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




Age: 9 & up

Prerequisites: The child should have considerable experience with design work using fraction circles and sectors together with polygons, including use of the third row of buttcons in the designer's pallette. The child should also be familiar with basic LOGO commands, including FORWARD, BACK, RIGHT, LEFT, PEN UP, PEN DOWN, and PEN SIZE.

Screen objects: A LOGO geometry microworld with a turtle in the middle. A SWEEPER attachment (described below) has been added to the microworld.

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch LOGO.
  3. Launch LOGO.
  4. Say, "In LOGO, how can you tell what path your turtle has taken?". Discuss. Say, "The pen shows that you have gone forward and back, and shows what turns you have made. The sweeper draws a sector when you make a turn." Enter the LOGO command BACK SWEEPER DOWN.
  5. Say "Now I'll turn right sixty degrees". Enter the RIGHT 60 command. As the turtle turns, the sweeper behind it draws a red sector of sixty degrees.
  6. Demonstrate the front sweeper, and the front and back sweepers used together.
  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 size of sweeper can be changed. Show how size of sweeper and degrees of sweep can be put into programs as variables to create designs.

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

Points of Interest: Discovery of relationships between sectors, external angles, and turtle turns.

Control of Error: Student's aesthetic judgement.

Direct Aims: Opportunity to apply understanding sectors, external angles, and turtle turns, experiment through design to discover relationships.

Indirect Aims: Relating LOGO geometry to Euclidean geometry.

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).

Tension between adoption and continuing research

Throughout her career, Montessori was constantly revising her materials and devising new ones as her research progressed.