Cut out the cards along the dashed lines. Pick a card. Read the prompt, try the example, then use the
starter to say your thinking out loud.
Reasoning prompt cards
1
REASON
2
EXPLORE
3
GUIDE
MATHS
AGES 7 TO 11
REASONING
Reasoning prompt cards
Twelve game cards that help you explain your maths thinking.
1
How do you know?
SAY “I know because ...”
TRY Is 36 an even number?
MODEL Yes. I know because it ends in 6, and
36 = 18 + 18.
1
2
Is there another way?
SAY “Another way is ...”
TRY 25 + 19
MODEL Way 1: 25 + 20 − 1 = 44. Way 2: move 1
across, 24 + 20 = 44.
2
3
Convince me
SAY “You can believe me because ...”
TRY Convince me that 3 × 4 = 4 × 3.
MODEL 3 rows of 4 dots, turned round, is 4 rows
of 3 dots. Both make 12.
3
4
Always, sometimes
or never?
SAY “It is ... because ...”
TRY An odd number plus an odd number
is even.
MODEL Always. 3 + 5 = 8, 7 + 9 = 16. The two odd
ones out make a pair.
4
5
What is the same and
what is different?
SAY “They are the same because ...”
TRY 24 and 42
MODEL Same: both use the digits 2 and 4, both
are even. Different: 42 is 18 more.
5
6
Spot the mistake
SAY “The mistake is ... It should be ...”
TRY 46 + 37 = 73
MODEL 6 + 7 = 13, so there is an extra ten.
46 + 37 = 83.
6
Page 1 of 2

Play in pairs. Take turns to turn over a card and explain the example. If your
partner agrees with your reason, colour a token.
Reasoning prompt cards
1
REASON
2
EXPLORE
3
GUIDE
MATHS
AGES 7 TO 11
CARDS 7 TO 12
Reasoning cards: explore
Six more prompts: test ideas, draw proofs and check with estimates.
7
What if ...?
SAY “If ..., then ... because ...”
TRY 9 − 4 = 5. What if both numbers go up by
10?
MODEL 19 − 14 = 5. The difference stays the
same.
7
8
Prove it with a picture
SAY “My picture shows ...”
TRY Prove that 1/2 = 2/4.
1/2
2/4
MODEL The shaded parts
are the same length.
8
9
Estimate first
SAY “I estimate ... because ...”
TRY 49 + 52
MODEL About 50 + 50 = 100. Exact answer: 101.
It is close, so it makes sense.
9
10
Which one does
not belong?
SAY “... does not belong because ...”
TRY 4, 9, 16, 20
MODEL 20, because 4 = 2 × 2, 9 = 3 × 3 and
16 = 4 × 4 are square numbers.
10
11
Explain it to a partner
SAY “First I ..., then I ..., so ...”
TRY 34 × 2
MODEL First I did 30 × 2 = 60, then 4 × 2 = 8, so
60 + 8 = 68.
11
12
Can you give an example?
SAY “One example is ... because ...”
TRY A number between 20 and 30 in the 4
times table.
MODEL 24, because 6 × 4 = 24. (28 works too.)
12
Page 2 of 2