How it works

Every problem here is worked the way it would be worked on paper — one step at a time, with the reason for each step written beside it.

Finding a problem

The problems page groups everything by the problem pattern it teaches — units and parts, constant total, guess and check, and so on. Two problems under one heading are solved the same way, where two that merely share a topic can need quite different work. The list of patterns down the left is the index: pick one and the page jumps to it.

Search: Matches the title, the question, the answer, the topic and the pattern — so ratio, guess and marbles all find something.
Topic: The 10 syllabus topics. Pick one to narrow the page to it; pick it again to clear it.
Difficulty: Standard, challenging, very challenging. Combines with a topic.
Revision list: A flat checklist of everything, by topic and easiest first, with tick boxes that remember where you are. It is the one to print.
Problem patterns: All of them on one page, most drawn in bars, with how to spot each one and the mistake children make. The four that differ only in which amount stays the same sit next to each other, because telling those four apart is the skill.

The two ways into a solution

A problem page opens with the question and one frame of the drawing, then these:

See the working: Drawn a step at a time, waiting for you between steps. This is the main one.
Practice: More questions that use the same pattern, with the working underneath — far enough underneath that you cannot read it while looking at the question.

The answer is on the problem page too, folded away under Show the answer, and the pattern it uses is named below it with a link to every other problem that uses the same one. Folding the answer away is deliberate: a page that tells you the trick before you have read the question has spent it.

The drawing, control by control

The bar sits under the page, left to right:

←: Back to the question — or, on a practice question, back to the practice list it came from.
↺: Start the whole solution again from step 1.
⏮: Back a step. Going back is instant — no re-drawing. ←
⏯: Play and pause. Let it run to the end if you would rather watch than tap. space
⏭: The next step. Press it while a step is still drawing and it finishes that one first. →
↻: Draw this step again — the one you are on, not the whole solution. R
⌖: Narrow screens only. Frames just the current step so the writing is big enough to read; it starts on. Tap it for the whole page. F
The label: Where you are — 3 / 6 · The key step. Every solution has a key-insight step: the pattern worth remembering, not just the answer.
− +: Zoom, up to 8×. Scrolling zooms where the pointer is; pinch does the same on a touchscreen; double-tap jumps in close and again to come back; drag to move around. − +
⤢: Back to fitting the window. 0
Slider: Seven speeds, a quarter through to double: 0.25× · 0.5× · 0.75× · 1× · 1.25× · 1.5× · 2×. [ and ] nudge it one step. Your choice, and whether it was playing, are remembered as you move between problems.

The keys talk to the drawing. Click the drawing once if the keyboard is not reaching it. The buttons always do what they say, whatever has focus.

On a phone and on a tablet

A tablet gets the drawing exactly as a laptop does: tap a problem, then use the bar to step through, and pinch to look closer.

A phone watches it the same way, and on a narrow screen the drawing frames one step at a time by itself so the writing is big enough to read. Tap ⌖ to see the whole page instead.

Sending in a problem

Submit: The button under the search box on the problems page. Type the question out or attach a screenshot — either on its own is enough, and you can do both.
Screenshots: Paste straight into the form, drop a file on it, or pick one. Up to three, shrunk in your browser before they are sent.
Optional: The answer, and the working you were taught — give the working and the solution follows that method rather than inventing its own.
After that: Every submission is read by hand before it appears, so it will not show up straight away. Approved ones are listed under Sent in by readers at the foot of the problems page, and link to the drawing once one exists.

The problem text becomes public once it is approved, so please do not put anything personal in it. Leave the name blank and it stays anonymous.

What gets checked

Every solution goes through these before it is published, and a check that has not run is recorded as not run rather than as a pass.

The answer: Worked out from the question alone, then worked out a second time from scratch. The two have to agree. If they do not, the solution does not go up.
The conditions: The answer is put back into the question and shown to fit every condition it states. That is drawn as the last step, so you can read it rather than take my word for it.
The page: A browser opens the finished drawing and checks nothing is cut off or overlapping, on four screen sizes including a phone. 588 of the 768 published solutions pass cleanly, and 177 have not been measured yet.
What it does not check: Whether the method is the one your child’s school teaches, or whether the explanation is the clearest one. Those are judgements. If a solution looks wrong to you, it may be — send it back and say so.