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GM6-6: Use trigonometric ratios and Pythagoras' theorem in two and three dimensions.

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Teaching resources for this Achievement Objective
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Cosine Rule

Level Six
Integrated
Units of Work
This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Cosine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. We note that the Cosine Rule is a generalisation of Pythagoras’ Theorem. Note that this...
  • solve triangles using the Cosine Rule
  • plan a practical exercise involving measurement
  • understand what a generalisation is
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Julie's wheels

Level Six
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply Pythagoras’ theorem to solve a problem.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, think).
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Tilted Squares and Right Triangles

Level Six
Integrated
Units of Work
This is an investigation, leading to the derivation and use of Pythagoras' Theorem in two and three dimensions. The initial focus of this unit involves students in aspects of geometry from levels 4 and 5 of the curriculum, to establish the groundwork necessary for the final stages of the unit.
  • Devise an algebraic rule to identify tilted squares that can fit on geoboards of different sizes.
  • Devise an algebraic rule to identify the size of the smallest square geoboard on which tilted squares can fit.
  • Devise and use an algebraic rule for Pythagoras’ theorem.
  • Devise algebraic rules to300