Macmillan Academy The Scholar Lab

Connect ideas · KS3–KS5

Cross-curricular prompts

The best questions don't fit in one subject. Here are ten that live in the gaps — each with a way in and a way further.

The most interesting questions rarely sit inside a single subject — they live in the gaps between them. Pick one that grabs you, follow it wherever it leads, and watch ideas from different lessons start to connect.

Maths × Music

The mathematics of music

Pluck a string and halve its length and you get the same note, one octave up. Pleasant-sounding chords turn out to hide simple whole-number ratios between frequencies — and dissonance hides messy ones.

Start here:

  • Why do a note and the one an octave above sound 'the same'?
  • What ratio links the notes in a major chord?
Take it further: Investigate why the piano had to be 'tempered' (slightly out of tune) so it could play in every key — a genuine clash between maths and music.
Computing × Philosophy

The ethics of AI

Algorithms now help decide who gets a loan, a job interview, or even bail. They can be faster and more consistent than people — but they learn from past data, and the past was not fair.

Start here:

  • If an AI is trained on biased decisions, what will it learn to do?
  • When an algorithm gets it wrong, who is responsible — the coder, the company, or the machine?
Take it further: Research a real case where an algorithm was found to be biased, and propose one rule you'd make law.
History × Statistics

History through data

A parish register, a price index or a set of shipping records can reveal patterns that no diary mentions — how long people lived, when famine struck, how trade moved.

Start here:

  • What can a graph of wheat prices tell you that a king's letters can't?
  • How might the same dataset mislead you if you ignore who collected it?
Take it further: Find a historical dataset online and draw one graph that tells a story — then write the caption a historian would.
Chemistry × Art

The science of forgery

A painting 'from 1500' that contains a pigment invented in 1820 is a fake — and chemistry can prove it. Scientists use X-rays, UV light and pigment analysis to see beneath the surface.

Start here:

  • How can the chemical make-up of paint reveal its true age?
  • What can an X-ray show that the naked eye cannot?
Take it further: Look up a famous art-forgery case (e.g. Han van Meegeren) and explain exactly how the fake was caught.
Languages × Psychology

Language and thought

Some languages have no word for 'left' or 'right' and use compass directions instead; some have many words for a colour English lumps together. Does the language you speak shape how you think?

Start here:

  • If your language had no future tense, would you save money differently?
  • Is this idea (the 'Sapir–Whorf hypothesis') strong, weak, or wishful thinking?
Take it further: Find one striking example of a language carving up the world differently, and judge how far it really shapes thought.
Physics × PE

The physics of sport

A curving free kick, a javelin's flight, the perfect basketball arc — all obey the same physics of forces, spin and projectiles. Elite athletes are, in effect, solving equations with their bodies.

Start here:

  • What launch angle gives a thrown object the greatest range, and why?
  • How does spin make a football bend in the air?
Take it further: Model one sporting action mathematically, predict the best technique, then test it and compare.
Geography × Politics

Maps, power and persuasion

Every flat map distorts the round Earth — and the choices about how are never neutral. The familiar Mercator map makes Europe look far bigger than Africa, which is in fact about 14 times its area.

Start here:

  • Which countries look larger than they really are, and which shrink?
  • Could a map ever be a form of propaganda?
Take it further: Compare the Mercator and Gall–Peters projections and argue which a school should put on the wall.
Economics × Science

The economics of climate

If a factory can pour pollution into the air for free, it will make too much of it — economists call this an 'externality'. Carbon pricing tries to put the hidden cost back onto the polluter.

Start here:

  • Why does something being 'free' to use often lead to too much of it?
  • Who ends up paying for pollution if no one is charged for it?
Take it further: Explain how a carbon tax or 'cap and trade' scheme works, and weigh one strength against one weakness.
Chemistry × Food

The chemistry of cooking

Browning a steak, baking bread, caramelising onions — cooking is chemistry you can eat. The 'Maillard reaction' between sugars and proteins creates hundreds of new flavour compounds.

Start here:

  • Why does food brown and taste richer when it's hot and dry, but not when boiled?
  • What's actually happening when bread dough rises?
Take it further: Pick one kitchen transformation and explain the chemistry behind it well enough to teach a Year 7.
Maths × Law

Probability and the law

A DNA match 'one in a billion' sounds like certain guilt — but courts have jailed innocent people on exactly this kind of statistic, misread. Probability in the courtroom is dangerous when misunderstood.

Start here:

  • If a match is 'one in a million', does that mean a one-in-a-million chance the suspect is innocent? (No — why not?)
  • How could the same true statistic be presented to sound guiltier or more innocent?
Take it further: Research the 'prosecutor's fallacy' and explain, with a clear example, how a true number can mislead a jury.

How to use these

Choose one prompt and spend an hour on the "start here" questions. Then push further with the challenge — and if it really grips you, grow it into a full independent research project. Bring your thinking to a teacher in either subject; they'll be delighted.

Produce & share

Make something: Pick one prompt, take on its 'take it further' challenge, and turn it into a short outcome — a one-page write-up, a model, a slide, or a two-minute explainer video.

When it's ready, email it to Mr King. The best work may be featured in the student showcase.

What you'll practise

Connecting ideas across disciplines, transferring methods from one subject to another, and the flexible, creative thinking that universities and employers value most.