Math // Addition & Subtraction

Missing number problems (age 7+)

Solve addition and subtraction problems including missing-number problems, using number facts, place value, and more complex methods

Ages
7 to 8
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

Can the learner work out sums with a hidden number — like '? − 38 = 24' or '53 + ? = 91' — by thinking carefully about what the equation is asking?

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 missing-number problem such as 245 + ? = 380
  • Choose an appropriate method (mental, written, or combination) based on the numbers
  • Solve multi-step problems combining addition and subtraction of three-digit numbers

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

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Missing number problems (age 7+)

Ages 7 to 8 // Method

Leads to

2 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

Missing-number problems (e.g. 245 + □ = 380) move children from 'compute the answer' to reasoning about an equation's structure: what is unknown, where it sits, and how an inverse operation or a count-on finds it. The equals sign is read relationally ('is the same as / balances'), not as 'the answer comes next'. Children choose a method from the numbers — count-on for a missing addend, inverse to undo, or a written method — check by substituting back, and increasingly combine steps with three-digit numbers.

Common misconceptions

  • Operator view of '=': for 245 + ? = 380 computing 245 + 380 ('the answer goes after the equals')
  • Not using the inverse — guessing/trial instead of 380 − 245 or counting on
  • Position confusion: treating ? − 120 = 250 as 250 − 120
  • Choosing subtraction/addition by habit rather than by where the unknown sits

Useful representations

  • Bar model / part-whole (unknown part vs unknown whole)
  • Balance scale image (both sides equal)
  • Number line (count-on to find a difference)
  • Equation with a box for the unknown
  • Base-ten / columns for the calculation

Teaching practices

  • Establish the equals sign as 'is the same as / balances', using balance and bar-model images, so a missing addend isn't read as 'add the two numbers shown'
  • Teach missing addend as either count-on (245 up to 380) or inverse (380 − 245); missing minuend/subtrahend via the inverse
  • Represent with a bar model so the unknown's position (part vs whole) dictates the operation
  • Choose method by the numbers — near numbers invite counting up, others a written method
  • Check by substituting the found number back into the original equation

Activities to try

  1. 1

    Balance the equation: find the missing number

    Why it works: The equals sign means the two sides are the same value; the position of the unknown (part vs whole) decides whether you add or subtract, and you can verify an answer by putting it back.

    1. Work with a balance or bar model showing 245 and an empty box on one side and 380 on the other, with the beam tilted.
    2. Try putting 380 in the box and observe that the side becomes far too heavy (245 + 380 = 625) — much more than 380.
    3. Adjust the box until the two sides match, finding 135, and say in words why 135 balances it.
    4. Use a number-line route for the same problem: start at 245 and count on to 380, noticing the jump is 135.
    5. Repeat with the unknown in other positions, e.g. □ − 120 = 250 (answer 370) and 500 − □ = 340 (answer 160), deciding each time whether the missing quantity is a part or the whole.
  2. 2

    True-or-false equations and choosing a strategy

    Why it works: Equations assert that both sides are equal and can be judged true or false; the choice between counting on and using the inverse depends on where the unknown sits and on how near the numbers are.

    1. Sort equations as true or false — e.g. '245 + 135 = 380' (true) and '245 + 380 = 380' (false, since 245 + 380 = 625) — to challenge the 'answer-next' habit.
    2. For each of several missing-number problems with the box in different positions, say whether you would count on or use the inverse, and explain what about the numbers made you choose.
    3. Solve and then justify: in 245 + □ = 380 the box is a part; in □ − 120 = 250 the box is the whole.
    4. Check each solution by substitution before moving on.
  3. 3

    Static balance/bar model as a reference

    Why it works: A clear diagram of what balances and of part-vs-whole gives a stable mental image to reason from when identifying the unknown.

    1. Study a labelled balance or part-whole bar diagram that shows which quantity is a part and which is the whole.
    2. Tap or point to each side to reveal its total and whether the two sides match.
    3. Use the diagram as a reference while solving problems, naming part and whole before choosing an operation.

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
Ma/KS2/Y3/AS/4

Math // Addition & Subtraction

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