Counting cubes
Structures drawn in 3D: first cubes that are all in sight, then cubes hidden under others and, at the top level, how many more would fill a cuboid.
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Teaching guide: spatial reasoning worksheets
Spatial reasoning is the ability to picture objects in three dimensions, turn them round in your head and see them from somewhere else. It is the part of geometry PISA assesses under "Space and shape" and it turns up in reasoning tests. This free spatial reasoning worksheet generator makes A4 worksheets for Grades 2 to 8: cube structures to count, views, rotated shapes and the cubes that nets fold into, with an answer key.
- For
- Elementary 2nd, 3rd, 4th, 5th, 6th · Middle & High 7th, 8th (ages 7-13)
- Subject
- Mathematics › Geometry & Measurement
- Includes
- Student sheet and answer key
- Format
- A4, to print or save as PDF; new exercises every time
- Price
- Free, no sign-up
- Available in
- Catalan, Spanish, English
Student worksheet 
Answer key Which view is it?
A structure with an arrow marking its front and four drawings: pupils pick the one seen from the front, from above or from one side.
Mental rotation
Of four shapes, only one is the model turned round. The others have a cube added, taken away or moved, or are its mirror image, which no turn can give.
Cubes and nets
A cube with marks on its faces and four nets to fold in your head. At Grades 7-8, the other way round: which of four cubes the net makes.
One answer only
Every drawing reads one way: the generator checks that no other cube structure gives the same drawing and that the wrong options really are wrong.
Answer key
The number of cubes (and how many are hidden) and the right letter circled in blue. Black lines and light greys that print well in black and white.
Frequently asked questions about spatial reasoning
What is spatial reasoning?
It is the ability to picture objects in three dimensions and handle them in your head: turn them round, see them from another point of view or fold up a net. It belongs to geometry, and PISA assesses it as part of mathematical literacy.
How do you count hidden cubes?
Every cube is on the floor or on another cube, and the cubes you cannot see are under other cubes. So a stack you see three cubes high has three cubes, even if you only see the top one. Counting stack by stack helps: the height of each stack, then add them up.
Which grades are these worksheets for?
Grades 2 to 8 (Years 3 to 9). Each activity has three levels with their grades: counting cubes starts in Grade 2, views in Grade 3, cube nets in Grade 4, and mental rotation of larger shapes goes up to Grade 8.
Why is a mirror image not the same shape?
Because no turn makes it match the model, just like your right and left hands. At levels 2 and 3 of "Which shape is the same?", one of the options is the mirror image of the model.
How can I tell whether a net folds into the cube shown?
The three marks you can see on the cube must land on faces that touch (not opposite ones) and go round their corner in the same order. For which shapes of six squares fold into a cube, and opposite faces, see the nets of 3D shapes.
Which other geometry worksheets go well with these?
The views and isometric drawing worksheets to draw front, top and side views, symmetry and grid drawing. Find every resource under maths worksheets.
Is any pupil data sent anywhere?
No. Worksheets are generated in your browser and templates are saved in your browser's memory.
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