GeoGebra

Unit 28 - Circumference and Pi

Autor:STEPAM Education

Circumference and Pi

Objective At the end of the lesson, the students are expected to: measure the circumference of various circular objects using various tools recognize and explain the consistent ratio between the circumference and diameter of circles, known as apply the formula C = π × d or C = 2 × π × r to calculate the circumference of a circle Materials cans with different sizes, hula hoops with different sizes, measuring tapes, ruler, meter stick, ropes Activity In this activity, students will measure the circumference and diameter of different circular objects. The teacher will define these terms at the beginning of the activity. While circumference was defined in the previous activity as a set of points, it can also refer to the distance around a circle, which will be emphasized in this activity.

Students will begin by measuring the circumference of smaller cylindrical objects, such as cans, and then move on to larger objects like hula hoops. They can use various instruments to measure the circumference, such as measuring tapes, meter sticks, or apps. Students should be instructed to record their measurements. Discussion
  1. Ask the students to discuss their strategies for measuring the circumference of the circle. Be sure to highlight the strategy of rolling the objects to convert the circumference into a straight line (e.g https://www.geogebra.org/m/PVgpPjeq). This approach is crucial for accurate comparison.
  2. Encourage students to examine their measurements and identify any patterns. At this stage, they should use their measuring instruments, such as tape measures or rulers, to compare measurements.
  3. Have the students organize their data on a table. Ask them to look for relationships between the circumference and the diameter and confirm their observations through calculations. They should discover that the ratio of the circumference to the diameter is slightly more than 3, approximately 3.14. Ask them if this ratio is consistent across all circles.
  4. Introduce the constant ratio that they have discovered which is around 3.14 known as pi and then introduce the symbol . Explain that this ratio is the same for all circles regardless of the size.
Consolidation Emphasize that for a circle of any size, the ratio of the circumference of a circle to the diameter is equal to which is about 3.14. This means that the circumference (C) of a circle is the product of and the length of its diameter (d). That is C = π × d Since the diameter is twice the radius, then d = 2 × r. So, we can also write C = 2 × π × r As an exercise, let the students calculate the circumference of a circle given its radius/diameter. STEPAM Components
  • Science - collecting/recording data
  • Technology - using apps to measure length
  • Engineering - finding a way to measure the circumference especially for large objects
  • Physical Education - performing the measurement outside the classroom, rolling the hula hoop to draw straight line
  • Art - n/a
  • Mathematics - performing simple calculations (circumference divided by diameter), finding the formula for circumference

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