Math // Mathematical Thinking

Working with money

Model real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context

Ages
7 to 8
Type
Thinking skill
Builds on
3 topics
Leads to
1 topic

Quick check

When the learner solves a real-life maths problem — like calculating how much fabric is needed for a project — can they choose the right representation (a diagram, a table, an equation) and explain what the answer means in the real situation?

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 whether to use a bar model, number line, or equation for a measurement problem
  • Model a multi-step money problem with equations and interpret the final answer as change or total cost
  • Create a line plot from measurement data and use it to answer questions about the real-world situation

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

Working with money

Ages 7 to 8 // Thinking skill

Leads to

1 topic

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 7-8, model real-world measurement, money, and time problems by choosing and justifying a representation (bar model, number line, or equation), carrying multi-step calculations with units attached, and crucially interpreting the final number as the RIGHT quantity (total cost vs change). The signature hazard is suspension of sense-making: computing to a number without naming which quantity the question asked for or checking its reasonableness. Line plots extend modelling to reading answers off a data display.

Common misconceptions

  • Reports the wrong quantity — gives the total cost when the question asks for the change
  • Stops after the first step of a multi-step problem
  • Computes without sense-checking whether the answer is reasonable in context
  • Drops or muddles units (mixing pounds and pence, or minutes and hours)

Useful representations

  • Bar model for multi-step and comparison money/measurement problems
  • Number line for time and measurement jumps
  • Equation with units for total cost / change
  • Line plot of measurement data

Teaching practices

  • Have the child choose AND justify a representation for the problem (bar model / number line / equation), matching tool to structure (MP4 identify and map quantities)
  • For multi-step money, name each interim result ('that's the total cost') before the next step, and interpret the final answer as the quantity asked (change vs total)
  • Keep units attached throughout and sense-check the final answer against the situation (CDE)
  • Use line plots so children read answers off a data display back into the real-world question
  • Reason about the situation before computing; avoid reducing the problem to keywords (CDE)

Activities to try

  1. 1

    Multi-step money modeller: name the quantity, then check it

    Why it works: In a multi-step problem each number along the way means something specific; the answer is only right when you name the quantity the question actually asked for and check it is reasonable in context.

    1. Set up a shopping problem: two items at 65p and 20p, paying with £1
    2. Choose a representation and say why it fits (e.g. a bar model with a £1 whole, an 85p part for the shopping, and a mystery part)
    3. Pause at the interim number and label it: 'that 85p — what is it?' Answer: the total cost (65p + 20p = 85p)
    4. Carry on to the second step: change £1 into 100p, then work out 100p − 85p = 15p as the change
    5. Interpret the final number with its unit ('15p change') and sense-check it: the cost and the change together should make the £1 paid (85p + 15p = 100p = £1)
  2. 2

    Shopkeeper who tries it on (spoken correction)

    Why it works: Distinguishing which quantity the answer names is a reasoning skill you can articulate and defend, not just compute.

    1. Play out a shop exchange where a shopkeeper rings up two items and states the subtotal as if it were the change
    2. Catch and correct the error out loud, explaining which quantity the stated number actually is
    3. Keep units straight (pounds and pence) while justifying the fix
    4. Explain aloud how a bar or equation would separate the cost from the change
  3. 3

    Worked multi-step walkthrough (scaffold)

    Why it works: Each number in a worked solution carries a meaning; following the labels shows how an interim quantity differs from the final answer.

    1. Step through a worked multi-step money or measurement problem
    2. Reveal what each step's number means (e.g. tap a step to show 'this is the total cost', 'this is the change')
    3. Describe in your own words what the interim number means before seeing the next step

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