Count stacks of cubes, find the hidden ones, fill a block, pick the top or front view, and solve painted cube puzzles. Six levels and printable worksheets.
Cube Counting builds one skill: seeing a three-dimensional stack in a flat drawing and reasoning about the parts you cannot see. A child counts the cubes in a picture, works out which ones must be hiding behind others, decides how many more would make a full block, and matches the stack to a view from above, in front or from the side. The top levels ask the kind of question used in children's maths contests, such as how many small cubes of a painted block have exactly two painted faces. The game is made for children of about 6 to 8. It is a spatial skill, and it grows fastest when a child also builds the same stacks with real blocks.
Level 1, Count them, shows a small stack where every cube can be seen. Level 2, Hidden cubes, shows a stack where some cubes are hidden behind others, with one rule that is printed and read aloud: every cube sits on the table or on another cube. So a tower with a visible top is solid all the way down. Level 3, Fill the block, draws dotted lines around a full block as tall as the tallest tower and asks how many more cubes make it full. Level 4, Which view, shows a stack with its front and side marked and asks which of four flat pictures is the top view, the front view or the side view. Level 5, Painted cubes, shows a block that is painted on every side, even underneath, and then cut into small cubes. It asks how many cubes have exactly two painted faces, exactly one, or none. Level 6, Fewest cubes, gives only a front view and a side view on a three by three table and asks for the fewest cubes the stack could have, or the most. Levels 5 and 6 are hard for adults who have not seen them before.
Levels 1 to 4 draw stacks from a bank of 158 stacks on tables of 2 by 2, 3 by 2 and 2 by 3 spots, with towers up to 3 cubes high. The picture is a proper isometric drawing: the cubes are painted from the back to the front, and each face is shaded as light on top, mid on the left and dark on the right, so it still reads on a black and white print. A stack goes in the bank only if its picture could not be drawn by any other stack on the same table, with towers up to 4 high. That is how the game makes sure the answer is certain, and the tests re-check every stack in the bank with their own model of the picture. Level 5 counts the cubes of a block from 2 by 2 by 2 up to 4 by 4 by 4, and the tests count every small cube one by one. Level 6 answers come from a search over every possible 3 by 3 stack. Wrong views on level 4 are close to the right one, but never a mirror image of it and never the picture of another view of the same stack.
By default the game moves up a level after three right answers in a row and down after two wrong in a row, and a child or parent can pick a level. Today's 5 is five puzzles made from the date on your device, so everyone with the same date gets the same five. Print a worksheet makes a page of 4, 6 or 8 puzzles on Letter or A4 paper with new puzzles each time and an answer key at the end. The drawings are shaded in greys, so they print well without colour.
It does not rotate the stack or let a child build one, and it does not test reading, because the questions are short and are read aloud with the speaker button. The tables are small on purpose, up to 3 spots wide, so a child can think about every cube. Real wooden or plastic blocks teach the same ideas better, so the printed puzzles are a good prompt to build the stack and look at it from the front, the side and above. Nothing is uploaded, and no account is needed.
It is written for ages 6 to 8. Level 1 is a stack of 3 to 9 cubes where every cube shows. Level 5, the painted block, is a puzzle that many adults get wrong the first time.
The rule is that every cube sits on the table or on another cube, and every stack in the game was checked against all other stacks that fit the same table. If a different number of cubes could draw the same picture, that stack is not used.
The block is painted on all six sides, then cut into small cubes. A small cube on the edge of the block, but not at a corner, has two painted faces. A 3 by 3 by 3 block has 12 of them, 6 with one painted face, 1 with none and 8 corners with three.
The front view is how the stack looks from the side marked front, the side view is how it looks from the side marked side, and the top view is how it looks from straight above. A tall tower hides what stands behind it, so each view only shows the tallest tower in each line.
Yes. Choose a level, then 4, 6 or 8 puzzles and Letter or A4 paper. Each print has new puzzles and an answer key on the last page, and the shading works in black and white.
It stays in this browser on this device. Nothing about your child is uploaded, and no account is needed. The page counts visits with Google Analytics, never answers.