Scheme of Work—Pythagoras and Trigonometry
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Current revision as of 21:12, 2 February 2010
Title
| | | | Geometry: Ma3 Shape, Space and Measures: Pythagoras’ Theorem and Trigonometry | | | | |
Key Objectives:
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Detail
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| 1 | recall and understand Pythagoras’ Theorem | Ma3-2f |
| recall and understand Pythagoras’ Theorem | C | Bostock L. (2002) STP National Curriculum Mathematics 8A Chapter 21 |
| apply Pythagoras' theorem | C | |||||
| visualise the theorem using Perigals’ dissection | C | |||||
| 2 | Deciding whether triangles are right-angled, and proving Pythagoras' theorem. | Ma3-2f |
| determine whether triangles are right-angled | C | Bostock L. (2002) STP National Curriculum Mathematics 8A Chapter 21 |
| prove Pythagoras’ theorem using algebraic methods | C | |||||
| history of Pythagoras and applications for everyday life | C | |||||
| 3 | Finding hypoteneuse. Finding missing side lengths. | Ma3-2f | given the lengths of three sides, determine whether a triangle is right-angled. | calculate the length of the hypotenuse using Pythagoras' theorem | C | Johnson T. (2006), Edexcel GCSE Mathematics Higher Tier, Linear Course, Chapter 19 |
| recall Pythagorean triples | C | |||||
| find hypotenuse using the (x, y) coordinates of two points. | C | |||||
| 4 | calculate the length of an unknown side of a right-angled triangle | Ma3-2f | find length of missing side | calculate the length of an unknown side of a right-angled triangle | C | Muschla, A. (1999) Math Starters, Jossey-Bass |
| calculate the height of an isosceles triangle using Pythagoras' theorem | C | |||||
| calculate the area of a triangle given the lengths of all three sides | C | |||||
| 5 | Use Pythagoras’ theorem to solve problems in 3D | Ma3-2f | multi-stage problems: finding the length of an unknown side | Use Pythagoras’ theorem to solve problems in 3D | C | Porkess R. (2007) Higher MEI GCSE Mathematics, Hodder Murray Chapter 7 |
| a2 + b2 + c2 = d2 | C | |||||
| find the length of a diagonal inside a square or rectangular based pyramid | C | |||||
| 6 | Introducing trigonometry | Ma3-2g | Identify pairs of similar triangles | identify similar triangles | B | Smith, A. (2006) Higher GCSE Mathematics for Edexcel, Hodder Arnold, Chapters:16 and 17 |
| define the tan ratio | B | |||||
| recall use of trigonometric functions on a calculator | B | |||||
| 7 | Introducing Sine and Cosine ratios | Ma3-2g | construct a triangular spiral | define and calculate the SINE ratio in a right-angled triangle | B | Websites:
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| define and calculate the COSINE ratio in a right-angled triangle | B | |||||
| choose the correct trigonometric ratio in calculations | B | |||||
| 8 | SOHCAHTOA | Ma3-2g | quiz: which formula would you use to calculate the length of x? | SOHCAHTOA | B | - |
| recall SIN, COS and TAN ratios using the SOHCAHTOA mnemonic | B | |||||
| find lengths of sides of right-angled triangles using the appropriate ratio | B | |||||
| 9 | Arctan, Arcsin and Arccos | Ma3-2g | trigonometry BC (before calculators) | use of SIN-1, COS-1, and TAN-1 methods to determine unknown angles | B | - |
| calculate missing angles in right-angled triangles | B | |||||
| multi-stage problems in trigonometry | B | |||||
| 10 | Bearings | Ma3-2g | accurate bearings drawings | bearings | A | - |
| angles of depression and elevation | A | |||||
| word problems | A | |||||
| 11 | Consolidation | Ma3-2g | pupil lead lesson, to address specific learning needs | Consolidation | A | - |
| multi-stage problems using Pythagoras' theorem and trigonometry | A | |||||
| real-life situations and bearings | A | |||||
| 12 | Test | Ma3-2f Ma3-2g | - | - | - | - |
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