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Using PUMA KS3 questions as building blocks for early familiarisation with GCSEs

Mike Collett, one of our PUMA KS3 authors, discusses the creation of questions for PUMA KS3. He focuses on how the tests can help to act as building blocks for familiarising students with GCSE-style questions at a level appropriate for their current knowledge and skills.

Planning for writing a test

Assessments and tests, and the questions in them, come in many forms and are used for different purposes. Test writers start with an understanding of the purpose and scope.
For PUMA KS3, the main input was the KS3 mathematics curriculum programme of study.
To help support progression and to provide spikey profiles of individual learners and groups, a set of granular curriculum descriptions are organised by 6 sections: number; algebra; ratio, proportion and rates of change; geometry and measures; probability; statistics. Quotas were created for each section and in some case sub-sections items for each year and each test.
The questions are designed to be varied, from straightforward arithmetical operations to more contextualised questions that might involve more than one step.
For each year, the three tests show progression and include a small selection of topics from previous terms, so the final summer term test includes topics over the whole year.

A range of problems

PUMA tests include some fairly short and straightforward questions that are designed to be very similar to GCSE questions. For example:

PUMA Autumn Year 7

GCSE AQA Foundation 2017

These kinds of PUMA questions will therefore help learners by providing early and continued familiarisation with GCSE-style content that is at the appropriate level for the year and term within KS3 mathematics.

Step by step transformations

Like other topics, transformations are introduced progressively in the PUMA assessments. Translation, reflections and rotations are included from Spring Year 7 to Spring Year 8, with enlargements included in Summer Year 8. Here is an enlargement question.

PUMA Summer Year 8

Being able to construct an enlargement and to understand other transformation are skills needed for GCSE. Here is a typical GCSE question that is more demanding and includes 2 transformations in the same question.

GCSE AQA Foundation 2017

The understanding needed for the PUMA questions provides building blocks towards questions at a GCSE level.


Some PUMA questions include more than one part and are organised in a similar way to GCSE questions.

PUMA Autumn Year 9

GCSE AQA Foundation 2017

Some PUMA questions will prepare the learner for using the same reference material in a question to derive answers to more than one part of a question as found in some GCSE questions.


Here is a more complex question.

PUMA Summer term Year 9

This involves several steps and some demanding problem solving. In particular, learners need to realise that the curved edges sum to the circumferences of two circles and know the formula for the circumference of a circle. They also need to deduce that the two straight lines are each 10cm, the same as the radius of the circles, then add the parts together.
The style of questions through the 9 PUMA tests progresses to include some of these more demanding problems. In this way, learners are introduced to the multi-step questions that are typical of GCSE. For example:

GCSE AQA Higher 2017

This GCSE question carried 5 marks and candidates would be given credit for appropriate methods and approaches in a more granular way. This is perfectly suitable for marking a large number of GCSE papers that are very high stakes, but marking multi-mark questions is more time consuming and more difficult to mark consistently in the classroom. On a standardised test, marking must be consistent to ensure accurate results.
The PUMA mark schemes are deliberately simple and apply one mark to each question or part question. This reduces the marking burden for teachers and ensures accuracy and reliability of results.
After learners have completed each test, and the results have been analysed, teachers can use these multi-step questions to help learners understand how to tackle them and show their working effectively as further preparation for KS4 and GCSE.
For more information about PUMA KS3 here.