Count the Cubes

Free puzzles to print

Each set: a Learn sheet with a worked example, 10 puzzles from easiest to hardest, and the answers.

• Level 1

  Ages 4–6 · Pre-K–K

  

  2 to 8 cubes, every cube shows; the child picks from three number cards that show small cubes under each number.

  On the sheet: “How many cubes? Put a check on the card.”

  Print Level 1 (Letter)Other paper size: A4

• Level 2

  Ages 6–8 · Grades 1–2

  

  7 to 14 cubes, and from the middle puzzles some cubes are hidden under ones you can see.

  On the sheet: “How many cubes? Write the number.”

  Print Level 2 (Letter)Other paper size: A4

• Level 3

  Ages 8–10 · Grades 3–4

  

  Count a stack on a 3 × 3 mat (8 to 14 cubes, some hidden). Then work out how many more make a 3 × 3 × 3 big cube. Then write a building plan: how many cubes stand on each square.

  On the sheet: “How many cubes?”

  Print Level 3 (Letter)Other paper size: A4

The thinking it works on

• Reading a flat drawing as a solid

  Reads a flat drawing of cubes as a solid stack with layers and columns.

  Battista and Clements (1996) found that children at first see a drawing of a box made of cubes as a loose set of faces. Only later do they put the views together into one solid they can count. Source

• Reasoning about what is hidden

  Works out that a cube must be there even though no part of it shows.

  Ben-Chaim, Lappan and Houang (1985) found that even students in grades 5 to 8 often struggle to work out how many cubes build a box in a drawing. Source

• Perspective taking

  Imagines looking down on the stack or walking around it to count the back.

  Frick, Möhring and Newcombe (2014) found that 4-year-olds mostly cannot pick what a scene looks like from another spot. The skill starts to grow around age 6, and children still differ a lot at 8. Source

• Systematic counting

  Counts layer by layer and keeps track so nothing is counted twice.

  Battista and colleagues (1998) found that many students do not 'see' the rows and columns in a grid of squares. They traced several levels in how children organize and count such a grid. Source

• Working memory

  Holds the running total, the rule and the current layer in mind at once.

  Gathercole and colleagues (2004) found that working memory (holding and using a few things in mind at once) grows steadily from age 4 to 15. Source

• Reading and writing a plan

  Writes a building plan: a number on each square saying how many cubes stand there.

  Alon (2026) tested 1,064 children in grades 1 to 6 on picking how a 3-D object looks from another viewpoint, and found steady gains across the grades. Source

Where is this thinking used?

• Architecture: A building is drawn flat as plans and elevations, then built in three dimensions.
• 3D modeling and game design: A flat screen stands for a solid world.
• Packing and inventory: Counting boxes in a van or items on a shelf when some sit behind others.
• Building from a plan: A number on a square stands for a column of bricks that isn't drawn.