A hula hoop is like a racetrack: Calculating the circumference, radius, and area of a circle

Student can use hula hoops to explore basic geometry concepts and indirect measurement.

In this lesson, students will use hoops of different sizes to explore geometry concepts such as circumference, area, and radius. They will also use indirect measurement and calculate percent of error.

Learning outcomes

Students will:

Use a couple different techniques to calculate the diameter, circumference, and area of several circular objects
Calculate percent of error

Teacher planning

Time required

one class period

Materials needed

For the first activity each group will need:

string
meter stick
calculator
three differently sized hula hoops or other circular objects

For the second activity each group will need:

masking tape
meter stick
three differently sized hula hoops or other circular objects
string
calculators

Student handouts

A hula hoop is like a racetrack worksheet: Document by the author; Open as PDF (79 KB, 3 pages; also available as Microsoft Word document)

Quiz: A hula hoop is like a racetrack: Document by the author; Open as PDF (14 KB, 1 page; also available as Microsoft Word document)

Pre-activities

Assemble the materials for this lesson before class begins.
Mark a wide path for the second activity of this lesson.

Activities

Activity one

Begin the day’s activities by asking students to volunteer examples of when they had to calculate accurate proportions.
Explain that in the following two activities they will be applying math concepts as they evaluate objects similar in shape to a race track: hula hoops. Yes, they must use their imagination! In the first activity, they will measure the diameter of three differently sized hula hoops (or other circular objects) and record the data on the worksheet. They will then calculate each circle’s circumference and area. Finally, they will determine the relationship between radius and area.
Have students get into groups while you pass out materials and the worksheets. Allow students fifteen minutes to complete this first activity.

Activity two

In the second activity, students will use a different method to measure the circumference of a circle. Show students the path you have marked out for them. Have them measure the path and record this information.
Students will mark a location on the first hoop to be the starting point. They will place that point on the starting point of the path and roll the hoop the distance of the path counting the number of complete rotations. On the last rotation, students determine what fraction or decimal of a rotation the hoop has traveled. They then record the mixed number or decimal of the total number of rotations of the hula hoop for the whole path on the worksheet.
Next students will calculate the circumference of the hula hoop by dividing the length of the path by the number of rotations of the hula hoop. They will record the results in the chart on their worksheet.
To assess the accuracy of their measurement and calculations, students should wrap a string around the circumference of the hoop and mark the string. They will pull the string in a straight line and use the meter stick to measure the circumference. The closer this measurement is to the calculated circumference, the more accurate the measurements.
Students will repeat steps 2–4 for each hula hoop.

Assessment

When the class has finished the two activities, have students take the short quiz. Look over their answers for accuracy and understanding.

North Carolina curriculum alignment

Mathematics (2004)

Grade 8

Goal 2: Measurement - The learner will understand and use measurement concepts.
- Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.
- Objective 2.02: Apply and use concepts of indirect measurement.