Math // Mathematical Thinking

Using objects to model real problems

Use objects, drawings, or simple number sentences to represent a real-world situation (early mathematical modelling)

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

Quick check

If you describe a simple real-life situation to the learner — like "there are 3 birds on a fence and 2 more land" — can they write a number sentence like 3 + 2 = 5 to represent it?

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.
  • Draw a picture or use objects to represent a simple real-world situation involving counting or comparing
  • Write or dictate a number sentence to describe a real-world situation (e.g. 'I had 5 apples and ate 2')
  • Use the model to answer a question about the situation

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

You are here

Using objects to model real problems

Ages 5 to 6 // Thinking skill

Leads to

1 topic
  • Connecting maths to real lifeRequired

    Mathematical Thinking // Ages 6 to 7

    Age 6-7 modelling with bar models/diagrams builds on age 5-6 modelling with objects and pictures

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

Early mathematical modelling for ages 5-6: children use objects, drawings, or dictated/written number sentences to REPRESENT a real situation, and then read an answer back off the model as something about the real objects. The whole modelling cycle appears in miniature: the model must preserve what actually happens in the story (a taking-away action, not just the numbers 5 and 2), and the answer must be interpreted in context ('three apples left', not a bare 'three'). The central hazard to head off is 'suspension of sense-making' — computing without checking the story — addressed by habitually asking 'does your model match what happened?' and 'three what?'. Teaching is concrete, story-driven, and two-way (situation→model and model→story).

Common misconceptions

  • Models the numbers but not the action — draws 5 and 2 as if adding when the story takes away
  • Gives a bare number ('three') without saying what it means about the apples
  • Accepts an answer that contradicts the story (more apples after eating some) — doesn't check the model against the situation
  • Draws the objects decoratively without preserving the quantities in the story

Useful representations

  • Counters/cubes acted on to show joining or taking away
  • Simple drawings that show the action of the story
  • Dictated or written number sentence (5 − 2 = 3) tied to the story
  • Five-frame/ten-frame to structure the quantities

Teaching practices

  • Model the ACTION, not just the numbers: act the story out so 'ate 2' is a taking-away, and check the model shows what happened (CCSS MP4 map the situation)
  • Always read the answer back into the story ('three apples left'), not as a bare number — the interpret-in-context habit starts here
  • Ask 'does your model match my story?' to build sense-making from the outset (CDE: head off suspension of sense-making early)
  • Work both directions — story→objects and objects→story — so the model is understood as standing for the situation
  • Use fingers, counters, and drawings as the models, then dictate/write the matching number sentence

Activities to try

  1. 1

    Act the story on cubes, then read the answer back

    Why it works: The model must preserve the ACTION of the story (taking away), not just the numbers; and the answer is three apples still in the bowl, not the bare number 3.

    1. Listen to or watch a short story, e.g. 'I had 5 apples in a bowl and I ate 2 of them'
    2. Show the story with counters/cubes: start with five, then physically remove two to model the eating as a taking-away
    3. Optionally arrange the counters on a five-frame or ten-frame to structure and see the quantities clearly
    4. As the model settles on three, say or build the matching number sentence 5 − 2 = 3
    5. Answer the question 'three what?' by saying 'three apples left' and pointing to the three remaining in the model
  2. 2

    Work both directions: invent a story from a model

    Why it works: A model carries the whole situation — action and all — both ways: a story can be turned into a model, and a model can be read back as a story.

    1. Receive a model, e.g. a bowl that started at five and now holds three cubes
    2. Decide what could have happened and tell the story aloud: 'I ate two apples'
    3. Build or dictate the matching number sentence (5 − 2 = 3) for the story you invented
    4. Explain what each part of the model stands for in your story
  3. 3

    Puppet tells a story and sometimes gets it wrong

    Why it works: Telling a matching story and interpreting what the answer means is a two-way, sense-making conversation; an answer that contradicts the story (more apples after eating some) must be rejected.

    1. Listen to a puppet tell a story and ask you to show it with objects or a drawing
    2. Build the model and say what the answer means ('three apples left')
    3. Catch the puppet when it models the story wrongly, e.g. 'I had 5 apples and I ate 2, so now I have 7?' — explain why that can't be right
    4. Tell the puppet your own story for a model it shows you

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