Seven principles, each with a question beside it so you can see the principle at work rather than take it on trust. Tap an option to check it; the worked answer sits underneath.
1. Start where the child is, then climb
The same topic is practised at three levels, from where a child in Year 3 or 4 starts to what the papers ask in Year 6. A child moves up as they get things right, never by being thrown in at the top. Here is one topic at both ends of that ladder.
Foundation
Question 1Aim for about 60 seconds
What is 323 as an improper fraction?
Show the worked answer
Answer: E, 113
How to work it out
Each whole is 33, so 3 wholes are 93.
Add the 23: 9 + 2 = 11, giving 113.
Why the other options are wrong
A (53): This just adds the whole number to the top. Each whole is worth 3 parts, not 1.
B (23): This drops the whole number altogether.
C (119): This multiplies the bottom as well; the bottom number stays the same.
D (93): This multiplies the whole number by the top instead of by the bottom.
Exam standard
Question 2Aim for about 60 seconds
What is 256 as an improper fraction?
Show the worked answer
Answer: D, 176
How to work it out
Each whole is 66, so 2 wholes are 126.
Add the 56: 12 + 5 = 17, giving 176.
Why the other options are wrong
A (56): This drops the whole number altogether.
B (166): This multiplies the whole number by the top instead of by the bottom.
C (126): This leaves out the 56.
E (76): This just adds the whole number to the top. Each whole is worth 6 parts, not 1.
2. Reason before speed
Speed comes last, once the thinking is secure. A good share of every drill asks the child to reason rather than to repeat a method: what must be true, where the mistake is, what you would need to know.
Reasoning
Question 3Aim for about 60 seconds
A whole number is a multiple of 6. Which statement must be true?
Show the worked answer
Answer: C, It is a multiple of 3
How to work it out
Test each statement with examples.
Only “it is a multiple of 3” is true for every case.
Why the other options are wrong
A (It is odd): Every multiple of 6 is even.
B (It is a multiple of 9): 6 is not a multiple of 9.
D (It ends in 6): 12 is a multiple of 6 and ends in 2.
E (It is a multiple of 12): 6 itself is a multiple of 6 but not of 12.
Reasoning
Question 4Aim for about 60 seconds
Dev works out (33 + 47) × 3 − 10 in three lines. One line has a mistake. Which line?
Line 1: 33 + 47 = 80
Line 2: 80 × 3 = 241
Line 3: 241 − 10 = 231
Show the worked answer
Answer: D, Line 2
How to work it out
Check each line on its own.
Line 2 is wrong: 80 × 3 = 240, not what is written.
Why the other options are wrong
A (No line is wrong): Check line 2 again: the calculation on that line does not give the number written.
B (Line 3): Line 3 is worked correctly from the line before it; the slip is earlier or later.
C (Two lines are wrong): Only line 2 fails its own calculation; the other two are worked correctly from the line before.
E (Line 1): Line 1 is worked correctly from the line before it; the slip is earlier or later.
3. Explain every answer, and every wrong one
The letter is the least useful part of an answer. Every question on Prism carries its working in steps and a reason for each wrong option, so a child learns from the slip they actually made.
Worked answer
Question 5Aim for about 60 seconds
Pack A has 10 apples for £5.80. Pack B has 8 apples for £5.04. Which is better value?
Show the worked answer
Answer: A, Pack A: 58p each against 63p
How to work it out
Work out the cost of one.
A: £5.80 ÷ 10 = 58p.
B: £5.04 ÷ 8 = 63p.
The lower cost for one is the better value.
Why the other options are wrong
B (They are the same value): They are not: £5.80 ÷ 10 = 58p and £5.04 ÷ 8 = 63p.
C (Pack A, because it has more apples): More in the pack is not better value on its own; the pack with more may cost more for each one.
D (Pack B, because it costs less): Cheaper overall is not better value when it holds fewer apples; compare the cost of one.
E (Pack B: 63p each against 58p): The prices for one are the wrong way round: the lower price for one is the better value.
4. Practise questions that change shape
A bank that only changes the numbers teaches a method, not a skill. The same topic is asked in many ways: find the rule rather than the next number, undo the change rather than make it, choose the calculation rather than do it.
Which rule
Question 6Aim for about 60 seconds
Which rule explains this sequence?
6, 11, 21, 41, 81
Show the worked answer
Answer: B, Double, then take away 1
How to work it out
Write the gaps: 5, 10, 20, 40.
The rule that fits every step is: double, then take away 1.
Why the other options are wrong
A (Add 5 each time): From 6 to 11 is 5, but from 11 to 21 is 10, so the gap is not always the same.
C (Double, then take away 2): 6 × 2 − 2 = 10, which is not 11.
D (Multiply by 2 each time): 6 × 2 is 12, which does not give 11 and 21 together.
E (The gap grows by 2 each time): The gaps are 5, 10, 20, 40; they do not grow by 2.
Which breaks it
Question 7Aim for about 60 seconds
The sequence should add the same number each time. One number is wrong. Which one?
15, 24, 33, 40, 51, 60
Show the worked answer
Answer: C, 40
How to work it out
The rule is add 9.
40 should be 42: 33 + 9 = 42.
Why the other options are wrong
A (51): 51 fits the rule: it is 9 more than the number before it (or the first number), so it belongs.
B (15): 15 fits the rule: it is 9 more than the number before it (or the first number), so it belongs.
D (33): 33 fits the rule: it is 9 more than the number before it (or the first number), so it belongs.
E (60): 60 fits the rule: it is 9 more than the number before it (or the first number), so it belongs.
Which calculation
Question 8Aim for about 60 seconds
A box holds 12 eggs. There are 8 boxes. How many eggs? Which calculation gives the answer?
Show the worked answer
Answer: B, 12 × 8
How to work it out
The story has equal groups, so multiply: 12 × 8.
Why the other options are wrong
A (12 + 8): This adds the two numbers, but the story does not put two amounts together.
C (12 × 8 × 8): This uses 8 twice; it appears once in the story.
D (12 ÷ 8): This divides, but the story does not share or split anything.
E (12 − 8): This takes one from the other, but the story does not take anything away.
Work it backwards
Question 9Aim for about 60 seconds
A figure becomes striped, then gains a dashed outline, and became the figure shown. Which figure was it before?
Show the worked answer
Answer: D
How to work it out
Undo the change in reverse order: undo "gains a dashed outline", then undo "becomes striped".
Why the other options are wrong
A: Only the last change has been undone; the first must be undone too.
B: This is the mirror image of the original.
C: This is the original turned a quarter turn too far.
E: This is the figure after the change, not before it.
5. Read anything
The papers do not only set stories. Prism's 96 reading texts cover 44 kinds of writing, among them Fiction, Non fiction, Poetry, Biography, Letter, Non fiction (biography), Non fiction (persuasive letter), Fiction (diary), Fiction (classic), mystery, survival, diary, and the questions move from finding and inferring to weighing evidence. See the reading texts.
6. Measure honestly, against a named school
Readiness on Prism is a percentage of the way to the standard of the schools a family names, worked from the child's own practice and labelled as Prism's estimate. There is no pass rate and no promise. Parents see every result, every mistake and the next step, in the same words their child sees.
7. Short, often, and in the open
Lessons are a few minutes, drills are ten questions, and the 26 games last a minute or two. Little and often beats a long weekend, and everything a child practises is shown in the open on the question types pages, so a family can judge it for themselves.
Verbal reasoning
Question 10Aim for about 45 seconds
Two words have been written in the same code. What is the rule?
BELL → LLEB LAMP → PMAL
Show the worked answer
Answer: D, The word is written backwards
How to work it out
Compare each letter with its code letter in both examples.
The only rule that fits both is: the word is written backwards.
Why the other options are wrong
A (Each letter moves 3 forward): If each letter moves 3 forward, BELL would become EHOO, not LLEB.
B (Each letter moves 2 back): If each letter moves 2 back, BELL would become ZCJJ, not LLEB.
C (The first letter moves 1 forward, the second 2, the third 3, and so on): If the first letter moves 1 forward, the second 2, the third 3, and so on, BELL would become CGOP, not LLEB.
E (Each letter moves 1 back): If each letter moves 1 back, BELL would become ADKK, not LLEB.
Non-verbal reasoning
Question 11Aim for about 45 seconds
This net is folded into a cube with the symbols on the outside. Which symbol is on the face opposite the ring?
Show the worked answer
Answer: B, The hollow square
How to work it out
Fold the net around the ring: the four squares that touch its edges or wrap round to them become its neighbours, and the one left, the hollow square, closes the far side.
Opposite faces never share an edge.
Why the other options are wrong
A (The dot): The dot shares an edge with the ring once the net is folded, so it sits next to it, not opposite.
C (The plus sign): The plus sign shares an edge with the ring once the net is folded, so it sits next to it, not opposite.
D (The cross): The cross shares an edge with the ring once the net is folded, so it sits next to it, not opposite.
E (The black square): The black square shares an edge with the ring once the net is folded, so it sits next to it, not opposite.
Prism starts with a free assessment across maths, English, verbal and non-verbal reasoning, then builds a weekly plan for your target schools. Parents follow progress free.