Exploring Circumference (IM Grade 7, Unit 3, Lesson 3, Activity 2 and 3)
Task
Lesson Purpose In this lesson, students discover that there is a proportional relationship between the diameter and circumference of a circle. They use their knowledge from the previous unit on proportionality to estimate the constant of proportionality. Then they use the constant to compute the circumference given the diameter (and vice versa) for different circles. Students learn that pi ( ) is the value of the constant and discusses various commonly used approximations. Students will relate the circumference to the radius in a future lesson, so it is not necessary to do so in this lesson. Determining that the relationship between the circumference and diameter of circles is proportional is an example of looking for and making use of structure and repeated reasoning (MP7, MP8). How Tuva Enhances the lesson Tuva enhances this lesson by providing students with real-world measurements of circular objects, allowing them to explore the relationship between diameter and circumference even if physical materials aren’t available. By working with this dataset, students can quickly visualize and manipulate the data without spending time plotting each individual point by hand. This efficiency allows for deeper analysis and discussion of the relationship between the two variables—helping students focus on recognizing patterns and understanding the constant ratio that connects diameter and circumference.
In this activity, we’re going to explore the circumference of circles. Before we start, let’s review some words that we will need to know. A circle is made of all the points that are the same distance from a given point. That given point is the center of the circle. The circumference of a circle is the distance around the circle. A diameter is a line segment that goes from one point on a circle to another and passes through the center. A radius is a line segment that goes from the center of a circle to any point on the circle.’s review some words that we will need to know.
Topics and standards: Grade 7, Illustrative Math & Tuva