Math // Mathematical Thinking

Showing Your Working

Show and tell how a mathematical answer was found using objects, drawings, and spoken words

Ages
5 to 6
Type
Thinking skill
Builds on
3 topics
Leads to
1 topic

Quick check

After the learner solves a maths problem, can they explain how they got their answer — using counters, a drawing, or words — rather than just writing down the final number?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Use objects or drawings to demonstrate how an addition or subtraction was solved
  • Respond to 'how do you know?' by pointing to objects or a drawing and describing what was done
  • Listen to a peer's explanation and say whether they agree or disagree

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics
  • Number bonds to 9Helpful

    Addition & Subtraction // Ages 4 to 6

    Explaining how to find number bonds to 10 exercises showing thinking with objects

  • Numbers up to 10 into pairsHelpful

    Addition & Subtraction // Ages 4 to 6

    Explaining part-part-whole decompositions exercises showing and telling

  • Listening and respondingHelpful

    English // Speaking & Listening // Ages 4 to 11

    Explaining mathematical reasoning orally requires basic listening and responding skills

You are here

Showing Your Working

Ages 5 to 6 // Thinking skill

Leads to

1 topic
  • Explaining Mathematical ReasoningRequired

    Mathematical Thinking // Ages 6 to 7

    Age 6-7 explaining with diagrams/logic builds on age 5-6 showing and telling with objects

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For 5-6 year olds, 'showing your working' means demonstrating and narrating HOW an answer was found — with objects, drawings, or spoken words — and beginning to answer 'how do you know?' by pointing to what was done rather than restating the answer. A key teaching insight is that at this age reasoning can often run ahead of the ability to communicate it: a quiet child may have reasoned soundly. Teaching therefore separates two threads — building the habit of demonstrating a method concretely, and separately scaffolding the language to narrate it — and treats listening to a peer and agreeing/disagreeing as the first seed of evaluating reasoning, not just answers.

Common misconceptions

  • Restating the answer ('because it's 8') when asked 'how do you know?' instead of showing the method
  • A quiet or brief response mistaken for weak reasoning, when it is really communication that lags
  • Judging a peer's work only by whether the answer matches, not by whether the method makes sense
  • Believing 'showing your working' means writing the sum again rather than revealing the thinking

Useful representations

  • Concrete objects / counters moved to enact and show a method
  • Ten frame and part-part-whole drawing
  • Number sentence alongside the objects
  • Spoken sentence stems ('first… then… so…')
  • The describe → explain step of the NRICH reasoning ladder

Teaching practices

  • Ask 'how do you know?' and 'show me' routinely, accepting objects, pointing, and drawings as valid ways to show working
  • Separate reasoning from its communication — judge whether a quiet child needs help thinking or help putting it into words, and support each differently
  • Model narrating a method aloud ('first I… then I…') and provide simple spoken stems
  • Use concrete referents (counters, ten frames, drawings) as the medium of explanation, as elementary arguments legitimately rest on objects and actions
  • Have children listen to a peer's method and say whether they agree, beginning to evaluate reasoning rather than just answers
  • Value the demonstration itself; do not treat limited vocabulary as limited mathematics

Activities to try

  1. 1

    The curious listener who wants to know HOW

    Why it works: 'How do you know?' is answered by demonstrating the method, not by restating the answer; and a method can be judged by whether its steps make sense, not only by whether the final number is right.

    1. Solve a within-10 problem such as 5 and 3 using counters (physical objects or on-screen draggable counters).
    2. When asked 'how did you get 8? show me!', move or point to the counters to re-enact the method — for example, 'I put 5, then counted on 3 more'.
    3. Hear the method echoed back as a little story ('first you put 5, then you counted on 3 more, so you got 8') and notice that explaining = showing the doing, not repeating the answer.
    4. Watch the listener solve a problem its own way — sometimes by a muddled or wrong route — and answer 'do you agree with how I did it? how can you tell?'
  2. 2

    Show-how workspace with a compare-two-methods panel

    Why it works: A method can be made concrete, repeatable, and comparable; evaluating reasoning means looking at the steps, not only matching the final answer.

    1. Move counters or fill a ten frame to solve an addition or subtraction, then use a 'show how you did it' replay to retrace the steps.
    2. Narrate the recaptured steps aloud using stems such as 'first… then… so…'.
    3. View a peer's or character's method beside your own and decide 'do you agree?', then 'show why' by pointing to a step that does or does not make sense.
  3. 3

    Tap-to-reveal a worked method (modelling scaffold)

    Why it works: Seeing the stages of a worked method named out loud shows what 'showing your working' can look like before producing one's own.

    1. Tap each stage of an already-solved problem to reveal 'what I did and why' at that step.
    2. Afterwards, re-solve a fresh problem and show your own steps with objects or a drawing, narrating as you go.

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