Math // Addition & Subtraction

Mental addition and subtraction (age 6+)

Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations

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

Quick check

Can the learner work out '36 + 7' or '42 − 5' in their head — keeping the tens in place and only adjusting 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 36 + 7 = 43 using objects or mentally
  • Calculate 52 − 4 = 48 using a number line or mentally
  • Explain bridging through 10 when adding ones to a two-digit number

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
  • Adding and subtractingRequired

    Addition & Subtraction // Ages 5 to 6

    Adding ones to a two-digit number extends Y1 adding within 20

  • The two digits of a two-digit numberRequired

    Number Representation & Place Value // Ages 6 to 7

    Adding ones to two-digit numbers requires understanding tens and ones

You are here

Mental addition and subtraction (age 6+)

Ages 6 to 7 // Method

Leads to

1 topic
  • Adding two two-digit numbersRequired

    Addition & Subtraction // Ages 6 to 7

    Adding two two-digit numbers requires ability to add ones to a two-digit number

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

Children aged 6–7 add and subtract a two-digit number and ones by bridging through a multiple of ten: partition the ones to land on the decade, then add or subtract the remainder (36 + 7 → 36 + 4 = 40, + 3 = 43; 52 − 4 → 52 − 2 = 50, − 2 = 48). Core activities use a manipulable number line and base-ten blocks — with ten-frames and a hundred square as alternative views — so the new ten is seen forming and the tens digit updates for a visible reason, with mixed bridging and non-bridging items (43 + 5) so children decide when a boundary is actually crossed. Fluency practice, a static anchor image, and a narrate-your-method conversation are retained as complementary approaches with distinct purposes.

Common misconceptions

  • Adding the ones digits and ignoring the new ten (36 + 7 → 33 or '313').
  • Counting on/back in ones and slipping by one at the tens boundary.
  • Failing to change the tens digit when the ones cross a multiple of ten.
  • Bridging when it isn't needed, or not bridging when it is.
  • For subtraction, stopping at the decade (52 − 4 → 50) or miscounting past it.

Useful representations

  • Base-ten blocks (ones regrouping into a ten)
  • Empty number line with a jump to the decade then on
  • Ten-frames / partially filled frames showing the ones
  • Hundred square (move along a row, drop to next row at the boundary)
  • Part-whole splitting the ones (7 as 4 + 3)

Teaching practices

  • Teach bridging explicitly: partition the ones to land on the decade, then add/subtract the remainder.
  • Use base-ten blocks so ten ones visibly regroup into a new ten (and vice versa when subtracting).
  • Use the empty number line to show the two-part jump to and past the decade.
  • Mix bridging and non-bridging items so children decide when a boundary is crossed.
  • Connect the mental bridging steps to later column methods (regrouping).

Activities to try

  1. 1

    Bridge the decade on a number line with a base-ten mat

    Why it works: When adding makes the ones fill up to a whole ten, a new ten is formed and the tens digit increases by one; when subtracting takes away more ones than there are, a ten is broken into ones and the tens digit decreases by one (52 − 4 = 48). Partitioning the ones to reach the decade makes this regrouping explicit for both addition and subtraction.

    1. Work 36 + 7 by first jumping from 36 to the next decade (40), then completing the jump with the remaining ones (to 43).
    2. On a base-ten mat, watch four loose ones combine with the existing ones to make a whole new ten-stick as the jump reaches 40, so the tens digit change has a visible cause.
    3. Switch to subtraction mode for 52 − 4: jump back to the decade first (52 − 2 = 50), then take the remaining 2 to reach 48.
    4. Mix in non-bridging items such as 43 + 5 and decide for each item whether the ones cross a decade before choosing to bridge.
    5. Optionally view the same bridging in another representation: a ten-frame filling up to a complete ten of ones, or a hundred square where you move along a row and drop to the next row as you cross the decade, so the new ten is seen forming in more than one way.
  2. 2

    Fluency practice: fill in, draw the jump, choose the decade

    Why it works: Once the bridging strategy is understood, spaced and varied practice builds fluency in partitioning the ones and updating the tens digit accurately.

    1. Complete fill-in results such as 36 + 7 = ___ mentally or with a jotting.
    2. Draw the two-part bridging jump on an empty number line to show reaching the decade and then continuing.
    3. Choose which decade you bridge through for a given calculation, with decade options as the choices (for 36 + 7 the decade is 40).
    4. In a separate results question, identify the correct total, where a distractor such as 33 for 36 + 7 reflects the ignore-the-new-ten error (keeping the original tens digit).
    5. Include at least one non-bridging item so you practise recognising when no bridge is needed.
  3. 3

    Anchor image: a worked bridging number line

    Why it works: A clear worked picture shows what a bridging jump looks like and names the new ten, giving a reference model for the two-part method.

    1. Study a number line showing 36 → 40 → 43 with the regrouped ten labelled, revealing each step in turn.
    2. Describe in your own words why the jump stops at 40 before continuing to 43.

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/4

Math // Addition & Subtraction

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