Math // Multiplication & Division

Multi-step problems: choosing operations

Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts

Ages
10 to 11
Type
Method
Builds on
3 topics
Leads to
2 topics
Standards
1 code

Quick check

If the learner is given a multi-step problem mixing different operations — like working out the total cost of several items at different prices — can they plan and carry out each step 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 three-step word problem involving a mix of all four operations
  • Explain why particular operations were chosen for each step of a multi-step problem
  • Identify and correct an error in a multi-step solution that used the wrong operation

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
  • Division with remaindersRequired

    Multiplication & Division // Ages 9 to 10

    Y6 multi-step four-op problems extend Y5 multi-step problems

  • Division with remainders (age 10+)Required

    Multiplication & Division // Ages 10 to 11

    Mixed operation problems require long division skill

  • Order of operationsHelpful

    Multiplication & Division // Ages 10 to 11

    Choosing operations benefits from order-of-operations understanding

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Multi-step problems: choosing operations

Ages 10 to 11 // Method

Leads to

2 topics
  • Using inverse operationsRequired

    Multiplication & Division // Ages 11 to 12

    Fluency with all four operations in context is required before formalising inverse relationships between them

  • Advanced Multi-Step ProblemsHelpful

    Mathematical Thinking // Ages 10 to 11

    Multi-step problems draw on four-operation problem-solving

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 10–11, develop strategic multi-step problem solving: deciding WHICH of the four operations each step needs, in what ORDER, and WHY. The skill is planning, justifying and monitoring a solution — not just executing arithmetic. Learners move words → structural model (bar/part-whole) → operation choice → execution → reasonableness check, can record the plan as a number-sentence chain (a letter for the final unknown, with each step's result feeding the next), and also analyse flawed solutions to spot a wrong-operation step.

Common misconceptions

  • Keyword-matching instead of modelling the situation ('share' → always divide even when it means 'each gets, so total = ×').
  • Losing the thread across steps — using the wrong intermediate value or forgetting a step in a three-step chain.
  • Choosing an operation by which numbers are 'easy' to combine rather than by the situation's structure.
  • Skipping the reasonableness check, so a wrong-operation answer (often wildly off) goes unnoticed.
  • Mishandling the remainder at a step (rounding up vs down vs keeping) because the context isn't re-examined.

Useful representations

  • Bar model / part-whole diagram translating the situation into visible structure (comparison bars, equal-group bars) from which the operation follows.
  • A step-planner / flow layout: box per step showing the operation chosen, the reason, and the intermediate result feeding the next step.
  • Worked-and-flawed solution pairs for error analysis — one correct, one with a wrong-operation step — placed side by side.
  • Number-sentence chain with a letter for the final unknown, linking each step's result to the next (connects to representing with equations).

Teaching practices

  • Teach a problem-solving routine (understand → represent → plan → do → check) rather than answer-hunting; the deliberate representation and planning steps are where operation choice is decided.
  • Use bar models / part-whole diagrams to expose STRUCTURE — a comparison bar signals subtraction or division, equal groups signal multiplication or division — so operation choice follows from the model, not from keyword-spotting.
  • Explicitly kill keyword strategies ('altogether = add', 'left = subtract'): give problems where the keyword misleads, forcing the child to reason from the situation's structure.
  • Make justification routine — 'why this operation here?' after every step — and use error-analysis tasks (a worked solution with a wrong-operation step) so children articulate WHY an operation is right or wrong.
  • Always close with a reasonableness check via estimation or inverse operations, connecting to the estimation topic (mt_ilPrU0cbtT) so checking becomes automatic and catches wrong-operation slips.

Activities to try

  1. 1

    Problem planner: build the model, then choose the operation

    Why it works: The situation's STRUCTURE — not a keyword — dictates which operation each step needs, and a multi-step problem is one connected chain where each result feeds the next.

    1. Read a rich context, e.g. 'A school buys 6 boxes of 24 pencils. They share them equally between 8 classes. Then each class uses 5 pencils on the first day. How many are left in each class?'
    2. Before computing, represent the situation as a bar / part-whole model: drag the quantities into comparison bars or equal-group bars so the structure is visible.
    3. For step one, choose the operation and state a reason tied to the structure (e.g. 'multiply, because there are 6 equal groups of 24').
    4. Carry the intermediate result forward into the next step's model, then choose the operation for that step, and repeat to the final answer.
    5. Record the plan as a number-sentence chain in which each step's result feeds the next and the final unknown is a letter — for example 6×24 = p; p÷8 = c; c−5 = n, where n is the final unknown you are solving for — so the connection between steps is explicit.
  2. 2

    Spot and fix the wrong-operation step

    Why it works: Being able to justify why an operation is right also means being able to detect why one is wrong — monitoring a solution is part of solving it.

    1. Examine a completed multi-step solution placed beside the problem, where one step used the wrong operation (e.g. subtracted where it should have divided).
    2. Locate the flawed step and explain why that operation does not match the situation's structure.
    3. Correct the step, re-run the remaining chain with the fixed intermediate value, and confirm with an estimate.
  3. 3

    Socratic planning dialogue

    Why it works: Verbalising the reason for each operation and what each intermediate value means builds the metacognitive control that multi-step problem solving requires.

    1. Work through a word problem with a questioner who never supplies the answer.
    2. Answer probes at each step: 'Why that operation here?', 'What does the number you just found actually represent?', 'Is that reasonable?'
    3. State a plan as a sequence of questions ('first, how many pencils in total across the boxes? then…') and solve one question at a time, writing each intermediate answer.

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
Ma6/2.2h

Math // Multiplication & Division

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