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



More Shapes Design

Age: 6 & up

Prerequisites: The child should have considerable experience with design work using fraction circles without separable sectors together with polygons, including use of the third row of buttcons in the designer's pallette. The child should also be able to match sectors with supplementary internal angles of polygons.

Screen objects: Pallette and blank document. Pallette has eight outlines of polygons in one column, ten outlines of fraction circles in next. Fraction circles and polygons line up so that the triangle is next to fraction circle with three sectors, etc. To the left of the one sector fraction circle is a buttcon with a cursor on it. This is the moving/resizing tool. Below this and to the left of the two-sector fraction circle is the buttcon for printing. The third row of buttcons from the previous design exercise is also present. There are also buttcons for grouping and ungrouping figures.

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch the fraction circles and polygons design work.
  3. Launch the application.
  4. Say, "I think I'll make a pentagon". Drag a pentagon from pallette to document.
  5. Demonstrate moving, resizing, adding additional figures to make patterns.
  6. Say, "Now I'll add matching sectors". Drag a five-sector fraction circle onto the document. The circle appears with small black rectangles to indicate grouping. Click on the ungrouping pallette so that sectors can be dragged around independently. Place sectors around the pentagon to show the external angles of the pentagon. Two five-sector fraction circles will be needed, since there are two external angles for every internal angle.
  7. Say "I can print the document, or quit the application, or I can do it again." Depending on the interest shown by the child(ren), print the document or push the "Try Again" button and repeat the presentation.
  8. Be sure to quit the application and return to the launcher when finished.
  9. Show how printed document can be used in the same way that preprinted pictures are used for coloring.
  10. Offer the child(ren) the opportunity to perform the exercise.

Variations: In subsequent presentations, show how arbitrary sets of figures can be grouped and ungrouped.

Extensions: Work with tesselations, islamic patterns, African textile designs.

Points of Interest: Discovery of relationships between figures.

Control of Error: Student's aesthetic judgement.

Direct Aims: Opportunity to apply understanding of fraction circles, sectors and polygons, experiment through design to discover relationships.

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

Software Affordance: The figures can be perfectly formed to allow children to discover true relationships between them. Figures of many sizes can be drawn (e.g., a number of concentric pentagons can be drawn inside a circle with five sectors).

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.