Tes Maths: Inspect the spec - trigonometry

Craig Barton
05th September 2016
TES Maths, inspect the spec, GCSE, new specification, trigonometry, secondary, KS4, Year 10, Year 11

Hand-picked resources to support the teaching of trigonometry as part of the new GCSE specification

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, Tes Maths aims to find out.

What does the specification say?

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

G20: Know the formulae for: Pythagoras’ theorem, a2 + b2 = c2, and the trigonometric ratios... apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

G21: Know the exact values of sinq and cosq for q = 0°, 30°, 45°, 60° and 90°; know the exact value of tanq for q = 0°, 30°, 45° and 60°

What's the same?

In many ways, questions on trigonometry will look exactly as they always have. Students will still be presented with right-angled triangles and be expected to work out missing sides and angles. And the highest attaining students will still have to deal with the twists and turns of 3D and non-right-angled triangles. It is likely that questions will continue to be asked in this context, fused together with topics such as bearings.

What has changed?

The biggest change is that 2D trigonometry with right-angled triangles is now a topic in the foundation course. While only those sitting the higher paper will be expected to "develop confidence and competence" in the topic, all students - no matter which tier they're in - will be faced with the delights of SOHCAHTOA.

In terms of content, all students now have to understand the exact values of trigonometric ratios, which were previously reserved for A-level courses. The introduction of exact values drastically increases the likelihood of trigonometry making an appearance on the non-calculator paper, and I wouldn't be surprised if questions on the higher paper require students to not only demonstrate their knowledge of exact values using cos(30) or sin(60), but also their ability to work with surds.

Additionally, higher students will also have to find the angle between a line and a plane. Although 3D trigonometry may have been covered as part of the previous specification, it's worth double-checking that it is included this time round as well.

How can Tes Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

  1. Introduction to trigonometry
    ​With foundation students now expected to know trigonometry, the way that you introduce the topic will be crucial. This well-structured lesson provides an excellent starting point.
  2. Complete trigonometry unit
    This fully resourced lesson sequence takes students on a journey from SOHCAHTOA, to the sine and cosine rules, via 3D trigonometry and angles of elevation and depression.
  3. Trigonometry investigation
    Get your students measuring angles and lines in order to become familiar with the values of sin(30), cos(60) and tan(45).
  4. Finding and applying trigonometric ratios
    Demonstrate where the three exact trigonometric values come from, using this well-designed lesson presentation and worksheet pack. 
  5. Discovering exact trigonometric values
    Encourage students to become familiar with "special triangles", in order to calculate exact trigonometric values without a calculator, using this set of worksheets.
  6. 3D trigonometry introduction
    Including a starter and plenary activity, this step-by-step lesson uses illustrations to explain the relationship between trigonometry and 3D shapes.
  7. Full 3D trigonometry lesson
    Starting with a recap of the basics, this detailed lesson covers many aspects of trigonometry, including how to find the angle between a line and a plane.
  8. Solving 3D problems
    Consolidate students' understanding of 3D trigonometry by setting them these higher-level problems, guaranteed to make them think.

Trigonometry Introduction Lesson

A lesson that introduces sin,cos and tan, with a little quiz and questions at the the end.
By bcooper87

Trigonometry - Sequence of Lessons

This is a PPT I made on Trigonometry for my Year 10s. It goes right from the basics of SOHCAHTOA through angles of elevation and depression, Trig in 3D to area of triangles, the Sine and Cosine rules. Included are a couple of worksheets I made to use to support the PPT.
By Daniel Burke

Trigonometry Intro Investigation

These two worksheets should be printed out. It has been scaled so that when pupils measure with a ruler each 'box' is 1cm x 1cm. Pupils take the required measurements and are asked if they have observed any similarities between O/A. The tan ratio is then introduced! Lots of calculator use is encouraged. Find out the tan of 30º, what about 45º? 1? What does that mean? Feedback would be appreciated as I am a student teacher.
By mallan824

Finding and applying the 3 trigonometric ratios - GCSE Mathematics 1 - 9 (NEW CONTENT)

Full lesson on finding and using the 3 trigonometric ratios that has been added to the new GCSE Maths specification.

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Visit weteachmaths.co.uk for

- Lessons and worksheets suitable for the 9 - 1 GCSE Specification
- A-Level teaching resources for Core 1, Core 2, Core 3, Core 4, Decision 1 and Statistics 1
- Teaching resources for Level 3 Core Mathematics
- Schemes of work for Higher and Foundation GCSE Maths (adapted for the 9 - 1 specification)
- Topic tests for GCSE Maths and A-Level Maths
- Support for the teaching and coursework in GCSE Statistics
By We Teach Maths

Finding Exact Trig Values - Discovery Learning

This worksheet encourages students to become familiar with 'special triangles' to calculate exact trig values without a calculator. By focusing on multiples of 30, 45 and 60, it also helps students spot symmetry in graphs. I created this resources to introduce double angle formula/additonal formula. Answers attached :)
By emcnicholl

3D Trigonometry

Powerpoint to be used to explain how to use Trigonometry in 3D shapes. Includes a starter, main explanation and a plenary. If you like this resource then please check out my other stuff on here! :)
By Owen134866

IGCSE Further Maths - 3D Trigonometry, Pythagoras and Sine/Cosine Rules

Covers 3D Trigonometry, 3D Pythagoras, angles between a line and a plane, angles between two planes and sine/cosine rules.
By DrFrostMaths

Trigonometry 3D problems lesson

Three part lesson with grade A questions. Starter includes questions to recap and consolidate previous learning in accordance with the route map (scheme of work) i have uploaded.
By mistrym03

Craig Barton, TES Maths adviser

Craig is a secondary maths teacher in the North of England.

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