Contents
- Choose the problem and make the thinking inspectable
- 1. Compare routes through a maths story problem
- 2. Predict, test and review a digital science model
- 3. Work through a Double Diamond design brief
- 4. Explain a logic puzzle before opening the next clue
- 5. Build and retest a limited-materials bridge
- 6. Find the first error in a calculation
- 7. Model a metacognitive think-aloud
- 8. Plan and debug a robotics maze
- 9. Plan a mystery-bag research process
Choose the problem and make the thinking inspectable
Choose a task with a clear goal, ask pupils to plan before acting, and finish by comparing the first approach with the revised one. The 15 activities below include maths discussion, logic puzzles, science and design challenges, robotics, storytelling and team investigations.
Select tasks using pupils’ demonstrated knowledge rather than a fixed year-group label. Before starting, check that they understand the vocabulary, materials and mathematical operations involved. Offer counters, drawings, oral explanations or written working as appropriate, without removing the central problem.
Use this short recording frame across the activities:
Goal: What must our solution do?
Plan: What will we try, and why?
Evidence: What happened?
Revision: What will we change?
Check: How will we know whether it works?
1. Compare routes through a maths story problem
Give pairs counters or scrap paper. Ask everyone to prepare an approach before sharing answers, then compare solutions against every condition in the problem.
The classroom examples and pupil responses below are hypothetical. Copyable problem:
A class needs exactly 24 pencils.
Pencils come in packs of 4 for £3 or packs of 6 for £4.
You may buy either type or a mixture, but no loose pencils.
What is the cheapest way to buy exactly 24 pencils?
Show how you checked that another combination would not cost less.
Answer guide: Four packs of 6 cost £16. Six packs of 4 cost £18. The only mixed combination is three packs of 4 and two packs of 6, costing £17. One route is to list possible numbers of 6-packs: 0, 1, 2, 3 or 4, then check whether the remaining pencils can be bought in 4-packs. Another is to compare equal bundles: 12 pencils cost £9 in 4-packs but £8 in 6-packs.
A pupil might say, “I counted in sixes until I reached 24.” Accept that as a valid counting route, then ask, “How did you calculate the cost? How could you check the mixed packs?” If a pupil jumps from a calculation to a conclusion, ask them to annotate the missing step or demonstrate it with counters.
Treat an explanation as evidence of the reasoning a pupil expresses, not as a complete record of everything they thought. Compare what they say with their drawings, calculations and demonstrations before deciding what to ask next.
2. Predict, test and review a digital science model
Build a simple computer simulation called the Tank Refill Model in a spreadsheet. Use columns for minute and water amount. Enter minute 0 with 0 units of water. Each following row represents one minute: add the chosen inflow and subtract an outflow of 1 unit. Begin with an inflow of 3 units per minute and copy the rule down for six minutes. Demonstrate one row before pupils investigate.
Investigation:
How does changing the inflow affect the time needed to reach at least 12 units?
Predict the result for inflows of 3, 4 and 5 units per minute.
Keep the starting amount and outflow unchanged.
Record the amount after each minute and the first minute at which the target is reached.
Explain any difference between your prediction and the model.
Answer guide: With inflow 3, the amount rises by 2 each minute and reaches 12 after 6 minutes. With inflow 4, it rises by 3 and reaches 12 after 4 minutes. With inflow 5, it rises by 4 and reaches 12 after 3 minutes. Ask, “Which setting did you change? What stayed the same? Which rows support your conclusion?”
This is a deliberately simplified model with stipulated constant flows and whole-minute observations. Use it to investigate the model’s rules, not to claim how every real tank fills. Prepare and check the spreadsheet before the lesson; no particular commercial simulation or interface is required.
A 2026 study compared 12 science teachers with 12 middle-school students using simulations. The teachers showed more comprehensive task understanding and more logical reasoning, while the students often ran simulations without recording specific details. This was an expert–novice comparison, not a trial showing that simulation use or logging improves primary pupils’ confidence or resilience. Cognitive processes of scientific problem-solving while using simulations: an expert-novice comparison
3. Work through a Double Diamond design brief
Set this design brief: Make a freestanding desk organiser from one cereal-box panel, two sheets of paper and masking tape. It must hold six pencils and allow a partner to remove one without the organiser falling over. Provide scissors and the same materials for each team.
Organise the work into four stages:
Discover: Ask a partner what makes pencils difficult to store or retrieve. Observe the current arrangement.
Define: Write one specific need, such as “The pencils need to stay upright and be easy to grasp.”
Develop: Sketch two possible structures, compare them, and build a prototype.
Deliver: Test against the brief, revise one feature, and demonstrate the result.
Ask, “Which user need does this feature address? What did your test make you reconsider?” A pupil might explain, “We liked the tall tube, but it tipped when someone pulled a pencil. We widened the base instead of adding decoration.”
Use this as a non-AI classroom design routine. The university research on a structured Double Diamond strategy within generative-AI-supported design learning does not establish the effects of this primary adaptation or require pupils to use AI. Effects of integrating a structured design thinking strategy into generative AI-supported design learning on students’ design achievement, creative self-efficacy, and problem-solving skills
If cutting, folding or holding parts becomes a separate barrier, use Fine Motor Skills vs Gross Motor Skills: Activities to choose a specific hand action to rehearse or adjust the materials. For this challenge, you might provide pre-cut card or hold a piece steady while the pupil decides where it should go.
4. Explain a logic puzzle before opening the next clue
Give pupils the puzzle below and three coloured cards to move around. Ask them to explain which clue they use first. Leave it untimed initially; add a time limit only if speed is part of your intended task.
Copyable puzzle:
A red bag, a blue bag and a green bag each contain one different object: a coin, a shell or a key.
The red bag does not contain the key.
The blue bag contains the shell.
The green bag does not contain the coin.
What is in each bag? Explain how you know.
Answer guide: Blue contains the shell. That leaves the coin and key for red and green. Red cannot contain the key, so red contains the coin and green contains the key. Check the answer against all three clues, not just the first clue used.
For an escape-room-style variation, place the next clue in an envelope that pupils receive after explaining their answer. Ask, “Which possibility did you rule out? Can you mark that on your cards?” Keep the challenge in the clues rather than requiring pupils to leave a room.
5. Build and retest a limited-materials bridge
For each team, provide four sheets of A4 paper, 60 cm of masking tape, two equal-height blocks or books, a ruler and one 100 g test mass. Set the supports 15 cm apart. The bridge must span the gap without a support underneath; teams may fold or roll the paper but must not tape it to the supports.
Success criterion: The bridge holds the 100 g mass at its centre for 10 seconds without the mass falling or the bridge touching the surface below. Test close to the work surface. Give each team the same mass and placement procedure so results can be compared.
Before building, ask teams to sketch their structure and mark where they expect it to bend. After testing, ask, “Where did the structure change shape? What single feature will you alter?” A pupil might say, “The middle sagged. We will keep the same span but fold the deck differently.” For a preliminary building task, use blocks or interlocking bricks to explore possible support arrangements.
6. Find the first error in a calculation
Choose this task only when pupils have worked with partitioning and subtraction across a tens boundary. Ask pairs to identify the first incorrect step, rather than simply replacing the final answer.
Copyable error-spotting task:
52 − 28
= (50 − 20) + (8 − 2)
= 30 + 6
= 36
Which step is incorrect?
Correct it and check your answer another way.
Answer guide: The first rewritten line is incorrect. It reverses the subtraction of the ones, so it no longer represents 52 − 28. One correction is to exchange a ten: 52 = 40 + 12, so (40 − 20) + (12 − 8) = 20 + 4 = 24. Another route is 52 − 20 = 32, then 32 − 8 = 24. Check by adding: 24 + 28 = 52.
Ask, “Can you draw or build the exchange? Where does your diagram show the 28 being removed?” Distinguish the actual error from a different valid strategy: counting up from 28 to 52 is also acceptable if the pupil accounts for the full difference.
7. Model a metacognitive think-aloud
The Education Endowment Foundation’s guidance on mathematical think-alouds recommends modelling planning, monitoring and evaluation: understanding the problem, checking progress while working, and reviewing the method afterwards. Thinking Aloud to support mathematical problem-solving
Problem: There are 29 pupils travelling in minibuses. Each minibus has space for 8 pupils. How many minibuses are needed?
Teacher think-aloud:
Plan: “I need enough seats for everyone. I’ll draw groups of eight and keep track of the total.”
Monitor: “One bus gives 8 seats, two give 16, and three give 24. I have three full groups, but I must check whether I have seated everyone.”
Revise: “There are still 5 pupils without seats. I need another bus even though it will not be full.”
Evaluate: “Four buses provide 32 seats, enough for 29 pupils. Three provide only 24. My answer must be four buses, not three buses with five pupils left over.”
Give pupils a related problem with 34 pupils and 10 places per bus. Ask them to annotate the moment when they decide whether an extra bus is necessary. The answer is four buses: three hold only 30 pupils. Follow up with, “What does the remainder mean in this story?”
8. Plan and debug a robotics maze
Make a four-by-four floor grid, with squares matched to one forward movement of your robot. Label columns A–D from left to right and rows 1–4 from bottom to top: A1 is the bottom-left square, A4 is the top-left square and D4 is the top-right square. Put the robot at A1 facing upwards towards A2. Mark B2 and B3 as blocked squares and D4 as the destination. Check movement distance and turning behaviour before teaching; if needed, rehearse with a paper robot first.
Challenge: Plan and program a route from A1 to D4 without entering either blocked square or leaving the grid. Success means the robot finishes inside D4. Pupils must draw the intended route, predict the final position, run the program, then record any change.
One route is A1 → A2 → A3 → A4 → B4 → C4 → D4. With the robot facing upwards on the grid as specified, the sequence is forward three squares, turn right by a quarter turn to face column B, then forward three squares. Adapt the command entries to your robot rather than assuming one button press always equals one square.
After a failed run, ask, “Where did the actual route first differ from your drawing? Was the problem in the route, the command sequence or the movement distance?” A pupil might say, “Our route was clear, but we turned after two squares instead of three.” Change one part before retesting.
9. Plan a mystery-bag research process
Put a wooden block, fabric square and spoon into separate opaque bags. Give groups the research question, “How could we identify an object without seeing it?” Ask them to plan what information to collect, how to describe it and how to check their conclusion after the reveal.
Make a mind map with branches for shape, texture, flexibility and possible use. Pupils can investigate by touch or direct a partner’s observations. Require a distinction between observation and inference: “It has a long, narrow handle” is different from “It is a spoon.”
Use two checkpoints: before collecting evidence, ask, “Which question would rule out a possibility?” After the reveal, ask, “Which observations were useful, and which were ambiguous?” For a longer research project, keep the same planning frame but add a question about which books or other resources pupils will consult and how they will record where information came from.
10. Pause a making task to revise the strategy
Give pairs a sheet of card, scrap paper and tape. Ask them to make a standing display for a paper picture. The display must stand unsupported and keep the picture visible from the front.
Pause after the first prototype for a suggested two-minute review. Ask each partner to complete: “We intended…”, “The test showed…” and “Our next change will be… because…”. Require a visible alteration or a reasoned decision to retain the design before work continues.
A pupil might explain, “We were adding colour, but the stand still fell backwards. We will move the support before decorating.” Use the pause to inspect the decision and resulting change, rather than treating the length of the discussion as a measure of success.
11. Compare evidence in a mock investigation
Present a fictional museum case: A replica display coin was returned to a different tray after an activity. Decide which route best fits the records, or whether more than one remains possible. Give pupils the evidence cards below rather than asking them to guess who is responsible.
Copyable evidence cards:
Display record: The coin was in the activity room at 10:00 and found on the library return tray at 10:15.
Transfer mark: A blue mark on the coin’s paper sleeve smeared when rubbed with a dry cloth.
Classroom material test: Samples from the trolley and box handles were transferred onto matching paper sleeves. Each sample was rubbed with a dry cloth in the same way. The blue chalk sample from the art trolley smeared; the blue wax-crayon sample from the book box did not smear.
Route A record: The art trolley passed the activity room at 10:05 and reached the library at 10:10. Its handle had blue chalk on it.
Route B record: The book box passed the activity room at 10:07 and reached the library at 10:12. Its handle had blue wax crayon on it.
Route C record: The sports basket left the activity room at 10:20. Its handle had blue chalk on it.
Answer guide: Route A best fits both the timing and the stated sample-test result. Route B fits the timing, but its tested handle sample did not smear, unlike the mark on the coin’s sleeve. Route C matches the chalk clue but leaves too late. The sample results are observations within this fictional case, not rules for every chalk or crayon. They do not prove the coin travelled on Route A: an unrecorded transfer remains possible. Ask pupils to distinguish “best supported by these records” from “certain”.
A university forensic-science study collected post-course self-reports from 260 undergraduate and postgraduate students. The authors explicitly noted that the absence of pre-course measurements prevented definitive claims about growth over time. It does not show that school mock cases or spoken checkpoints increase confidence in critical judgement. Investigating interdisciplinary learning outcomes in a forensic science programme
12. Log changes during a practical science investigation
Ask pairs to predict whether a wooden block, metal spoon, plastic lid and ball of modelling clay will sink or float in a tray of water. Record each prediction before testing the actual objects; do not supply a universal answer based only on the material name.
Copyable strategy log:
Object:
Prediction and reason:
What we observed:
Was the test clear enough to interpret?
What we changed or repeated, and why:
What we can conclude about this object:
A pupil might record, “I pushed the lid under the water, so I could not tell what it would do by itself. I repeated the test by placing it on the surface and letting go.” Ask, “Did you change the object or correct the test procedure? What claim does your observation actually support?”
13. Use team checkpoints in storytelling and role-play
Give teams this story problem: Two characters find a wallet in a fictional school corridor. They disagree about what to do next. Write a six-sentence story in which both characters explain a concern, consider two possible actions and agree on a next step. Alternatively, make a six-panel mural or act out the same sequence.
Assign rotating roles: proposer, questioner, recorder and checker. Stop after sentence or panel three. Each pupil must summarise the group’s current plan and one unresolved question before the team continues.
Ask, “Does the next event follow from what happened earlier? Have both characters’ concerns been considered? What would you do, and what information would you need?” A pupil might say, “Our first ending ignored the character who was worried about the owner. We added a line explaining how they would ask for help.” Use your school’s actual procedure if you extend the fictional discussion to real lost property.
14. Let pupils set and test a clue challenge
Invite groups to design a three-clue classroom hunt for another group. Give boundaries: use agreed locations, make each clue solvable from information available in the room, and provide an answer key. Begin with a mind map of possible locations and clue types.
Starter clue: “Find the classroom clock. Move to the place where we keep dictionaries. Look for the envelope marked with a triangle.” The answer key should identify the exact intended location. Ask the testing group to note any instruction that could point to more than one place.
For a tabletop strategy-game alternative, pupils can create a hidden three-shape sequence using a circle, square and triangle once each. Players guess the order and receive only the number of shapes in the correct position. Require designers to record the hidden sequence and check every piece of feedback against it.
After another group tests the hunt or game, ask designers, “Where did players need information you had not provided? Which revision makes the challenge clearer without giving away the answer?” Let pupils propose the next challenge from an ambiguity or difficulty they observed.
15. Make feedback lead to a visible revision
Return one piece of work from any activity with feedback about a specific decision, test or explanation. Ask pupils to revise that part and show what changed. Keep the original version beside the revision so the response is inspectable.
Feedback examples:
Maths: “You found a cost of £16. Add a check showing why the mixed packs are not cheaper.”
Bridge: “Your second bridge held the mass. Mark the feature you changed and explain why you chose it.”
Logic puzzle: “You named the objects correctly. Add the deduction between the blue bag clue and your answer for the red bag.”
Science: “Your log says ‘we tried again’. State what you changed and which observation led to that decision.”
Finish with a short pupil response: “I changed… because… The evidence is…”. If the explanation remains unclear, ask for an annotated calculation, drawing or demonstration rather than accepting more talk alone. Use the response to choose the next task: another example with the same structure, a different representation, or a challenge with one added constraint.
Related resources
International Journal of Instruction
Educational Research and Reviews
Educational Research Quarterly
International Journal of STEM Education
