Math // Mathematical Thinking

Connecting maths to real life

Represent real-world problems with number sentences, bar models, or diagrams, and interpret the mathematical result back in context

Ages
6 to 7
Type
Thinking skill
Builds on
3 topics
Leads to
1 topic

Quick check

When the learner solves a word problem by drawing a bar model or writing an equation, can they also explain what their answer means in the real-world context — like "that means each child gets 4 sweets"?

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.
  • Choose and write an appropriate number sentence for a measurement or money word problem
  • Draw a bar model or diagram to represent a two-step or comparison problem
  • Interpret the numerical answer in context (e.g. '15 cm means the ribbon is 15 centimetres long')

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

You are here

Connecting maths to real life

Ages 6 to 7 // Thinking skill

Leads to

1 topic
  • Working with moneyRequired

    Mathematical Thinking // Ages 7 to 8

    Age 7-8 modelling builds on age 6-7

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 ages 6-7, this topic develops the full mathematical modelling cycle: represent a money or measurement word problem with a number sentence, bar model, or diagram, AND complete the 'return trip' by interpreting the numerical answer back in context with its unit ('5p change', '15 cm long') and checking whether it is reasonable. The defining new demand is that a bare number is not an answer; the remedy to 'suspension of sense-making' is to reason about the situation before computing and always interpret and sense-check the result afterwards.

Common misconceptions

  • Stops at a bare number without interpreting it in context or attaching a unit
  • Grabs the numbers and applies the operation a keyword suggests, without modelling the situation
  • Doesn't sense-check — accepts an answer that can't be true in the situation (change larger than the money paid)
  • Reports the wrong quantity (gives the total when the question asks for what's left)

Useful representations

  • Part-whole and comparison bar models for two-step problems
  • Number sentence with units attached to the quantities
  • Number line for measurement/money jumps
  • Simple diagrams of the situation (coins, ribbon lengths)

Teaching practices

  • Insist on the return trip: every numerical answer is interpreted in context with its unit ('5p change', '15 cm long') — the interpret-in-context half of MP4
  • Reason about the situation before computing; resist keyword-stripping, which the CDE guide identifies as a cause of suspension of sense-making
  • Use bar models to expose two-step and comparison structure so the child models the relationships, not just grabs numbers (NCETM)
  • Build the reasonableness check: 'could you have MORE money after spending some?' — sense-check the answer against the situation
  • Ask 'what does this number mean here?' at the end of every problem, not just 'what's the answer?'

Activities to try

  1. 1

    Model a shop story, then make the return trip

    Why it works: A calculation is not finished when the number appears; it is finished when the number is read back into the story and checked for whether it could possibly be true. You cannot end up with MORE money after spending some.

    1. Read a shop story, e.g. 'Sam has 20p in his purse and buys a sticker costing 15p. How much change does he get?'
    2. Build a bar model of the situation: 20 as the whole, split into a 15 part and a mystery (change) part; or write a matching number sentence.
    3. Work out the missing part to land on 5.
    4. Complete a mandatory 'what does your 5 mean?' step: attach the unit and quantity, finishing the sentence '5p change'.
    5. Pass a reasonableness check before the answer is accepted: decide whether a candidate answer could possibly be true in the story (e.g. flag that change greater than the amount paid is impossible).
  2. 2

    Argue with the shopkeeper: catch the impossible change

    Why it works: Defending why an answer does or does not make sense out loud strengthens the reasonableness habit; a contrasting impossible answer provokes the check that compute-and-stop skips.

    1. Talk with a shopkeeper character (role-played by a partner, teacher, or on-screen character) who offers a plausible-sounding but impossible answer: 'You gave me 20p for a 15p sticker, so your change is 35p, right?'
    2. Decide out loud whether 35p can be right, and explain why change cannot be larger than the money paid.
    3. State the correct change in context ('5p change') and justify it.
    4. Respond to a follow-up: 'If the sticker cost 25p, could Sam buy it with his 20p? How do you know?'
  3. 3

    Bar models for part-whole and comparison problems

    Why it works: Bar models expose the structure of a situation — including part-whole and comparison relationships — so the child models the relationships rather than grabbing numbers and applying a keyword operation.

    1. Draw a part-whole bar model for a word problem, labelling which part is the known quantity, which is the whole, and which is the unknown.
    2. Use a comparison bar model to show two quantities side by side for a comparison problem (e.g. one ribbon longer than another).
    3. Use a number line to represent money or measurement jumps when that fits the story better.
    4. Attach units to each quantity on the model and to the final answer.

Math // Mathematical Thinking

More in Mathematical Thinking

All 48 topics