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



Match Regular Polygons

Age: 4 & up

Prerequisites: Launching and quitting an application; clicking and dragging; counting with red and blue rods; ability to identify regular polygons in the geometric cabinet.

Screen objects: Eight solidly colored polygons down left side of screen. First polygon is an equalateral triangle, second polygon is a square, third polygon is a regular pentagon, etc. At bottom of screen are eight matching polygons placed in random order. All of these polygons are colored blue to match the geometric insets. Next to the left hand column is another column of polygons. These polygons are simply blue outlines.

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch the regular polygons.
  3. Launch the regular polygons application.
  4. Move the cursor to the triangle at the top left of the screen. Click on each side of the triangle in turn. Count the sides as you click: "One, two, three. Three sides". The sides of the triangle will darken when pressed like sticky buttons.
  5. Ask the child(ren) to find another polygon with three sides. After it is found, ask "What else do we call a polygon with three sides"?
  6. Drag the triangle to the blue outline of a triangle next to the solid triangle at the top left of the screen. The system will darken the sides in turn as if it they were clicked and say "One, two, three. Three sides".
  7. Continue with the rest of the regular polygons.
  8. 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.
  9. Be sure to quit the application and return to the launcher when finished.
  10. Offer the child(ren) the opportunity to perform the exercise.

Variations: Matching the physical fraction circles to a chart with divided circles on it, counting sectors as they put them over corresponding circles in chart. Matching polygons of various sizes by number of sides.

Extensions: Sectors and numerals matching. Making polygons with geometry sticks.

Points of Interest: Sticky buttons stay pressed when clicked. Marking items as they are counted. First exposure to sides as components of a polygon.

Control of Error: System responds by counting sides when polygon is placed in outline (darkening them and counting out loud). If count does not match number of sides in polygon to its left, the polygon falls back down to the bottom of the screen.

Direct Aims: Practice in counting. Introduction to sides of a polygon.

Indirect Aims: Preparation for exercises in recognition of external angles of regular polygons.

Software Affordance: The counting of the number rods requires teacher verification. This exercise uses control of error to support the child's autonomy.

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.