Math // Addition & Subtraction

Adding and subtracting tens mentally

Add and subtract a two-digit number and tens 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 quickly work out '54 + 30' or '78 − 20' 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 45 + 30 = 75 mentally
  • Calculate 82 − 40 = 42 mentally
  • Explain that only the tens digit changes when adding/subtracting tens

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 two digits of a two-digit numberRequired

    Number Representation & Place Value // Ages 6 to 7

    Adding/subtracting tens requires place value understanding

  • 10 More or 10 LessRequired

    Number Representation & Place Value // Ages 6 to 7

    Adding/subtracting tens builds on mentally finding 10 more or less

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Adding and subtracting tens mentally

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 tens 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

For ages 6–7: add and subtract a two-digit number and a multiple of ten (e.g. 45 + 30, 82 − 40) mentally and with concrete/pictorial support, building from '10 more/10 less'. The key insight is that adding or subtracting whole tens leaves the ones digit fixed and, while the answer stays between 0 and 99, changes only the tens digit (crossing 100, e.g. 85 + 30 = 115, also changes the hundreds). The classic error is treating the added tens as ones (45 + 30 → 48) or changing both digits. A deliberate contrast with adding ones (45 + 3) keeps the two procedures distinct.

Common misconceptions

  • Changing the ones digit as well as the tens when adding tens.
  • Adding the tens digit to the ones (45 + 30 → 48 or 75... e.g. treating 30 as 3 ones).
  • Miscounting the number of tens jumps.
  • Confusing add-tens with add-ones procedures.
  • For subtraction, borrowing into the ones unnecessarily.

Useful representations

  • Base-ten ten-sticks added/removed beside a fixed ones pile
  • Hundred square with vertical jumps
  • Empty number line with jumps of ten
  • Place-value (Gattegno) chart sliding the tens
  • Arrow cards separating tens and ones

Teaching practices

  • Build from '10 more/10 less' to adding/subtracting several tens at once.
  • Use base-ten blocks: add or remove ten-sticks while the ones pile stays untouched.
  • Use a hundred square with vertical moves (down = +10, up = −10).
  • Draw attention to the invariant ones digit as the key check.
  • Contrast with adding ones (which changes the ones) so children don't confuse the two.

Activities to try

  1. 1

    Add and remove tens while the ones stay put

    Why it works: Adding or subtracting a multiple of ten moves only the tens; the ones digit is invariant. Adding ones is a different move that changes the ones instead.

    1. Start with a base-ten representation of 45: four ten-sticks and five single ones, with the numeral 45 shown alongside.
    2. Before acting, predict the answer to 45 + 30 and say which digit you think will change.
    3. Add three more ten-sticks one at a time for +30, saying the running total aloud: 45 → 55 → 65 → 75, and notice that the five single ones never move.
    4. Switch to subtraction: start from 82 (eight ten-sticks, two ones) and remove four ten-sticks for 82 − 40, reaching 42, with the two ones untouched.
    5. Repeat the same moves on a hundred square numbered with 1 at the top: for +30 move three rows straight down (45 → 55 → 65 → 75); for −40 move four rows straight up (82 → 72 → 62 → 52 → 42), watching that the ones column stays the same.
  2. 2

    Fluency practice: one-step add/subtract tens

    Why it works: The one-step mental move for adding/subtracting tens can become more automatic, while deliberate contrast with adding ones keeps the two procedures from merging.

    1. Complete fill-in items such as 45 + 30 = ___ and 82 − 40 = ___, aiming to answer in one step.
    2. Answer 'which digit changes?' questions for an add-tens item, resisting a distractor answer that alters the ones digit.
    3. Work through a short sequence of +10 steps (e.g. 45, 55, 65, 75) and then a −10 sequence, saying each total.
    4. Mix in an occasional add-ones item (45 + 3) so you have to decide which digit changes each time.
  3. 3

    Explain and predict the invariant digit

    Why it works: Being able to articulate why the ones stay fixed (because whole tens are being added) demonstrates secure place-value reasoning beyond getting the right number.

    1. Work out 45 + 30; 82 − 40; and 45 + 3 mentally and state which digit changed each time.
    2. Explain why only the tens change when adding or subtracting tens, and why the ones change for 45 + 3.
    3. Predict the ones digit of 82 − 40 before calculating, then check.
    4. Show 45 + 30 on a hundred square and describe which way you move and why.

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/5

Math // Addition & Subtraction

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