The foundations
The maths computer science actually rests on.
Not maths for its own sake, and not maths you have to finish before you start. Each topic below is learned by building something that uses it — an image is a grid of numbers, a spam filter is probability, a model learning is a slope you walk down. Start anywhere.
Number, Proportion & Functions
5 CasesFractions, percentages, area, and how one quantity changes with another.
Where you meet it: Everything else stands on this. Prices, scaling, units, and reading a formula.
- Happy or sad message?Add +1 and −1 to a running total and read its sign.
- Bag a bargain!Find a percentage of an amount (a discount) and work out the new price.
- Where does your day go?Show parts of a whole (a day) as fractions/percentages on a pie chart.
- Will the carpet fit?Find the area of a rectangle with length × width.
- Make a wave danceChange a number in a formula and watch the graph it draws change with it.
Data & Statistics
13 CasesSummarise a pile of numbers, and see the shape hiding in it.
Where you meet it: Every dataset you will ever load. Averages, spread, correlation, and knowing when a chart is lying.
- Whose tower is tallest?Read and compare a bar chart; find the tallest bar.
- A rainbow of favoritesCount into categories and read a bar chart / pictogram.
- Which word wins?Tally items into categories and compare the totals on a chart.
- Am I growing faster than my sister?Read and compare two line graphs; which climbs more steeply?
- Which day was the hottest?Interpret a line graph and find the maximum value.
- Where does my allowance go?Group data into categories, total each and rank them.
- How spread out are the marks?Calculate the mean, median and range; read a histogram.
- Do taller kids run faster?Plot a scatter graph and judge the correlation.
- Can I predict next month's temperature?Fit a line of best fit and extend it to predict.
- Can a computer tell two flowers apart?Read a scatter of two features and separate the groups.
- Can the computer find hidden groups?Spot clusters on a scatter graph of two measurements.
- Capstone: investigate your weekRun a full data investigation: chart, summarise, correlate.
- Ask a database a questionFilter and group records to answer a question about a table of data.
Probability & Uncertainty
6 CasesReason about what might happen, and how sure you are.
Where you meet it: Spam filters, language models choosing the next word, and any model that outputs a confidence.
- The creativity dialTurn scores into chances that add up to 100%.
- Is this dice fair?Use relative frequency from many trials to judge fairness.
- Guess the next wordPick outcomes by how often they occurred (frequency).
- Why AI makes things upReason about uncertainty and unseen (zero-frequency) cases.
- Catch the spamUse how often words appear to weigh a likely outcome.
- Answer using real notes, not guessesGround an answer in retrieved evidence instead of unsupported guessing.
Vectors, Matrices & Grids
6 CasesNumbers arranged in rows, grids and directions — and what you can do to them at once.
Where you meet it: Images, embeddings, similarity search, and the inside of every neural network.
- A picture is just numbersRead a value at a position on a 2-D grid of numbers.
- Colour in just the ballIdentify a region of a grid by its position and colour.
- Draw a box around itFind the min/max coordinates of a shape to bound it.
- See a real AI spot objects (live)Boxes are coordinates on a grid; percentages show confidence.
- Find the right pageScore how well each page matches a query, then rank by that score.
- Chop it up and rank the piecesSplit text into pieces, score each piece for relevance and order them.
Graphs & Discrete Structures
4 CasesThings joined to other things, and finding your way between them.
Where you meet it: Social networks, recommendations, search, routing, and how an agent plans its next step.
- People you may knowCount shared items (mutual friends) and rank by how many.
- An AI that reaches the goalMove on a grid using coordinates and direction (translation).
- How connected are you?Count steps along connections to find the shortest path.
- An agent that picks a toolChoose between branches based on a condition, and follow the path that results.
Rates of Change & Optimisation
2 CasesHow fast something changes, and how to steer it towards better.
Where you meet it: How a model actually learns: follow the slope downhill until the error stops shrinking.
Also mapped to school
Following the UK curriculum?
Every Case is also tagged to the UK National Curriculum, so you can see what a given school year covers and which Cases reinforce it. Useful for parents; ignore it if you're learning for yourself.
Pick your child's school year
Year 5 maths
Comparing with line graphs, tables and timetables; percentages begin.
What they learn at school
- Statistics: solve comparison, sum and difference problems using line graphs
- Complete, read and interpret information in tables and timetables
- Percentages, decimals and fractions as parts of a whole
- Reading coordinates and simple translations
Practise it on Astra
Why bother with maths?
Because it's the machinery behind things you already use.
Games
Every jump, score and collision is maths doing its job.
Money
Budgets, discounts, interest — maths keeps your money honest.
AI
The AI in these Cases is built entirely on the topics above.
Sport
Angles, stats and records — coaches live on this.
Music
Beats, rhythm and sound waves are maths you can hear.
You don't just do maths here — you use it to solve a real problem in code, and watch it work.
School-year mapping follows the DfE programmes of study (KS1–KS4) and is a guide for parents — worth checking against your own school.