Math // Addition & Subtraction

Adding two two-digit numbers

Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods

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

Quick check

Can the learner add or subtract two two-digit numbers — like '43 + 28' — using counters, a drawing, or working it out in their head?

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 34 + 27 using base-ten blocks or column addition
  • Calculate 63 − 28 using a number line or partitioning
  • Explain a strategy for adding or subtracting two two-digit numbers

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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Adding two two-digit numbers

Ages 6 to 7 // 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

Ages 6–7 add and subtract two two-digit numbers (e.g. 34+27, 63−28) by giving meaning to 'carrying' and 'borrowing' as fair exchange: ten ones can be swapped for one ten and vice versa. Learners partition into tens and ones, combine like with like, then compose a ten when the ones exceed nine, or decompose a ten when there are too few ones to subtract. Concrete base-ten work and pictorial jottings for the SAME calculation let the recording mirror the physical action, so regrouping is felt as a swap rather than rehearsed as a digit trick.

Common misconceptions

  • Failing to compose the ten: adding tens (50) and ones (11) and writing them side by side (511) or keeping 51
  • Smaller-from-larger subtraction: 63−28 done as 8−3 in the ones, answer 45
  • Counting every unit and losing the ten-structure (not treating a ten-rod as one ten)
  • Misaligning tens and ones when recording without a place-value mat

Useful representations

  • Base-ten blocks with a place-value mat (compose/decompose a ten)
  • Number line (jumps for adding; count-up for difference)
  • Part-whole / partitioning jottings (30+20 and 4+7)
  • Bar model (comparison and missing-part subtraction)
  • Hundred square

Teaching practices

  • Establish the exchange principle with base-ten blocks: ten ones can be fairly swapped for one ten, and one ten for ten ones (NRICH: exchange/unitising)
  • Partition both numbers into tens and ones, combine like with like, then compose/decompose a ten as needed (NCETM Spine 1.15/1.16)
  • Use a number line for subtraction as finding a difference (count up 28→63) as an alternative to take-away
  • Move concrete → pictorial → jotting for the SAME calculation so the recording mirrors the action
  • Ask the child to explain their strategy and why 34+27 is not 511 — the recombination is where meaning is tested

Activities to try

  1. 1

    Exchange on a place-value mat: compose and decompose a ten

    Why it works: Composing a ten (addition) and decomposing a ten (subtraction) are the same exchange run in opposite directions; 'carrying' and 'borrowing' are fair swaps between ones and tens, not separate digit tricks.

    1. Set out 34 + 27 on a place-value mat using base-ten blocks (or draggable on-screen tens and ones).
    2. Pile the ones together to find there are eleven; because that is ten or more, perform a 'make a ten' action that swaps ten loose ones for one ten-rod moved into the tens column, leaving one loose one, then read the answer as 61 (not 511, not 51).
    3. Set out 63 − 28; find there are not enough ones to give eight, so take a ten-rod and break it into ten loose ones, so 63 is now 50 and 13.
    4. Hand over eight ones (13−8=5) and subtract the tens (50−20=30) to reach 35.
    5. Record each physical step as a matching jotting: 30+20=50, 4+7=11, exchange → 61; and 63 = 50+13, 13−8=5, 50−20=30 → 35.
  2. 2

    Subtraction as finding a difference on a number line

    Why it works: Subtraction can be read as the difference between two numbers found by counting up, which offers a second route to the same answer and a self-check against the smaller-from-larger error.

    1. Place 28 and 63 on a number line.
    2. Count up from 28 to 63 in convenient jumps (e.g. 28 → 30 is 2, 30 → 60 is 30, 60 → 63 is 3).
    3. Total the jumps (2 + 30 + 3 = 35) and state 63 − 28 = 35.
    4. Compare this count-up answer with the take-away/exchange answer from the mat and confirm they agree.
    5. Optionally model the same subtraction with a bar model (whole 63, known part 28, missing part found as the difference) or on a hundred square, as further representations of the same difference.
  3. 3

    Annotated worked example and targeted consolidation

    Why it works: A clearly staged worked example makes the partition and exchange visible for reference, and a focused problem set surfaces whether the compose-a-ten and smaller-from-larger errors have really been overcome.

    1. Study a worked example of 34+27 and 63−28 where the partition and exchange step are revealed one stage at a time (e.g. reveal 4+7 becoming 'one ten and one'; reveal the tens as 30+20+10).
    2. Explain in your own words what happened at the exchange step before moving on.
    3. Then work a short set of two-digit ± two-digit items, including 34+27 and the decomposition of 63 into 50+13, choosing or writing the answer and giving the exchange reasoning.
    4. When a '511', '51' or '45' answer appears, say why it is wrong rather than only marking the correct one.

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/6

Math // Addition & Subtraction

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