Math // Addition & Subtraction

Mental addition and subtraction (age 7+)

Mentally add and subtract a three-digit number and ones

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

Quick check

Can the learner work out '436 + 7' or '521 − 8' in their head — keeping the hundreds and tens unchanged while adjusting just the ones?

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.
  • Calculate 345 + 7 mentally
  • Calculate 462 − 5 mentally
  • Explain that only the ones digit changes (unless bridging through a ten)

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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Mental addition and subtraction (age 7+)

Ages 7 to 8 // Method

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

Year 3 pupils mentally add or subtract ones to a three-digit number. The core insight: only the ones digit changes UNLESS the calculation bridges a ten, in which case the tens digit (and possibly the hundreds) also changes. Children anchor the hundreds and tens as a stable 'larger part' and operate only on the ones, reusing secure within-20 make-ten bonds for the bridging cases. Contrasting a non-bridging case directly with a bridging case is what refines the rough rule 'only the ones change' into the accurate 'only the ones change unless we cross a ten'.

Common misconceptions

  • Changing the wrong digit (adding the ones to the tens or hundreds digit)
  • Failing to bridge: 345+7 given as 342 or 3412 (keeps 2, drops the extra ten) instead of 352
  • Smaller-from-larger on the ones when subtracting bridges down (462−5 given as 463: does 5−2)
  • Believing 'only the ones digit ever changes', so bridging cases are mishandled

Useful representations

  • Place-value chart / Gattegno chart (only the ones row moves; bridging cascades)
  • Number line segment around the nearest ten
  • Base-ten blocks (add/remove ones, exchange at the ten)
  • Bead string near a decade
  • Partitioning jotting (345 = 340 + 5)

Teaching practices

  • Anchor the hundreds/tens and operate only on the ones — 345+7 keeps '34_' fixed and works 5+7
  • Reuse within-20 make-ten bonds for the bridging cases (345+7 = 345+5+2 = 350+2)
  • Contrast a non-bridging case (345+3) with a bridging case (345+7) so the child notices when more than the ones digit changes
  • Use a marked number line / hundred-square segment to show the small jump near a decade
  • Ask the child to predict which digits will change before calculating (DfE evidence: explain that only the ones digit changes unless bridging)

Activities to try

  1. 1

    Anchor the larger part, spin only the ones

    Why it works: A change to the ones stays local: the hundreds and tens act as an untouched anchor, so for a non-bridging case only the ones digit moves.

    1. Show 345 on a place-value chart (e.g. a Gattegno chart) with the hundreds, tens and ones rows visible.
    2. Work 345 + 3: change only the ones from 5 to 8, keeping '34_' fixed, and say aloud which digits stayed the same and which changed.
    3. Name the value of each digit before adding (the 3 you add is three ones, so it joins the ones), to guard against adding to the wrong column.
    4. Predict, before calculating, which digits will change.
  2. 2

    Bridge a ten with make-ten bonds

    Why it works: When a calculation crosses a ten, the ones 'fill up' to the next decade and the tens digit also changes; make-ten bonds the child already knows handle the split.

    1. Work 345 + 7 on a marked number line (or a hundred-square segment near the decade): jump +5 to land on 350, then +2 more to reach 352.
    2. Connect this to the within-20 bond already known: split 7 into 5 + 2, so 345 + 7 = 345 + 5 + 2.
    3. Notice the moment the tens digit changes (4 becomes 5 as you cross 350) — this is the exception to 'only the ones change'.
    4. Optionally watch a place-value chart where the ones roll past 9 and cascade a carry of +1 into the tens, with a number-line toggle showing the same jump onto 350 then stepping to 352.
  3. 3

    Contrast non-bridging and bridging side by side

    Why it works: Directly comparing a case where only the ones change with one that bridges turns the rough rule into the accurate rule and exposes the 'only the ones ever change' overgeneralisation.

    1. Place 345 + 3 and 345 + 7 next to each other and predict, for each, which digits will change before calculating.
    2. Calculate both, then state which digits actually changed and why they differed.
    3. Articulate the refined rule: 'only the ones change, unless we cross a ten'.
    4. Try a mixed set of items sorted by whether they bridge, predicting each time.

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/1a

Math // Addition & Subtraction

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