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.

Example 1

easy
Look at this sequence of shapes: triangle, square, pentagon. How many sides does the next shape have? Draw a rough sketch.

Example 2

medium
A cube is painted red on all 6 faces and then cut into 27 smaller equal cubes. How many small cubes have paint on exactly 2 faces?

Example 3

easy
If you fold a square piece of paper in half and then in half again (both folds along the middle), how many layers of paper are there when unfolded? How many crease lines are visible?

Example 4

medium
A rectangular box is 6 cm long, 4 cm wide, and 3 cm tall. What is the length of the space diagonal (corner to opposite corner)?