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

 

Drawing Polygons with Logo

[Below is my description of an exercise explained to me by Bob Blodget (1998).]

Age: 8 & up

Prerequisites: The child should understand what a LOGO turtle turn is.

Screen objects: Left side of screen has a column of four regular polygons. Each polygon has one side more than the previous polygon, so the first one is a triangle, the next one a square, and the last one a hexagon. In the next column is a text box for the student to type in the number of sides for the figure. The column next to that is the number of degrees a turtle should turn each time it turns a corner when tracing the polygon. The next column has buttons to tell the system to try to draw the polygon with the angle given. In the next column appears the figure drawn. If the number of degrees given is not correct, the figure will not close or will cross itself. The student can keep adjusting the angle untill the figure closes. The last column shows the total number of degrees turned by the turtle.
 

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch the application for drawing polygons with turtles.
  3. Launch the application
  4. Start with the triangle. Count the number of sides (clicking on a side will highlight it as you count). Count "One, two, three. Three sides". Type 3 into the text box next to the triangle.
  5. Move on to the column headed "Number of degrees in one turn". Ask the children to guess at some number. Enter some number other than 120.
  6. Say, "Now we can draw it". Press the "Draw It" button next to the text box. The figure will not close or two lines of the figure will cross each other. Try other values until coverging on 120.
  7. Continue with the rest of the polygons.
  8. When finished, note that sum of all turtle turns (value in last column) is always 360.
  9. 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.
  10. Be sure to quit the application and return to the launcher when finished.
  11. Offer the child(ren) the opportunity to perform the exercise.

Variations: After the child has experience with decimal division, the regular polygons with seven to ten sides can be added (a septagon has a turtle turn of 360 / degrees).

Extensions: Design work with turtles and sweepers.

Points of Interest: Total of all turtle turns is 360 degrees for all polygons.

Control of Error: Figure that is drawn when "Draw It" button is pressed.

Direct Aims: Show relationship between turtle turns, number of sides, and 360 degrees.

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

Software Affordance: Feedback of drawn figure.

Software Constraints: Extremely constrained LOGO environment to scaffold learning about drawing regular polygons.