GCSE Mathematics B – Modular Delivery Options Modular specification allows you to deliver the course in the way that best suits you and your students with the option of Teaching Unit 1 or 2 first, though we advise that Unit 3 is taken towards the end of the course. Start the course early in Year 9 Make greater use number of assessment windows available for entries and mock examinations Mix-and-match tiers, to improve student’s final grade. Using ResultsPlus Progress – diagnostic tests before you start teaching a unit Using ResultsPlus & ResultsPlus booster to improve performance on resits

Delivery Model 1:Two year course (starting with Unit 1 or 2) Year 11 November Year 10 March Year 10 June Year 11 March Year 11 June Resit opportunity for second unit Unit 3 mock or live exam Unit 3 exam or resit opportunity Teach Units 1 & 2 Second unit exam (resit opportunity for first unit) First unit exam

Delivery Model 2: Start teaching the GCSE course in Year 9 (starting with Unit 1 or 2) Year 9 Year 11 November Year 10 November Year 10 March Year 10 June Year 11 March Year 11 June 2012 Unit 3 exam or resit opportunity Unit 3 live or mock exam Resit opportunity for Units 1 & 2 Second unit exam (resit opportunity for first unit) First set of live practice papers for Units 1 & 2 Start teaching first unit First unit exam

Delivery Model for linear centres (from June 2012 onwards) Year 9/10 Year 11 June Year 10 June Year 11 November Year 11 March Mock exam Opportunity/ Enter for live exam Mock exam opportunity Start teaching the GCSE linear course Enter students on a 1 year accelerated course for the exams Enter for live exam Year 12 November Resit opportunity Mock examinations can be taken in a number of ways: (a)In the traditional way by setting the mock papers internally (b)Using the Mock Paper Analysis – setting a past paper as a mock, and we will provide the full ResultsPlus analysis at cohort and individual student level (c)Enter students for the live exams. If they do well, they can keep their grades. Otherwise ResultsPlus analysis can help with remediation ahead of the live exam

Impact on teaching and learning We are moving from AO1Using and applying (20% included within subject knowledge) (i)Problem solving(ii) Communicating(iii) Reasoning AO2Number and algebra50 – 55% AO3Shape Space and Measures25 – 30% AO4Handling Data18 – 22%

Impact on teaching and learning To AO1 Recall and use their knowledge of the prescribed content 45 –55% Number and algebra Geometry and measures Statistics and probability AO2 Select and apply mathematical methods 25 –35% in a range of contexts AO3 Interpret and analyse problems 15 – 25% and generate strategies to solve them

Impact on teaching and learning In essence About 50%Techniques split about Number and algebra50 – 60% Geometry and measures20 – 30% Statistics and probability15 – 25% About 30%Choose an appropriate method to solve a problem About 20%Analyse a problem and find a method of solution

Impact on teaching and learning In addition Functional skills 30 – 40% Foundation 20 – 30%Higher Quality of written communication About (5% included within the total paper)

Quality of Written Communication (QWC) QWC will… account for around 5% of the marks in total generally on questions that are worth 4 marks or more be indicated with asterisk by the question number on the examination paper, and shown in mark scheme

Quality of Written Communication (QWC) Students will be assessed on their ability to: i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labelling conventions e.g. where mathematics shown supports a decision

ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. e.g. algebraic/geometric proofs iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used. e.g. charts are drawn

Impact on teaching and learning This means there will be more questions that are set in a context will have elements of functional skills will have more words will be problems to solve will need more than one skill area in its solution will expect candidates to show their working

Instead of Find 65% of £120. (2 marks) You might get Jules buys a new jacket in a sale. The original cost of the jacket was £120 In the sale the price is reduced by 35%. What is the sale price of the jacket? (3 marks) Both these questions would be AO1 with the second having functional skills. Sale 35% off

Instead of Solve 10x + 14 = 22 You might get The perimeter of this shape is 22 cm. 2x + 7 x 3x x All measurements Find the area.are in centimetres The second question is AO2 because there are different methods of solution and candidates would have to choose which method to use.

This question can be seen on old and new specs £3.80 £ g 175g Large Regular A Large tub of popcorn costs £3.80 and holds 200g. A Regular tub of popcorn costs £3.50 and holds 175g. Which is the better value for money? (3 marks) This would be AO3 as it is a problem to solve and candidates would have to decide on their strategy. Best buy questions may become a regular feature on our papers though with frequent use they will possibly become routine and cease being a problem to solve.

Questions that are problems to solve Eggs for sale Example Question Sam and Linda keep hens and sell the eggs that the hens lay. They have 140 hens. Each hen lays an average of 6 eggs each week. The hens each eat about 100g of food each day. The hen food costs £6.75 for a 25kg bag. What is the least Sam and Linda need to charge for a dozen eggs so that they cover the cost of the hen food? (6 marks)

Mark schemes Outline mark scheme Per day M1 140 hens eat 100 × 140 = g = 14 kg each day M1 A1Cost of 14 kg of hen food = 6.75 ÷ 25 × 14 = £3.78 M1Number of eggs 140 × 6 ÷ 7 = 120 each day 120 eggs = 10 dozen M1Food for 1 dozen eggs costs £3.78 ÷ 10 = 37.8p C1Cost for one dozen 38p Per hen M11 hen eats 100g each day M1 A125 kg ÷ 100 g = ÷ 100 = 250 days M1 A16.75 ÷ 250 = 2.7 p each day It takes 14 days to lay a dozen eggs. M1Cost of food = 2.7 × 14 = 37.8p C1Cost for one dozen 38p Per week M1140 × 6 = 840 eggs per week or 70 dozen M1 A1Weight of food 100 × 140 × 7 = 98 kg M1Cost of food = 6.75 ÷ 25 × 98 = £26.46 M1Cost of food for 1 dozen eggs ÷ 70 = 37.8p C1Cost for one dozen 38p

Implications for teaching and learning The new programme of study at Key Stage 3 and the new programme of study at Key Stage 4 flags up the changes in the assessment objectives

Changes in emphasis More emphasis on problem solving More emphasis on finding an appropriate method More emphasis on showing your working More emphasis on proof and explaining your results More emphasis on using different skill areas

How can this be achieved in the classroom? Use problem solving strategies and investigations throughout KS3 and KS4 Use old GCSE investigations Emphasise the importance of showing your working Register for the UK Maths challenge at KS3 & 4 Teach students how to split a question up into its component parts.

Summer 2009 Paper 1380/1F 18. Diagram NOT accurately drawn A D 88 O 96 O B C James says, “The lines AB and DC are parallel.” Ben says, “The lines AB and DC are not parallel.” Who is right, James or Ben? Give a reason for your answer. (Total 2 marks)

Success rate ? 93.2% scored 0 marks 1.1% scored 1 mark 5.7% scored 2 marks This was out of over candidates

The question was testing the understanding of angles on parallel lines including elements of ‘using and applying’ mathematics.

The original mark scheme B2 for Ben and a valid reason, eg ‘it should be 180’ or ‘they are not supplementary (allied, co-interior) oe This could be implied by 184 or 84 or 92 seen [B1 for Ben and or 180 – 88 or 180 – 96 seen or for just a valid reason (eg. Without Ben or James)]

High tariff topics at Foundation High success rates: Number Long multiplication (50+%) Find value of a calculation given another (50-60%) Exchange rate/money calculations (50+%) Use of calculator (50+%)

High tariff topics at Foundation High success rates: Algebra Derive an algebraic expression (50-60%) Basic laws of indices (45-50%)

High tariff topics at Foundation High success rates: Shape and Space Angles on a straight line/triangle, with reasons (50+%) Enlargements with given scale factors (70+%)

High tariff topics at Foundation High success rates: Data Handling Two-way tables (75%) Questionnaires (50+%) Scatter graphs (65+%)

High tariff topics at Foundation Low success rates: Number Fractions (<30%) HCF, LCM and Product of prime factors (20%) Ratio (33%) Significant figures (25%)

High tariff topics at Foundation Low success rates: Algebra Solving equations such as 4x + 1 = 2x + 12 (15-20%) Substituting negative values (<20%) Expanding a single bracket (10-25%)

High tariff topics at Foundation Low success rates: Shape and Space Describing transformations (2- 10%) 2D representations of 3D solids (25%) Constructions (10%) Area and circumference of a circle (2-10%)

High tariff topics at Foundation Low success rates: Data Handling Probability (20-30%) Estimating the mean (<5%)

Mid to High tariff topics at Higher High success rates: Number Standard Form conversions (65+%) Use of calculator (80+%) Compound Interest (65+%)

Mid to High tariff topics at Higher High success rates: Algebra Factorise a 2-term quadratic expression (50%) y = mx+ c (50+%) Indices (rules of) (60-65%)

Mid to High tariff topics at Higher High success rates: Shape and Space Pythagoras (60%) Trigonometry of a right angle triangle (50-55%)

Mid to High tariff topics at Higher High success rates: Data Handling Cumulative Frequency (60+%) Probability tree diagrams (50+%) Box plots (basic information) (60+%)

Mid to High tariff topics at Higher Low success rates: Number Bounds (<20%) Surds (rationalising, etc.) (<15%)

Mid to High tariff topics at Higher Low success rates: Algebra Solving inequalities (<30%) Rearrange complex formulae (<15%) Transformation of graphs (10-20%) Algebraic proofs (5-10%) Simplifying algebraic fractions (<15%)

Mid to High tariff topics at Higher Low success rates: Shape and Space Use of Circle theorems (10- 20%) Congruency proofs (5-10%) Trig graphs (10-20%) Vector algebra (5-15%) Complex mensuration (15-25%)

Mid to High tariff topics at Higher Low success rates: Data Handling Histograms (5-15%) Conditional Probability (10- 15%)

Task 3 Write a 3, 4 or 5 mark question, that could appear on either a Foundation or Higher tier paper, on each of the following areas: Fractions and Ratio Area and/or circumference of a circle Probability and/or Averages Wherever possible, try to address AO2 and/or AO3 together with functional elements

Sample Question which could be answered in a variety of ways in KS3. How about Trial & Improvement or using an Excel spreadsheet formula? A room is 2 metres longer than it is wide. The area of the room is 52 m². What is the perimeter of the room? Source:-2010 Edexcel GCSE Maths SAM