Math // Addition & Subtraction

Number bonds to 9

Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)

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

Quick check

If the learner has 6 strawberries and needs 10 for a recipe, can they quickly tell you they need 4 more — without counting all the way up from 1?

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.
  • Given 7, respond '3' to make 10
  • Use a ten-frame to find the complement to 10
  • Record pairs that make 10 as equations (e.g. 6 + 4 = 10)

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

1 topic
  • Numbers up to 10 into pairsRequired

    Addition & Subtraction // Ages 4 to 6

    Making 10 is a specific application of decomposing numbers into pairs

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Number bonds to 9

Ages 4 to 6 // Method

Leads to

5 topics
  • Number bondsRequired

    Addition & Subtraction // Ages 5 to 6

    Number bonds within 20 builds on knowing bonds to 10

  • Addition and subtraction within 20Required

    Addition & Subtraction // Ages 6 to 7

    Making-ten strategy requires knowing bonds to 10

  • Fluent adding and subtracting within 10Required

    Addition & Subtraction // Ages 6 to 7

    Fluency within 10 requires knowing number bonds to 10

  • Showing Your WorkingHelpful

    Mathematical Thinking // Ages 5 to 6

    Explaining how to find number bonds to 10 exercises showing thinking with objects

  • Adding Three Small NumbersHelpful

    Addition & Subtraction // Ages 6 to 7

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

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

Number bonds to 10 for ages 4-6 (Reception/Y1): for any number 1-9, find the number that makes 10 when added to it (7→3, 6→4). The ten-frame is the key structure because the empty cells make the complement visible, moving children from counting-on to seeing/recalling the bond. Bonds should become a fact family linking addition and subtraction (7+3=10 ⇔ 10−7=3) and be built toward rapid both-directions recall, because they underpin the making-ten strategy, column carrying and mental calculation through KS1/KS2.

Common misconceptions

  • Counting on from the given number every time rather than recalling the bond, so speed never develops.
  • Knowing 7 + 3 = 10 but not the related 10 − 7 = 3 (bond not held as a fact family).
  • Confusing bonds to 10 with bonds to other totals when the ten-frame isn't present.
  • Thinking there is only one 'way to make 10' rather than a full set of pairs.
  • Miscounting the empty cells on the ten-frame, giving a complement off by one.

Useful representations

  • Ten-frame with filled and empty cells showing a number and its complement
  • Part-part-whole model with the whole fixed at 10
  • Rekenrek (two rows of 5) for showing bonds to 10
  • Bead string of 10 partitioned into two colours
  • Systematic equation list of all bonds to 10 (1+9 … 9+1)

Teaching practices

  • Use the ten-frame as the canonical structure so the complement is SEEN as empty cells, moving children from counting-on to recognising the bond.
  • Practise both directions and link addition to subtraction (7 + 3 = 10 ⇔ 10 − 7 = 3) so bonds are a fact family, not a one-way fact.
  • Work systematically through the pairs (1+9, 2+8, …) to reveal the symmetry and give a sense of the complete set.
  • Build toward automaticity through frequent short retrieval practice grounded in the ten-frame image, not isolated rote drill divorced from meaning.
  • Connect to bonds to 20 and the making-ten strategy explicitly so children see WHY these facts are worth knowing by heart.

Activities to try

  1. 1

    Ten-frame 'make ten' practice

    Why it works: The empty cells of the ten-frame ARE the answer: once the ten-frame becomes a mental picture, the complement is recognised at a glance rather than counted up.

    1. Look at a ten-frame holding some counters (e.g. 7 counters, so 3 cells are empty).
    2. Before counting, predict how many more counters are needed to make 10.
    3. Add (drag, tap, or place physical counters) the missing counters to fill the frame to 10, then check.
    4. Say and record the matching equation, e.g. 7 + 3 = 10.
    5. Repeat with different starting numbers 1-9, working toward naming the complement without counting the empty cells one by one.
  2. 2

    Link each bond to its subtraction partner

    Why it works: Each pair that makes 10 is one fact family, not several separate facts: knowing 7+3 means you also know 3+7, 10−7 and 10−3.

    1. Start from a known bond shown on a ten-frame, e.g. 7 + 3 = 10.
    2. Remove the added part (the 3) and state the matching subtraction fact: 10 − 3 = 7.
    3. Also state the commutative partner, 3 + 7 = 10, and the other subtraction fact, 10 − 7 = 3 (take away the 7 to see the 3 that remains).
    4. Write the full fact family for the pair.
    5. Answer quick questions in both directions, e.g. '__ + 6 = 10' and '10 − 6 = __'.
  3. 3

    Work through the complete set systematically

    Why it works: There is a complete, finite set of ways to make 10 with its own symmetry — not just one 'way to make 10' and not an endless list.

    1. List the bonds in order: 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1.
    2. Notice the symmetry (each pair appears both ways around) and that 5+5 is the one pair of equal parts.
    3. Use a partitioned ten-strand, a two-colour ten of beads, or one row of a rekenrek (ten beads grouped as five and five in two colours) to show the same pairs physically.
    4. Keep a reference display of the full set and tap/reveal a partner for any starting number.
    5. Tell the whole set from memory as it becomes secure.

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
K.OA.4
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y1/AS/2

Math // Addition & Subtraction

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