Primary 6 Solids Study Guide
Primary 6 solids in four short steps, each one answered by counting rather than by eye. Every step has a figure to tap, and worked examples follow.
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What are solids questions in Primary 6 maths?
Every solids question is answered by counting, not by how the figure looks.
A drawing of a solid can fool the eye, so each method here turns the picture into numbers. A cube has 6 faces. A face meets 4 others along an edge. A column of cubes is only as tall as its views allow. A slanted side is a count of squares across and up.
In this chapter, your child learns to:
- find the face opposite a given face on the net of a cube;
- use the front and side views to find the most cubes added, or the least removed;
- count the painted faces of each cube in a glued solid;
- draw a side on a grid as a run across and a rise up, for parallel and right-angled sides.
Step 1
Nets of a cube: finding the opposite face
List the 4 faces that touch it; the one left over is opposite. A cube has 6 faces, so its net has 6 squares, and the arrangement of those squares decides whether it folds. On the folded cube, each face shares an edge with 4 faces and never touches the sixth. So name the 4 faces sharing an edge with the face you are given. The face nobody named is directly opposite it.
When the net is folded, which face is directly opposite face L?
Tap the faces that share an edge with L
Faces sharing an edge with L: none yet
A net of a cube has a row of four squares, A, B, C and D. E is joined above B, and F below B. Which face is opposite B?
Step 2
Most cubes added without changing the views
Each column can stand only as tall as the smaller of its two views. Read each square of the top view as one column of cubes standing on the table. The front view gives the tallest column in each line from left to right; the side view gives it from front to back. A column taller than either would change that view. Fill every column to its cap, then subtract the cubes you started with. To remove the least, keep as many cubes as the two views allow.
Solid A has 9 unit cubes. Add as many as you can without changing the front view or the side view.
Tap a column to add a cube
Cubes added: 0. Solid A now has 9 cubes.
In a solid of unit cubes, one column's line in the front view is 3 cubes high, and its line in the side view is 2 cubes high. How tall can that column be without changing either view?
Step 3
Painted cube questions: counting painted faces
Start every unit cube at 6 faces, then take off what is covered. Gluing two cubes together hides a face on each of them, so 1 join hides 2 faces. A face resting on the table is not painted either. Count each cube on its own: 6, minus 1 for each cube it is glued to, minus 1 more if it stands on the table. Keep the two subtractions separate so both stay visible.
Seven unit cubes are glued together. The outside is painted, but faces on the table are not. Find every cube with exactly 4 painted faces.
Tap a cube's name
Found: 0
Ten unit cubes are glued into a staircase one cube deep, with columns 4, 3, 2 and 1 cubes high. The outside is painted, but not the faces on the table. How many cubes have exactly 4 painted faces?
Step 4
Drawing shapes on a grid
Describe a slanted side as a run across and a rise up, counted in squares. Count the squares before drawing anything. A parallel side has the same run and the same rise. A side twice as long doubles both. A side at a right angle swaps the two counts and turns one direction round, so 4 right and 2 up becomes 2 left and 4 up. Then check which side of the line the question asks for.
A is at (4, 4), B at (2, 1) and C at (8, 6). Draw the trapezium ABYC: BY is parallel to AC and twice as long.
Move the pen from B
Pen at (2, 1): 0 across and 0 up from B.
On a square grid, side PQ goes 4 right and 3 up. A square PQRS is drawn on it. Which could side QR be?
Primary 6 solids questions, worked step by stepCount it out on paper first. Then open a hint, or reveal the working a line at a time.
Four unit cubes are glued in a straight row on a table. The outside is painted, but the faces resting on the table are not. How many painted faces are there altogether?
- Each end cube = 6 − 1 − 1 = 4 painted faces.
- Each middle cube = 6 − 2 − 1 = 3 painted faces.
- Altogether = 4 + 4 + 3 + 3 = 14.
A net of a cube has a row of four squares P, Q, R and S. Square T is joined above Q, and square U is joined below R. When the net is folded, which face is opposite T?
- The row P, Q, R, S folds into a ring of 4 faces.
- T folds over one end of the ring, so T shares an edge with P, Q, R and S.
- U is the only face left, so U is opposite T.
A solid of 9 unit cubes stands on a table. The table shows how many cubes stand in each column. What is the greatest number of cubes that can be added without changing the front view or the side view?
| 2 | 0 | 0 |
| 1 | 0 | 0 |
| 3 | 1 | 2 |
front
- Front view, left to right: 3, 1 and 2. Side view, front to back: 3, 1 and 2.
- Caps, front row: 3, 1, 2 = 6. Middle row: 1, 1, 1 = 3. Back row: 2, 1, 2 = 5.
- Cubes when full = 6 + 3 + 5 = 14.
- Cubes added = 14 − 9 = 5.
On a square grid, A is at (1, 2) and B is at (4, 1). Draw the square ABCD on the side AB, above AB. Write down the coordinates of C and D.
- AB: 3 right and 1 down.
- At a right angle, BC goes 1 right and 3 up.
- C = (4 + 1, 1 + 3) = (5, 4).
- AD is parallel to BC, so D = (1 + 1, 2 + 3) = (2, 5).
A solid of 18 unit cubes stands on a table, with the column heights shown. Some cubes are removed so that the front view is 3, 2 and 1 squares high from left to right, and the side view is 3, 2 and 1 from front to back. Every cube left rests on the table or on another cube. What is the least number of cubes removed?
| 2 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 3 | 2 |
front
- Least removed = most left.
- Each column: no taller than now, than its front view, or than its side view.
- Front row: 3, 2, 1 = 6. Middle row: 2, 2, 1 = 5. Back row: 1, 1, 1 = 3.
- Most left = 6 + 5 + 3 = 14, so removed = 18 − 14 = 4.
Step 5
Check yourself
Five quick solids questions. Nothing is saved, and each reply points to the matching set of questions.
A net of a cube has a row of four squares A, B, C and D. E is joined above A, and F below D. Which face is opposite E?
A column has 1 cube. Its line in the front view is 2 high and in the side view is 4 high. How many cubes can be added to it without changing either view?
Six unit cubes are glued into a 2 by 3 block, one layer, on a table. The outside is painted, but not the faces on the table. How many cubes have exactly 3 painted faces?
On a square grid, side DE goes 3 right and 1 up. Side FG is parallel to DE and twice as long. How does FG go?
Three unit cubes are stacked in a tower on a table. The outside is painted, but not the face on the table. How many painted faces are there altogether?
How to use this guide. Before each tap, ask your child to say the count out loud: which faces touch, how tall a column may be, how many faces are covered, how many squares across. The figure then confirms it. Each step takes a few minutes.
On paper, ask your child to write the count down before drawing or answering: the four faces that touch, a table of column heights, or 6 minus each covered face. A written count is easy to check, and in a drawing question it shows how each point was found.
More study guides
P6 Solids lessons and practice
4 lesson videos and 24 questions across four subtopics, from Basic to Challenge, each with a worked solution.
Watch and practise →