Core Maths for physical education?

Ruth Wroe, Maths Subject Advisor

In this blog I’ll be outlining why physical education students should be encouraged to take core maths and how it will support their studies. I’ll also highlight some useful cross-curricular resources and promotional materials. 

I’ll be focusing on our A Level Physical Education specification (H555), but core maths will support equivalent Level 3 qualifications in PE from other awarding organisations that you may be teaching at your centre.

Why take core maths?

Students who achieve a grade 4 or better at GCSE Maths but don’t wish to continue studying maths at AS or A Level need a convincing argument to take a Level 3 maths course. The fact that it covers the kind of maths that they will need in their other Level 3 subjects, which should help them to do better, is a compelling argument though.

What are the aims and content?

The aim of Core Maths A and B is to take students who have attained at least a grade 4 at GCSE and enable them to confidently tackle the kinds of mathematical problems they are likely to encounter in their other subjects or in their future lives. It does not have the algebraic focus of AS Level Maths, but it is a Level 3 qualification which introduces some new Level 3 content, as well as reinforcing the required GCSE Maths content used in other A Level subjects and vocational qualifications. So, for many students, core maths is a much better option than AS Level.

What will your students learn?

In core maths lessons students will practise applying their skills in different contexts so they become more confident at tackling problems set in a range of situations, and more adept at mathematical reasoning. As a result, they’ll become more competent at dealing with the maths in the context of physical education – identifying the maths involved, carrying out the required steps, understanding how their answer relates to the problem asked and interpreting what their answer means in the context of PE.

A Level PE students will have prior learning from GCSE Maths (9-1) and most, but not all, will have acquired data analysis skills from GCSE PE. However, studying core maths alongside physical education helps to instil and reinforce the maths met in A Level PE. It complements its key mathematical requirements of interpreting data and graphs, using data to evaluate performance, and analysing motion.

Mathematical skills requirements of A Level Physical Education

The A Level PE specification states that: 

“The assessment of quantitative skills will represent 5% of the overall marks. The use of quantitative skills is spread across the components.”

Quantitative skills will not only be required in the three examined components but also in the non-exam assessment on ‘Evaluating and Analysing Performance for Improvement’. Although most of the required mathematical skills will have been met at GCSE Maths, the focus will be on revisiting and mastering their application in a physical education context.

What’s covered in Core Maths A and B?

These are the mathematical skills required in physical education that are included in both Core Maths A and B:

• Compare the outcomes from a model with actual data. 
• Interpret sample data in terms of properties of the parent population. 
• Plot, label and interpret graphs. 
• Work with equations and formulae. 
• Work with commonly used units and compound units. 
• Calculate displacement, distance, velocity, speed and acceleration. 
• Work with percentages. 
• Work with ratios. 
• Work with representations of 3D objects in 2D.

Core maths students will interpret data in a variety of contexts and representations (including tables, graphs, diagrams and spreadsheets). They will have an understanding of the modelling cycle, samples and the Normal distribution. The assessments they undertake will specifically address interpreting results in the context of a given problem and interpreting and communicating information accurately (assessment objective AO3). The skills developed in core maths will help PE students when comparing their performance calculations with normative data and when evaluating physical training and performance.

There is a whole section dedicated to working with graphs and gradients. Core maths students work with graphs drawn from a variety of contexts, including graphs representing motion along a straight line, time series graphs, step graphs, periodic graphs, graphs of exponential growth and decay and piecewise graphs. These will be particularly useful in PE where a range of graphs are used, such as pulmonary function test graphs, energy continuum graphs, EPOC graphs, linear motion graphs (distance/time, speed/time and velocity/time). 

Parabolas are referenced in biomechanics (projectile motion) and sports psychology (inverted U theory). Although parabolas are not explicitly included in core maths, all students will have met these in GCSE Maths (9-1). They will be able to recognise and sketch quadratic functions and identify turning points using symmetry. 

As mentioned, core maths is not heavily focused on algebraic manipulation, but students will work with formulae. They will be able to evaluate (find the value) and rearrange simple formulae involving the four operations, powers and roots. Various formulae are used across the physical education specification, such as estimated maximum heart rate, cardiac output, aerobic capacity and maximal oxygen uptake (VO₂ max), target heart rate and linear motion (speed, velocity and acceleration). 

Core maths students will work with commonly used units and know that quantities being compared should have the same units. They will understand that the units of quantities arise from the way they are calculated which is particularly useful in physical education where a range of compound units are used, such as heart rate (bpm), stroke volume (mℓ/beat), cardiac output (ℓ/min), breathing frequency (breaths/min), tidal volume (ℓ/breath), minute ventilation (ℓ/min), VO₂ (ℓ/min) speed and velocity (m/s or m s^-1), acceleration (m/s/s or m/s² or m s^-2). 

Percentage and ratio work undertaken in core maths will reinforce understanding of various physical education concepts, such as work-relief ratio, interval-relief ratio, target heart rate depending on % intensity, interval intensity proportional to 1 Repetition Maximum (% of 1RM) and % efficiency in levers. Likewise, work with representations of 3D objects in 2D, may help in limb kinematics which uses 3D images.

What’s not covered in Core Maths A or B?

The following topics are not covered in our core maths qualifications: 

• Biomechanical principles: 
  • Newton’s laws of motion (inertia, acceleration, reaction) 
  • Free body or force diagrams 
  • Calculations of force and momentum 
• Angular motion: 
  • Calculations of angular velocity, angular momentum, and moment of inertia 
  • Radian measure
    
• Fluid mechanics 
• Projectile motion: 
  • Free body or force diagrams 
  • Resolution of forces.

Core maths students will have some useful prior knowledge for analysis of motion calculations though, as they will be familiar with velocity and acceleration, units of measure and using formulae. However, most of the topics listed above are covered in detail in other Level 3 maths qualifications: 

• Newton’s laws of motion: AS/A Level Maths 
• Force diagrams: AS/A Level Maths 
• Calculation of force: AS/A Level Maths 
• Calculation of momentum: AS/A Level Further Maths 
• Angular motion: AS/A Level Further Maths 
• Radian measure: A Level Maths 
• Projectile motion: A Level Maths 
• Resolution of forces: A Level Maths

Which specification is most appropriate for A Level Physical Education?

The ‘Introduction to quantitative reasoning’ component is common to both specifications. It covers interpretation of data and graphs, and use of data to evaluate quantitative statements which are required in A Level PE. 

The choice of specification should therefore be based on what other Level 3 subjects are being taken alongside A Level PE. 

Students taking other Level 3 subjects which have a statistical element would be advised to take Core Maths B because this is covered in statistical problem solving. 

Critical maths, on the other hand, offers support in developing critical maths skills for reasoning and making judgements. This centres around discussing a real-life problem and then deciding on and using the required maths to solve the problem. Core Maths A supports a wide range of Level 3 subjects that have quantitative and problem-solving requirements.

Core maths resources for physical education

Resources on Integral’s Core Maths Platform and the activities and exercises in the OCR Core Maths A and B (MEI) textbook can be used for practising the maths encountered in physical education.

Core maths takeaways for physical education teachers

The Advanced Mathematics Support Programme (AMSP) has produced a postcard and poster that you can display in classrooms and use at open events to promote core maths with students. They also run a variety of free CPD events for both core maths teachers and PE teachers to help in delivering the maths in their subject.

Stay connected

If you have any questions, you can email us at maths@ocr.org.uk, call us on 01223 553998 or tweet us @OCR_Maths. You can also sign up for subject updates and receive information about resources and support.

About the author

Ruth supports the Level 3 maths qualifications and has chief responsibility for Core Maths A and B. She joined the maths team in 2014, working on the development of A Level Maths. Previously, Ruth taught maths in the UK, New Zealand, Kuwait, Oman and Qatar. Outside of work she cares for elderly parents but in her spare time she enjoys travelling, live music, real ale and dog walking.

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