Contents
Make the listening part visible
Teach pupils to do more than exchange answers: explain a method, listen closely enough to retell it, then compare it with another method for the same problem. Use this sequence: think → explain → retell and check → swap → compare.
K20 Center’s Partner Speaks strategy asks pupils to explain their reasoning to a partner and then share their partner’s explanation. Its procedure explicitly includes teacher modelling of active listening. NRICH’s Picture Your Method similarly invites pupils to share a partner’s calculation method and ask clarification questions. Partner Speaks | K20 LEARN Picture Your Method | NRICH
The sequence and materials below are an adaptable teaching design, not an evaluated programme. Begin with addition that pupils can already attempt, so you can rehearse the conversation without also introducing an unfamiliar calculation method. If both partners use the same method, offer the second worked method below rather than requiring them to invent a different one.
Teach, model, rehearse and review
Prepare one problem, the two role cards below and a recording slip. Make paper, pencils and any familiar calculation representations available. Assign partners A and B, and establish a pause cue such as “Finish this step, then pause.” Allow thinking time before either partner speaks.
The classroom examples and pupil responses below are hypothetical. Say: “Our job is to understand two ways of solving the same problem. A explains first. B listens, asks about a step and retells the method. A checks that retelling. Then we swap. At the end, you will describe something that is the same and something that is different.”
Introduce the listening actions explicitly: let the speaker finish a step, follow their marks or objects, ask a specific question, and check your retelling with them. Permit pupils to point, draw or use objects alongside speech; do not make eye contact a requirement of the routine.
Model both roles using the worked problem below. You can move between two labelled positions or rehearse with another adult. Show the listener doing mathematical work: identifying a step, asking why it works and retelling it accurately—not simply saying “I agree.”
Rehearse one exchange before the full routine. Ask A to explain the first method and B to retell it. Pause and ask: “Did the retelling include what changed and why?” Model a missing detail if needed. Then swap roles, use the second method and complete the comparison together.
Review by inviting a pupil to share their partner’s method. Ask the partner, “Have we represented your thinking accurately?” Then select one observed feature to model again: taking turns, explaining a step, retelling accurately or comparing methods. Use the checklist at the end to choose which.
Copy-ready speaker and listener cards
SPEAKER CARD
When it is your turn:
1. Say which problem you are solving.
2. Show and explain your steps: “First I… Then I…”
3. Explain a choice: “I split ___ into ___ because…”
4. Pause for your partner’s question and retelling.
5. Check: “Yes, that is my method” or “Let me clarify this part…”
Hand over: “Now explain your method. I will listen.”
LISTENER CARD
While your partner explains:
1. Let them finish a step. Follow their writing, drawing or objects.
2. Ask about a step you need to understand:
“Where did ___ come from?”
“Why did you split ___ that way?”
“Can you show that step?”
3. Retell: “You started with ___. Then you ___. You did that because…”
4. Check: “Have I understood your method?”
Swap roles after your partner checks your retelling.
COMPARE TOGETHER
Use both methods where you can see them.
“Both methods…”
“One difference is…”
“This step matches that step because…”
“For this problem, I would choose ___ because…”
Give a mathematical reason for your choice, such as a useful number fact or an easier step to keep track of. You may prefer different methods.
Worked addition: two methods for 38 + 27
Problem: 38 + 27
Method A: partition both numbers
38 = 30 + 8
27 = 20 + 7
30 + 20 = 50
8 + 7 = 15
50 + 15 = 65
Explanation: Add the tens and the ones separately, then combine the two totals.
Method B: add on and bridge through 60
38 + 20 = 58
58 + 2 = 60
60 + 5 = 65
Explanation: Split 27 into 20, 2 and 5. Add 20 first, then split the remaining 7 into 2 and 5 to reach 60 before adding the rest.
Teacher modelling script
Speaker: “I split both numbers into tens and ones. The tens total 50 and the ones total 15. Then I add those totals to get 65.”
Listener: “Where did the 15 come from?”
Speaker: “From adding the ones: 8 + 7.”
Listener: “So you added the tens, added the ones, then combined 50 and 15. Is that right?”
Speaker: “Yes.”
Teacher, stepping out of role: “Notice that the listener asked about one particular number, then checked the whole method before swapping.”
Pupil dialogue for the second turn
B: “I kept 38 together and added 20 to make 58. Then I added 2 to reach 60 and another 5 to reach 65.”
A: “Why did you add 2 and then 5?”
B: “I still needed to add 7. I split it into 2 and 5 because 58 needs 2 to reach 60.”
A: “You added all 27, but in three parts: 20, 2 and 5. Have I got it?”
B: “Yes.”
Comparison dialogue
A: “Both methods split numbers into parts and get 65.”
B: “Your method splits both starting numbers. Mine keeps 38 together.”
A: “I would choose mine because I know 8 + 7.”
B: “I would choose mine because adding from 60 is easy for me to keep track of.”
Teacher: “You have compared the steps and explained your preferences. Different choices can both be valid.”
Restart talk without taking over the mathematics
When one partner dominates
Pause: “Keep your method visible. It is your partner’s turn to tell us what they understood.”
To the listener: “Start with ‘You began by…’ You can point to the working.”
To the original speaker: “Listen to the retelling. Then confirm it or clarify one part.”
Restart: “Now swap cards. The other partner explains their method.”
When an explanation is unclear
Pause: “Let’s stop at the first step we cannot yet follow.”
To the listener: “Point to the number or mark you want explained. Ask, ‘Where did this come from?’”
To the speaker: “Show that step with writing, a drawing or objects.”
Restart: “Retell just that step and check it before moving on.”
When partners disagree
Pause: “Are you disagreeing about the answer, whether a step works, or which method you prefer?”
If answers or steps differ: “Put both workings where we can see them. Check each step using a familiar representation or calculation. Where do they first differ?”
If preferences differ: “Explain why you would choose your method for these numbers. You do not have to choose the same one.”
Restart: “Retell the other method accurately before giving your reason.”
Do not treat a valid counting strategy as an error merely because another method uses larger steps. Ask the pupil to show how the count matches the calculation, then compare the steps with the alternative. If neither partner can resolve a disputed step, ask them to mark that exact point and request help. A help-request routine for independent maths offers a way to make the sticking point visible and establish what pupils do while waiting.
NRICH’s guidance on classroom problem-solving culture asks teachers to check their interpretation of a pupil’s explanation rather than silently adjusting it to fit a better answer. Use that same check when restarting talk: “Can I check that you mean…?” Developing a Classroom Culture That Supports a Problem-Solving Approach to Mathematics | NRICH
A fresh rehearsal and reusable recording slip
Practice problem
46 + 28
1. Work out the total. Keep your steps visible.
2. Take turns explaining and retelling.
3. Compare two methods. If you used the same method, ask for an alternative to examine.
4. Complete the recording slip.
Answer guide
46 + 28 = 74
Partitioning: 40 + 20 = 60; 6 + 8 = 14; 60 + 14 = 74.
Adding on: 46 + 20 = 66; 66 + 4 = 70; 70 + 4 = 74.
In the second method, the remaining 8 is split into 4 and 4 to bridge through 70. Both methods add the full 28. One splits both starting numbers; the other keeps 46 together. Accept other mathematically valid methods and comparisons.
PARTNER RECORDING SLIP
Names: __________ Problem: __________
Method A: write or sketch the steps.
________________________________
Method B: write or sketch the steps.
________________________________
A retold B’s method; B checked it: __________
B retold A’s method; A checked it: __________
Both methods: ______________________
One difference: _____________________
For these numbers, I would choose ___ because ___
A step or question we still need to check: __________
Decide what to model again
TEACHER OBSERVATION CHECKLIST
Pair/problem: __________
For each item, note “observed”, “needs a prompt” or “not yet observed”, with a short example.
Both partners had an explanation turn: __________
Speaker showed steps, not only an answer: __________
Speaker explained a mathematical choice: __________
Listener asked about a specific step when needed: __________
Listener retold the method accurately: __________
Speaker checked or clarified the retelling: __________
Pair identified a mathematical similarity or difference: __________
Pair checked a disputed step or marked it for help: __________
Exact words or working to revisit: __________
Next feature to model: __________
Choose the next model from what you actually notice. If pupils only exchange answers, model showing and explaining one step. If retellings change the method, model the confirmation check. If comparisons stop at “both got 74”, place the workings side by side and model a difference in how the numbers were split. If turn-taking is the obstacle, rehearse the handover using a familiar solved problem.
At the next opportunity, keep the same talk sequence and change the problem to match the mathematics you are teaching. Revisit the selected feature while listening to another exchange; use the checklist to plan further modelling, not to assign a score to pupils’ mathematical talk.
