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

Research

  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

Montessori

 

Design with Shapes

Age: 5 & up

Prerequisites: The child should have considerable experience with matching fraction circles and polygons, as well as associating numerals with fraction circles and 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. A third column of buttoncons on the pallette shows color tablets of various colors, as well as buttcons for filling in a figure (a bucket of paint emptying into a container), creating new document, opening a document, saving a document, printing, cutting, copying, and pasting. There is a menu selection to hide or show the third column. For initial presentation, the third column is hidden.

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 "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.
  7. Be sure to quit the application and return to the launcher when finished.
  8. Show how printed document can be used in the same way that preprinted pictures are used for coloring.
  9. Offer the child(ren) the opportunity to perform the exercise.

Variations: In subsequent presentations, introduce the third column of buttcons. Teachers can customize buttcon set to add any or all of the third column buttcons. This exercise is related to the artistic composition with geometric insets.

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 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.

Leone Learning Systems, Inc. (LLS) is a North Shore company that provides online courses for kids anywhere and local teaching and tutoring services for students in Chicago and the Northern Suburbs of Chicagoland. LLS also provides a free geometry software package for children age 6 and up, and free resources for teachers and parents. This site includes information about classes taught, availability for tutoring, learning activities for kids, lesson plans, and an ongoing software and curriculum research and development effort.