Practice Spatial Reasoning in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The cognitive ability to visualize, manipulate, and reason about two- and three-dimensional objects mentally in space.

Imagining how furniture will fit in a room before physically moving any of it.

Showing a random 20 of 64 problems.

Example 1

easy
How many edges does a cube have?

Example 2

medium
A rectangular box is 66 cm long, 44 cm wide, and 33 cm tall. What is the length of the space diagonal (corner to opposite corner)?

Example 3

medium
Your shoes are on the floor below your bed. Are the shoes above or below the bed?

Example 4

easy
How many corners (vertices) does a cube have?

Example 5

easy
If you unfold a cube flat, how many square faces are in the flat pattern (net)?

Example 6

easy
A cat is inside the box. Is the cat in or out of the box?

Example 7

medium
A cube is painted red on all 6 faces and then cut into 2727 smaller equal cubes. How many small cubes have paint on exactly 2 faces?

Example 8

easy
A balloon floats above your head. Is the balloon above or below you?

Example 9

easy
Maya stands in line. The teacher is in front of her. Where is the teacher: in front of or behind Maya?

Example 10

medium
A rectangle has how many corners?

Example 11

hard
An arrow points UP. You turn it a quarter turn to the right, then flip it over a horizontal line (top-bottom flip). Which direction does the arrow now point?

Example 12

medium
A hexagon has how many sides?

Example 13

easy
You put two squares of the same size right next to each other so their sides touch. What new shape do they make?

Example 14

medium
A square piece of paper is folded in half, then in half again. How many layers thick is it now?

Example 15

medium
A net has 6 squares in a cross shape. When folded, what solid does it form?

Example 16

medium
Two shapes look identical but one is shown rotated. What spatial skill confirms they're the same shape?

Example 17

hard
A sun is in the sky. A flower is on the ground. Is the sun above or below the flower?

Example 18

medium
A cube is painted red, then cut into 8 small equal cubes (2ร—2ร—22 \times 2 \times 2). How many small cubes have exactly 3 red faces?

Example 19

medium
A rectangle is standing tall (long side up-down). You turn it 9090 degrees. Is the rectangle now tall or wide?

Example 20

medium
A solid is built from 4 unit cubes stacked in an L-shape. How many cubes touch the ground if it sits on its longest side?