Lesson Ideas

  1. Match Fraction Circles
  2. Match Regular Polygons
  3. Polygons and Fraction Circles
  4. Fraction Circles and Numerals
  5. Polygons and Numerals
  6. Design with Shapes
  7. External Sectors
  8. More Shapes Design
  9. Measure Sector Angles
  10. Drawing Polygons with Logo
  11. Sweepers


  1. Design Problem
  2. Literature Review
  3. Work Models
  4. Design Patterns
  5. Design Experiments
  6. Lesson Ideas
  7. Montessori Computes
  8. Thinking About Circles

Related Links

Patterns and Design



External Sectors

Age: 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)

  1. Invite the child(ren).
  2. Announce that you are going to launch the supplementary angles application.
  3. Launch the application.
  4. Start with the fraction circle with three sectors. Count the sectors -- "One, two, three. Three sectors." Drag the upper left sector into the half-circle in the adjacent column.
  5. Ask the child(ren) to find a polygon with three sides.
  6. Drag the blue triangle to the circle with the red half-circle and the 1/3-circle sectors One third of a circle covers the external angle of a triangle, so the 1/3-circle sector and the internal angle of the triangle are supplementary. Show how the bottom left corner of the triangle fits into the remaining sixty degree angle.
  7. Continue with the rest of the fraction circles and regular polygons.
  8. When finished, notice that there are no polygons matching the fraction circles with one and two sectors. Note that the whole circle will not fit into the half-circle. Move cursor to fraction circle with two sectors. Drag the half-circle sector over the half-circle in the right hand column. Note that no room is left for a polygon.
  9. Say to yourself "I can quit the application, or I can do it again." Depending on the interest shown by the child(ren), quit the application or push the "Try Again" button and repeat the presentation.
  10. Be sure to quit the application and return to the launcher when finished.
  11. Offer the child(ren) the opportunity to perform the exercise.

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.