Math // Addition & Subtraction

Finding a missing number in addition

Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)

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

Quick check

Can the learner see that '10 − 8 = ?' is the same as asking 'what do I add to 8 to reach 10?' — so they can use their adding knowledge to help with subtraction?

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 10 − 8 by thinking 'what do I add to 8 to make 10?'
  • Explain that subtraction can be thought of as a missing-addend problem
  • Use known addition facts to solve related subtraction problems

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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Finding a missing number in addition

Ages 6 to 7 // Concept

Leads to

1 topic

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 understand subtraction as an unknown-addend problem: 12 − 9 = ? asks the same question as 9 + ? = 12 — find the missing PART of a known whole. Anchor the equivalence on a part-whole model, teach counting up from the subtrahend when the numbers are close, and repeatedly pair each subtraction with its addition twin. A linked part-whole/number-line display can make the 'same gap, two routes' insight concrete; dialogue draws out the justification; matching and missing-number tasks consolidate; a static part-whole picture (with a double ten-frame and fact-family triangle as further representations) anchors both equations against one diagram.

Common misconceptions

  • Believing subtraction can only mean 'take away / count back', so refusing to count up.
  • Not seeing 8 + ? = 10 and 10 − 8 = ? as the same question.
  • Counting back inefficiently for close numbers (12−11 counted back eleven steps) and making errors.
  • Confusing which quantity is the whole and which is a part in the part-whole model.
  • Treating the answer to 8 + ? = 10 as 10 (writing the whole) rather than the missing part.

Useful representations

  • Part-whole (cherry) diagram with the missing part as the unknown
  • Bar model: total bar with one part shaded and the gap to find
  • Empty number line showing a count-on jump from subtrahend to minuend
  • Double ten-frame with one frame filled and the gap to ten visible
  • Fact-family triangle linking the whole and its two parts

Teaching practices

  • Anchor on the part-whole model: subtraction reveals a missing PART when the whole and one part are known.
  • Teach counting-up (shopkeeper's method) explicitly as the efficient strategy when subtrahend and minuend are close.
  • Pair each subtraction with its unknown-addend twin (13 − 9 = ? ↔ 9 + ? = 13) so the equivalence is repeatedly seen.
  • Use missing-number equations in varied positions to force the additive reading rather than a take-away action.
  • Delay pure take-away drilling; contrast 'how many are left' with 'how many more to reach' so difference/missing-part meanings are established.

Activities to try

  1. 1

    Two routes, one gap: linked part-whole and number line

    Why it works: A subtraction and its unknown-addend twin ask the same question — the missing part of a whole — and counting up from the subtrahend is often the shortcut, especially when the numbers are close.

    1. Look at a part-whole bar with whole 10 and known part 8, and a number line beside it.
    2. First try to count BACK from the whole by the known part (back 8 from 10) to find the missing part; notice this is fiddly for some pairs.
    3. Then start at the known part (8) and hop UP to the whole (8→9→10), counting the jumps to find the gap.
    4. See both routes highlight the SAME gap of 2, and read the two printed sentences 10 − 8 = 2 and 8 + 2 = 10 together.
    5. Repeat with a close-number case such as 12 − 9: count back nine steps, then instead start at 9 and hop up 9→10→11→12 (three easy jumps), and see 12 − 9 = 3 printed above 9 + 3 = 12.
  2. 2

    Explain why counting up works

    Why it works: Being able to justify the equivalence — not just produce the number — shows the child reads subtraction additively rather than only as take-away.

    1. Solve a close-number subtraction such as 12 − 9 using whatever method you choose.
    2. Answer aloud: 'You could take 9 away — but is there a quicker way to get from 9 up to 12?'
    3. State the matching addition sentence (9 + ? = 12) for the subtraction.
    4. Explain in your own words why 12 − 9 and 9 + ? = 12 are the same question.
  3. 3

    Match, fill, and choose the quicker route

    Why it works: Consolidate the pairing of subtraction with its addition twin and the strategic choice of counting up when numbers are close.

    1. Match each subtraction to its unknown-addend twin, e.g. 13 − 9 ↔ 9 + □ = 13.
    2. Fill in the missing addend: 9 + □ = 13 (answer 4), then write the matching subtraction 13 − 9 = 4.
    3. Decide which is quicker for 12 − 9 — counting up or counting back — and give a reason.
    4. Given a known fact such as 8 + 5 = 13, write a subtraction you can now answer straight away.

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.4

Math // Addition & Subtraction

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