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Decide what maths is 'at the top of the tree' for this topic - think about conceptual understanding and what you want students to be able to do.  

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Decide what maths is 'at the top of the tree' for this topic - think about conceptual understanding and what you want students to be able to do.  

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Consider what gaps students might have - procedural understanding 

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Consider what gaps students might have - procedural understanding 

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Plan a lesson for your chosen area. If your area is large, pick a topic within it. 

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Plan a lesson for your chosen area. If your area is large, pick a topic within it. 

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The subject content of this specification matches that set out in the Department for Education's Mathematics GCSE subject content and assessment objectives document. This content is common to all exam boards.

The content has been organised into broad topic areas and given a reference as follows:

Number references start with N

Algebra references start with A

Ratio, proportion and rates of change references start with R

Geometry and measures references start with G

Probability references start with P

Statistics references start with S.

All content can be assessed on any of the three question papers. As such, some questions will draw together elements of maths from different topic areas.

The weighting of the topic areas has been prescribed by Ofqual and is common to all exam boards. The table below shows the approximate weightings of the topic areas for the overall tier of assessment, not for each individual question paper.

Topic Area

Foundation Tier (%)

Higher Tier (%)

Number

25

15

Algebra

20

30

Ratio

25

20

Geometry

15

20

Probability and statistics (combined)

15

15

The subject content, aims and learning outcomes, and assessment objectives sections of this specification set out the knowledge, skills and understanding common to all GCSE Mathematics exams.

Within this specification, the assessment will reflect the key concepts of the subject as articulated in the subject content and assessment objectives document.

In line with the requirements set by the Department for Education, the expectation is that:

all students will develop confidence and competence with the content identified in the "basic foundation content" column

all students will be assessed on the content identified by the "basic foundation content" and "additional foundation content" columns; more highly attaining students will develop confidence and competence with all of this content

only the more highly attaining students will be assessed on the content identified in the "higher content" column. The highest attaining students will develop confidence and competence with this content.

Students can be said to have confidence and competence with mathematical content when they can apply it flexibly to solve problems.

The content in the "basic foundation content" column and "additional foundation content" column can be assessed on Foundation tier question papers.

All content can be assessed on Higher tier question papers.

Notes are added to exemplify some of the specification references.

In addition to this subject content, students should be able to recall, select and apply mathematical formulae. See the Appendix for a list of the DfE prescribed formulae.

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The subject content of this specification matches that set out in the Department for Education's Mathematics GCSE subject content and assessment objectives document. This content is common to all exam boards.

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AQA Maths revision past exam papers for the new 1-9 GCSE Specification.

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Pupils plan when they should start preparing a meal in order to have it ready by a stated time.

Suitability

National Curriculum levels 5 to 6

Time

30 minutes to 1 hour

Resources

Ruler, pencil and paper; scissors available but provided only on request.

Representing

Select a way of representing the sequence of jobs using a table or diagram showing times, constraints and which jobs may be done in parallel.

Analysing

Work logically towards a result, sequencing the jobs using the constraints given on the job cards; explore the effects of varying the order.

Interpreting and evaluating

Relate findings to the original context: they look at the organisation of jobs, recognise which jobs may be done in parallel and deduce the latest time they can start preparing the meal.

Communicating and reflecting

Communicate reasoning clearly, showing the order in which jobs can be done and which may be done in parallel.

Check that Pupils fully understand the context, for example with questions such as:

How long does it take to boil a potato? How about frying a piece of fish?

Would you start them both at the same time? Or which would you start first? Why?

Show your working so that I can understand your reasoning - don't just write down the answer!

This task requires pupils to demonstrate their proficiency in the Key Processes using fairly elementary mathematical techniques. They might be expected to:

create and interpret graphs and diagrams and draw conclusions

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Pupils plan when they should start preparing a meal in order to have it ready by a stated time. Suitability National Curriculum levels 5 to 6 Time 30 minutes to 1 hour Resources Ruler, pencil and paper; scissors available but provided only on request.

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Pupils determine the optimum time to visit Hilbre Island, taking account of given considerations.

Suitability

National Curriculum levels 4 to 7

Time

30 minutes to 1 hour

Resources

Paper and calculator

Representing

Understand the problem and consider the constraints given.

Analysing

Work logically taking account of the constraints.

Communicating and reflecting

Communicate their findings throughout and summarise their outcomes.

To help pupils understand the task, you might choose to introduce it with a short video, with comments:

Hilbre Island is a small island in the Dee estuary, near Liverpool. It is very important for the birds that migrate and nest there. People can only reach it by foot for a few hours a day, when the tide is out, so they must plan carefully when to walk across.

You are given all the information you need to decide when to start your journey to Hilbre with friends; plan it to have as much time as possible to enjoy the island, but also make sure you can get back safely and do not get stuck there overnight!

The task requires calculations involving time.

During the task, the following probing questions may be helpful:

What do you need to consider in making your choice? What are the key points?

Are any of the three dates not possible? Why?

Why have you chosen this date rather than one of the other dates?

Will Jon and Lu understand your reasoning?

Further notes for teachers can be found in the Annex to the teacher guide.

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Pupils determine the optimum time to visit Hilbre Island, taking account of given considerations. Suitability National Curriculum levels 4 to 7 Time 30 minutes to 1 hour Resources Paper and calculator Representing Understand the problem and consider the constraints given. Analysing Work logically taking account of the constraints.

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Pupils determine how long it would take a panel of judges if they saw every act that auditioned for the "Z factor" programme.

Suitability

National Curriculum levels 3 to 8

Time

45 minutes to 1 hour

Resources

Paper and calculator

Representing

Simplify the problem by making appropriate assumptions

Analysing

Combine assumptions and work logically to solve the problem

Communicating and reflecting

Throughout, present arguments and reflect on findings, recognising the impossibility of the scenario presented

You could start by showing pupils relevant pictures or videos from http://xfactor.itv.com/

For the TV programme, there are thousands of people wanting to audition. How do they decide which acts get through this first set of auditions?

To answer the question, you will need information that is not given, so you will have to make assumptions (sensible guesses) - and explain them.

The task requires multiplicative calculations involving time.

The following probing questions may be helpful:

What do you need to know? As you work through the problem, write down the questions for which you need answers

Make sensible guesses for the answers; what assumptions are you making? Why?

Have you decided to ignore any factors? Why?

What does your solution tell you about the auditions for the Z Factor?

Two key assumptions are needed: 1) How long an audition lasts; 2) The number of hours in a judges' working week. Pupils' assumptions should be vaguely realistic! Pupils might work backwards, assuming all auditions are seen and finding how long each one would need to be; this does not answer the question asked, but it does show insight into the situation and the mathematics is equally complex.

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Pupils determine how long it would take a panel of judges if they saw every act that auditioned for the "Z factor" programme.