Math // Mathematical Thinking

Making Sense of Problems

Make sense of a problem by identifying what is being asked, choosing concrete objects or pictures to represent the situation, and explaining a pathway to the solution

Ages
5 to 6
Type
Thinking skill
Builds on
5 topics
Leads to
2 topics

Quick check

When the learner gets a maths problem they don't immediately know how to solve, do they stop and think about what the question is asking — maybe drawing a picture — before diving in?

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 10, explain what the problem is asking before attempting to solve
  • Choose objects, fingers, or drawings to represent a problem situation
  • After finding an answer, check it makes sense (e.g. re-count objects to verify a total)

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
  • Addition as combining or putting together twoHelpful

    Addition & Subtraction // Ages 4 to 6

    Making sense of addition problems requires understanding addition as combining

  • How Many in Total?Helpful

    Counting & Cardinality // Ages 4 to 6

    Problem sense-making at 5-6 requires cardinality understanding to make sense of 'how many' problems

  • Persisting When It's HardHelpful

    Learning to Learn // Learning to Learn // Ages 5 to 6

    Mathematical perseverance with problems is the domain-specific application of the universal persistence habit

  • Checking Your Own WorkHelpful

    Learning to Learn // Learning to Learn // Ages 5 to 6

    Checking whether a maths answer makes sense applies the universal self-checking habit to a mathematical context

  • Listening to Texts Read AloudHelpful

    English // Reading Comprehension // Ages 5 to 10

    Making sense of word problems requires listening comprehension skills

You are here

Making Sense of Problems

Ages 5 to 6 // Thinking skill

Leads to

2 topics
  • Guided Multi-Step Problem SolvingRequired

    Mathematical Thinking // Ages 6 to 7

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

  • Growth MindsetHelpful

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

    Growth mindset understanding (SEL) is grounded in the concrete experience of persevering through mathematical problems — the abstract principle is made real through mathematics

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 5-6 year-olds, 'making sense of a problem' means treating a word problem as a real situation to understand before touching any number. Proficient young solvers restate what the story asks in their own words, represent it with objects or a drawing, work toward an answer, then check whether it makes sense in the story. The main teaching risk is the opposite habit — grabbing the numbers and 'doing a sum' (suspension of sense-making / compulsion to calculate). The core activity is a patient spoken 'thinking partner' routine that refuses a blurted number and builds comprehension first; concrete counters, numberless/progressively-revealed staging, a worked-example reveal, and a single reasonableness check are supporting approaches with different purposes.

Common misconceptions

  • 'I look for the special word — altogether means add, left means take away' (keyword strategy, applied before the story is even read)
  • 'Every problem is just a sum with the numbers in it' — computes an answer even for an unanswerable or nonsensical story (suspension of sense-making / compulsion to calculate)
  • Restating a salient number from the story instead of the quantity actually asked for
  • Treating being stuck as 'I can't do it' rather than a cue to represent the story a different way

Useful representations

  • Concrete objects / counters the child physically moves to enact the story
  • Part-part-whole picture (two groups combining into a whole)
  • Simple bar or strip drawing linking the known and unknown quantities
  • Numberless word-problem staging (reveal the story, then the question, then the numbers last)
  • A four-move frame: understand → represent → solve → check

Teaching practices

  • Comprehension first: have the child retell the problem in their own words and say what is being asked BEFORE any calculating
  • Represent the situation concretely — act it out with counters, fingers, or a simple drawing so the story structure (part-part-whole) is visible
  • Use numberless / progressively-revealed story problems so children reason about the relationship between quantities before a number invites them to compute
  • Model a short self-questioning routine aloud ('What is happening? What do I need to find? Does my answer make sense?') and have the child echo it
  • Deliberately pose the occasional unanswerable or 'silly' story so children learn that not every set of numbers yields a sum — sense-making is required
  • Never teach cue-word rules ('altogether means add'): build understanding of the situation, not word-to-operation mapping

Activities to try

  1. 1

    The thinking partner who won't take a number yet

    Why it works: A word problem is a situation to understand, not just numbers to do a sum with; sense-making and a reasonableness check come before and after calculating.

    1. Listen to a tiny within-10 spoken story from a friendly partner character, e.g. 'Three frogs were on a log and two more hopped on.'
    2. Before giving any answer, retell the story in your own words and say what is being asked ('what are we trying to find out?').
    3. Show the story with counters/frogs or fingers ('show me with your frogs') so the part-part-whole structure is visible.
    4. Work out an answer for a solvable story, then answer the partner's closing question: 'Does your answer make sense in the story?'
    5. When the partner occasionally tells a deliberately silly story ('...so what colour is the pond?' or '...so how old is the cat?'), catch that it cannot be worked out and say why.
  2. 2

    Numberless, progressively-revealed story with a part-whole workspace

    Why it works: Children reason about the relationship between quantities before a number invites them to compute, building a visual representation of the situation.

    1. See the story picture first, then the question, with the numbers revealed last.
    2. With a workspace of draggable counters and a part-whole mat, place objects to model the situation and the relationship between the quantities.
    3. Only after modelling, use the number pad that appears to find the answer.
    4. Respond to a 'does this match the story?' check that compares your model to the situation, not just the final number.
  3. 3

    Tap-to-reveal worked example of the four moves

    Why it works: The understand/represent/solve/check routine becomes visible as a sequence a solver actually follows.

    1. Work through one story where each phase can be revealed: understand → represent → solve → check.
    2. At each phase, see what a good solver asks themselves ('What is happening? What do I need to find? Does my answer make sense?').
    3. Echo the self-questioning routine aloud after seeing it modelled.

Math // Mathematical Thinking

More in Mathematical Thinking

All 48 topics