Introduction—Pythagoras and Trigonometry

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Contents

Assignment 2, Task 2: Design a Scheme of Work which supports teachers in providing a quality learning experience

Produce a quality scheme of work that would be suitable for supporting staff in their teaching of a selected topic in school in the 14-16 range. make use of appropriate elements of the National Curriculum and, where appropriate, a GCSE syllabus.

Provide evidence of your abiliy to:

  1. Demonstate a secure understanding of the nature of your subject in the context of the school curriculum.
  2. Provide teacher with clear, insightful and effective ways in which they can teach the subject.
  3. Design learning activities which motivate pupils and allow them to progress well in the subject.
  4. Demonstrate how teacher can be supported through schemes of work and how such schemes might effectively be designed and presented.

Sue Potter, Despina Steiert and Gavin Wilson—PGCE Secondary Mathematics

Organisation of this Binder

  1. Table of Contents
  2. Introduction
  3. Scheme of Work
  4. Individual Lesson Plans
  5. End of Unit Test (with answers)
  6. Worksheets, Handouts and other resources

Ma3 Shape, Space and Measures: Pythagoras’ Theorem and Trigonometry

Summary Learning Objectives:

  • Use Pythagoras' Theorem in a range of contexts to find lengths of unknown sides in right-angled triangles.
  • Recall and use trigonometric ratios.
  • Solve problems in both two and three dimensions using Pythagoras' theorem and simple trigonometry.

Recommended Lesson Structure

11 lessons followed by a test:

  1. Recall and understand Pythagoras’ Theorem
    • apply Pythagoras' theorem
    • visualise the theorem using Perigals’ dissection
  2. Determine whether triangles are right-angled
    • prove Pythagoras’ theorem using algebraic methods
    • history of Pythagoras and applications for everyday life
  3. Calculate the length of the hypotenuse using Pythagoras' theorem.
    • recall Pythagorean triples
    • find hypotenuse using xy coordinates of two points in an xy diagram
  4. Calculate the length of an unknown side of a right-angled triangle.
    • calculate the height of an isosceles triangle using Pythagoras' theorem
    • calculate the area of a triangle given the lengths of all three sides
  5. Use Pythagoras’ theorem to solve problems in three dimensions.
    • a2 + b2 + c2 = d2
    • find the length of a diagonal inside a square or rectangular based pyramid
  6. Identify similar triangles.
    • define the tangent ratio
    • recall use of trigonometric functions on a calculator
  7. Define and calculate the SINE ratio in a right-angled triangle.
    • define and calculate the COSINE ratio in a right-angled triangle
    • choose the correct trigonometric ratio in calculatuons
  8. SOHCAHTOA
    • recall SIN, COS and TAN ratios using the SOHCAHTOA mnemonic
    • find lenths of sides of right angled triangles using the appropriate ratio
  9. Use SIN-1, COS-1, and TAN-1 to determine unknown angles.
    • calculate misssing angles in right- angled triangles
    • multi-stage problems in trigonometry
  10. Bearings
    • angles of depression and elevation
    • word problems
  11. Consolidation
    • multi-stage problems using Pythagoras' theorem and trigonometry
    • real-life situations and bearings.

Assumptions

We have assumed that these lessons will be delivered in the Spring Term, although this is not essential. They are intended for a Year 10 class taking the Edexcel Higher Tier Linear GCSE (2010 specification). We have designed this module to consist of eleven 50-minute lessons followed by a test, spread over three consecutive weeks. We have scheduled homework after every even-numbered lesson, which we assume will be handed in at the next lesson. There is some applied and practical content which recognises the arrived of Functional Maths. The main textbook is Smith, A. (2006) Higher GCSE Mathematics for Edexcel, Hodder Arnold. As far as prior knowledge is concerned, we assume that some, if not most, of the pupils will have already been introduced to Pythagoras' Theorem. But we also assume that no pupils have encountered trigonometry before.

The extent of this module

This module covers the fundamentals of trigonometry but does not provide the final say on the subject before GCSE exams are taken. In particular, the Sine and Cosine Rules are omitted from thus module on the assumption that they will be covered in Year 11.

Position in the school curriculum

It is not for us to proscribe the sequence of subjects schools should teach maths at Key Stage 4. A typical and highly practical sequence might proceed as follows around this module:

  • .
  • .
  • Similar triangles
  • Pythagoras
  • Trigonometry
  • Area of triangle
  • Convert between area units
  • Volume of prism
  • Sectors of circles
  • .
  • .

Guidance for the Teacher

Although we have recommended a particular textbook (Smith 2008), this module can instead be taught with another GCSE textbook. These alternative textbooks are listed in the lesson plans.

There is more than enough material included in this binder to fill up 11 lessons, keep the learners engaged and help them achieve their target levels in this topic.

Resources

  1. All the materials for this module—scheme of work, lesson plans, exercises and other elements&mdash' are available on a USB memory stick for each of access.
  2. All the material, except for any copyright, items are also available on a website at http://editthis.info/teach/Scheme_of_Work%E2%80%94Pythagoras_and_Trigonometry to enable teachers, wherever they are, to access and use these lesson plans.
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