Lesson Ideas
Research
Related LinksPatterns and DesignMontessori

External SectorsAge: 6 & up Prerequisites: Matching fraction circles with polygons, matching numerals with fraction circles and polygons. Screen objects: Ten numerals from 1 to ten down left side of screen. To the right is a column of red fraction circles. Next to this column is a column of circles outlined in black with the bottom semicircle colored a solid black. The top of the circle is the color of the background. At bottom right of screen are eight blue polygons in random order. Presentation: (Individual or small group)
Variations: Use physical fraction circles and polygons from geometric cabinet to match supplementary angles. Subsequent exercises could include measurement of internal angle of polygon and angle of corresponding sector, demonstration of the fact that the two angles always add up to 180 degrees. Extensions: Design work with fraction circles and polygons. Points of Interest: Fitting the blue and red pieces together. Control of Error: Child may make a mistake by "fitting" a polygon whose internal angle is too large (e.g., putting a pentagon over the space left by a 1/3 sector). However, if this happens, then some other piece won't fit at the end of the exercise (e.g., the triangle will not take up all of the space left by a 1/5 sector). Direct Aims: Introduction to supplementary angles. Indirect Aims: Preparation for exercises in recognition of external angles of regular polygons. Software Constraints: Unlike the polygons in the geometric cabinet, the polygons cannot be rotated. Unlike the polygons made of geometry sticks, the sides of the polygons are rigid and cannot be added or removed. The sectors of the fraction circles cannot be removed from the circles. The sectors and circles cannot be rotated. 