Maths · Composing Transformations
The Transformation Deck
Drag the track to play the cards and watch the outline move. Then say where corner C finished.
Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere. What you may do with it, in full.
Loading the interactive exercise. Nothing you do here is saved or scored.
Why this works
The programme is “Flip in the line y = x”, then “Slide 2 right, 3 down”. Taking the cards one at a time, a flip in y = x SWAPS the two numbers: (x, y) becomes (y, x), and no sign changes at all; and then a slide adds the same pair of numbers to every corner: (x, y) becomes (x + 2, y − 3). Corner C starts at (-2, 3) and finishes at (5, -5). The order matters as much as the cards do: each card acts on wherever the shape has got to, not on where it started, so playing them the other way round can leave the shape somewhere else entirely.
Helping a child through The Transformation Deck
It runs in 2 steps
- 1. Play it. Drag the fold track all the way across to play both cards, then scrub back and forth.
- 2. Where did it land?. Now the question: where does corner C finish?
Hints, least revealing first
- Scrub the track slowly, and back again. The pale outlines show every place the shape stopped.
- Follow corner C on its own rather than the whole shape - it leaves a dotted trail.
- a slide adds the same pair of numbers to every corner: (x, y) becomes (x + 2, y − 3).
When they finish it: “Both cards, in the right order!”
7 11+ skills this exercise practises
Each of these has its own page, with a worked example on it. 1 of the 7 names the mistake that skill attracts.
- Compose coordinate transformationsApply two stated coordinate transformations in order.
- Plot or read a coordinateRead or place one point on a coordinate grid.
- Reflect a coordinateDetermine a point image after reflection in a stated coordinate axis.
- Rotate a coordinateDetermine a point image after a stated rotation about the origin.
- Translate a coordinateDetermine a point image or translation vector on a coordinate grid.
- Compose a visual transformation sequenceApply three stated rotations or reflections in order.
- Compose two visual transformationsApply two stated rotations or reflections in order.
You can reuse this. Here is exactly how far that goes
Tutors, teachers and editors keep asking, so this is the answer in writing rather than by email. You do not need to ask permission, and you do not need to tell us.
- Embed it
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- Use it in class
- One child or a full set, in a school, in a tutoring session, in a homework club, or at the kitchen table.
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- Quote it, rewrite it, translate it, cut it up, or build something different on top of it. Treat the wording, the worked examples and the question ideas as yours to work with.
The one thing we ask is a link back to the page you took it from, so a reader can find the live, playable version and the rest of the 11+ skills next to it. That is a request, not a condition: nothing above depends on it.
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Embed this exercise
Paste this into your own page and the exercise runs there, playable, for your readers or your students. It is 900 pixels tall by default and as wide as the column you put it in; change the height if your layout wants a different one.
The embedded copy has no header, no footer and no sign-up prompt. It records nothing about the child using it, on your page just as on ours.
The Transformation Deck touches 7 skills at once
Which means a child who struggles with it could be stuck on any one of them. A free diagnostic across all four subjects narrows it to the one.