1. New GCSE Mathematics GCSE Mathematics (First teaching Sept 2017)
First assessment Summer 2018 (M1, M2, M3, M4 only)
Assessment January (M1, M2, M3, M4 only)
First full award all units M1 – M8 Summer 2019

2. Legacy GCSE Mathematics
Assessment T units January 2018
Assessment T units Summer 2018
Final assessment for T units January 2019

3. Agenda Revision of GCSE Mathematics Qualifications (for first teaching September 2017)
10.00am – 11.15am GCSE Mathematics specification
and Specimen Assessment Materials
11.25am – 12.15pm Planning Frameworks – Ruth Crooks
12.15pm – 12.45pm Lunch
1.00pm – 2.30pm GCSE Mathematics Problem Solving
2.30pm – 3.00pm Plenary Q & A

4. Timeline for new GCSE Maths specification
Legacy specification will be assessed until summer 2018
There will be a mop up in January 2019
New GCSE first full award will be in summer 2019

5. GCSE Mathematics Unique features Employability New specification
Four distinct pathways
Flexibility retained within these pathways
Foundation level – level 1 or level 2 in functional mathematics
New grading A* and C*
Qualification is linked to and builds on the learning experiences from Key Stage 3 as required for the statutory Northern Ireland Curriculum
Potential pathway into a range of careers in the STEM sector
Programme For Government targets –
20. Increase uptake in economically relevant Science, Technology, Engineering and Mathematics (STEM) places (DEL)
21. Increase the overall proportion of young people who achieve at least 5 GCSEs at A* - C or equivalent including GCSEs in Maths and English by the time they leave school including increase the proportion of young people from disadvantaged backgrounds who achieve at least 5 GCSEs at A* - C or equivalent including GCSEs in Maths and English
42 Improve literacy and numeracy levels among all school leavers, with additional resources targeted at underachieving pupils

6. GCSE Mathematics Foundation
Specification at a glance
55%
2019)
2019)
Grades D, E, F, G
Level 1 in Functional Maths
2019)
Grades C*, C, D, E, F
Level 1/2 in Functional Maths

7. GCSE Mathematics Higher
Specification at a Glance
2019)
Grades B, C*, C, D, E
2019)
Grades A*, A, B, C*, C

8. New GCSE Mathematics
The assessment structure of the qualification has changed. Content has been divided into 8 units – M1, M2, M3, M4, M5, M6, M7 and M8.
M1, M2, M5 and M6 are Foundation Papers. M3, M4, M7 and M8 are Higher Tier papers.
The completion papers: M5, M6, M7 and M8 must be taken after M1, M2, M3, and M4. This is because the completion papers are synoptic.
The completion papers are of greater demand – M8 is now the most demanding paper because of the volume of content and the additional content which has been added to M8. Some of this content is new; other content has been moved from T4.

9. New GCSE Mathematics
The grading structure has changed. Grades now include a C* and a new A* based on a new formula
A ‘functional elements’ profile will be extracted from the M1 and M2 papers. These papers allow for extra reading time.
Level 1 functional mathematics will be awarded for attainment in M1 and level 2 functional mathematics will be awarded for attainment in M2 with level 1 if a designated standard is reached.
The new assessment objectives present greater demand and challenge.
QWC will be assessed through AO2. There will be no starred questions on the front cover indicating QWC.

10. Assessment objective weightings
The table below sets out the assessment objective weightings
for each assessment component and the overall GCSE qualification.
Assessment Objective
Unit Weighting
Foundation Tier
M1 and M5 or
M2 and M6
Higher Tier
M3 and M7
M4 and M8
AO1
47 – 53%
37 – 43%
AO2
22 – 28%
27 – 33%
AO3
Currently AO1 45 – AO2 25 – 35 AO

11. GCSE Support Materials
Planning Frameworks
Newly added content and content removed
Progression of subject content document e.g M1 → M2 → M3 → M4 etc
Mapping of content in legacy specification to the new specification (e.g T4 → M8)
BBC Bitesize
List of terminology/mathematical language
Guidance on new topics in the specification
Problem solving workshops

12. Specimen Assessment Materials (SAMS)
Overview of the SAMS
Q & A

13. Modules
Max UMS
400
Target A*
M4/M8 A
320
M4/M8 or M4/M7 B
292
M3/M7 C*
268
M2/M6 or M3/M7 C
240
M2/M5 or M2/M6 D
200
M1/M5 E
160 F
120 G 80

14. Modules
Max UMS
Max Grade M1
107 D M2
131 C* M3
143 B M4
180
A/A* M5 M6
160 M7
175 M8
220

15. Possible Combinations
Max UMS
Max Grade
M1 and M5
238 D
M1 and M6
267 C
M1 and M7
282 C*
M1 and M8
327 A
M2 and M5
262
M2 and M6
291
M2 and M7
306 B
M2 and M8
351
A*/A
M3 and M5
274
M3 and M6
303
M3 and M7
318
M3 and M8
363
M4 and M5
311
M4 and M6
340
M4 and M7
355
M4 and M8
400 A*

16. Top ⅓ of grade Cs and bottom ⅓ of grade Bs

17. New Awarding Structure
SUMMER 2016 MATHS
old
new
A* UMS Boundary
360
378
cum% at A*
11.9
6.5
cum% at A
29.8

18. The Planning Framework
The GCSE Mathematics Planning Framework is a flexible planning tool
Designed to support delivery of the Revised GCSE Mathematics specification

19. The Planning Framework is not …
Mandatory
Prescriptive
Exhaustive

20. The Planning Framework is …
Based on the Revised GCSE Mathematics Specification
Draws on the ‘Guidance on Teaching, Learning and Assessment at Key Stage 4’ publication

21. The Planning framework
Outlines the progression of subject content
Identifies newly added content
Indicates how content in the legacy specification maps to the new specification

22. The Planning Framework
Provides suggestions for activities:
Knowledge and understanding
Subject specific skills
Cross-Curricular Skills
Thinking Skills and Personal Capabilities

23. Subject-specific skills
Content and Process skills
Mathematical techniques and Mathematical thinking

24. Subject-specific skills
Using and applying standard techniques
Reasoning, interpreting and communicating mathematically
Solving problems within mathematics and in other contexts

25. Using and applying standard techniques
Accurately recalling facts
Accurately recalling terminology
Accurately recalling definitions
Using notation correctly
Interpreting notation correctly
Accurately carrying out routine procedures
Accurately carrying out set tasks requiring multi-step solutions

26. Reasoning, interpreting and communicating mathematically
Making deductions to draw conclusions from mathematical information
Making inferences to draw conclusions from mathematical information
Constructing chains of reasoning to achieve a given result
Interpreting information accurately
Communicating information accurately
Presenting arguments
Presenting proofs
Assessing the validity of an argument
Critically evaluating a given way of presenting information

27. Solving problems within mathematics and in other contexts
Translating problems in mathematical contexts into a process
Translating problems in mathematical contexts into a series of processes
Translating problems in non-mathematical contexts into a mathematical process
Translating problems in non-mathematical contexts into a series of mathematical processes

28. Solving problems within mathematics and in other contexts
Making connections between different parts of mathematics
Using connections between different parts of mathematics
Interpreting the results in the context of the given problem
Evaluating methods used
Evaluating results obtained
Evaluating solutions to identify how they may have been affected by assumptions made

29. Becoming functional with Mathematics
Subject-specific skills
Content and Process skills
Mathematical techniques and Mathematical thinking

30. Becoming functional with Mathematics
Use and apply standard mathematical techniques1 to carry out routine mathematical procedures and set tasks.
Embed the procedures or set tasks into a mathematical problem.
Use and apply mathematical thinking2 and mathematical techniques to solve a mathematical problem.
Embed the mathematical problem into a real-life problem.
Use and apply mathematical thinking and mathematical techniques to solve a real-life problem in a mathematical way.

31. Becoming functional with Mathematics
Every Mathematics lesson is an opportunity to develop Mathematical Techniques
Every Mathematics lesson is an opportunity to develop Mathematical Thinking

32. The Planning Framework
Provides suggestions for a range of teaching and learning activities
Provides flexibility to adapt and develop ideas for your educational setting

33. PROBLEM SOLVING

34. Problem-solving skills A problem is something you do not immediately know how to solve. There is a gap between where you are and getting started on a path to a solution. This means that your students require thinking and playing-with-the-problem time. They need to test out ideas, to make conjectures, to go up ‘dead ends’ and adjust their thinking in the light of what they learn from this, discuss ideas with others and be comfortable to take risks. When students are confident to behave in these ways they are then able to step into problems independently rather than immediately turning to us as teachers to ask what to do!
As teachers we can support our students to develop the skills they need to tackle problems by the classroom culture we create. It needs to be one where questioning and deep thinking are valued, mistakes are seen as useful, all students contribute and their suggestions are valued, being stuck is seen as honourable and students learn from shared discussion with the teacher, Teaching Assistant(if present) and peers.

35. New neighbours moved in next door to me.
I asked the mother how old were her three sons?
She told me that the product of their ages was (all ages are whole numbers)
I told her that she hadn’t given me enough information so she told me that the sum of their ages was the same as my house number.
I told her that I still couldn’t figure their ages so she told me that her eldest son played the piano.
With that, I said “Now, I know their ages! They’re x, y and z

36. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 & 36
Different products could be
1 X 1 X 36
1 X 2 X 18
1 X 3 X 12
1 X 4 X 9
1 X 6 X 6
2 X 2 X 9
2 X 3 X 6
3 X 3 X 4

37. House number is sum of ages
1 X 1 X 36 = 38
1 X 2 X = 21
1 X 3 X 12 = 16
1 X 4 X = 14
1 X 6 X = 13
2 X 2 X 9 = 13
2 X 3 X 6 = 11
3 X 3 X 4 = 10

38. I live in number 13
1 X 1 X 36 = 38
1 X 2 X = 21
1 X 3 X 12 = 16
1 X 4 X = 14
1 X 6 X = 13
2 X 2 X 9 = 13
2 X 3 X 6 = 11
3 X 3 X 4 = 10

39. Polya’s First Principle: Understand the problem
Polya’s Second Principle: Devise a plan
Polya’s Third Principle: Carry out the plan
Polya’s Fourth Principle: Look back

40. PROBLEM SOLVING
Gather information
Draw sketch, visualisation
Write analysis – steps to solve problem, solve a parallel problem, perhaps formulae, own knowledge
Solve numerically including units
Check – does the answer make sense?

41. Language
ADDITION: sum, plus, and, total, increase, more, raise, both, combined, in all, altogether, additional, extra, appreciate
SUBTRACTION: less than, more than, decrease, difference, reduce, change, lost, nearer, farther, left, remain, fell, dropped, discount, depreciate
MULTIPLICATION: multiplied, of, product, times, as much, by, twice, three times, tripled, every
DIVISION: divide evenly, cut, split, each, every, average, equal pieces, out of, ratio, shared, quotient
Toolkit
Properties of triangles, quadrilaterals, Pythagoras, area, circle details, prime, even and odd numbers, difference of 2 squares, symmetry ……….

42. Making an orderly list
How many ways can you arrange the letters A, B and C?
ABC (A first)
ACB (A first)
BAC (B first)
BCA (B first)
CAB (C first)
CBA (C first)

43. Foundation Paper Summer 2016

44. What does the question ask? Mark it on the diagram!
12cm
7cm x x
What does the question ask?
Mark it on the diagram!

45. 12cm
7cm x x

46. What do I know about a parallelogram
What do I know about a parallelogram? My toolkit - 4 sides, opposite sides equal, opposite sides parallel, total of 360o, opposite angles equal, adjacent angles add up to 180o

47. Method 1 Angles add up to 360o
4x – x + 2x x = 360
12x + 12 = 360
12x = 348 so x = 29

48. Method 2 Opposite angles equal
4x – 23 = 2x + 35
2x = 58
x = 29

49. Method 3 Adjacent angles sum is 180o
2x x = 180
5x =
5x = 145 so x = 29

50. The Great Race There are nine cars in the race.
The white car finished six places behind the blue car.
It was raining on the day of the race.
The yellow car was in the middle of the order of finishing
5. The green car finished ahead of the black car.
6. All the cars finished the race.
7. The orange car finished between the green and the yellow cars.
8. Only one car finished ahead of the blue car
The purple car finished behind the white car.
The pink car finished between the yellow and the black cars.
11. The average speed of the cars was 102mph.
12. The red car finished four cars ahead of the yellow car
13. The green car finished before the yellow car
14. Find the finishing order of the cars.

51. Over the course of numbering every page in a book, a mechanical stamp printed 2929 individual digits. How many pages does the book have?
For a set of five whole numbers, the mean is 4, the mode is 1, and the median is 5.
What are the five numbers?
A farmer has hens and sheep. There are sixteen heads and thirty-eight feet between these creatures. How many hens does
the farmer have?

52. ABCD is a trapezium of area 28m2
BC is parallel to AD. BA is perpendicular to AD.
Given that BC is 6cm and AD is 8cm, what is the exact length of CD? B C A D

53. ABCD is a trapezium of area 28m2
BC is parallel to AD. BA is perpendicular to AD.
Given that BC is 6cm and AD is 8cm, what is the exact length of CD?
6 cm B C
4 cm A D
2 cm
Area of trapezium = ½(6 + 8) x AB = 28
AB = 4
Drop perpendicular from C onto AD.
CD2 =
CD2 = 20
CD = √20 = √4 x √5 = 2√5

56. If R is the radius of the large circle and r is the radius of
the small circle then area
required is πR2 - πr2 r O R
R2= r2 + 52
R2 - r2 = 52
πR2 - πr2 = 25π

60. Let’s solve a parallel problem. Suppose there were 10 sweets in the bag.
Probability of choosing 2 orange sweets = 6/10 x 5/9 Letting sweet numbers be n
Probability of choosing 2 orange sweets = /n x (6-1)/(n-1) Hence 6/n x 5/(n-1) = 1/3

61. At a birthday party, one-half drank only lemonade, one-third drank only cola, fifteen people drank neither, and nobody drinks both. How many people were at the party?

62. At a birthday party, one-half drank only orange, one-third drank only cola, fifteen people drank neither, and nobody drinks both. How many people were at the party? Solution As 1/2 + 1/3 = 3/6 + 2/6 = 5/6, we know that 1/6 drank neither. So there must have been 6 x 15 = 90 people at the party

63. Mr. and Mrs. Oeuf have two daughters and three sons.
At Easter time every member of the family buys one cream egg for each other member.
How many cream eggs will be bought in total?

64. Solution
There are seven members of the family and each person must buy six cream eggs.
Therefore, total number of cream eggs is 7 x 6 = 42.
You could use this idea to work out the following,
(i) In a season, 12 schools play home and away matches in a rugby league. How many matches that take place in a season?
(ii) In a netball tournament there are 6 teams and each team plays each other team once. How many matches will take place?
(iii) In a form class there are 30 girls and 2 are picked at random. How many ways are there of picking them?

65. Find the area of the shape above9 3 5 2 6 4
Find the area of the shape above

66. Find the area of the shape above Area = 5 x 9 + 6 x 4 + 2 x 6 + 9 x 4 3 5 2 6 4
Find the area of the shape above
Area = 5 x x x x 4
Area = = 117

67. Find the area of the shape above 9 3 5 2 6 9 4 17
Find the area of the shape above
Area = 17 x 9 = 153 minus 3 x 2 and 5 x 6
Area = 153 – 6 – 30 = 117

68. Let number of boys be 9n and number of girls be 10n
Extra 17 boys come so there are now 9n + 17 boys
New ratio is 9n + 17:10n and that equals 8:7
7(9n + 17) = 8(10n)
63n = 80n
119 = 17n
n = 7
Hence 10 x 7 = 70 girls

69. Divisible by 2
Divisible by 3
Divisible by 4 Prime factors 2 x 2
Divisible by 5
Divisible by 6 Prime factors 2 x 3
Divisible by 7
Divisible by 8 Prime factors 2 x 2 x 2
Divisible by 9 Prime factors 3 x 3
Divisible by 10 Prime factors 2 x 5
Number is 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520

71. Higher Paper Summer 2014

72. Right angled triangle Pythagoras Half a rectangle Area = ½bh
Even & Odd numbers can be written 2n and 2n + 1 O x O = O O x E = E E x E = E

73. Pythagoras (y + 1)2 = y2 + x2 y2 + 2y + 1 = y2 + x2 2y + 1 = x2
Even & Odd numbers can be written 2n and 2n + 1 So 2y + 1 is an odd number Hence x2 is an odd number And since O x O = O, x is odd

74.
Maths challenge.net

75.
mathematics/curriculum/seniorsecondary#page=1
http%3A%2F%2Fwww.asianscholarship.org%2Fasf%2Fejourn%2Farticles%2FLim%2520Chap%25 20Sam2.doc&ei=HSBNVeXNApCV7Abd44PACg&usg=AFQjCNHeTGCRJguHPQYvePOhFXVT3VYkdA

76. Why choose CCEA? mbvbmvbmvb
We support Learners - CCEA puts the learner at the centre of everything we do. We think about what learners need for life and work and then build solutions to meet those needs. We do this for the entire curriculum – from Foundation and Early Years to A level and beyond.
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We are Local - CCEA is Northern Ireland’s awarding body. We understand local needs and we are focused on providing services and products for learners in Northern Ireland. This also means we’re near you, should you need help or support.
We are Listening - CCEA listens to those who use its products and services; this means listening to teachers, employers and learners, and taking action to ensure better outcomes for learners. This approach ensures that we develop relevant, high quality and innovative specifications and support.

77. Keeping you informed The ReVision microsite – ccea.org.uk/therevision
Essential updates
Specifications & SAMs
Monthly e-Vision newsletter
Subject specific e-alerts Face to face
Social media
Twitter @ccea_info
Facebook ccea.info
Don’t forget to register for your updates on the microsite – ‘keep up to date’ section

78. Contacts: GCSE Mathematics
Education Manager: Joe McGurk
Telephone: Ext (2106)
Subject Support Officer: Nuala Tierney
Telephone: Ext (2292)
Specification, sample assessment and support materials available on the subject microsite at