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Exact Trig Values in Depth

Craig Barton

@mrbartonmaths

Jo Morgan

@mathsjem

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2013

Gove announces GCSE reform

2015

First teaching of new GCSE maths specification to Year 10

2017

First new GCSE maths exams

2020

Global pandemic

2023

Now

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1MA0

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1MA1

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"Memorisation is a necessary precondition of understanding."

“Knowledge is a necessary precondition of understanding."

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When is knowing about (but not necessarily memorising) exact trig values helpful?

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Why else learn exact trig values?

Opportunity to deepen understanding of trigonometry�

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Exact trig values on Foundation Tier?

Exercise in memorisation: doesn’t test what we want to test.
Unnecessary distraction.
It leads nowhere.
Without knowledge of surds it makes no sense.

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	AQA F	AQA H
Nov 22	Y	Y
Jun 22	N	Y
Nov 21	Y	Y
Nov 20	Y	N
Nov 19	N	Y
Jun 19	N	Y
Nov 18	N	Y
Jun 18	N	Y
Nov 17	N	N
Jun 17	Y	Y

Appearance of Exact Trig Values on GCSE Paper 1

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1. Exact trig values in GCSE exams��2. Sequence planning��3. Memorisation…?��4. Resources, problems, opportunities

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Exact Trig Values in Higher GCSE Exams

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AQA JUN 17 1F

Av score: 0.06

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AQA NOV 20 1F

Av score: 0.13

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AQA NOV 21 1F

Av score: 0.38

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AQA NOV 19 1H

Av 0.46

AQA JUN 18 1H

Av 1.02

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Memorisation
Substitution
Surds
Fractions
Multiplication

Trigonometry

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AQA JUNE 17 1H

0.97

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AQA JUNE 17 1H

0.97

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AQA JUNE 19 1H

Av 1.01

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AQA NOV 18 1H

Av score 0.29

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AQA NOV 21 1H

Av score 0.61

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Sequence Planning

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Typical approach…?

Year 7	Angles in triangles
Year 8	Pythagoras’ Theorem
Year 9	Introduction to right angled trigonometry
Year 10	More right angled trigonometry (including bearings and possibly 3D trig)
Year 11	Non right-angled trigonometry + trig graphs + exact values

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n = 791

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GCSE sequencing…?

1	Recap surds	8	Method selection: non-RAT
2	Recap right-angled trig	9	3D Trigonometry
3	Exact values: derive	10	½absinC
4	Calculations with exact values	11	Trig graphs*
5	Right-angled probs (inc exact values)	12	Exact values & trig graphs
6	Sine Rule	13	Ambiguous case
7	Cosine Rule	14	Consolidation + problems

* Revisit at graph transformations

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n = 791

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Use exact trig values throughout teaching of non right-angled triangle trigonometry.

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AQA Certificate in Further Maths

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AQA Cert FM

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Interleaving opportunities

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Memorisation

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How to spell?

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Things to remember:

What goes in the top row
Order (sin vs cos)
Numbers in each row
Steps – root, divide by two
How to derive tan

Maths skills/knowledge required:

Simplification

Things to remember:

Which two triangles to draw

Maths skills/knowledge required:

Pythagoras’ Theorem
Right-angled trigonometry

1 mark for stating a correct value

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Resources, Problems, Opportunities

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Boss Maths

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sin90, sin60, sin45, sin360

The above shows all irrational numbers except for one. Which one?

Brilliant.org

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MathsPad

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Don Steward ♥

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2

1

3

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Resourceaholic.com

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Final Thoughts…

Higher

Give exact trig values some time (if you can).
Use this topic to recap and deepen understanding of trigonometry and surds.
Order lessons to maximise interleaving opportunities.

Foundation

Consider whether it’s worth the time and brain space.
Prioritise.