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Session 3

Preparing students for the new GCSE specifications

What works well?

Sharing resources & good practice; resources to support functionality

The new programmes of study for mathematics build mathematical understanding and competence by developing pupils’ skills in mathematical processes and applications.

Where are we with Functional Mathematics?

- - is this still a high priority for you and your department?
- - remember the new GCSE!
- - where are you with the process of modifying SoLs?
- - how has classroom practice changed? Is further development necessary? What CPD are you providing?
- - is it more than sets of new resources?

Questions from the March / Jan Units

- To consider questions on recent module exams that test the AO2 and AO3 skills
- To benefit from examiners’ feedback
- To consider implications for teaching and learning
- To share existing good practice

Key messages

- Teach strategies for selecting information
- Encourage the use of two way tables
- Develop clear and logical setting out
- Label calculations – eg Ticket cost =
- Develop understanding of proof – both geometric and algebraic
- Teach algebraic methods for problem solving
- Ensure pupils actually answer the question – particularly in QWC questions
- Develop fluent calculation skills

How do you develop these skills?

Problem solving strategies cannot be taught directly - that is by describing them and rehearsing them as procedures.

The teaching is indirect, drawing attention to strategies as possibilities for action in the

context of solving problems.

Teaching strategies for problem solving

- Include problem solving in every lesson
- Have regular problem solving lessons
- Provide opportunities for pupils to experience a wide range of problems which will develop specific skills
- Make links between topics and mix topics
- Ask questions which make students think
- Ask questions without an exact answer
- Ask open questions
- Teach algebra as a problem solving tool

Teaching strategies to develop exam skills

- Focus on selecting key information from wordy questions
- Teach key exam vocabulary
- Use a graphic organiser to approach complex multi-step problems
- Give pupils diagrams or tables and ask them ‘what could the question be?’
- Ask pupils to identify parts a, b and c for a multi-step problem

What do you need to find out?

Question:

What mathematics will you use?

What if…..?

Working and solution:

(Ensure the solution relates back to the original problem. Consider the form of the answer i.e.should it be an explanation, a diagram, a percentage etc, and the units i.e money, ratio, algebra, cmsetc)

What do you need to find out?

Step 1

Step 2

Pupils need to choose what information they require from the question. This may include words, algebra and diagrams (or words translated into diagrams)

Pupils need to decide what it is they are looking for. They may wish to record intermediate steps towards the final answer.

Question:

What mathematics will you use?

What if…..?

Step 3

Step 5

What range and content do they require to solve the problem?

Place the question in this box

Pupils are asked to consider what if questions in relation to the context given.

Working and solution:

Step 4

Pupils use this space to record their working and final solution.

(Ensure the solution relates back to the original problem. Consider the form of the answer i.e.should it be an explanation, a diagram, a percentage etc, and the units i.e money, ratio, algebra, cmsetc)

What do you need to find out?

What mathematics will you use?

What if…..?

Working and solution:

(Ensure the solution relates back to the original problem. Consider the form of the answer i.e.should it be an explanation, a diagram, a percentage etc, and the units i.e money, ratio, algebra, cmsetc)

Actual Question

Possible questions:

Solution to actual Question

Solution to chosen question:

CREATE A QUESTION

Actual Question

Use a diagram, table or other information

Provide the actual question

Possible questions:

Solution to actual Question

Ask pupils to ‘create questions’ around the information given and choose one to solve.

Pupils write in their working and give the solution to the actual question.

Solution to chosen question:

CREATE A QUESTION

Pupils solve their question or that of another group.

Actual Question

Possible questions:

Solution to actual Question

Solution to chosen question:

CREATE A QUESTION

Martha sells jars of jam at a farmers’ market.

She has 80 jars to sell at £3 each.

She sells 50 jars and then reduces the price by 40%.

Martha then sells the remaining jars at the reduced price.

It costs her £95 to make the jars of jam.

Her target is to make a profit of at least £100.

Does she meet her target?

You must show your working.

(AQA Unit 2 November 2010 – 5 marks)

Martha sells jars of jam at a farmers’ market.

She has 80 jars to sell at £3 each.

She sells 50 jars and then reduces the price by 40%.

- How much money has she taken?
- What is the new price?

Martha then sells the remaining jars at the reduced price.

(c) How much money does she take from the reduced jars?

It costs her £95 to make the jars of jam.

Her target is to make a profit of at least £100.

(d) Does she meet her target?

You must show your working.

Sharing Good practice

- What have you done that has worked with your students?
- What have you done that has worked with your department?

Key elements for success

- Mediate the specification and objectives language for pupils
- Graded examples – level descriptors, level ladders, graded objectives
- Misconceptionshighlighted
- Functional – real life contexts, cross strand problem solving
- Exam board questions
- Resources – to address literacy, thinking skills, PLTS, enterprise, probing questions and rich tasks

- Differentiation
- Assessment – summative (to track progress) and formative (to identify learners on-going needs and inform planning)
- Progression – ensure teachers and pupil understand how to progress and make explicit the programme that will, for instance, enable set 2 to access the higher paper.

Action Points

- What will you do differently in your own lessons to prepare your students for problem solving exam questions?
- How will you move your department forward?
- What further points do you need to consider?

Where are we with Functional Mathematics?

- - is this still a high priority for you and your department?
- - remember the new GCSE!
- - where are you with the process of modifying SoLs?
- - how has classroom practice changed? Is further development necessary? What CPD are you providing?
- - is it more than sets of new resources?

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