# Recognise Rotations of Combined 2D Shapes

In this worksheet, students will join simple 2D shapes together to make a compound shape. Students will also identify the matching shape, which may have been rotated, from a selection.

Key stage:  KS 2

Curriculum topic:   Spatial and Non-Verbal Reasoning

Curriculum subtopic:   Joining 2D Shapes

Difficulty level:

### QUESTION 1 of 10

Prepare to be a 2D shape builder!

Look at the shapes below:

In this question type, we need to join these three shapes together to make a new shape.

Matching letters have to touch, so, in this example, both the sides labelled a have to be touching each other and both the sides labelled b have to be touching each other.

Which of the following options would the new shape look like?

a)         b)         c)

The trick is to imagine joining all of the shapes together, and then try rotating the entire new shape, to see if it matches one of the options.

If we join all of the shapes together, without rotating anything, it would look like this:

As this doesn’t match any of the options, let’s try rotating it to see if we can match it to anything.

If it is rotated a quarter turn in an anti-clockwise direction, it looks exactly like option b - bingo!

So the correct answer is b.

Let’s try another example now.

This one is more challenging as there are four shapes to join.

Look at the shapes below:

What would this shape look like if all the correct letters were joined together?

a)         b)         c)

Remember to join them all together first and then try to rotate it.

If we imagine putting all of the shapes together with the corresponding letters, our shape would look like this:

As this doesn’t match any of the options, let’s try rotating it to see if we can match it to anything.

If it is rotated 180 degrees, it looks exactly like option b - job done!

So the correct answer is b.

It’s now your turn to join shapes together.

Good luck 2D shape builder!

Psst! Here’s a handy hint to help you reach superstar status: remember to join the shapes first and then try to rotate your new shape to match one of the options.

Hi there, 2D shape builder!

We're glad you're here to help us put the 2D shapes in this activity together in their correct positions.

Look at these three shapes:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

Here is another trio of shapes to consider:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

​Look at our next set of shapes:

What will these shapes look like once they've been joined together?

​Look at this final group of shapes:

What will these shapes look like once they've been joined together?

​Look at this new trio of shapes:

What will these shapes look like once they've been joined together?

Here's another set of shapes for you to feast your eyes on:

What will these shapes look like once they've been joined together?

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

Consider this new trio of shapes now:

What will these shapes look like once they've been joined together?

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

• Question 1

Hi there, 2D shape builder!

We're glad you're here to help us put the 2D shapes in this activity together in their correct positions.

Look at these three shapes:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

EDDIE SAYS
How did you get on with this first challenge, 2D builder? We need to join up the sides with matching letters. The trick is to focus on the shape which has two sides labelled with letters as this will be in the centre, then imagine the other shapes moving around this. The square will need to tumble over to join the vertical, left-hand side of the triangle. The rectangle will then need to rotate as well to fit on the diagonal side of the right-angled triangle. If we join these three shapes together in this sequence, our combined shape will look like option d. Can you imagine the shapes moving around the central triangle to fit together in this way, detective?
• Question 2

Here is another trio of shapes to consider:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

EDDIE SAYS
Let's use the power of our minds to mentally move these shapes. We need to keep the shape labelled with two letters (the arrow crossroad) in the same position, then move the other shapes around it. The long side of the trapezium needs to join with the base horizontal line of our arrows (both labelled a.) This means that the trapezium needs to rotate 180 degrees or a half turn. The triangle then needs to sit on the upper left horizontal side of the arrows, both labelled b. If we follow these steps, the combined shape will look like option b. Does this match the image in your head?
• Question 3

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

Remember that all the sides labelled with the same letters must be touching each other

EDDIE SAYS
Let's try keeping the larger, circular shape in the centre this time, so that we only have to move the smaller shapes around it - it's always good to mix things up, isn't it?! The shorter left edge of the rectangle needs to sit on the short horizontal cut-out of the circle (both labelled a.) This means that the rectangle needs to rotate so that it is standing tall on its edge to fit in this gap. The triangle will then sit on top of the upper short edge of the standing rectangle (both labelled b). This will look like option e. Did you spot that?
• Question 4

​Look at our next set of shapes:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Again, let's keep the larger block arrow shape fixed, and move the other, smaller shapes around it. The diamond needs to rotate 90 degrees or a quarter turn anti-clockwise so that it can join with the inner, upper diagonal of the arrow (both labelled a). The rectangle also needs to rotate 90 degrees anti-clockwise so that it is sitting on top of the upper horizontal edge of the block arrow (both labelled b). Once we have completed these movements, our combined shape will look like option a.
• Question 5

​Look at this final group of shapes:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Both the block arrow and the rectangle need to be touching the triangle. Are there any options where this is not the case? Yes! All of the options except for d do not show this relationship, which means we have found our correct answer already! Well done for being a fantastic 2D builder! You've learnt to eliminate options by seeing which shapes must be touching each other. You've also learnt that sometimes you have to join the shapes and then rotate the entire combined shape to find the correct answer.
• Question 6

​Look at this new trio of shapes:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Here, the trapezium will need to turn upside down so that its longer horizontal edge can join with the lower horizontal side of the cross shape, which is labelled a. This means that we can rule out options b, d and e straight away as suspects, as their trapeziums are not upside down. Now we must choose between options a and c. The triangle needs to sit on top of the upper horizontal edge of the cross, labelled b. In option a, the triangle is joined to the right vertical edge instead so this cannot be correct. This makes option c the correct answer. Keep using your shape-moving powers and ruling out the options one-by-one as you go.
• Question 7

Here's another set of shapes for you to feast your eyes on:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Let's start by moving the small arrow shape. It will need to rotate to sit on the horizontal side labelled with an a on the large L-shape. As it is much skinnier than the line of the L-shape, any options with the arrow positioned anywhere on this line will be correct. The parallelogram then needs to sit on the top horizontal edge of the L-shape (labelled b). If we follow this through, then our final shape will look like option d. Don't let sneaky option c catch you out here - it's very close to being right, but the parallelogram has been rotated so that its wrong side has joined with the L-shape.
• Question 8

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Let's keep our curvy, half-cylinder still here, and move the simpler shapes around it. We need to rotate the oval so that its edge labelled b can join with the right-hand concave curve of the central half cylinder. This means that we can rule out option a, as its oval has not been turned to fit in this gap. Then we need to turn the triangle around so that its base labelled a can join with the flat top edge of the half cylinder. Option b shows the triangle joined to the bottom edge of the half cylinder, so cannot be our answer. Can you see how the triangle in options d and e are different from the one given in the question? This makes option c the correct answer.
• Question 9

Consider this new trio of shapes now:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Let's start by ruling out any obviously incorrect answers here. Both the square and the triangle need to be touching the four-pointed star shape, which rules out option b as this is not the case here. Now there's only four options to consider. Let's imagine joining the shapes together. The square needs to rotate so that its base joins the left side of the pointed star (both labelled a). The triangle needs to turn upside down to join the lower side of the right-hand point (both labelled b). Can you imagine this combined shape in your head? It would look like this: However, none of our options show this exactly so we must be looking for a rotation. If we rotate the image above as a whole, without moving any of the shapes separately, it will look like option e. Remember that you must join the shapes first and then rotate the entire image, detective.
• Question 10

​Look at this new group of shapes:

What will these shapes look like once they've been joined together?

EDDIE SAYS
Again, let's start by ruling out any obviously incorrect answers. Both the triangle and the thinner curve need to join with the thicker curve. In options a, c, d and e this is not the case - so we can immediately focus on option b as the correct answer. Let's check this by joining the shapes. Imagine the thicker curve rotating to join with the left side of the thinner curve, then the triangle turning upside down to join with the other end of the thicker curve. Remember the order of this process, master builder: 1) Eliminate the obviously incorrect options; 2) Join the shapes by matching letters and rotating; 3) If no answers match this, rotate the entire combined shape until you find a match. Simple!
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