Every question here is written by Prism in the style of the tests. None is copied from a real paper, and a fresh one is drawn each time a child practises.
From foundation to exam standard
Two questions at each level. Tap an option to check it.
Foundation where a child in Year 3 or 4 starts
Question 1Aim for about 45 seconds
How many cubes make this shape? Every cube is resting on the ground or on another cube.
Show the worked answer
Answer: E, 7
How to work it out
Count each column from the back: 2 + 2 + 1, then 1, then 1.
That makes 7.
Only 6 can be seen; the rest are hidden underneath.
Why the other options are wrong
A (6): This counts only the 6 cubes you can see. 1 more are hidden underneath, holding the others up.
B (5): This counts the 5 columns, one cube for each top you can see, not every cube in each column.
C (9): Two too many. 2 + 2 + 1 + 1 + 1 makes 7: no cube is hidden unless it holds another up.
D (8): One too many. Counting column by column, 2 + 2 + 1 + 1 + 1 makes 7, not 8.
Question 2Aim for about 45 seconds
How many cubes make this shape? Every cube is resting on the ground or on another cube.
Show the worked answer
Answer: C, 8
How to work it out
Count each column from the back: 2 + 2 + 1, then 1 + 1 + 1.
That makes 8.
Only 6 can be seen; the rest are hidden underneath.
Why the other options are wrong
A (6): This counts only the 6 cubes you can see. 2 more are hidden underneath, holding the others up.
B (7): One too few. 2 + 2 + 1 + 1 + 1 + 1 makes 8; a cube at the bottom of a column was missed.
D (9): One too many. Counting column by column, 2 + 2 + 1 + 1 + 1 + 1 makes 8, not 9.
E (10): Two too many. 2 + 2 + 1 + 1 + 1 + 1 makes 8: no cube is hidden unless it holds another up.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 45 seconds
A stack of cubes is seen from the front and from above. Every cube rests on the ground or on another cube. What is the most cubes the stack could have?
From the front
From above
Show the worked answer
Answer: B, 9
How to work it out
Take each column of the front view in turn: it shows the tallest stack in that column, and the view from above shows how many squares the column uses.
Most: every used square is built to the full height.
Adding the columns gives 9.
Why the other options are wrong
A (6): 6 is the number of squares in the front view; cubes hidden behind the front ones do not show there.
C (10): One more than the views allow: a column cannot be taller than its front view shows.
D (7): 7 is the fewest cubes the views allow, with one tall stack in each column and the other used squares one cube high.
E (4): 4 is the number of squares seen from above; stacked cubes are counted once in that view.
Question 4Aim for about 45 seconds
A stack of cubes is seen from the front and from above. Every cube rests on the ground or on another cube. What is the most cubes the stack could have?
From the front
From above
Show the worked answer
Answer: B, 9
How to work it out
Take each column of the front view in turn: it shows the tallest stack in that column, and the view from above shows how many squares the column uses.
Most: every used square is built to the full height.
Adding the columns gives 9.
Why the other options are wrong
A (10): One more than the views allow: a column cannot be taller than its front view shows.
C (7): 7 is the fewest cubes the views allow, with one tall stack in each column and the other used squares one cube high.
D (8): 8 is one possible count, but it is not the most: every used square can be built to its column height.
E (5): 5 is the number of squares in the front view; cubes hidden behind the front ones do not show there.
Exam standard what the papers ask in Year 6
Question 5Aim for about 45 seconds
How many cubes make this shape? Every cube is resting on the ground or on another cube.
Show the worked answer
Answer: D, 9
How to work it out
Count each column from the back: 2 + 2, then 2 + 1, then 2.
That makes 9.
Only 7 can be seen; the rest are hidden underneath.
Why the other options are wrong
A (8): One too few. 2 + 2 + 2 + 1 + 2 makes 9; a cube at the bottom of a column was missed.
B (5): This counts the 5 columns, one cube for each top you can see, not every cube in each column.
C (7): This counts only the 7 cubes you can see. 2 more are hidden underneath, holding the others up.
E (10): One too many. Counting column by column, 2 + 2 + 2 + 1 + 2 makes 9, not 10.
Question 6Aim for about 45 seconds
How many cubes make this shape? Every cube is resting on the ground or on another cube.
Show the worked answer
Answer: D, 8
How to work it out
Count each column from the back: 2 + 2 + 2, then 1 + 1.
That makes 8.
Only 6 can be seen; the rest are hidden underneath.
Why the other options are wrong
A (5): This counts the 5 columns, one cube for each top you can see, not every cube in each column.
B (9): One too many. Counting column by column, 2 + 2 + 2 + 1 + 1 makes 8, not 9.
C (6): This counts only the 6 cubes you can see. 2 more are hidden underneath, holding the others up.
E (7): One too few. 2 + 2 + 2 + 1 + 1 makes 8; a cube at the bottom of a column was missed.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Fewest and most cubes
From the front view and the view from above, the fewest and the most cubes the stack could hold.
Exam standard
Question 7Aim for about 45 seconds
A stack of cubes is seen from the front and from above. Every cube rests on the ground or on another cube. What is the most cubes the stack could have?
From the front
From above
Show the worked answer
Answer: E, 12
How to work it out
Take each column of the front view in turn: it shows the tallest stack in that column, and the view from above shows how many squares the column uses.
Most: every used square is built to the full height.
Adding the columns gives 12.
Why the other options are wrong
A (10): 10 is one possible count, but it is not the most: every used square can be built to its column height.
B (5): 5 is the number of squares in the front view; cubes hidden behind the front ones do not show there.
C (8): 8 is the fewest cubes the views allow, with one tall stack in each column and the other used squares one cube high.
D (6): 6 is the number of squares seen from above; stacked cubes are counted once in that view.
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