Math // Addition & Subtraction

Fluent addition and subtraction

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

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

Quick check

Can the learner quickly recall facts like '9 + 7 = 16' and '16 − 7 = 9', and use those to help work out bigger sums like '90 + 70'?

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.
  • Rapidly recall 7 + 8 = 15 and 15 − 8 = 7
  • Use 6 + 4 = 10 to derive 60 + 40 = 100
  • Derive 35 + 5 = 40 from knowledge that 5 + 5 = 10

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

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Fluent addition and subtraction

Ages 6 to 7 // Method

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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

Two linked goals for ages 6–7: automatic recall of addition and subtraction facts to 20 (so 7+8 and 15−8 come without calculating) and derivation of related facts to 100 by scaling and using known bonds — 6+4=10 → 60+40=100 by scaling the bond to tens, and 5+5=10 → 35+5=40 by using the ones bond inside a larger number. Recall is built from a secure make-ten strategy plus spaced, untimed retrieval rather than speed drills; derivation is built by treating tens as units so a known bond reappears at a larger scale.

Common misconceptions

  • Recall not automatic — still counting on fingers every time for 7+8
  • Failing to scale the bond: knowing 6+4=10 but giving 60+40=10 or 70 or 700
  • Treating addition and subtraction as unrelated, so 15−8 is re-counted despite knowing 7+8=15
  • Applying a derived pattern blindly (e.g. 35+5=40 but then 35+50=40)

Useful representations

  • Ten-frame / double ten-frame (make-ten)
  • Fact-family triangle (shows the three related facts)
  • Bead string / Rekenrek
  • Base-ten ten-rods (scaling a bond to tens)
  • Number bonds part-whole diagram

Teaching practices

  • Build automaticity from strategy, then retrieval: secure make-ten within 20 first, then space low-stakes recall practice so facts move to memory (DfE: emphasis on practice aids fluency)
  • Teach fact families so + and − are learned together (7+8=15, 15−8=7, 15−7=8) and the inverse is available
  • Derive decade facts by scaling a known bond: 6+4=10 becomes 60+40=100 because six tens plus four tens is ten tens
  • Use the same visual at two scales (ten-frame counters vs ten-rods) to show 6+4 and 60+40 are one picture
  • Avoid timed pressure that induces anxiety; keep finger/strategy use welcome while retrieval matures

Activities to try

  1. 1

    Same bond, bigger units: scaling 6+4 to 60+40

    Why it works: Deriving a decade fact like 60+40 is scaling a known bond, not memorising a new fact: six tens plus four tens is ten tens = 100. A different move is using a bond inside a larger number — 35+5 uses the ones bond 5+5=10 to give 40. Which unit you add (ones vs tens) decides the result, so 35+5=40 and 35+50=85 are different.

    1. Complete 6+4 on a ten-frame by sliding four counters in to fill all ten; confirm this is a known, secure bond making 10.
    2. Switch the counters to tens: let each counter become a ten-rod (or restate each counter as 'one ten') so the same full frame now reads 100.
    3. Say aloud what changed: 'six tens plus four tens is ten tens, which is 100' — the gesture and picture are identical, only the unit changed.
    4. Repeat the tens-scaling with another known bond: 5+5=10 → 50+50=100 (five tens plus five tens is ten tens).
    5. Separately, derive 35+5 by using the ones bond 5+5=10: 30 + (5+5) = 40, so here the 5 is added as five ones, not scaled to tens.
  2. 2

    Fact-family triangle: one trio, both operations

    Why it works: Addition and subtraction are the same relationship between three numbers; knowing one fact hands you the inverse, so 15−8 need not be re-counted once 7+8=15 is known.

    1. Lay out the three numbers 7, 8 and 15 on a fact-family triangle (part–part–whole).
    2. Cover one corner and read off the fact it reveals: cover 15 to get 7+8=15 and 8+7=15; cover 7 to get 15−8=7; cover 8 to get 15−7=8.
    3. State explicitly: because 7+8=15, you already know 15−8 and 15−7 without re-counting.
    4. Build a second family (e.g. 6, 9, 15, giving 6+9=15, 9+6=15, 15−6=9, 15−9=6) and name all its related facts the same way.
  3. 3

    Spaced, untimed retrieval to build automatic recall

    Why it works: Automaticity grows from secure strategy plus spaced, untimed retrieval; a fact becomes 'known' when recalling it needs noticeably less effort on later encounters.

    1. Practise recalling facts to 20 in short, low-stakes sessions spread over days (e.g. 7+8, 15−8, 6+4, 9+4), rather than one long timed drill.
    2. Mix in derive-a-fact prompts such as '6+4=10, so 60+40=?' and '5+5=10, so 35+5=?', choosing or writing the answer.
    3. After each prompt, say which ones you just knew and which you had to work out.
    4. Keep finger and make-ten strategy use welcome; the aim is that repeated facts need less effort each time, not beating a clock.

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
Maths/Y2/AS/3

Math // Addition & Subtraction

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