Plans and Elevations Worksheet Generator
A structure built from cubes can be drawn three ways on squared paper: the plan from above, the front elevation and the side elevation. This makes structures of up to twelve cubes and asks for those views — from a picture on isometric paper, or from a plan with the number of cubes on each square — and the reverse: given the three views, build a structure that has them. That last question usually has more than one answer, so the sheet asks for the fewest and the most cubes it could use, which have exactly one answer each, and says how many different structures fit.
What this generator does
Grows a connected structure of stacks on a small grid, so every cube stands on the table or on another cube, and keeps it only if every stack can be seen in the isometric picture. Each view is worked out twice — once from the stack heights and once by projecting every cube on its own — and the two must agree. For building questions, every possible set of stack heights on the plan is tried to count the structures with the same three views.
How to use this tool
- Choose a task, a level and how many structures.
- Press Make the sheet. Blank squared grids for the answers are printed with each question.
- Show the answers to see the three views, the number of cubes and, for building questions, one structure that fits.
- Print the questions and the answers, or type a sheet code to make the same sheet again.
Understanding the controls
- Task
- Draw the plan and both elevations from an isometric picture; draw the elevations from a plan with heights; or build from three views and give the fewest and most cubes.
- Level
- Gentle structures fit on 3 × 2 squares and are 2 cubes high with 4 to 6 cubes; standard 3 × 3 and 3 high with 6 to 9; stretch 4 × 3 and 3 high with 8 to 12.
- How many structures
- 1 to 4, two to a printed page, with blank grids large enough not to give away the size of the answer.
- Sheet code
- Leave empty for a fresh sheet from the browser's secure generator; with a code, the same code and settings make the same sheet again while the generator is unchanged.
Worked examples
- Code harbour, draw, standard, structure 1
- Back row 3, 3, 1 cubes, front row 0, 0, 1: front elevation heights 3, 3, 1; side elevation 1 (front) then 3; 8 cubes.
- Code harbour, build, standard, structure 1
- Plan with one square at the back left and three at the front; front view 3, 2, 2; side view 2 (front), 3. The back stack must be 3; the front-left stack can be 1 or 2, so the fewest is 8 and the most 9.
Common use cases
- Plans and elevations practice with cubes the class can also build
- Reading isometric drawings of cube structures
- Discussing why three views do not always fix a solid
How this generator works
The plan marks every square with at least one cube. The front elevation shows, for each column from left to right, the tallest stack in it; the side elevation, seen from the right, shows the tallest stack in each row with the front of the structure on the left. For a building question the plan fixes which squares hold cubes, and each stack can be no taller than its column in the front view or its row in the side view; every combination within those limits is tried, and those whose views match are counted.
Randomness and fairness
Structures come from the browser's secure generator, or a seeded one when you type a code. A code repeats a sheet while the generator is unchanged. Codes are deterministic, not cryptographic, and not a secret.
For how randomness is produced across the whole site, see how Generate Random works.
Assumptions this tool makes
- Every cube stands on the table or on another cube: no overhangs and no gaps under a cube.
- The front is the face the arrow labelled Front points at; the side view is from the right.
Limitations and good to know
- Views are drawn as filled squares on a grid, not technical drawings: lines where the depth changes and hidden edges are not shown, and first- and third-angle layouts are not used.
- Structures are stacks on the table; shapes with overhangs or holes are not made.
- The isometric picture shows the structure from one direction only.
Common mistakes
- Drawing the front elevation as the front row only
- A tall stack further back still shows above a short one in front; each column shows its tallest stack.
- Drawing the side elevation the wrong way round
- From the right-hand side, the front of the structure is on your left.
- Assuming three views fix the structure
- Stacks hidden behind taller ones can often be several heights; count what the views allow.
Privacy and your data
Structures are built in your browser. With analytics consent, a count records how many structures a sheet had; the structures and any code are not sent.
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