Partitioning A Circle Into Two and Four Equal Parts
- Kailee Loberg
Throughout the activity you will be able to explore the differences between one half and one fourth of a circle. You will be able to see these differences from angles to the number of parts making up the circle. You will use a straight line which has an angle of 180 degrees to construct the bisection of the circle. You will use the straight line, which was used to create halves to represent 1/2 of the circle to form a perpendicular line. All four angles that are created should equal 90 degrees. If they do not equal 90 degrees then you know that your circle is not split into four equal parts (representing 1/4). CCSS.MATH.CONTENT.1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Task: Partitioning a circle into two equal parts. 1. Create a circle of any size by using the "Circle with Center Through Point" tool. 2. Use the "Line" tool to cut your circle in half. While placing your line be sure that it goes through points A and B by clicking on the points while placing your line. By clicking the two points, your line will show up. 3. Your circle should now be split into two. Now we need to make sure that the two parts of your circle are equal. Before doing so you need to add an extra point onto your circle. Use the "point" tool to add a point where the line and circle intersect. You should now have a straight line of points (a, b, and c). 4. Click on the "angle" tool, then select the points B, A, and C in that order. You should now have a 180 degree angle. 5. Now label each half of your circle by using the "pen" tool to write 1/2 in each half. 6. Move the circle around by dragging point B using the cursor. Does your circle change? Does the angle of your circle change? Is your circle still divided into two equal parts? Task: Partitioning a circle into four equal parts. 1. On a new page, create a new circle. 2. Use the "Line" tool to cut your circle in half. While placing your line be sure that it goes through points A and B by clicking on the points while placing your line. By clicking the two points, your line will show up. Point C needs to be created opposite of the point B. 3. To split your circle into four equal parts you will need to make a perpendicular line. To do this, use the "perpendicular line" tool. Select the center point of the circle and the line that goes through the points B and C. Your circle should now be split into four parts. 4. Create two more points where your circle and lines intersect. You should now have four points on the outside of your circle where your circle and lines intersect and one point in the middle of the circle. 5. To be sure that we have four equal parts in our circle we need angles. 6. Select the "angle" tool. Select points B, A, and D in that order. Your angle should read 90 degrees. If your angle does not read 90 degrees, your circle is not split into four equal parts. 7. Label each fourth of your circle by using the "pen" tool. 8. Move the circle around by dragging point B using the cursor. Does your circle change? Do the angles of your circle change? Is your circle still divided into four equal parts?