Drawing solids made of cubes
Most exercises on this paper start from a model built with interlocking cubes. Draw the cube nearest to you first, then add the others one at a time, only drawing the edges you can see. Shade the three visible faces differently, for example the tops light, the left faces medium and the right faces dark, and the drawing reads as a solid straight away. Count cubes you can’t see too: a drawing of an L-shaped block might hide one cube underneath another, and a volume question depends on it.
Plans and elevations
In England, the GCSE mathematics subject content asks students to “construct and interpret plans and elevations of 3D shapes”. The plan is the view from directly above, the front elevation the view from the front and the side elevation the view from one side. A typical question gives an isometric drawing and asks for the three views, or gives the views and asks for the solid:
- From drawing to views: count the cubes in each column seen from above for the plan, and the tallest cube in each column for the elevations. Draw the views on squared paper, one square per cube: the graph paper generator prints 1 cm squares.
- From views to drawing: sketch the plan’s footprint on the dots first, then build each column up to the height its elevation shows.
Getting clean prints
The dots print at Large size in your usual line color (blue unless you changed it). For photocopying a class set, choose black or gray and keep Large dots, because thin dots fade on copies. Draw in pencil and go over the final edges in pen, so construction lines can be erased. If you prefer guide lines to dots, use isometric graph paper, which draws the full triangle grid.
How this page sets up the sheet
- Isometric dots, vertical columns, the way round for isometric drawing.
- In inches: 1/2 in (12.7 mm) dots apart, 2 per inch.
- In millimetres: 1 cm (0.394 in) dots apart, 1 per cm.
It opens in inches in the US and other countries that use Letter paper, and in millimetres everywhere else (or in whichever unit you last used on this site). The paper size follows your browser too: Letter in the US, A4 elsewhere. Everything stays editable. Your own page settings, such as margins, are remembered for next time; the grid itself always opens as set up here. To start from a blank setup, use the graph paper generator.