Maths
Reasoning prompt cards
Use twelve prompt cards to explain, test and compare mathematical thinking. Each card has a question, a sentence starter and a worked model, with topics ranging from even numbers and addition to fractions and square numbers.
Use the equal-length bars to explain why one half and two quarters show the same amount.
Read the complete materialRead the material
Use twelve prompt cards to explain, test and compare mathematical thinking. Each card has a question, a sentence starter and a worked model, with topics ranging from even numbers and addition to fractions and square numbers.
Activity. Use the preview for diagrams and layout.
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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
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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
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Reasoning prompt cards Teacher companion Mathematics | Pupils aged 7 to 11 Use with the exact 2-page original file. Keep pupil or staff activity pages separate from this teacher companion. When to use it Use these during paired maths talk after pupils have met the number ideas on the cards. Choose a prompt that fits current learning, and ask pupils to explain how they know rather than only state an answer in the current unit. Purpose Explain a mathematical claim using an example, representation or calculation, then listen to a partner’s reasoning, compare approaches and explain why. Start here Choose one card and read its prompt, try question and model. Discuss which part shows the mathematical reason. A teaching sequence 1. Use a reasoning card such as “How do you know?” or “Is there another way?” and give each pupil time to think. 2. Try the example and use the sentence starter to say the reasoning aloud. 3. Swap roles and choose a card that asks pupils to compare, estimate, find a mistake or prove an idea with a picture. 4. Use a further prompt to test whether the explanation works with another number or example. Ask a partner to restate the reasoning in their own words. Checking guidance Look for a reason connected to the mathematics, such as showing that 3 × 4 and 4 × 3 make the same total. Ask, “Can you show that another way?” If the partner agrees without explanation, invite them to point to a calculation, drawing or example. Illustrative reasoning: 3 x 4 and 4 x 3 both give 12. Ask for an array or grouped picture, then have the partner restate why the representation supports the claim. Support Start with a familiar number fact and use the printed sentence starter. Let pupils draw or use counters before explaining. An adult can read the prompt aloud and help partners take turns. Take it further Ask pupils to create a new example for a statement and test whether it always works. They can challenge a partner's reasoning respectfully by asking for another representation or a counterexample. Things to keep in mind Worked examples model approaches but do not cover every possible explanation. Review calculations and vocabulary against the lesson before use. Partner agreement alone does not verify an answer; ask pupils to justify reasoning with a calculation or representation. Reasoning prompt cards Teacher companion | Page 1
A teaching sequence
Explain a mathematical claim using an example, representation or calculation, then listen to a partner’s reasoning, compare approaches and explain why.
Choose a reasoning card and think
Choose a reasoning card and give both pupils thinking time. Read its prompt before trying the printed example.
What does the selected prompt ask you to explain?
Try the example and say the reason
Try the example and use the sentence starter to say the reasoning aloud.
Which calculation or representation supports your explanation?
Use the equal-length bars to explain why one half and two quarters show the same amount.
Read the complete materialSwap roles and explore another approach
Swap roles and choose a card that asks pupils to compare, estimate, find a mistake or prove an idea with a picture.
How could a picture show the equal fraction lengths?
Test and restate the reasoning
Use a further prompt to test whether the explanation works with another number or example. Ask a partner to restate the reasoning in their own words.
Does the explanation still work with another suitable example?
Before you teach
Look for the thinking behind an answer, choose the support your class needs and leave room for an independent response.
What to look for
Look for a reason connected to the mathematics, such as showing that 3 × 4 and 4 × 3 make the same total. Ask, “Can you show that another way?” If the partner agrees without explanation, invite them to point to a calculation, drawing or example. Illustrative reasoning: 3 x 4 and 4 x 3 both give 12. Ask for an array or grouped picture, then have the partner restate why the representation supports the claim.
Give a little support
Start with a familiar number fact and use the printed sentence starter. Let pupils draw or use counters before explaining. An adult can read the prompt aloud and help partners take turns.
Take the idea further
Ask pupils to create a new example for a statement and test whether it always works. They can challenge a partner's reasoning respectfully by asking for another representation or a counterexample.
Things to keep in mind
Worked examples model approaches but do not cover every possible explanation. Review calculations and vocabulary against the lesson before use. Partner agreement alone does not verify an answer; ask pupils to justify reasoning with a calculation or representation.
Keep the idea. Make it yours.
Bring your topic, learning goal and class context to PLAI™, then review what you create.
Ideas to try with your class
Sample teaching perspectives on what to try, what to adapt and what to watch for.
Meet The Creators
Meet a creator whose teaching interests connect with this template.
Glue Stick Club
The two-page maths set contains twelve cut-out cards with a prompt, a worked or try-it example and a speaking starter. One asks whether 36 is even and models using its final digit as a reason.
Bright Margins
The cards prompt pupils aged 7 to 11 to explain how they know, compare approaches and listen to a partner's reasoning. A familiar numerical example gives a concrete start for explaining rather than only stating an answer.
The Curious Pencil
Ask the pupil to use a drawing, objects or calculation alongside the speaking starter. Give a partner time to restate the reasoning before either pupil decides whether the explanation is convincing.
Good Question
The example on a card illustrates one claim and does not establish every possible rule or method. Check mathematical accuracy for the chosen prompt and assess the reasoning given, not confidence or speaking speed.