Curriculum update A level Mathematics and Further Mathematics from September 2017
General points All A levels will be linear from September 2017 AS can be co-taught with A level, but will have a separate exam which will not count towards the A level AS is the first half of A level AS content will be examined at a higher level in A level, but at a lower level for the AS exam AS can be taught over 1 year or 2 years
Content - General Content is 100% specified for Mathematics and 50% specified for Further Mathematics Building on the new GCSE, Mathematics will now contain compulsory applied elements, specifically Mechanics and Statistics Ensuring your students are A level ready will now match preparing them for GCSE more effectively
APPLICATIONS CONTENT IN THE NEW A LEVEL
Comparison with M1 content M1 topics (current specifications) Edexcel AQA OCR MEI Motion-time graphs Constant acceleration (s.u.v.a.t) Vectors & Forces in 2D Newton s Laws Problem solving with Newton s laws Friction Projectile motion Variable acceleration (calculus) Impulse and Momentum (*Momentum only) * * Moments
Comparison with M1 content Mechanics topics in new AS level Edexcel AQA OCR MEI Vectors & Forces (inc. simple 2D problems) M1 M1 M1 M1 Constant acceleration (s.u.v.a.t.) in 1D M1 M1 M1 M1 Motion-time graphs M1 M1 M1 M1 Kinematics with variable acceleration (calculus) M2 M2 M1 M1 Newton s Laws M1 M1 M1 M1 Equilibrium (simple cases) M1 M1 M1 M1
Comparison with M1 content Additional Mechanics topics in full A level Edexcel AQA OCR MEI Constant acceleration (s.u.v.a.t.) in 2D M1 M1 M1 M1 Variable acceleration (with calculus) in 2D M2 M2 M1 M1 Resolving Forces M1 M1 M1 M1 Dynamics for motion in a plane M1 M1 M1 M1 Friction M1 M1 M1 M2 Moments (simple statics cases) M1 M2 M2 M2 Projectiles ( motion under gravity using vectors ) M2 M1 M2 M1
Comparison with S1 content S1 topics (current specifications) Edexcel AQA OCR MEI Representation of Data in graphical form Averages and Spread; Outliers and Skewness The laws of Probability; conditional probability Discrete Random Variables The Binomial Distribution Correlation and Regression * The Normal Distribution Sample means; Central Limit theorem Hypothesis testing for the Binomial Distribution
Comparison with S1 content Statistics topics in new AS level Edexcel AQA OCR MEI Representation of Data in graphical form S1 S1 S1 S1 Averages and Spread; outliers and Skewness S1 S1 S1 S1 Probability; independence of events S1 S1 S1 S1 Correlation and Regression S1 S1 S1 S1 Discrete Random Variables S1 S1 S1 S1 The Binomial Distribution S2 S1 S1 S1 Hypothesis testing for the Binomial Distribution S2 S2 S2 S1 Methods of sampling S3 S2 S2 S2 Using large data sets; cleaning data - - - -
Comparison with S1 content Additional Statistics topics in full A level Edexcel AQA OCR MEI Conditional probability; Venn diagrams S1 S1 S1 S1 Probability models for data - - - - The Normal Distribution S1 S1 S2 S2 Hypothesis test for the mean of a Normal Distribution S3 S2 S2 S2 Hypothesis tests for correlation coefficient S3 S3 S2 S2
INTERLUDE
Exploring Connections: Binomial Interlude
Distinct arrangements In your groups take your two colours of cubes and make all the possible linear arrangements of 2, 3, 4 or 5 cubes Choose one colour: sort your arrangements in order of decreasing numbers of that colour If you finish quickly, you can try to find all the arrangements for another number of cubes
Linking to the binomial expansion Consider the 4-cube combinations. Before we make our selections, the cube line could be considered to look like this: Each cube is red-or-white. Compare this with the expansion of (a+b) 4 (a+b) (a+b) (a+b) (a+b) Each term in the expansion contains a different combination of a and b.
Linking to the binomial expansion This combination: represents one of the possible combinations where 2 of the cubes are red and 2 are white. Compare this with the expansion of (a+b) 4 (a+b) (a+b) (a+b) (a+b) Selecting a from 2 brackets and b from 2 brackets gives us the term in a 2 b 2. How many ways are there of doing this?
Linking to the binomial expansion (a + b) 0 = 1 (a + b) 1 = 1a + 1b (a + b) 2 = 1a 2 + 2ab + 1a 2 (a + b) 3 = 1a 3 + 3a 2 b + 3ab 2 + 1b 3 (a + b) 4 = 1a 4 + 4a 3 b + 6a 2 b 2 + 4ab 3 + 1b 4 (a + b) 5 = 1a 5 + 5a 4 b + 10a 3 b 2 + 10a 2 b 3 + 5ab 4 + 1b 5
Linking to the binomial distribution: Picking two beads out of a bag, with replacement: p pink Probability: p 2 p q pink q p quartz pink 2pq quartz q quartz q 2
Content General (Maths and FM) Specifications must encourage students to: reason logically and recognise incorrect reasoning generalise mathematically construct mathematical proofs
Content General (Maths and FM) Specifications must encourage students to: decide on the solution strategy solve a problem in context understand the relationship between problems in context and mathematical models to solve them
Content General (Maths and FM) Specifications must encourage students to: read and comprehend mathematical arguments read and comprehend mathematical articles use technology such as calculators and computers effectively
Use of technology Calculators used must include the following features: an iterative function the ability to compute summary statistics and access probabilities from standard statistical distributions the ability to perform calculations with matrices up to at least order 3 x 3 (FM only)
Use of technology The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics
INTERLUDE
Planning a Linear Scheme of Work: Tracking Kinematics from GCSE to A level
Think about these ideas: Kinematics and motion graphs Gradient/tangent questions s.u.v.a.t. formulae Deriving the s.u.v.a.t. equations Applications of calculus to displacement, velocity, acceleration Extended to 2D and 3D with use of vectors Gravity, friction, resistance forces, projectile motion
Motion graphs (distance/time; velocity/time)
More realistic Graphs
Interpreting kinematics graphs Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph Mathematics AS and A level content Department for Education, December 2014
v (m/s) The s.u.v.a.t. equations: v = u + at v - u s = ut + 1 2 at2 u v 2 = u 2 + 2as t s = 1 2 (u + v)t s = vt 1 2 at2
velocity (m/s) What if the acceleration is not constant? We can still use gradient and area time (s)
Projectile motion
Where are these topics taught at the moment? Tick to show which modules contain the necessary maths for the topics named.
Where are these topics taught? Kinematics in GCSE Gradient/tangent questions in GCSE and M1 s.u.v.a.t. formulae in GCSE Physics Deriving s.u.v.a.t. in AS Mathematics (M1) Applications of calculus to displacement, velocity, acceleration in A level Mathematics (M2) Extended to 2D with use of vectors at A level (M2) Projectiles (M1 or M2)
Where will these topics be taught? In future, the integrated nature of the course and the linear structure of the exam will mean that kinematics topics will be in: GCSE Mathematics A Level Mathematics Schemes of work can adopt a thematic rather than modular approach and examiners will be able to set synoptic questions which test both pure and applied mathematics.
Further Mathematics 50% content specified, all pure Awarding bodies can decide on the other 50% so they may (or may not) be significant differences There may be some element of choice retained in FM All exam boards should be producing at least one specification that can run alongside Mathematics Awarding bodies choose, may be pure or applied Prescribed content, all pure.
AS FM A level FM This is designed to be a separate, valuable qualification It must be able to be cotaught with the full A level in Further Mathematics AS Further Mathematics must be at least 30% Pure Mathematics Awarding bodies choose, may be pure or applied Prescribed content, all pure. AS FM Optional prescribed content Specifically prescribed content
AS FM A level FM The 30% Pure Mathematics content of AS Further Maths has to be constructed from some compulsory content: Matrices Complex Numbers together with some additional Pure Maths content chosen from the compulsory content for A Level Further Maths. Awarding bodies choose, may be pure or applied Prescribed content, all pure. AS FM Optional prescribed content Specifically prescribed content
AS FM Additional FP content What additional 10% of content would you select? It must fulfil the following criteria: About half the size of the prescribed AS content Can be co-taught with AS Mathematics Forms a coherent course (along with some applied content) Optional prescribed content Specifically prescribed content
THINGS TO THINK ABOUT AND DISCUSS
Discussion Points What will the new A levels mean for you and your department? Is there a whole school approach? What are the implications for planning and staffing? How will you go about delivering a linear specification? Will you enter all students for AS at the end of year 12? How will you incorporate Further Maths into your offer? Has your department considered running a separate AS Level qualification in Maths (possibly over 2 years)?
Which awarding body? Remember content is 100% specified for Mathematics, so all boards will cover the same content At the moment there seem to be only minor reasons for using the same awarding body for Maths and Further Maths as there are no modules to swap around Using more than one awarding body gives you access to both sets of resources.
Which awarding body? Consider choosing the awarding body which looks: the best match for your department s skills the most useful for your students likely career path the best value resources, long term the most fun to teach rather than the easiest or most familiar?
Professional development The awarding bodies are due to submit their specifications to OFQUAL in June 2016.Following this the FMSP will be offering: A pack and associated training to be used by teachers to support the development of their department. One-day courses in the Autumn term looking at the new AS and A Level Maths and at the new AS and A Level Further Maths. LOPD courses in all aspects of the new courses (including using technology)
What now? Wait for the awarding bodies to release their specifications and plan time to look at them all when they become available Don t rush to buy books: online resources are more flexible and may be better value in the long run. Think about the development needs of your department, especially preparing for a linear course where applications are integrated with pure. Talk to your Area Coordinator about local plans for PD. Allow time to reflect on what will work for you.
The Further Mathematics Support Programme Our aim is to increase the uptake of AS and A level Further Mathematics to ensure that more students reach their potential in mathematics. The FMSP works closely with school/college maths departments to provide professional development opportunities for teachers and maths promotion events for students. To find out more please visit www.furthermaths.org.uk