# Visualise Rotating and Joining Irregular 2D Shapes

In this worksheet, students will join simple 2D shapes together to make a compound shape. They will 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 correct answer is c, as the triangle moves to the right of the rectangle and the trapezium goes on top of the rectangle.

Let’s try another question now.

This time it is more challenging, as the shape can rotate.

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.

Here are the possible options:

a)         b)         c)

If we join all of the shapes together, without rotating them, 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.

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 given 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 this pair of shapes:

We need to join these shapes together to make a new, combined shape.

Sides with matching letters have to touch.

This means that both the sides labelled a have to be touching each other.

Once the shapes have been joined together, where will the square be?

On the top

In the middle

On the bottom

Now it's time to join our pair of shapes from the previous question together.

Look at these two shapes again:

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

Remember that both the sides labelled a must be touching each other

Here's a new duo of sneaky 2D shapes to consider in this case.

Look at these two shapes:

We need to join these shapes together to make a new, combined shape.

Sides with matching letters have to touch.

Once the shapes have been joined together, where will the triangle be?

On the top

On the right

On the bottom

On the left

Now it's time to join our shapes from the previous question together.

Look at these two shapes again:

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

Remember that both the sides labelled a must be touching each other

Look at these two new shapes:

We need to join these shapes together to make a new, combined shape.

Once the shapes have been joined together, where will the triangle be?

On the top left edge of the diamond

On the top right edge of the diamond

On the bottom left edge of the diamond

On the bottom right edge of the diamond

Now it's time to join our shapes from the previous question together.

Look at this duo of shapes again:

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

Look at this new pair of shapes:

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

Look at this final duo of suspect shapes:

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

Look at this fresh duo of shapes:

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

Look at this penultimate pair of 2D 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 this pair of shapes:

We need to join these shapes together to make a new, combined shape.

Sides with matching letters have to touch.

This means that both the sides labelled a have to be touching each other.

Once the shapes have been joined together, where will the square be?

On the top
EDDIE SAYS
How did you get on with this first challenge, 2D builder? The bottom side of the square needs to join with the top right side of the pentagon, as they are both labelled with a letter a. This means that the square will move on top of the pentagon to join with it. Can you imagine the square moving up and rotating to join with the side labelled a? Keep a mental image of how these shapes are joined to help you identify your prime suspect in the next challenge...
• Question 2

Now it's time to join our pair of shapes from the previous question together.

Look at these two shapes again:

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

Remember that both the sides labelled a must be touching each other

EDDIE SAYS
Both of the sides labelled a must join together. So the square needs to rotate so that it can perfectly slot onto the side of the pentagon on the top right, which is also labelled with an a. This means that our final combined shape will look like option b. Does this image match the picture in your head, detective?
• Question 3

Here's a new duo of sneaky 2D shapes to consider in this case.

Look at these two shapes:

We need to join these shapes together to make a new, combined shape.

Sides with matching letters have to touch.

Once the shapes have been joined together, where will the triangle be?

On the left
EDDIE SAYS
We need to imagine joining these shapes together so that we can picture where the triangle will be positioned. The bottom side of the triangle (labelled a) needs to join with the left side of the arrow. This means that the triangle will have to rotate in an anti-clockwise direction to join with the vertical edge of the arrow. Can you visualise this movement in your head? This means that the triangle will end up on the left. Make sure you've got your lefts and rights down in this question, or it can quickly become confusing! Remember the position of these shapes to help you in your next mission...
• Question 4

Now it's time to join our shapes from the previous question together.

Look at these two shapes again:

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

Remember that both the sides labelled a must be touching each other

EDDIE SAYS
Did you notice something strange and sneaky about option d? The triangle shown in this option is completely different! It uses a right-angled triangle to build with, rather than an equilateral triangle - very sneaky! This means that we can rule this suspect out immediately. In the previous question, we decided that the triangle needed to rotate in an anti-clockwise direction to join with the left-hand, vertical edge of the arrow (labelled a). As options a and c show the triangle positioned either above or below the arrow, rather than to the left of it, we know that option b must be the correct answer. Great shape building so far, detective - keep it up!
• Question 5

Look at these two new shapes:

We need to join these shapes together to make a new, combined shape.

Once the shapes have been joined together, where will the triangle be?

On the top left edge of the diamond
EDDIE SAYS
The bottom side of the triangle needs to join with the top left edge of the diamond (both labelled a). This means that the triangle will sit on the top left edge of the diamond. Can you image the triangle turning anti-clockwise to slide over and join with the diamond? Keep your detective's eyes peeled to find out what these shapes will look like after they have been joined in our next challenge...
• Question 6

Now it's time to join our shapes from the previous question together.

Look at this duo of shapes again:

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

EDDIE SAYS
If the bottom side of the triangle joined with the top left side of the diamond, what would our combined shape look like? The triangle needs to rotate slightly in an anti-clockwise direction. Use your shape-moving superpowers to imagine this process in your head. Can you see how it will look like option a? Keep up the excellent shape joining 2D builder - you're over halfway through!
• Question 7

Look at this new pair of shapes:

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

EDDIE SAYS
The five-sided shape on the right is called a pentagon, and its flat bottom side is labelled with the letter a. So this side needs to join with the lower right side of the hexagon (six-sided shape). In options a and b, the pentagon has sneakily been switched for another shape so we know that these red herrings cannot be correct answers. Our pentagon will have to rotate in an anti-clockwise direction to join with the lower right side of the hexagon. This will look like option d. Can you imagine the shapes moving in this way in your head?
• Question 8

Look at this final duo of suspect shapes:

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

EDDIE SAYS
Did you find the correct version of our final joined shapes here? All of these faces look like they have a banana resting on their head in different positions! You may need to get your detective's magnifying glass out here, as they all look quite similar. The smaller curve of our second shape needs to sit on top of our smiley face. This means it will rotate perfectly to sit on top of the head, which will look like option c. Congratulations on all your shape-joining and rotation skills in this activity, detective! You can now visualise rotating and joining irregular 2D shapes by linking sides with the same letter.
• Question 9

Look at this fresh duo of shapes:

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

EDDIE SAYS
Here, the rectangle needs to rotate to join with the top of the semi-circle. Can you imagine the rectangle turning so that its side (labelled a) can sit on top of the flat top of the semi-circle? This joined shape would look like option c.
• Question 10

Look at this penultimate pair of 2D shapes:

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

EDDIE SAYS
Here, the triangle needs to turn upside down so that its base (labelled a) can join with the base of the trapezium. Can you visualise this movement in your detective's head? This new, combined shape would look like option a. You just have one more pair of suspects to join now, detective - nearly there!
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