Math // Addition & Subtraction

Unknown in Addition & Subtraction

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

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

Quick check

If the learner sees '? + 6 = 14' or '9 − ? = 4' written on paper, can they figure out what number goes in the gap?

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 8 + ? = 11 and write 3
  • Solve 5 = □ − 3 and write 8
  • Solve 6 + 6 = □ and write 12

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

Unknown in Addition & Subtraction

Ages 6 to 7 // Method

Leads to

1 topic
  • Connecting maths to real lifeHelpful

    Mathematical Thinking // Ages 6 to 7

    Representing unknown-number problems with equations exercises modelling at age 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

Help 6–7 year olds find the unknown whole number in addition/subtraction equations where the unknown appears in any position (8 + ? = 11; 5 = □ − 3; 6 + 6 = □). The target is a flexible method built on reading '=' as 'both sides balance' and choosing the inverse move, not an 'add the two numbers I can see' habit. Vary the unknown's position deliberately (result, change, start, answer-on-left) and insist on checking by substituting the answer back.

Common misconceptions

  • Adding the two visible numbers regardless of the box's position (8 + ? = 11 → 19).
  • Reading answer-left forms as backwards (5 = □ − 3 → writes 2, i.e. 5 − 3).
  • Always subtracting or always adding by keyword rather than by the unknown's role.
  • Not checking the solution by putting it back into the equation.
  • Treating '=' as 'work out the total' so a box before '=' is confusing.

Useful representations

  • Bar model / part-whole diagram with the unknown segment shaded
  • Pan balance with an unknown mass on one side
  • Empty number line for count-on / inverse jumps
  • Fact-family triangle to pick the needed operation
  • Equation cards with the box in varied positions

Teaching practices

  • Systematically vary the unknown position (a+b=□, a+□=c, □+b=c, and answer-left forms) so pupils build a flexible method, not a keyword habit.
  • Represent each equation on a bar / part-whole model first to see which quantity is unknown before calculating.
  • Teach solving-by-inverse explicitly: convert □ + 9 = 14 into 14 − 9.
  • Insist on substituting the answer back to check the equation balances.
  • Use non-standard forms (5 = □ − 3) early to defeat the left-to-right 'answer-comes-next' reading.

Activities to try

  1. 1

    Balance the unknown with counters

    Why it works: The box holds whatever value makes the two sides equal; '=' means balance, so an answer-on-left form like 5 = □ − 3 is not 'backwards' — it is the same balancing task. One balancing method works for every position.

    1. Set out an equation with a box, e.g. 5 = □ − 3, on a two-pan balance or bar model where one side already shows 5.
    2. Add or remove counters in the box until both sides match: too few and the box side is too light, too many and it tips down.
    3. State the value that makes both sides balance (for 5 = □ − 3 the box must hold 8, because □ − 3 has to equal 5).
    4. Repeat with the unknown in every position: 8 + ? = 11, □ + 6 = 12, 6 + 6 = □.
    5. Check each solved equation by putting the found number back in and confirming both sides match.
  2. 2

    Solve by the inverse, then check

    Why it works: Once you know which quantity is the whole and which is a part, you can go straight to the answer with the inverse operation instead of slow trial-and-error.

    1. Given □ + 9 = 14, convert it to the inverse: 14 − 9, and compute □ = 5.
    2. Given 8 + ? = 11, use 11 − 8 = 3 rather than guessing and testing values.
    3. Use a fact-family triangle (whole 14; parts 9 and 5) to pick the operation needed for the unknown's position.
    4. Substitute the answer back and confirm the sentence is true.
    5. Practise a mixed set covering result-unknown, change-unknown, start-unknown and answer-left forms.
  3. 3

    Explain your move (strategy talk)

    Why it works: Articulating the reasoning surfaces whether a child is using a keyword/positional habit or genuinely reasoning from which quantity is missing.

    1. Solve a varied-position equation aloud, e.g. 5 = □ − 3, then explain how you decided what to do.
    2. Answer probes: 'Which of these could you check with an addition, and how?' and 'What if it were □ − 3 = 5 instead of 5 = □ − 3 — would the answer change?'
    3. Show how you'd check that your answer to 8 + ? = 11 makes the sentence true.

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.8

Math // Addition & Subtraction

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