Math // Addition & Subtraction

Mental and written addition and subtraction

Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures

Ages
6 to 7
Type
Method
Builds on
2 topics
Leads to
0 topics
Standards
2 codes

Quick check

If the learner is given a problem involving lengths, weights, or prices, can they decide whether to add or subtract and carry out the calculation correctly?

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.
  • Solve a two-step problem: 'I had 35p, spent 12p, then found 5p. How much now?'
  • Choose an appropriate method (mental or written) for a given problem
  • Solve problems involving measures, e.g. 'a ribbon is 45cm, I cut off 18cm'

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

2 topics
  • Adding two two-digit numbersRequired

    Addition & Subtraction // Ages 6 to 7

    Solving real problems with mental/written methods requires the procedural skill of adding/subtracting two-digit numbers

  • Early Word ProblemsHelpful

    Addition & Subtraction // Ages 5 to 7

    Problem-solving in context extends from Y1 word problems

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Mental and written addition and subtraction

Ages 6 to 7 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Addition & Subtraction

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

Year 2 children learn to apply addition and subtraction to real problems — two-step problems, money, and measures — and to choose between a mental and a written method. The core challenge is modelling: reading the situation, deciding what each step needs, and tracking an intermediate result, rather than picking an operation from keywords. Bar models and part-whole diagrams represent the structure before any computing.

Common misconceptions

  • Keyword strategy: picking the operation from words ('left'→subtract, 'altogether'→add) rather than the situation — breaks on multi-step and compare problems
  • Doing only the first step of a two-step problem and stopping
  • Losing or misusing the intermediate result
  • Ignoring units, or mixing units in measures/money problems
  • Defaulting to a written method when a mental one is far quicker (or vice versa)

Useful representations

  • Bar model (comparison, part-whole, two-step)
  • Part-whole diagram
  • Number line (count-on for change/difference)
  • Coins / ruler as concrete context for money and measures
  • Jottings vs mental — an anchor chart of when to use each

Teaching practices

  • Teach the child to represent the situation first (bar model / part-whole) before choosing numbers or method — structure before calculation
  • For two-step problems, make the intermediate result explicit ('how much after spending, before finding?')
  • Discuss method choice: some problems are quicker mentally (35p−12p), some warrant a jotting/written method — build the judgement
  • Attend to units and context in measures/money (cm, p) so answers are labelled and sensible
  • Use the DfE problem vocabulary (total, difference, more/less, change) so the operation is drawn from the situation, not from keywords

Activities to try

  1. 1

    Build the story as a bar model (money two-step)

    Why it works: Drawing the situation turns a confusing word problem into visible parts; seeing the middle number (23p) appear is what stops a child from stopping after step one, and labelling keeps the units correct.

    1. Take the problem 'I had 35p, spent 12p, then found 5p — how much now?' and draw a bar to represent the starting 35p.
    2. Cut 12p off the bar for the spending, and label the segment that is left — write 35−12=23 and mark 23p as the intermediate result.
    3. Add a 5p bar for 'then found 5p' and compute the final total: 23+5=28p. Label the answer with its unit.
    4. Repeat with a lengths story, e.g. 'a ribbon is 45cm, I cut off 18cm — how long is left?', drawing and labelling the bar and giving the answer in cm (45−18=27cm).
  2. 2

    Compare problems that defeat keyword guessing

    Why it works: The operation comes from the situation, not from a trigger word; a bar model makes compare problems (where keywords can mislead) solvable by showing the structure.

    1. Solve 'Sam has 24 stickers. Tom has 8 more than Sam. How many does Tom have?' by drawing Sam's bar and building Tom's bar as Sam's amount plus 8 more.
    2. State the operation you used (24+8=32) and explain why 'more than' here means add, even though 'more than' can sometimes cue the wrong choice.
    3. Try a contrasting compare problem where the cue word misleads, e.g. 'Tom has 32 stickers. He has 8 more than Sam. How many does Sam have?' Draw both bars and notice that, even though it says 'more', Sam's bar is shorter, so you subtract (32−8=24). Modelling, not the cue word, tells you whether to add or subtract.
  3. 3

    Mental or written? Choosing an efficient method

    Why it works: Method choice is a judgement about efficiency, not a rule; small, friendly numbers often suit mental work while larger or multi-digit ones may warrant a written method.

    1. For each problem decide: can I do this quickly in my head, or should I jot it down? Then solve it.
    2. Compare 35p−12p (quick mentally) with a larger measures problem such as 45cm−18cm that may be easier with a jotting or bridging step.
    3. Build a short anchor chart of 'when I use mental' versus 'when I jot/write', and justify one of your choices aloud.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y2/AS/1Maths/Y2/AS/2

Math // Addition & Subtraction

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