One Pie, Thirty Plates: Scaling a Melton Mowbray Pork Pie for a Leicester Maths Club

A maths club session that begins with a recipe and ends with a slice of warm pork pie has a lot going for it. The numbers are real, the mistakes are edible, and nobody argues about whether the answer is useful. Our plan is to scale a Melton Mowbray-style pork pie for a Leicester Maths club night in November 2026 — not by guessing, but by deciding what kind of scaling we actually mean.

Melton Mowbray pork pie is a local food with protected geographical indication status, and Leicester is close enough that it feels like home cooking. That makes it a good hook for students who might switch off at the words ‘ratio and proportion’. The aim is not to train pastry chefs. It is to make students choose a model, defend an assumption and then check the answer against a real tin.

First question: what is scaling?

If you double the diameter of a round pie but keep the depth the same, the area of the top and bottom multiplies by four. The volume of filling also multiplies by four, because volume is area times depth. But if you scale every dimension — diameter, depth and pastry thickness — by two, the volume multiplies by eight. Those are very different answers, and the difference is the whole lesson.

For a club bake, the sensible model is usually this: keep the pastry thickness roughly the same, keep the depth roughly the same, and change the diameter. That means filling scales with area. It also means pastry does not scale in the same simple way, because a larger pie has less crust per mouthful of filling than a small one.

Tin sizes and portion maths

Start with a baseline. A 20 cm pie, cut into eight generous slices, is our unit. The club has 24 sign-ups, so if we keep the slice size the same we need an area factor of three: 24 divided by eight.

Now compare tins by area, relative to the 20 cm tin. The factor is (diameter ÷ 20) squared.

A single 30 cm pie gives about 18 portions — not enough for 24 hungry students. Two 23 cm pies give about 21 portions, which is still short. One 30 cm pie plus one 20 cm pie gives 2.25 + 1.00 = 3.25 area units, or about 26 portions. That is a useful buffer for second helpings and for the student who always arrives late.

A single 35 cm pie gives 3.06 area units, or about 24.5 portions. Mathematically that is neat. Practically, check your oven shelf and your tin supply before you commit. The best answer in a maths club is the one you can actually bake.

Pastry is not filling

This is where the arithmetic gets interesting. Suppose the 20 cm recipe uses 500 g of pastry and 800 g of filling. That is a pastry-to-filling ratio of 500:800, or 1:1.6.

Scale the filling for a 30 cm pie by the area factor of 2.25: 800 g × 2.25 = 1800 g. Good. Now try to scale the pastry the same way and you will over-crust the pie. Pastry mass depends on surface area, not volume, and the top and bottom grow faster than the sides.

A workable estimate: split the original pastry into 300 g for top and bottom and 200 g for the sides. For the 30 cm pie, the top and bottom scale by 2.25, while the sides scale by 1.5 because the circumference grows with diameter, not area. That gives 300 × 2.25 + 200 × 1.5 = 675 + 300 = 975 g of pastry. The new ratio is 975:1800, or about 1:1.85. The larger pie has proportionally less pastry. That is not a failure of the recipe; it is geometry doing its job.

For the 30 cm plus 20 cm plan, total pastry is 975 + 500 = 1475 g and total filling is 1800 + 800 = 2600 g. The overall ratio is about 1:1.76. Ask students to predict whether the combined ratio will be closer to the small pie or the large pie before they calculate. The answer is a weighted average, and the weighting is the thing worth discussing.

Cost per slice

Use illustrative prices and let students update them with real supermarket or Leicester Market figures. For the 30 cm plus 20 cm bake, suppose pork shoulder comes to £7 per kilogram, pastry ingredients to £3.50, seasoning to £1 and oven energy to 60p. If the filling needs 2.6 kg of pork, that is £18.20. Total cost is about £23.30. Divide by 26 portions and you get roughly 90p per slice.

That number is a model, not a quote. It ignores labour, waste, tin lining and the cost of running to the shop because someone forgot the pepper. Ask students which omission changes the price most. This is a gentle way to introduce sensitivity: a small change in one assumption can move the final answer more than a big change in another.

Oven energy and the cost of doing maths

A 2.2 kW oven running for 65 minutes uses 2.2 × (65 ÷ 60) = about 2.38 kWh. At an illustrative 25p per kWh, that is roughly 60p. If both pies go in together, the energy cost is shared across 26 slices, or about 2.3p per slice. If you bake them separately, the energy cost roughly doubles.

Ovens cycle on and off, so this is an estimate. That is fine. The point is to show that ‘cost per slice’ is not only about pork and flour. It is also about time, temperature and how you use the oven.

A session plan that ends in slicing

Divide the club into four groups. Group one owns tin geometry and portion counts. Group two owns the pastry-to-filling ratio and must present the surface-area argument. Group three owns costing and must show a price per slice with assumptions listed. Group four owns oven energy and must compare one bake with two.

Give each group ten minutes, then ask for one number and one assumption. Write them on the board. Before the pie is cut, ask everyone to predict the actual number of portions from the tins in front of them. Then cut, count and compare. The gap between prediction and reality is where the learning lives.

And if the pastry shrinks or the filling leaks, that is not a failed maths session. It is a reminder that models are useful precisely because reality is messier. The club still gets a slice, and the numbers still get checked.