The idea in brief. A view is one flat side of the solid. It has one square for each column you can see from that side, never one square for each cube, so a view cannot tell you how many cubes there are. The count comes from the layers instead, and a layer is full whether or not the drawing shows it, because nothing floats. In the lesson. A view is a shape, and the number of cubes is not in it.
Lesson video, with the working
Front, side and top views of a solid
2 min 41 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Solid P is built from unit cubes. The arrows show where you look from. (a) Draw the front view of Solid P. (b) Draw the side view of Solid P. (c) Draw the top view of Solid P. (d) How many unit cubes are used to build Solid P?
Total cubes = 4 (base) + 2 (middle) + 1 (top) = 7
Ans: 7
Example 1
Solid Q is built from 5 unit cubes. Draw the top view of Solid Q on the grid.
The top view is a 2 by 2 square of 4 unit squares.
Ans: 2 by 2 square
How to solve it
A view is the solid drawn flat from one side. Draw only what you see from the arrow's direction.
In the front view, a cube behind another lines up with it, so two cubes can show as one square.
For the side view, look in from the right. The front of the solid is on the left of the grid.
For the top view, you see the floor, 2 squares by 2 squares. It does not show how tall anything is.
To count the cubes, use the top view for the base layer, 4 cubes, then add the layers above: 7 unit cubes.
The top view has 4 squares. The solid has 5 cubes. A view is a shape, and the number of cubes is not in it.
Practice questions with worked solutions
Question 1 is free to try. The other 11 open in the free trial, each with its full working.
Question 1 of 12 · Basic · free to tryA solid is built from unit cubes. Its bottom layer is a rectangle 3 cubes…A solid is built from unit…
A solid is built from unit cubes. Its bottom layer is a rectangle 3 cubes long and 2 cubes deep. A second layer of 4 cubes sits on the left-hand 2 by 2 of it, and a third layer of 2 cubes sits on the left-hand column of that. How many unit cubes are used to build the solid?
How do you answer counting unit cubes from views questions in P6?
A solid made of unit cubes is shown as a drawing or as front, side and top views, and the question asks how many cubes it has.
What your child learns here
A solid made of unit cubes is shown as a drawing or as front, side and top views, and the question asks how many cubes it has. Some cubes are always hidden. These questions use building solids with unit cubes and measuring volume in cubic units from earlier years, as they appear in Primary 6 Volume papers.
Count a solid layer by layer from the bottom, including cubes no face of which can be seen.
Draw a view with one square for each column seen from that direction.
Know that a view shows a shape, not the number of cubes.
Use the depth: a full solid 2 cubes deep has twice as many cubes as its front view shows.
Sort the cubes of a painted cuboid into corners, edges, faces and inside cubes by the number of painted faces.
Does the answer make sense?
A view shows only the shape of the solid, so the number of cubes is at least the number of squares in the top view and can be more. When your child sorts a painted block's unit cubes into corner, edge, face and inside groups, the groups must add up to all the cubes.
How to practise these questions
The Basic questions train counting a solid one layer at a time, and drawing a view with one square per column. Intermediate questions add combining several views to fix a solid, and finding the fewest cubes to complete a cuboid. Challenge questions paint a large cube, cut it up, and sort the small cubes by their painted faces. When the three views do not match the solid, read the written step-by-step solution together.
Questions parents ask
How do you count cubes you cannot see in a drawing? Count layer by layer from the bottom. Any cube shown on an upper layer must stand on a cube below it, so those hidden cubes are counted even though no face of them is drawn.
What is the difference between a front view and a top view? The front view is the solid seen straight from the front; the top view is seen from directly above. The top view shows which columns stand on the table, but not how tall they are.
Is counting unit cubes in the syllabus? Yes. Building solids with unit cubes and measuring volume in cubic units are in the MOE syllabus under Volume of Cube and Cuboid, in Primary 5. The Primary 6 volume work builds on them.
