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Geometry

General Outcome: Develop algebraic and graphical reasoning through the study of relations.

Specific Outcomes: It is expected that students will:

1. Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
   [C, CN, PS, R]

• (It is intended that this outcome be integrated throughout the course by using sliding, rotation, construction, deconstruction and similar puzzles and games.)
  1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
  • guess and check
  • look for a pattern
  • make a systematic list
  • draw or model
  • eliminate possibilities
  • simplify the original problem
  • work backwarddevelop alternative approaches.

1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

2. Demonstrate an understanding of the Pythagorean theorem by:

• identifying situations that involve right triangles
• verifying the formula
• applying the formula
• solving problems.
  [C, CN, PS, V]

  2.1 Explain, using illustrations, why the Pythagorean theorem only applies to right triangles.

  Pythagorean Theorem Interactive - iFrame

Link: LearnAlberta

Note: There is a prototype/draft flash file from the Junior High Math Interactive project that did not make it to the website. There are some unique features in the Explore It file worth looking at.

Pythagorean Theorem

Pythagorean Theorem

2.2 Verify the Pythagorean theorem, using examples and counterexamples, including drawings, concrete materials and technology.

Pythagorean Theorem

Pythagorean Theorem

2.3 Describe historical and contemporary applications of the Pythagorean theorem.

2.4 Determine if a given triangle is a right triangle, using the Pythagorean theorem.

2.5 Explain why a triangle with the side length ratio of 3:4:5 is a right triangle.

Pythagorean Theorem Interactive - iFrame

Link: LearnAlberta

Pythagorean Triple

2.6 Explain how the ratio of 3:4:5 can be used to determine if a corner of a given 3-D object is square (90º) or if a given parallelogram is a rectangle.

2.7 Solve a problem, using the Pythagorean theorem.

March, 2008 http://www.education.alberta.ca/media/655889/math10to12.pdf

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf