GeoGebra

Unit 27 - Definition of a Circle

Author:STEPAM Education

Definition of a Circle

Objectives At the end of the lesson, the students are expected to:
  • understand the concept of circle, including the terms center, radius, and circumference
  • apply the understanding of the circle to ensure fairness in a game
  • use various tools to measure distance and lengths
Materials Coins or pingpong balls, basket, rope, chalk, meter stick, measuring tape, ruler Activity In this game, students (represented by blue dots) will aim to shoot coins into baskets (represented by red dots). A coin must successfully land in the basket to count as a score. Each student who scores three successful shots will advance to the next round, where they will compete against winners from other groups until a final winner is determined. The students will be positioned around the basket in various shapes, such as squares, triangles, and circles as shown in the figure below.



Students will realize that positions, except for the circular arrangement, may feel unfair. Ask them to think about why this might be the case.



Encourage them to measure the distance between each student's position and the basket to explore the differences and understand the impact of positioning on fairness. Discussion
  1. Ask the students which shape is more appropriate for ensuring fairness and why.
  2. Encourage the students to discuss how they can make the game fair for everyone. Guide the discussion so that they consider using a rope and chalk to create a circle around the basket where the students will stand when they shoot the coins. This will make the distance between the basket equal and will ensure that the game is fair.
  3. Introduce terms related to circles like center, radius, interior, exterior, and circumference. Have the students use various measuring devices (e.g. meter stick, measuring tape, ruler) and apps like
  4. Measure to measure the distance between the student and the basket (i.e. the radius) whenever possible.
Consolidation
  1. Emphasize that the purpose of drawing the circle is to ensure that the distance between the basket and every student is equal. This distance is called the radius of the circle.
  2. Define a circle as a set of points that are all the same distance from a fixed point, known as the center. Relate this definition to the activity: the basket is the center, and the students or the drawn curves represent the set of points. The set of points is also referred to as the circumference of the circle.
  3. Emphasize the difference between the phrases “inside the circle (or in the circle)”, “on the circle”, and “outside the circle.” Help students understand these distinctions in relation to their positions and the basket.
  4. Summarize the key terms: center, radius, and circumference
STEPAM Components
  • Science - collecting/comparing data (score/distance)
  • Technology - Using apps to measure lengths/distance
  • Engineering - Constructing the circle
  • Physical Education - Throwing the coins into the basket
  • Art - Constructing/drawing the circle(?)
  • Mathematics - collecting/comparing data (score/distance)
Note: Second image generated by ChatGPT.

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