RP.A.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <span>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</span>