Math // Addition & Subtraction

Mentally adding tens to 3-digit numbers

Mentally add and subtract a three-digit number and tens

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

Quick check

Can the learner quickly work out '354 + 40' or '628 − 30' in their head — knowing that only the tens digit changes?

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 + 40 mentally
  • Calculate 462 − 30 mentally
  • Explain that only the tens digit changes (unless bridging through a hundred)

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
  • The three digits of a three-digit numberRequired

    Number Representation & Place Value // Ages 7 to 8

    Mental add/sub of tens to three-digit numbers requires three-digit PV

  • 10 or 100 More or LessRequired

    Number Representation & Place Value // Ages 7 to 8

    Extends finding 10 more/less to adding arbitrary multiples of 10

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Mentally adding tens to 3-digit numbers

Ages 7 to 8 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Addition & Subtraction

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

Mentally adding or subtracting multiples of ten to a three-digit number extends the '10 more/less' idea one column up: usually only the tens digit changes, UNLESS the calculation bridges a hundred, in which case the hundreds digit also changes. Children anchor the hundreds and ones, reuse decade facts in the tens (e.g. 7 tens ± some tens), and use make-ten at the scale of tens when crossing a hundred. Teach with a place-value chart and a number line marked in tens around the nearest hundred, deliberately contrasting non-bridging and bridging cases so the exception is visible.

Common misconceptions

  • Changing the ones digit instead of the tens (345+40 given as 349)
  • Failing to bridge a hundred: 372+40 given as 3(11)2 or keeping the tens at 11
  • Smaller-from-larger in the tens when subtracting bridges down (a hundred not decomposed)
  • Believing 'only the tens digit ever changes', so bridging-a-hundred cases are mishandled

Useful representations

  • Place-value / Gattegno chart (tens row moves; bridging cascades to hundreds)
  • Number line marked in tens, around the nearest hundred
  • Base-ten blocks (add/remove ten-rods, exchange at the hundred)
  • Hundred-square rows (moving down = +10)
  • Partitioning jotting (372 = 370 + 2)

Teaching practices

  • Anchor the hundreds and ones; operate only on the tens — 345+40 keeps '3_5' and works 40+40 in the tens
  • Reuse decade bonds and the make-ten idea at the scale of tens for bridging a hundred (372+40 = 372+28+12... via 380/400)
  • Contrast a non-bridging case (345+40) with a bridging case (372+40) so the child sees when the hundreds digit moves
  • Build from '10 or 100 more/less' — adding 40 is four steps of ten
  • Ask the child to predict which digits change before calculating (DfE evidence)

Activities to try

  1. 1

    Contrast a non-bridging and a bridging case on a place-value chart

    Why it works: Adding or subtracting tens changes only the tens digit UNLESS the running total of tens crosses a hundred, in which case a hundred is composed (or decomposed) and the hundreds digit changes too — the same kind of exception children already met when crossing a ten.

    1. Start with 345 on a place-value chart and add 40 mentally: before calculating, predict which digits will change and which will stay the same.
    2. Confirm that only the tens change (4 tens + 4 tens = 8 tens), giving 385, with the hundreds (3) and ones (5) unchanged.
    3. Now try 372 + 40, again predicting first: notice the tens reach eleven, so a hundred is composed and the hundreds digit ticks up — resolve to 412 (reach 400 by adding 28, then add the remaining 12).
    4. Say aloud how 372 + 40 is like 7 tens + 4 tens = 11 tens, and point to where the extra hundred comes from.
  2. 2

    Bridge a hundred downwards when subtracting

    Why it works: Subtracting tens can bridge a hundred downwards, decomposing a hundred into ten tens; the hundreds digit then decreases, and the result must be smaller than the start.

    1. Work out 431 − 50 mentally, first predicting whether the hundreds digit will change.
    2. Check the size: subtracting 50 should make the answer exactly 50 less than 431, which takes it below 400. Is your answer below 400, and does adding 50 back give 431?
    3. Use a number line marked in tens to show the jump crosses below 400 (431 − 31 = 400, then − 19 more = 381).
    4. If using base-ten blocks, decompose one hundred into ten tens before removing five tens.
  3. 3

    Predict and sort: will the hundreds digit change?

    Why it works: Deciding in advance whether a calculation bridges a hundred builds the discriminating judgement that prevents the over-generalisation 'only the tens digit ever changes'.

    1. For a mixed set of items (e.g. 345 + 40, 372 + 40, 462 − 30, 431 − 50), predict for each whether the hundreds digit will change before calculating.
    2. Sort the items into 'bridges a hundred' and 'does not bridge a hundred'.
    3. Calculate each mentally, then check your sort against the answers (385, 412, 432, 381).
    4. Explain in your own words the rule: only the tens change unless the calculation crosses a hundred.

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/1b

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