What does a child have to do to compose two visual transformations in the 11+?

Apply two stated rotations or reflections in order. It is one of 22 named non-verbal reasoning skills in the 11+, in the transform strand, and this page carries 1 interactive exercise that practises it.

What is the trap in an 11+ compose two visual transformations question?

Doing the two steps the other way round gives a different figure - the order in the sentence is the order to work in. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What is not part of compose two visual transformations in the 11+?

The skill map draws the line here: Exactly two transformations; order matters. A question past that line is testing a different named non-verbal reasoning skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside compose two visual transformations?

The skill map connects it to reflect a visual figure and rotate a visual figure. A two-step transformation may include a reflection component. A two-step transformation may include a rotation component. Each of those has its own page here.

How can my child practise compose two visual transformations for free?

Use The Transformation Deck, embedded on this page. It is the exercise the skill map attaches to compose two visual transformations, it runs in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. It also has its own link, so you can send it to a child without sending them anywhere else first.

Non-verbal Reasoning · Transform

Compose two visual transformations

Apply two stated rotations or reflections in order.

Practise it now

Drag the track to play the cards and watch the outline move. Then say where corner C finished.

This exercise practises compose two visual transformations alongside its own main skill, Composing Transformations.

It covers most of this skill rather than all of it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Two transformations, one after the other

Follow the figure through both steps in turn: rotate 270 degrees clockwise, then reflect in the horizontal mirror line.

The second step acts on the figure the first step already produced, so swapping the order of a turn and a flip gives a different picture.

TransformRotate 270 degrees clockwise, then reflect in the horizontal mirror line

Option A, 270 degree rotationturned 270° clockwise
Option B, 90 degree rotation, mirrored across the x axisflipped, then turned 90° clockwise
Option C, 270 degree rotation, mirrored across the x axisflipped, then turned 270° clockwise
Option D, 180 degree rotation, mirrored across the x axisflipped, then turned 180° clockwise

Answer: flipped, then turned 270° clockwise

How you get there

After step 1, rotate 270 degrees clockwise, the figure is turned 270 degrees clockwise. After step 2, reflect in the horizontal mirror line, the figure is flipped, then turned 270 degrees clockwise. So the final figure is flipped, then turned 270 degrees clockwise. The second step acts on the first result, which is why reversing the order lands on a different option.

Why the other answers tempt

Doing the two steps the other way round gives a different figure - the order in the sentence is the order to work in.

If they are stuck, say this

Do the first step in your head and hold that picture, then apply the second step to it; one option is what you get if you carry out rotate 270 degrees clockwise, then reflect in the horizontal mirror line in the wrong order.

Now do it live in The Transformation Deck

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's try Compose two visual transformations together. Take a look at the picture. Here is what matters: Shape picture with transform Rotate 270 degrees clockwise, then reflect in the horizontal mirror line made from 0 parts. Here comes the question: Follow the figure through both steps in turn: rotate 270 degrees clockwise, then reflect in the horizontal mirror line. A handy clue is: Do the first step in your head and hold that picture, then apply the second step to it; one option is what you get if you carry out rotate 270 degrees clockwise, then reflect in the horizontal mirror line in the wrong order. Nice work. Here is the thinking: After step 2, reflect in the horizontal mirror line, the figure is flipped, then turned 270 degrees clockwise. So our answer is: flipped, then turned 270° clockwise. One sneaky trap is: Doing the two steps the other way round gives a different figure - the order in the sentence is the order to work in. Can you show me the first move in your own words? No rush; one calm step is enough.

What this exercise is doing

The Transformation Deck

Drag the track to play the cards and watch the outline move. Then say where corner C finished.

This engine’s own main skill is Composing Transformations. It practises compose two visual transformations alongside it, and covers most of it rather than all.

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.

Step 1. Play it. Drag the fold track all the way across to play both cards, then scrub back and forth.
Step 2. Where did it land?. Now the question: where does corner C finish?

What to say if they get stuck

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).

Open The Transformation Deck on its own page to share it

Where compose two visual transformations sits in the 11+

The 11+ does not test these skills in isolation, and practising one in the wrong order wastes the practice. These are the skills the curriculum map connects this one to.

This is built out of: Reflect a visual figure
A two-step transformation may include a reflection component.
Rotate a visual figure
A two-step transformation may include a rotation component.

How compose two visual transformations differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: apply two stated rotations or reflections in order, and it stops where exactly two transformations; order matters.

Compose coordinate transformations
Apply two stated coordinate transformations in order. Exactly two transformations are composed. Single transformations have separate skills.
Plot or read a coordinate
Read or place one point on a coordinate grid. Axis range and quadrant are explicit.
Reflect a coordinate
Determine a point image after reflection in a stated coordinate axis. One point and one stated mirror axis only.
Rotate a coordinate
Determine a point image after a stated rotation about the origin. The centre, direction, and turn are explicit.
Translate a coordinate
Determine a point image or translation vector on a coordinate grid. One point and one translation only.

Related non-verbal reasoning skills

Compose a visual transformation sequenceApply three stated rotations or reflections in order.

All non-verbal reasoning 11+ skills

Questions parents ask about compose two visual transformations

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

: Apply two stated rotations or reflections in order. It is one of 22 named non-verbal reasoning skills in the 11+, in the transform strand, and this page carries 1 interactive exercise that practises it.
: Doing the two steps the other way round gives a different figure - the order in the sentence is the order to work in. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Do the first step in your head and hold that picture, then apply the second step to it; one option is what you get if you carry out rotate 270 degrees clockwise, then reflect in the horizontal mirror line in the wrong order.
: The skill map draws the line here: Exactly two transformations; order matters. A question past that line is testing a different named non-verbal reasoning skill, which is worth knowing before you spend a week practising the wrong one.
: The skill map connects it to reflect a visual figure and rotate a visual figure. A two-step transformation may include a reflection component. A two-step transformation may include a rotation component. Each of those has its own page here.
: Use The Transformation Deck, embedded on this page. It is the exercise the skill map attaches to compose two visual transformations, it runs in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. It also has its own link, so you can send it to a child without sending them anywhere else first.

Non-verbal reasoning is the paper families most often leave until last

A free diagnostic covers matrices, series, odd one out, rotation, reflection and the 3D questions, and shows where the time is worth spending.

Start the free 11+ diagnostic