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Mathematics · KS3 to A Level · £6.99

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Secondary maths department handbook — KS3 to A Level

One book for the whole department: the head of maths who has to build the curriculum and the teacher who has to teach the bottom set on Friday afternoon. Built on what the specifications actually say, read from the current documents.

£6.99The whole playbook, 78 pages

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One purchase covers the school that buys it. Print it, copy it, hand it round your department. Not for passing to other schools or uploading anywhere.

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Read before publication by the serving head of that department and by senior leaders, in school.

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Schools that have bought from Empower Educators include Nottingham High School, Northampton High School GDST and Sutton Valence School.

Everything else this site has for Mathematics: Mathematics teaching resources

1 Curriculum
2 Fluency
3 Reasoning
4 Evidence
5 Standard

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Mathematics is the subject everyone has an opinion about, and the one where a scheme of work is most often mistaken for a curriculum. A list of topics in an order is not a sequence. A sequence records what has to be secure before the next thing can be taught.

This booklet is written for the whole department at once. A head of maths can read it as a curriculum and quality-assurance document; a teacher can open it at the page they need on a Friday afternoon. The specifications were read from the current documents rather than from summaries, and where the boards differ the difference is stated rather than blended.

Written to: The current GCSE and A Level mathematics specifications, read in full
Intended for: department CPD, planning and curriculum review
Extent: 78 pages · 75 sections

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The Maths playbook in thirty seconds

A quick look inside: common misconceptions drawn twice with the wrong rule beside the fix, the five pillars, a full lesson plan and templates you can print and write on.

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Contents

All 75 sections

Taken from the book’s own contents page, so the page numbers are the real ones.

THE CASE

01 The Subject Everyone Has an Opinion About p3

02 Where Mathematics Departments Drift p4

THE THEORY

03 How Mathematical Understanding Actually Builds p5

04 Fluency, Reasoning and the Space Between p6

THE PRACTICE

05 Pillar 1 — Curriculum: Sequence Before Coverage p7

06 Pillar 2 — Fluency: Automatic, Not Merely Correct p8

07 Pillar 3 — Reasoning: The Part That Is Not Optional p9

08 Pillar 4 — Evidence: Knowing What They Cannot Do p10

09 Pillar 5 — Standard: One Department, One Expectation p11

10 What Should a Year 7 Actually Arrive Knowing? p12

11 Three Years, Not a Run-Up to GCSE p13

TEACHING MATHEMATICS

12 Modelling: The Part Students Cannot See p14

13 Questioning That Reveals Thinking p15

14 Practice That Is Worth the Time p16

47 Lesson Structures That Are Not Formulas p49

48 Mathematical Language and Vocabulary p50

61 Six Topics, Three Ways p63

MISCONCEPTIONS

15 Number and Place Value p17

16 Algebra, Ratio and Proportion p18

17 Geometry, Statistics and Probability p19

62 The Bank — Number, Indices and Surds p64

63 The Bank — Algebra, Geometry and Data p65

REPRESENTATIONS

18 Models That Do Mathematical Work p20

REASONING

19 Problem Solving Without the Mystique p21

20 Proof, Generalisation and Mathematical Argument p22

59 The Problem-Solving Workflow p61

ASSESSMENT

21 Assessment That Changes Teaching p23

22 Feedback That Students Can Act On p24

THE FOUR BOARDS

23 GCSE Mathematics, Compared p25

24 The Tier Decision p26

64 Using Board Knowledge Strategically p66

71 GCSE Mathematics: The Difference Is the Mark Total p73

72 A Level Mathematics: Same Content, Three Different Shapes p74

EXAM PREPARATION

25 Using Past Papers Intelligently p27

A LEVEL

26 The GCSE to A Level Handover p28

27 Teaching the Three Strands p29

EVERY STUDENT

28 SEND, Dyscalculia and Working Memory p30

29 High Attainers: Depth, Not Acceleration p31

60 Tiering, Grouping and Genuine Challenge p62

CULTURE

30 A Classroom Where Being Stuck Is Normal p32

31 Routines, Equipment and the Calm Maths Room p33

32 Homework and Technology, Used Deliberately p34

33 AI in a Mathematics Department p35

50 Talking to Parents About Mathematics p52

FOR LEADERS

34 The Head of Mathematics p36

35 Data That Leads to a Decision p37

36 Quality Assurance Without Fear p38

37 Developing Mathematics Teachers p39

38 The First 90 Days p40

49 Department Meetings and CPD p51

65 Recommended Reading and Where It Helps p67

66 Ofsted and the Mathematics Department p68

SCENARIOS

39 Six Situations, and Where to Look First p41

40 Three More, and the Leadership Question Underneath p42

THE TOOLKIT

41 Templates 1–3 — Curriculum and Sequence p43

42 Templates 4–7 — Assessment and Misconceptions p44

43 Templates 7–10 — Monitoring and Meetings p45

44 Templates 10–12 — Self-Evaluation and Improvement p46

45 Templates 12–14 — For Teachers and New Staff p47

46 The Teacher’s Page — Mathematics p48

OUTSTANDING LESSONS

51 What an Outstanding Lesson Actually Looks Like p53

52 Lesson 1 — Ratio, Year 8 p54

53 Lesson 2 — Solving Equations, Year 7 p55

54 Lesson 3 — Trigonometry, Year 10 p56

55 Lesson 4 — Problem Solving, Year 9 p57

CURRICULUM

56 A Scheme of Work That Records Dependencies p58

57 Years 8 to 11, in Outline p59

58 A Five-Lesson Sequence: Algebraic Manipulation p60

THE MATHEMATICIANS

67 Eight Mathematicians, and What Each One Gives a Lesson p69

68 Four Thousand Years, and Where It Sits in Your Curriculum p70

DRAWING THE HARD IDEAS

69 Three Misconceptions, Drawn Twice p71

70 One Problem, Three Methods, One Discussion p72

THE EVIDENCE

73 Eight Recommendations, and the One Departments Get Wrong p75

CLOSING

74 One Department, One Standard p76

75 References and Evidence Base p77