Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Solve the Shape Equation

In this worksheet, students will identify combined shapes made from two given shapes or they will identify the missing shape from a combined shape. The focus will be on identifying shape, size, shading and line type.

'Solve the Shape Equation' worksheet

Key stage:  KS 2

Year:  Year 5 11+ worksheets

Curriculum topic:   Spatial and Non-Verbal Reasoning

Curriculum subtopic:   Combined Shapes

Difficulty level:  

Worksheet Overview

Hi there, shape mixer!

It’s time to combine some shapes with the magical powers of our minds!

 

This type of question is laid out like an addition sum in maths.

Look at the two shapes below:

 

Use your magical, shape-moving mind powers to imagine these two shapes combining together.

One, or both of them could rotate, and they are allowed to overlap each other too. 

 

How many different ways can you think of them combining together?

 

Look at the options below:

 

 

Which of these options can be made by combining our two original shapes together?

We need to focus on one of our original shapes at a time and investigate whether it has maintained the same shape, shade and size in our answer options.

 

It also must have the same line type - this includes the line thickness and line style.

Remember that one or both of the original shapes could also rotate when they combine.

 

Let’s start with the first shape in our sum.

This shape is made up of a tall, vertical line with two shorter, horizontal lines going through its middle.

Which of our five options show exactly the same shape?

 

Only options b and d do.

 

In option a, this shape has an extra line.

In option c, this shape has lost a line.

And, in option e, the line thickness has changed.

 

Now, we only need to focus on options b and d to see if they contain a match for our second shape.

There’s no point in wasting time looking at the other options when we can eliminate them straight away! 

 

Option b has different shading to the original second shape.

 

This makes option d our correct answer.

In this option, the first shape has rotated 90° anti-clockwise to combine with the second.

 

Now it’s time to take your shape-mixing skills to the next level with this new example:

 

 

This time, we have been given the combined shape and just one of the separate shapes used to make it.

Our job here is to find the missing shape which joins with the first shape to make the combined shape

 

We could treat this like a subtraction question in maths to help us figure out the missing shape.

Just like this:

 

 

Which of the following options would join with the single rectangle to make the combined shape?

 

 

First, we need to identify what we need to add to the shape on the right (the blank rectangle) to make it look like the combined shape.

Can you see how two medium-sized squares and a small square overlap the blank rectangle? 

 

Which options show two medium-sized squares and a small square?

 

Options a, b and e do.

 

This means we can eliminate options c and d straight away.

The line style is different in option e, so this can be eliminated too.

In option a, the small square is in the wrong position.

This leaves us with option b as our correct answer!

 

It’s now your turn to go on the hunt for combined or missing shapes.

 

11+ detective image

                                     Top tip!

Remember to check that the new images maintain the same shapes, sizesshading and line types as the originals.

 

Good luck, shape mixer!

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • National Tutoring Awards 2023 Shortlisted / Parents
    National Tutoring Awards 2023 Shortlisted
  • Private-Tutoring-WINNER-EducationInvestor-Awards / Parents
    Winner - Private Tutoring
  • Bett Awards Finalist / Parents
    Finalist
  • Winner - Best for Home Learning / Parents
    Winner - Best for Home Learning / Parents