Building a Trundle Wheel
10 min
Teacher Prep
Setup
Narrative
In this activity, students learn that a trundle wheel is a tool used in real-world situations to measure long distances. From an image and a description of what a trundle wheel looks like, students think about how the tool works and how they could build one. Students think about the tasks for which a trundle wheel is an appropriate measuring tool (MP5). This builds on work students did in an earlier unit, when they learned about the relationship between the circumference of a wheel and the distance it travels.
Launch
Keep students in the same groups of 3–4 from the previous lesson. Explain to students that a trundle wheel is a measuring device composed of a handle, a wheel, and a device that clicks each time the wheel completes one rotation. Give students 5 minutes of group work time followed by whole-class discussion.
Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language students use to discuss measurement. Display words and phrases, such as “measure,” “trundle wheel,” “measuring tape,” “circumference,” and “standard.”
Student Task
A tool that surveyors use to measure distances is called a trundle wheel.
-
How does a trundle wheel measure distance?
-
Why is this method of measuring distances better than the methods we used earlier?
-
How could we construct a simple trundle wheel? What materials would we need?
Sample Response
Sample responses:
- The wheel is pushed, and as it turns it keeps track of the number of rotations. If the circumference of the wheel is known, this can be multiplied by the number of rotations to find the distance walked.
- The circumference is constant, meaning it does not change, and each rotation follows the next without any gaps. Strides can be slightly different from step to step, and if a measuring tape is used, there might be a gap between iterations.
- A wheel, a handle, and a way to keep track of and count rotations are needed.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to remember the connection between the circumference of a wheel and the distance the wheel travels during one rotation so that they are prepared to use a trundle wheel to measure distances in the next activity.
Direct students’ attention to the reference created using Collect and Display. Ask students to share how a trundle wheel is used to measure distance. Invite students to borrow language from the display as needed and update the reference to include additional phrases as they respond.
Invite students to share their ideas about how to build a trundle wheel and ask them how their design will allow them to measure distances.
Consider asking the following questions:
- “What information about the wheel is needed? What quantities should be measured?”
- “Trundle wheels often have a clicking device that signals each time the wheel completes one rotation. How is this helpful?”
- “If there is a wheel that has a diameter of 25 cm and 11 clicks are counted to go across the classroom, what is the length of the room?” (Answer: 25π⋅11cm, or between 8 and 9 m.)
Distance can be measured by counting the rotations of the wheel and multiplying by the circumference of the wheel. The construction of the trundle wheel allows one to easily count the rotations as they walk.
Anticipated Misconceptions
If students do not recognize the relationship between the circumference of a wheel and the distance traveled by the wheel, consider asking:
- “What measurement of a circle tells us how far a wheel travels each rotation?”
- “How do we calculate circumference?”
Standards
- 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.
30 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Building a Trundle Wheel
10 min
Teacher Prep
Setup
Narrative
In this activity, students learn that a trundle wheel is a tool used in real-world situations to measure long distances. From an image and a description of what a trundle wheel looks like, students think about how the tool works and how they could build one. Students think about the tasks for which a trundle wheel is an appropriate measuring tool (MP5). This builds on work students did in an earlier unit, when they learned about the relationship between the circumference of a wheel and the distance it travels.
Launch
Keep students in the same groups of 3–4 from the previous lesson. Explain to students that a trundle wheel is a measuring device composed of a handle, a wheel, and a device that clicks each time the wheel completes one rotation. Give students 5 minutes of group work time followed by whole-class discussion.
Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language students use to discuss measurement. Display words and phrases, such as “measure,” “trundle wheel,” “measuring tape,” “circumference,” and “standard.”
Student Task
A tool that surveyors use to measure distances is called a trundle wheel.
-
How does a trundle wheel measure distance?
-
Why is this method of measuring distances better than the methods we used earlier?
-
How could we construct a simple trundle wheel? What materials would we need?
Sample Response
Sample responses:
- The wheel is pushed, and as it turns it keeps track of the number of rotations. If the circumference of the wheel is known, this can be multiplied by the number of rotations to find the distance walked.
- The circumference is constant, meaning it does not change, and each rotation follows the next without any gaps. Strides can be slightly different from step to step, and if a measuring tape is used, there might be a gap between iterations.
- A wheel, a handle, and a way to keep track of and count rotations are needed.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to remember the connection between the circumference of a wheel and the distance the wheel travels during one rotation so that they are prepared to use a trundle wheel to measure distances in the next activity.
Direct students’ attention to the reference created using Collect and Display. Ask students to share how a trundle wheel is used to measure distance. Invite students to borrow language from the display as needed and update the reference to include additional phrases as they respond.
Invite students to share their ideas about how to build a trundle wheel and ask them how their design will allow them to measure distances.
Consider asking the following questions:
- “What information about the wheel is needed? What quantities should be measured?”
- “Trundle wheels often have a clicking device that signals each time the wheel completes one rotation. How is this helpful?”
- “If there is a wheel that has a diameter of 25 cm and 11 clicks are counted to go across the classroom, what is the length of the room?” (Answer: 25π⋅11cm, or between 8 and 9 m.)
Distance can be measured by counting the rotations of the wheel and multiplying by the circumference of the wheel. The construction of the trundle wheel allows one to easily count the rotations as they walk.
Anticipated Misconceptions
If students do not recognize the relationship between the circumference of a wheel and the distance traveled by the wheel, consider asking:
- “What measurement of a circle tells us how far a wheel travels each rotation?”
- “How do we calculate circumference?”
Standards
- 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.