Math // Addition & Subtraction

Number bonds

Recall number bonds (addition and related subtraction facts) within 20

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

Quick check

Can the learner quickly recall facts like '8 + 7 = 15' and immediately know that '15 − 7 = 8' — without having to work out the subtraction from scratch?

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.
  • Quickly recall that 8 + 5 = 13
  • Given 13 – 5, respond 8 using knowledge of related addition fact
  • Know all pairs of single-digit numbers that sum to numbers up to 20

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

You are here

Number bonds

Ages 5 to 6 // Method

Leads to

2 topics
  • Adding and subtractingRequired

    Addition & Subtraction // Ages 5 to 6

    Adding/subtracting to 20 procedurally requires knowing the number bonds

  • Place value understanding and number factsHelpful

    Number Representation & Place Value // Ages 6 to 7

    Using number facts to solve problems benefits from known addition/subtraction facts

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 5-6 (Y1): recall number bonds within 20 as fact families, so each addition fact (8+5=13) hands over its related subtractions (13−5=8, 13−8=5) rather than being memorised separately. Facts should appear in all four forms and with the unknown in any position (7=16−9) to pre-empt the 'answer-after-equals' habit. Within-20 recall is built from bonds-to-10 plus making-ten (bridging) and doubles, then firmed with short, frequent interleaved retrieval, while a reconstructing strategy stays available for slips.

Common misconceptions

  • Learning additions and subtractions as separate lists rather than as fact families, doubling the memory load and leaving subtraction weak.
  • Recalling only the canonical form (8+5) and struggling with 5+8 or 13−8.
  • Rejecting missing-number/reordered forms (7 = 16 − 9) because = is read as 'answer here'.
  • Counting rather than recalling, especially for bridging facts.
  • Confusing bonds of different totals when facts aren't tied to a clear whole.

Useful representations

  • Fact-family triangle (whole and two parts) generating four facts
  • Part-part-whole model within 20
  • Ten-frames (one full, one partial) for bridging bonds
  • Bead string / rekenrek of 20
  • Equation sets showing a bond in all four forms and missing-number variants

Teaching practices

  • Teach every bond as a fact family (a+b, b+a, whole−a, whole−b) so one known fact yields four, and subtraction is derived from addition.
  • Present the facts in several forms including unknown-in-different-positions (7 = 16 − 9) to build flexibility and pre-empt the 'answer after =' habit.
  • Build within-20 recall from bonds to 10 + making-ten + doubles rather than as fresh rote facts.
  • Use fact-family triangles and part-whole models so the relationship among the three numbers is explicit.
  • Consolidate with short, frequent, interleaved retrieval; keep a reconstructing strategy available for slips.

Activities to try

  1. 1

    Fact-family machine: one relationship, four facts

    Why it works: One relationship among three numbers IS four facts: learning 8+5 gives you 13−5 and 13−8 for free, so subtraction is derived from addition rather than memorised as a separate list.

    1. Set a whole of 13 with two parts, 8 and 5, in a part-whole triangle (whole at the top, parts in the lower corners).
    2. Read the four facts that the relationship generates: 8+5=13, 5+8=13, 13−8=5, 13−5=8. Say each one aloud.
    3. Change a part (e.g. make the parts 7 and 6 with whole 13) and watch all four equations rewrite, so you see the same structure holds for every bond (for a double such as 6+6=12, the four forms reduce to two different facts: 6+6=12 and 12−6=6).
    4. Use a 'cover a corner' mode: hide one number and say the missing one. Then set a new, clearly labelled whole (e.g. whole 16 with parts 7 and 9) and practise missing-number forms such as 7 = 16 − ? and 16 − ? = 9.
    5. Practise shaky family members again in short interleaved rounds until the four facts come quickly from recall or near-instant derivation.
  2. 2

    Build within-20 recall from bonds-to-10, making-ten and doubles

    Why it works: Teen bonds are not fresh rote facts: they can be derived from secure bonds to 10 using making-ten and doubles, and derivation becomes faster recall with spaced practice.

    1. Re-secure bonds to 10 first (e.g. 6+4, 7+3) so they are instant.
    2. For a crossing-ten sum like 8+5, split the second number to make ten: 8+2=10, then 10+3=13. Use one full ten-frame and one partial frame to show the move.
    3. Use a known double to help a near-double: 6+7 is 6+6+1 or 7+7−1.
    4. State which facts you just KNEW and which you had to work out, then practise the worked-out ones more.
    5. Repeat in short, frequent, mixed sessions rather than one long drill.
  3. 3

    Mixed-form retrieval practice across the fact family

    Why it works: Recognising and completing a bond in any form — including the unknown in any position — is the mark of flexible, secure fact-family knowledge.

    1. Answer quick-fire items drawn from all four forms of a family: 8+5=?, 5+8=?, 13−5=?, 13−8=?.
    2. Answer missing-number items with the unknown in different positions: 7 = 16 − ?, 8 + ? = 13, ? − 5 = 8.
    3. Mix additions and their related subtractions back-to-back (8+5 then 13−5) to practise pulling the subtraction from the addition.
    4. Note any item that needed counting and return to it after a making-ten reminder.

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/Y1/AS/2

Math // Addition & Subtraction

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