My fourth grade crew started to explore circles this week. They looked at the circumference, diameter, radius and area of circles. They’ve had a bit of experience with them earlier in the year during Pi Day. That day was long forgotten this week. The class started with a large dose of reviewing the concept of area and circles. I noticed that some of the students wanted to immediately use the formula to find the area of a circle. For a few, the process of giving the formula to the kids has caused a headache down the road. They know the formula and some even have it memorized. When asked to define the area of a circle they revert back to formula. When asked what the formula means some of the students repeat the formula back to me. This is a red-alert in my mind – indicating a lack of conceptual understanding.
The class went back a few steps to the area of rectangles and triangles on a grid. After a brief review I observed that students were able to 1) describe what area is 2) Use a grid to count squares to determine the area. Students then said it would be much easier to use the formula. So we used the formula and then went back to circles.
Instead of jumping to the formula like I said earlier, the class took out centimeter grid paper. Students traced circular items onto the grid paper and counted the squares.
This seems boring looking back and as I write this but it was a worthwhile activity in retrospect. Students then found the radius of the traced item. It was fairly easy as students could count the centimeter squares. They used the radius, multiplied it by itself and found the product. They then multiplied that by 3.14, which is our abbreviated version of Pi.
The goal was to get our answers between three and four centimeters. Many of the students had trouble at first but refined their counting methods to be more accurate. I could see some of the students making the connections between using the formula and an understanding of the area of a circle. Eventually students started checking their work by using the area of a circle formula.
Near the end of class students started asking what happens when we can’t actually count the squares of an object. Another student mentioned that we use the formula. That brought out a quality discussion about understanding the formula and why it works. We’re making progress.