Math // Addition & Subtraction

Early Word Problems

Solve one-step word problems involving addition and subtraction to 20, including missing-number problems

Ages
5 to 7
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
2 codes

Quick check

If you say 'I had some sweets, ate 5, and now have 9 left — how many did I start with?', can the learner figure out the missing number?

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 'I have 12 sweets and eat 4, how many left?'
  • Solve missing number: 7 = [ ] – 9
  • Solve problems using concrete objects and pictorial representations

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
  • Adding and subtractingRequired

    Addition & Subtraction // Ages 5 to 6

    Word problems to 20 require the procedural ability to add/subtract to 20

  • Addition and subtraction word problemsHelpful

    Addition & Subtraction // Ages 4 to 6

    Word problems to 20 extend from word problems within 10 — same problem structures at a higher range

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Early Word Problems

Ages 5 to 7 // Method

Leads to

3 topics

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 5-7 (Y1/early Y2): solve one-step word problems involving addition and subtraction to 20, including missing-number problems such as 7 = ? − 9. The core objective is modelling the situation (acting out, drawing, bar/part-whole models) rather than keyword-matching, and crucially handling problems where the unknown sits in the start, change or result position — not only the answer slot. Bar/part-whole models make the unknown visible so children can reason to it using the inverse or a known bond.

Common misconceptions

  • Keyword-matching (fails on missing-number and compare problems).
  • Assuming the unknown is always the result, so start- and change-unknown problems stump them.
  • Rejecting missing-number forms because = is read as 'answer here'.
  • Combining the two given numbers regardless of the structure (e.g. adding in a start-unknown problem that needs subtraction).
  • Not using the inverse/known bond to find the unknown, instead guessing.

Useful representations

  • Bar/tape model showing known parts and an unknown
  • Part-part-whole model with the unknown in any slot
  • Objects/drawings acted on to match the story
  • Empty number line for counting on to find a difference/unknown
  • Equations with a box/letter for the unknown in varied positions

Teaching practices

  • Keep teaching modelling of the situation (act-out, drawing, bar/part-whole) over keyword strategies, extending to numbers to 20.
  • Introduce the unknown in all positions (result, change, start) and use part-whole/bar models to make the unknown visible so children can reason to it.
  • Connect missing-number problems to the inverse relationship and to known bonds (7 = ? − 9 → ? = 16 via 7 + 9).
  • Have children write the equation that matches the situation, placing the unknown where it belongs (not always after =).
  • Progress difficulty by problem structure, not just larger numbers, and discuss why a chosen model fits the story.

Activities to try

  1. 1

    Story-to-bar-model builder

    Why it works: A problem where the unknown is the START or the CHANGE, not the answer, is not impossible: the bar model shows exactly where the mystery sits. If the unknown is the whole, combining the known parts finds it. If the unknown is a part, taking the known part away from the whole (or counting on from it) finds it. Children learn to model any structure rather than hope a keyword tells them what to do.

    1. Listen to or read a one-step problem with numbers to 20, e.g. 'I had some sweets, ate 9, and 7 are left.'
    2. Drag the quantities you know into a bar or part-whole frame — for this story, split a whole into a '9 eaten' part and a '7 left' part.
    3. Mark where the unknown sits in the model (here the WHOLE — the number you started with — is the mystery).
    4. Act on the model to find the unknown — combine the two parts to fill the whole (7 + 9 = 16), or count on along a number line.
    5. Repeat with problems that rotate the unknown through result, change and start positions, and with pure missing-number equations like 7 = ? − 9.
  2. 2

    Hands-on modelling with counters, drawings and paper bars

    Why it works: Modelling the situation with concrete materials — rather than matching keywords — reveals the correct operation even when the unknown is not the result.

    1. Act out or draw the story with physical counters before choosing any operation.
    2. Lay out a paper tape/bar strip and partition it into known parts and an unknown part to match the story.
    3. Use an empty number line to count on and find a difference or an unknown.
    4. Say aloud what you know, what you are trying to find, and why the operation you chose fits the story.
  3. 3

    Coaching dialogue: 'What do we know, what are we finding?'

    Why it works: Reasoning aloud about knowns and the unknown can develop the modelling and inverse reasoning needed for harder problem structures.

    1. Respond to a coach who asks you to name what is known and what is unknown in a problem.
    2. Justify which operation you will use and where the unknown sits, especially for start-unknown and missing-number problems.
    3. Talk through 7 = ? − 9: identify that you need a starting number which, after removing 9, leaves 7.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.OA.1
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y1/AS/4

Math // Addition & Subtraction

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