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 Novembe

rYear 10

Year 10March

Year 10 June

Year 11March

Year 11

June

Resit opportunity for second unit

Unit 3 mock or live exam

Unit 3 exam or resit opportunity

Teach

Units 1 & 2Second 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 Novembe

r

Year 10Novembe

r

Year 10March

Year 10 June

Year 11March

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 10June

Year 11November

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

AO1 Using and applying (20% included within subject knowledge)

(i)Problem solving (ii) Communicating (iii) Reasoning

AO2 Number and algebra 50 – 55%

AO3 Shape Space and Measures 25 – 30%

AO4 Handling Data 18 – 22%

Impact on teaching and learning

To

AO1 Recall and use their knowledge of the prescribed content 45 –55%

Number and algebraGeometry and measuresStatistics 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 algebra 50 – 60%Geometry and measures 20 – 30%Statistics and probability 15 – 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 matterReasoning, 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 £120In 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 ofSolve 10x + 14 = 22

You might getThe perimeter of this shape is 22 cm.

2x + 7   

x  3x  x   All measurementsFind 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 £3.50 200g 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 schemesOutline mark schemePer day

M1 140 hens eat 100 × 140 = 14 000 g = 14 kg each dayM1 A1 Cost of 14 kg of hen food = 6.75 ÷ 25 × 14 = £3.78M1 Number of eggs 140 × 6 ÷ 7 = 120 each day

120 eggs = 10 dozenM1 Food for 1 dozen eggs costs £3.78 ÷ 10 = 37.8pC1 Cost for one dozen 38p

Per henM1 1 hen eats 100g each day M1 A1 25 kg ÷ 100 g = 25 000 ÷ 100 = 250 daysM1 A1 6.75 ÷ 250 = 2.7 p each day

It takes 14 days to lay a dozen eggs.M1 Cost of food = 2.7 × 14 = 37.8pC1 Cost for one dozen 38p

  Per week

M1 140 × 6 = 840 eggs per week or 70 dozenM1 A1 Weight of food 100 × 140 × 7 = 98 kgM1 Cost of food = 6.75 ÷ 25 × 98 = £26.46M1 Cost of food for 1 dozen eggs 26.46 ÷ 70 = 37.8pC1 Cost 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

88O 96O

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 130 000 candidates

The question was testing the understanding of

angles on parallel lines including elements of

‘using and applying’ mathematics.

The original mark schemeB2 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 88 + 96 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 HigherHigh 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 HigherLow 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