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
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
- 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
- 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
You are here
Mental and written addition and subtraction
Ages 6 to 7 // Method
Leads to
0 topicsNothing 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
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.
- Take the problem 'I had 35p, spent 12p, then found 5p — how much now?' and draw a bar to represent the starting 35p.
- 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.
- Add a 5p bar for 'then found 5p' and compute the final total: 23+5=28p. Label the answer with its unit.
- 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
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.
- 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.
- 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.
- 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
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.
- For each problem decide: can I do this quickly in my head, or should I jot it down? Then solve it.
- Compare 35p−12p (quick mentally) with a larger measures problem such as 45cm−18cm that may be easier with a jotting or bridging step.
- 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
- The national curriculum in England: Key stages 1 and 2 framework document
- Maths/Y2/AS/1Maths/Y2/AS/2
Math // Addition & Subtraction
More in Addition & Subtraction
- Addition and subtraction within 20Ages 6 to 7MethodAdd and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts
- Fluent adding and subtracting within 10Ages 6 to 7MethodFluently add and subtract within 10
- Adding within 100Ages 6 to 7MethodAdd within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10
- What the equals sign meansAges 6 to 7ConceptUnderstand the meaning of the equal sign as 'is the same as' and determine if equations are true or false
- Addition in any orderAges 6 to 7ConceptUnderstand and apply the commutative property of addition: addends can be added in any order
- Finding a missing number in additionAges 6 to 7ConceptUnderstand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)
- Inverse: addition undoes subtractionAges 6 to 7ConceptRecognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems
- Mental addition and subtraction (age 6+)Ages 6 to 7MethodAdd and subtract a two-digit number and ones mentally and using concrete/pictorial representations