Course Guide - USAID Teacher Education Project

e) There is an angle of 360° around any point. Students may limit their thinking aboutangles to acute, right, and obtuse. Perhaps older children may consider straight andreflex angles.But if they are given a point and asked to describe its surrounding angle, even adultsare likely to say 0°. (Just as they may have said 0-degrees when introduced to astraight angle.) To their eyes, the angle around a point is invisible...unless givenactivities (such as the ones arranging pattern blocks around a point) to help them "see"360°.3) What is essential to know or do in class?a) Dissect polygons into triangles in order to develop (not just provide) the angle sumformula.b) When given a variety of polygons with n sides, students can demonstrate why allthe polygons have a consistent angle sum.c) Show that there are always 360° around a point.4) Class Activities:a) Begin by reviewing the homework.Discuss the quadrilateral activity first. Ask about student discoveries. Have studentsextend their thinking by asking what would have happened if a square were not cut inhalf diagonally, but "crosswise" into two rectangular halves. What was the angle sumof the original square? What is the angle sum of the two resulting rectangles?Why did the two triangles, which resulted from cutting on the diagonal, have an anglesum equal to that of the original square whereas cutting it crosswise doubled the anglesum?b) Ask students about their assignment to find the angles and angle sums for each ofthe pattern blocks. What was the angle sum of the square, trapezoid, and the tworhombuses? Why do they think that was so? What was alike about those fourshapes?c) Ask students about the regular hexagon. What was the angle measurement at eachof its vertices? How did they determine that? Did they use benchmark angles? Lay thecorners of two equilateral triangles on the hexagon's internal angle? How did theyfind the hexagon's angle sum? Do they think this angle sum would be true for allhexagons (just as 180-degrees was true for all triangles and 360-degrees was true forall quadrilaterals)?d) In this next activity, students will develop the angle sum theorem. Again, it iscrucial that they experiment and not be given the formula beforehand.It may be necessary to define what is meant by the term "diagonal" and to review theangle sum of any triangle being 180-degrees. Divide the class into three groups. Haveone group work with triangles and hexagons, the second group work with pentagonsand decagons, and the third group work with quadrilaterals and octagons. (Note that