 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Solutions for Session 4, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5    Problem C1

 a. To form a square, try this: Repeat 4; Go Forward 4; Rotate Right 90; End Repeat. b. To form a non-square rectangle, try this: Repeat 2; Go Forward 5; Rotate Right 90; Go Forward 7; Rotate Right 90; End Repeat. c. To form a non-rectangular parallelogram, try this: Repeat 2; Go Forward 5; Rotate Right 60; Go Forward 7; Rotate Right 120; End Repeat. d. To form an equilateral triangle, try this: Repeat 3; Go Forward 5; Rotate Right 120; End Repeat. e. To form a regular pentagon, try this: Repeat 5; Go Forward 5; Rotate Right 72; End Repeat. f. To form a regular hexagon, try this: Repeat 6; Go Forward 5; Rotate Right 60; End Repeat. g. There are many different star polygons, but here's one way to do it: Repeat 5; Go Forward 5; Rotate Right 144; End Repeat. The angle must be a multiple of the angle used to form a regular polygon of the same number of sides. If you wanted a star polygon without intersecting lines, try this: Repeat 5; Go Forward 5; Rotate Left 72; Go Forward 5; Rotate Right 144; End Repeat. h. To form a regular n-gon, theoretically, the commands would be as follows: Repeat n; Go Forward 5; Rotate Right (360/n); End Repeat. To do this in the Interactive Activity, you need to select a specific value for n. Apply the commands as above, replacing n with the number you've chosen. You will need to do this as a multi-step process. For example, if you select n = 18, you'd need to write the following algorithm, which includes the same sequence twice: Repeat 9; Go Forward 2; Rotate Right 20; End Repeat; Repeat 9; Go Forward 2; Rotate Right 20; End Repeat. You can try this using different values for n. Alternatively, you could write a slightly shorter sequence to draw the same 18-gon: Repeat 2, Repeat 9; Go Forward 2; Rotate Right 20; End Repeat; Repeat 9; Go Forward 2; Rotate Right 20; End Repeat; End Repeat.   Problem C2

 a. If the turn is x degrees, the resulting interior angle measure is (180° - x°). b. Answers will vary, but one important observation is that such turns measure exterior angles. In order to build a polygon with the correct interior angles, we must first subtract from 180 degrees to find the exterior angles.   Problem C3 The sum of the measures of the exterior angles is 360 degrees for all polygons drawn this way. One explanation for why this is true is that the cursor must make a complete circle and return to its original position, and there are 360 degrees in a circle.   Problem C4 In a regular polygon, the measure of each central angle is equal to the measure of each exterior angle: Since the central angles total 360 degrees and the exterior angles total 360 degrees, each of these angles is also equal. (For non-regular polygons, these totals are still equal, but the individual angles are not.)   Problem C5 See commands in Problem C1 (h). The sum of the exterior angles is a multiple of 360 degrees, since the cursor will go around in a circle more than once as it moves through the points of the star. Answers will vary, depending on the size of the star polygon (specifically, the number of times the cursor must go around in a circle), but will always be a multiple of 360 degrees.     