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 Fraction Circles

Age: 4 & up

Prerequisites: Launching and quitting an application; clicking and dragging; counting with red and blue rods.

Screen objects: Ten circles down left side of screen. First circle is undivided, second circle is divided into two equal halves, third circle is divided into three equal thirds, etc. At bottom of screen are ten matching circles placed in random order. All of these circles are colored red to match the physical fraction circles. Next to the left hand column is another column of circles. These circles are simply red outlines.

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch the fraction circles.
  3. Launch the fraction circles application.
  4. Click on the full circle at the top left of the screen and say "One. One sector". The circle is a sticky button that will darken when pressed.
  5. Ask the child(ren) to find another circle with one sector.
  6. Drag the circle to the red outline of a circle next to the first full circle. The system will darken the circle as if it were clicked and say "One. One sector".
  7. Continue with the rest of the fraction circles. Click on sectors as you count them. After counting, say the count followed by the word "sectors" (e.g., for circle with three sectors, count "One, two, three. Three sectors").
  8. Say "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 physical chart with divided circles on it, counting sectors as they put them over corresponding circles in chart. Matching fraction circles to number rods by laying sectors on top of rod segments. Matching circles of various sizes by number of sectors.

Extensions: Sectors and numerals matching.

Points of Interest: Sticky buttons stay pressed when clicked. Marking items as they are counted. A whole is equal to the sum of its parts (a whole with more parts is not necessarily bigger than a whole with fewer parts). First exposure to angles represented as sectors.

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

Direct Aims: Practice in counting.

Indirect Aims: Preparation for 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: The sectors of the fraction circles cannot be removed from the circles. The sectors and circles cannot be rotated.