Math // Addition & Subtraction

Adding Three Small Numbers

Add three one-digit numbers using strategies including looking for pairs that make 10

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

Quick check

If the learner needs to add 4 + 6 + 8, can they spot that 4 and 6 make 10 first, then add 8 to get 18 — rather than just adding in order from left to right?

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 5 + 7 + 3 by first adding 7 + 3 = 10, then 5 + 10 = 15
  • Add any three single-digit numbers correctly
  • Identify useful pairs within three addends to make the calculation easier

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
  • Grouping numbers to addRequired

    Addition & Subtraction // Ages 6 to 7

    Adding three numbers uses the associative property to group pairs

  • Number bonds to 9Helpful

    Addition & Subtraction // Ages 4 to 6

    Looking for pairs that make 10 benefits from knowing number bonds to 10

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Adding Three Small Numbers

Ages 6 to 7 // Method

Leads to

1 topic
  • Adding numbersRequired

    Addition & Subtraction // Ages 7 to 8

    Adding four two-digit numbers extends adding three one-digit numbers

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

Teaches ages 6–7 to add three one-digit numbers efficiently by scanning for a pair that makes ten (or a double), adding that pair first, then adding on the third number — e.g. 5 + 7 + 3 → 7 + 3 = 10, then 5 + 10 = 15. The objective is the strategic habit of scanning and reordering (supported by commutativity/associativity and fluent bonds to 10), not merely getting a correct total. Includes a hands-on manipulative core, fluency/strategy-choice practice, a narration conversation, and a worked anchor, with each scaffold's role made explicit. Interactive and efficacy details are proposed, not validated.

Common misconceptions

  • Always adding left-to-right and never scanning for a make-ten pair.
  • Not recognising a pair that makes ten because bonds to 10 aren't fluent.
  • Losing or double-counting the third addend after making ten.
  • Thinking the numbers must be added in the written order.
  • Miscounting when crossing ten while adding the third number by ones.

Useful representations

  • Three movable number tiles that can be reordered
  • Ten-frame that fills to ten from the chosen pair, then takes the third
  • Empty number line with a jump to ten then on
  • Bar/part-whole with three parts
  • Bonds-to-10 pairs chart as a scanning aid

Teaching practices

  • Teach an explicit 'scan for a pair that makes ten (or a double)' habit before adding.
  • Rehearse bonds to 10 to fluency so the make-ten pair is spotted instantly.
  • Use rearrangeable counters/tiles so children physically move the useful pair together.
  • Contrast a make-ten route with a left-to-right route on the same triple to show the efficiency gain.
  • Keep sums within 20 initially so the third addition crosses ten at most once.

Activities to try

  1. 1

    Drag a pair to make ten on the ten-frame

    Why it works: Spotting the pair that makes ten (or a double) first turns an awkward three-number sum into an easier one: a make-ten pair leaves 'ten and a bit', and a double gives a known fact to add on to. The written order is not fixed, you are free to reorder, and any ordering still gives the same total.

    1. Start with three movable number tiles above a ten-frame, e.g. 5, 7 and 3.
    2. Scan the three tiles and decide which two you would add first: a pair that makes exactly ten, or, if there is no such pair, a double.
    3. Drag two tiles together; if they make ten the frame fills completely and leaves a simpler 'ten and a bit' (here 5 + 10).
    4. Deliberately try a less useful pairing first (e.g. 5 + 7 = 12) and notice the frame does not land on a clean ten, then find the better pair — it still gives a correct total, just by a slower route.
    5. Repeat with triples that reward a make-ten pair, and with at least one triple that rewards a double instead.
  2. 2

    Which pair makes it easiest? — fluency and strategy choice

    Why it works: Fluent recall of bonds to 10 lets you spot the useful pair quickly; deliberately choosing a make-ten pair can make the addition quicker and less error-prone than always adding left-to-right.

    1. Given a triple such as 5 + 7 + 3, choose which two numbers you would add first and say why.
    2. Complete fill-in-the-blank totals for a set of triples, each containing a make-ten pair that is not the first two written.
    3. Do a short, light timed set of spotting make-ten pairs to build quick recall of bonds to 10.
    4. For each item, state the pair chosen and the leftover number before giving the total.
  3. 3

    Narrate the pair you chose

    Why it works: Explaining the chosen pair makes the scanning strategy explicit and surfaces whether the child is truly scanning or just adding in written order.

    1. A tutor poses triples such as 5 + 7 + 3, 8 + 2 + 6 and 4 + 9 + 1.
    2. For each, work out the total and say which two numbers you added first and why that choice helps.
    3. Answer follow-ups: 'Is there a pair here that makes exactly ten?', 'Would you get the same total in a different order?', 'For 4 + 9 + 1, which pair makes ten and which number is left to add on?'

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
1.OA.2
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y2/AS/7

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