Student Work- Jones Week 10

Relating Circumference and Diameter

            We have worked on circles in my classroom. More specifically, how circumference and diameter are related. For classwork, students had to measure the diameter of circles and apply the 3 times rule to find the circumference. The three times rule was very interesting because it is connecting multiplication and circles. When students heard “three times” most of them thought that they had to multiply but they did not know what they had to multiply. We discussed the three times rule. The three times rule stated that the circumference is three times the diameter. When I first introduced this to students, they seemed skeptical that this idea could actually be true. After showing them examples, student believed the idea and were ready to try it on their own. Student were successful with this task. While walking around and watching students as they approached the activity with the three times rule, some students actually measured the diameter  of the circle and wrote out the multiplication problem to show their work. For example, if students measured a circle with a diameter  of 3 inches, they would write “3 X 3= 9, so the diameter is 9 inches. Other students did not need to do this because multiplication is a concrete concept for them and they are able to do multiplication in their heads. Some of the students were also able to think of the circumference as a straight line that when they measure it would be 3 times their diameter. This activity showed that students can take a concept that they understand such a multiplication and relate it to a not so familiar concept such as the circumference and the diameter of a circle to help it make sense. This shows that students current mathematical understanding is at a point where they can connect different concepts together which will be valuable to them as they continue in their academic career. The gaps that appear in their current mathematical understanding seems to be viewing circles as a concept in itself. Students wanted to connect circles to something that they knew which was wonderful however, I do not feel that students view circles as a concrete idea at this point. Students will need to do more work with circles so that circles will become its own idea and student will know when and where to use different ideas to find different parts of a circle such as its area. Based on this activity and what students took from it, two potential activities I could do with students to further students understanding of circles would be to have students define circles to make sure that they understood what a circle is. Some students view ovals as circles, but ovals are not circles. By having students have a solid understanding of what a circle is, students will be more likely to understand different aspects of circles in the future. Another activity would be to have students draw circles and find the diameter and circumference of circles that they draw. By doing this, they will see that in order for formulas of a circle to work, you have to have a perfect circle. What I mean when I say a perfect circle is that the students do not have any dents or edges. If a circle had these things and a student attempts to measure the diameter of the circle, the diameter will be wrong. Students need to see this for themselves so that in the future they will be able to understand circles and recognize circles and non circles when they see them.