Tuesday  September 13

• Measuring angles, lengths and areas.
• Squares, rectangles  : 90 degree/ right angle
• parallelograms: opposite angles are congruent, sum of consecutive angles =180 degrees
• triangles  : add to 180 degrees- straight angle [Illustrated physically and with wingeometry]
  
• Dissections, cut and paste methods of measurement.
• Cutting and reassembling polygons.
• The "Square Me" Puzzle
  
• The triangle, quadrilateral, pentagon, and hexagon.
• More on measurements of angles and areas of polygons.
• A quadrilateral can be made from two triangles...
  so the sum of its interior angles is 2 * 180 = 360.
• A pentagon can be made from 3 triangles... so the sum of its interior angles is 3* 180 = 540. If the pentagon has all angles congruent( of equal measurement) then each angle will be 540/5 = 108 degrees!

• A hexagon can be made from 4 triangles... so the sum of its interior angles is 4* 180 = 720. If the hexagon has all angles congruent( of equal measurement) then each angle will be 720/6 = 120 degrees!

Puzzles and Polygons 
• Dissections, cut and paste methods of measurement.
• Cutting and reassembling polygons.

Tangoes: a commercial game based on tangrams

Making Dissection Puzzles:

• Dissections (Junkyard)
• visit Dissection Animations
• visit The Puzzling World of Polyhedral Dissections by Stewart T. Coffin.

 

 

• Equidecomposable polygons (translation from Portugese)
  A Reference for a possible project or portfolio entry.

• Activity: Tile plane with playing cards.
• Discuss briefly: Symmetry of playing cards
• reflection (vertical line/ horizontal line)
• 180 deegree rotation 
• Preview ... Possible tiles and tilings.
• One Regular Convex Polygon.
• Two or more Regular Convex Polygons.
• Other Polygon Tilings.  
• Non polygonal tilings.