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

 

Measure Sector Angles

Age: 8 & up

Prerequisites: The child should be able to use the instrument for the measurement of angles and a calculator. The child should also have experience with the division material set.

Screen objects: Document and two floating windows. One floating window displays an online version of the instrument for the measurement of angles. The other window displays an online calculator. On the left hand side of the document is a column of six fraction circles divided into equal sectors of one, two, etc. To the right of this column are the following text and text boxes:
 

1 circle =   degrees and 360 degrees / 1 =   degrees
1/2 circle =   degrees and 360 degrees / 2 =   degrees
1/3 circle =   degrees and 360 degrees / 3 =   degrees
1/4 circle =   degrees and 360 degrees / 4 =   degrees
1/5 circle =   degrees and 360 degrees / 5 =   degrees
1/6 circle =   degrees and 360 degrees / 6 =   degrees

 

Presentation: (Individual or small group)

  1. Invite the child(ren).
  2. Announce that you are going to launch the sector measuring application.
  3. Launch the application.
  4. Say, "First, I'll measure the two-sector circle". Drag a semi-circle to the measuring instrument. When any sector is dropped into the instrument, it is positioned with the sector angle in the center of the instrument, and ends of the arc at zero degrees and the degree measure of the arc. The numeral on the instrument that gives the measure of the arc is then highlighted. For the two-sector circle, this number will be 180 degrees.
  5. Say "One hundred eighty degrees", and type 180 into the corresponding text box.
  6. Continue with circles of three, four, five, and six sectors.
  7. Try measuring the circle of one sector. Instead of highlighting the numeral 0, the instrument will alternately flash 0 and 360 at the 0 point. Ask why this happens. Discuss.
  8. Go to the first division problem, and say, "Three hundred sixty divided by one". Enter the problem into the online calculator.
  9. Continue with the rest of the division problems.
  10. 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.
  11. Be sure to quit the application and return to the launcher when finished.
  12. Show how printed document can be used in the same way that preprinted pictures are used for coloring.
  13. Offer the child(ren) the opportunity to perform the exercise.

Variations: After the child has experience with decimal division, the fraction circles with seven to ten sectors can be added (360 / 7 gives a an answer that has a decimal component).

Extensions: Exercise with turtle turns.

Points of Interest: Discovery of relationships between figures.

Control of Error: Measuring instrument and calculator.

Direct Aims: Show relationship between sector angles and division of 360.

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

Software Affordance: By incorporating measuring instrument and calculator into the software, space is saved and measurement and calculation made easier so that child can focus on relations to be learned.

Software Constraints: Sector is automatically positioned in the measuring instrument.

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.