Math // Mathematical Thinking

Guided Multi-Step Problem Solving

With teacher guidance, make sense of multi-step and more complex problems by planning a pathway to the solution, identifying relevant information, and choosing appropriate operations

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

Quick check

If the learner works out that 3 children each get 12 sweets and ends up with 5, does the learner pause and say "that doesn't seem right" rather than just writing it down?

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.
  • When given a word problem within 20 or 100, identify the known information and what needs to be found
  • Try a strategy (drawing, number line, known fact) and switch approach if the first attempt stalls
  • Check the reasonableness of an answer using estimation or a different method

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

5 topics
  • Making Sense of ProblemsRequired

    Mathematical Thinking // Ages 5 to 6

    Age 6-7 problem-solving builds directly on age 5-6 problem-sense-making

  • Early Word ProblemsHelpful

    Addition & Subtraction // Ages 5 to 7

    Planning approaches to word problems within 20 exercises this skill

  • Addition and subtraction within 20Helpful

    Addition & Subtraction // Ages 6 to 7

    Choosing strategies for adding within 20 requires planning and evaluating approaches

  • Feeling of not understandingHelpful

    Learning to Learn // Learning to Learn // Ages 6 to 7

    Evaluating whether a maths solution is reasonable applies the universal comprehension-monitoring habit

  • Planning a TaskHelpful

    Learning to Learn // Learning to Learn // Ages 6 to 7

    Planning a mathematical approach is the domain-specific application of the universal task-planning habit

You are here

Guided Multi-Step Problem Solving

Ages 6 to 7 // Thinking skill

Leads to

3 topics
  • Multi-Step Problem SolvingRequired

    Mathematical Thinking // Ages 7 to 8

    Age 7-8 problem-solving builds on age 6-7 problem-solving

  • Breaking Tasks into StepsHelpful

    Personal & Social Development // Self-Regulation & Resilience // Ages 7 to 9

    The SEL skill of breaking a big task into manageable steps parallels and builds on the mathematical practice of planning a step-by-step approach to complex problems

  • Choosing a StrategyHelpful

    Learning to Learn // Learning to Learn // Ages 9 to 10

    The LtL strategy evaluation skill (9-10) builds on the early scaffolded habit of checking reasonableness in maths introduced at 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 6-7 year olds, help children plan a pathway through two-step and more complex word problems: identify what is known and what must be found, decide which information is relevant (setting aside any red-herring number), choose and sequence operations, estimate first, and check the answer for reasonableness. Two documented habits work against this: keyword/number-grabbing (choosing an operation from a cue word or using every number present) and the compulsion to calculate (rushing to an answer with no estimate or sense-check). The strongest supports in the sources are teacher-modelled self-questioning and children building their OWN visual representations (strip/bar diagrams, or a number line for two-step jumps) that map relevant quantities and reveal the sequence of steps. Several activities below address the same objective through different media (a build-your-own workspace, a planning dialogue, a worked-example companion, and a reasonableness-judgement item); keep more than one because they exercise construction, talk, and recognition respectively.

Common misconceptions

  • Answering only the first step of a two-step problem (treating multi-step as single-step)
  • Using every number in the problem, including an irrelevant one, because 'they must all be needed'
  • Choosing the operation from a cue word rather than the problem's structure
  • Computing an answer and stopping, with no estimate or reasonableness check (compulsion to calculate)

Useful representations

  • Bar / strip diagram mapping known parts to the unknown
  • Part-part-whole and comparison ('more than') structures
  • Number line for two-step jumps
  • Numberless staged reveal to build relationships before numbers appear
  • A prompt list / four-move frame: understand → plan → solve → check

Teaching practices

  • Model self-questioning aloud and give a short prompt list: 'What do I know? What must I find? What shall I do first?' (WWC Rec 2, strong evidence)
  • Teach children to build their OWN visual representation (bar/strip diagram) that maps knowns to the unknown — building it beats being handed one (WWC Rec 3, strong evidence)
  • Use the representation to keep the WHOLE multi-step situation visible so the child does not stop after step one
  • Include problems with an irrelevant number so 'identify relevant information' is actually exercised, not assumed
  • Estimate first to set a reasonableness benchmark, then compute, then ask 'does this make sense?' and check by a different method
  • Encourage strategy-switching: if the first approach stalls, represent it a different way rather than abandoning — name this as normal

Activities to try

  1. 1

    Build-your-own 'plan-it' workspace with a red herring and an estimate-first step

    Why it works: Planning, relevance-sorting, and self-checking become things the child does and watches on a live representation, rather than rules they are told. Keeping the whole situation visible helps the child notice when they have stopped after step one on multi-step problems, and comparing to a self-made estimate can make an unreasonable answer stand out.

    1. Meet a problem revealed a piece at a time: first the story, then the question, then the numbers (a staged, numberless-to-numbered reveal).
    2. Build your OWN representation by dragging parts onto a canvas to map the known parts to the unknown — a bar/strip diagram, or a number line to show the jumps — rather than using a pre-made diagram.
    3. Identify and physically set aside the irrelevant number. For example, in 'There are 24 children and 3 teachers; 8 children go home. How many children are left?' the 3 teachers are not needed (this one is a single step, 24 − 8 = 16, chosen to practise spotting a red herring).
    4. Practise the sequencing on a genuinely two-step version, e.g. '8 children go home in the morning and 6 more go home at lunch; how many are left?' — here finding 16 is only step one (24 − 8), and 10 is the answer (16 − 6).
    5. Before computing, set an estimate ('about how big will the answer be?') to create a reasonableness benchmark.
  2. 2

    Planning dialogue with a 'detective partner' that models self-questioning

    Why it works: Rehearsing the monitoring routine in talk — planning the pathway, naming relevant versus irrelevant information, and sense-checking — builds the habit of reasoning about structure before numbers.

    1. Work with an in-role partner who models self-questioning aloud and asks you to answer: 'What do I know? What must I find? What shall I do first? Does that make sense?'
    2. Say which information is needed and which is a red herring, and justify your plan aloud before computing.
    3. Before computing, estimate ('about how big should the answer be?'), then close every problem by sense-checking the result against that estimate.
    4. When your first approach stalls, try 'let's show it another way' — represent the problem differently (for example, swap a bar model for a number line) rather than abandoning it.
  3. 3

    Worked-example companion: reveal a good solver's self-questions and why a number was ignored

    Why it works: Seeing the plan-then-check frame and the reasoning for discarding a spare number makes the usually-invisible monitoring moves explicit before the child performs them independently.

    1. Work through a tap-to-reveal worked two-step problem, uncovering each phase: understand → plan → solve → check.
    2. At each phase, reveal the self-question a good solver asks and why the irrelevant number was ignored.
    3. After viewing, retell the plan in your own words and then try a fresh problem where YOU do the planning and relevance-sorting.

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