Area of the Circle Grade 5 (Japan)
From APEC HRDWG Wiki
Teacher Yasuhiro Hosomizu's lesson in Japan was captured on video for the APEC Education Network (EDNET) project called Classroom Innovations through Lesson Study. The lesson is an example of using the Lesson Study process of professional development in the teaching of Mathematics. This lesson teaches students how to calculate the area of a circle by cutting the circle into sectors and rearranging those sectors into approximate shapes with known areas, such as a parallelogram.
This is the seventh of ten lessons on the circle: two lessons focus on circles and regular polygons; three focus on the circumference of a circle; three on the area of a circle and two lessons give students the opportunity to summarize and apply what they have learned. The current lesson is the second of the three lessons on the area of a circle. In previous lessons, students learned how to calculate the areas of basic shapes including squares, rectangles, triangles and parallelograms. The lesson plan and full lesson video are available below. Video highlights with descriptions and analysis are available at the end of this page.
[High Performing Economy  ] [Demonstration Practice  ] (see Resource Types)
|
|
(Video Clips and Highlights Available below. Right-click and select "Save Target As" to download.) |
Lesson Goals
Selected Video Clips
The clips below are selected from the full list of episodes. The Full Lesson Video may be downloaded for further study.
|
Description of Video Clip |
Video Links |
|
The lesson begins with a review of previous ideas from the first lesson on finding the area of a circle. During that lesson, the teacher asks students to explain various approaches to finding the area of a circle: 1) cutting the circle up and changing its pieces into a parallelogram, 2) counting squares (on graph paper) and 3) drawing the circle inside a square and sharing four points. The students extend the major idea to include parallelograms, triangles, trapezoids, and rectangles for which they already know the area formulas. |
Revision (1 of 7)
|
|
Students create parallelograms from a circle with pre-cut equal sectors of eight or 16 pieces. A student (Yoshizawa; 00:10:31) explains a way of calculating the area based upon the formula for a parallelogram and translates this into a formula using circumference and radius. He goes further by explaining that using more pieces gives a better approximation to the area of the circle (1/2 circumference x radius). The teacher calls upon other students to explain Yoshizawa's thinking. He later summarizes the students’ suggestions to increase the number of sectors; by doing so “it approximates a parallelogram gradually.” |
Gradual approximation (Yoshizawa) (2 of 7)
|
|
A second student (Miss Kamoda) explains the formula again, using the example on the board to show where she obtained the radius and half the circumference. Later, a third student (Iijima; 16:50) uses prior knowledge to show how the formula can be converted to radius x pi x radius. |
What comes next? (Miss Kamoda) (3 of 7)
|
|
The teacher says he is very happy because the students are building on what they have learned before. Based on the students’ presentations and explanations, the teacher writes on the board the expression leading to the formula for the area of a circle and highlights the key points. |
I'm very happy (4 of 7)
|
|
The teacher explains that the relevant measurements for finding the area of a circle includes radius, diameter, circumference and pi. |
Rewrite expression (5 of 7)
|
|
The teacher asks students to create a triangle using the sectors of a circle and to find its area. At 30:14 he asks four students to put up their figures. The first is Miss Kamoda who puts up a different parallelogram with two rows of sectors one above the other.
The teacher gives students three minutes to derive a formula for this new parallelogram. Only a few students finish so he asks the other students to go see and discuss the other students’ solutions. At 00:37:00, a student (Kudo) explains his solution. He measured the diameter as 20 cms and used a square to represent the circumference to get the formula 20 x square ÷ 4, which he writes as 5 x square. In the ensuing discussion, Yoshizawa explains how to change this formula into (diameter)÷4x(circumference) enabling the teacher to relate the two formulas. |
Kudo's solution (6 of 7)
|
|
He then calls another student (Iijima) to the board, who then show the two formulas are the same. This presentation elicits an "ah ha!" moment for some students. The teacher’s goal is to extend the idea to other figures such as triangles which have been constructed by other students, but the class runs out of time, and he finishes by saying that they will continue the next day.
|
Student explains (7 of 7) start 43:24, length 1' 29".
|
