Using a Trundle Wheel to Measure Distances

40 min

Teacher Prep
Setup
Students in same groups. 20 minutes to measure, 10 minutes to calculate, followed by whole-class discussion.
Required Preparation

Prepare to distribute the trundle wheels students built in the previous lesson. Make sure students can still get to the path (between 50 and 100 meters) that they measured the other day.

For the digital version of the activity, acquire devices that can run the applet.

Narrative

In this activity, students use the trundle wheels they made to measure a longer path of about 50–100 meters. This is the same path that they measured during an earlier lesson with a different method. As they return to measure the same path with a new approach, students make sense of and persevere in solving the problem (MP1).

After students measure, they spend the remainder of the lesson on computations and sharing results. Students get a chance to connect the mathematical formulas and computations with the aspects of the hands-on experience they had in making and using the wheels. They model with mathematics by deciding how to report their results after taking multiple measurements (MP4).

This activity works best when each student has access to a path to measure with a trundle wheel. If a path to measure is unavailable, consider using the digital version of the activity. In the digital version, students use an applet to measure a path with a trundle wheel. The applet allows students to count the rotations to determine the distance.

This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.

Launch

Keep students in the same groups from the previous lesson. Remind students of the path they should measure. Instruct them to come back to the classroom to finish their calculations as soon as they have recorded their measurements.

If several groups are sharing a trundle wheel, they each measure the given path once and compare their data with each other.

Give students 10–20 minutes to take turns measuring and 10 minutes of group work time to finish their calculations, followed by whole-class discussion.

Use Collect and Display to direct attention to words collected and displayed from an earlier lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson.

Action and Expression: Provide Access for Physical Action. Support effective and efficient use of tools and assistive technologies. To use the trundle wheel, some students may benefit from access to step-by-step instructions or modeling a systemic way to record the number of clicks to calculate an example distance.
Supports accessibility for: Organization, Memory, Attention

Student Task

Earlier you made trundle wheels to measure long distances. Your teacher will show you a path to measure.

  1. Measure the path with your trundle wheel three times and calculate the distance. Record your results in the table.

    trial number number of clicks   computation   distance
    1
    2
    3
  2. Decide what distance you will report to the class. Be prepared to explain your reasoning.
  3. Compare this distance with the distance you measured the other day for this same path.
  4. Compare your results with the results of two other groups. Express the differences between the measurements in terms of percentages.

Sample Response

  1.  Sample response: 
    • Diameter of wheel: 25 cm
      trial number number of clicks computation distance
      1 63 25π⋅6325\pi\boldcdot 63 4,945.5 cm, 49.5 m
      2 65 25π⋅6525\pi\boldcdot 65 5,102.5 cm, 51.0 m
      3 63.5 25π⋅63.525\pi\boldcdot 63.5 4,984.75 cm, 49.9 m
  2. Sample response: Distance to report: 50 m
  3. Answers vary.
  4. Sample response: If Group A’s measurement is 50 m and Group B’s measurement is 51 m, then Group B’s measurement is 2% larger than Group A’s since 51÷50=1.0251\div 50 = 1.02.
Activity Synthesis (Teacher Notes)

Direct students’ attention to the reference created using Collect and Display. Ask students to share their process for measuring the path. Invite students to borrow language from the display as needed, and update the reference to include additional phrases as they respond.

Ask each group to report their measurement for the length of the path and record their answers for all to see. Guide students to compare these answers by asking questions like these:

  • “Do all of these answers seem reasonable? Do any of these answers seem unreasonable? Explain your reasoning?”
  • “Why are these answers not all exactly the same? What are some sources of error?” (Not going in a straight line, the wheel wobbles, the ground is uneven, only counting number of clicks but not parts of rotations, etc.)
  • “What units did you use? What units would be most convenient for designing the course of a 5K walk-a-thon?” (Metric since we are designing a 5 kilometer course.)
  • “What degree of precision is appropriate to report?" (To the closest 1 meter at most. Reporting in centimeters or milimeters for such long distances using a tool like a trundle wheel would imply a degree of precision that would not be appropriate.)

If time permits, consider asking, “If you could choose your own diameter for a trundle wheel, what would it be?” (A diameter that creates a circumference of 1 meter would be convenient, about 32 centimeters.)

Collect and store students’ trundle wheels so they will have access to them again in the next lesson.

Anticipated Misconceptions

If students lose track of the number of rotations along the path, consider asking:

  • “Explain how your trundle wheel helps you measure distance.”
  • “How can you use your team to help you keep track of the number of rotations?”
Standards
Addressing
  • 7.G.4·Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • 7.G.B.4·Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
  • 7.RP.A·Analyze proportional relationships and use them to solve real-world and mathematical problems.
  • 7.RP.A·Analyze proportional relationships and use them to solve real-world and mathematical problems.