Math // Addition & Subtraction

Addition and subtraction within 20

Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts

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

Quick check

If the learner needs to work out '8 + 6', can they split the 6 into 2 + 4, use the 2 to fill up to 10, then add the remaining 4 to get 14?

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.
  • Solve 8 + 6 using making ten: 8 + 2 + 4 = 14
  • Solve 13 − 4 by decomposing: 13 − 3 − 1 = 9
  • Use a known fact (8 + 4 = 12) to derive 12 − 8 = 4

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

Addition and subtraction within 20

Ages 6 to 7 // Method

Leads to

5 topics
  • Adding within 100Required

    Addition & Subtraction // Ages 6 to 7

    Adding within 100 extends within-20 strategies to larger numbers

  • Fluent addition and subtractionRequired

    Addition & Subtraction // Ages 6 to 7

    Fluent recall of facts to 20 builds from strategic calculation within 20

  • Fluent adding and subtracting within 20Required

    Addition & Subtraction // Ages 7 to 8

    Fluency within 20 requires prior strategy-based adding/subtracting within 20

  • Guided Multi-Step Problem SolvingHelpful

    Mathematical Thinking // Ages 6 to 7

    Choosing strategies for adding within 20 requires planning and evaluating approaches

  • Generalising PatternsHelpful

    Mathematical Thinking // Ages 6 to 7

    Deriving facts within 20 from known facts (near doubles, make ten) exercises generalising from patterns

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 (Y1/Y2): add and subtract within 20 using strategies — making ten (8+6 = 8+2+4 = 14), decomposing to bridge ten (13−4 = 13−3−1 = 9), and deriving from known facts. The core insight is treating ten as a friendly landmark reached in both directions; this bridging reasoning later underpins column carrying and borrowing. The focus is the method, not just a correct answer, since counting all by ones can reach 14 without showing the intended understanding.

Common misconceptions

  • Counting on/back in ones across ten instead of using ten as a landmark (slow and error-prone at the boundary).
  • Splitting the wrong addend or splitting it wrongly when making ten (e.g. taking 4 not 2 from the 6 to fill an 8).
  • For subtraction, decomposing incorrectly across ten (13−4 done as 13−4 in ones with a boundary error).
  • Not connecting making-ten to known bonds to 10, so the strategy feels arbitrary.
  • Applying making-ten rigidly even when a known fact or near-double would be quicker.

Useful representations

  • Two ten-frames showing one filled to 10 and the extra spilling into the second
  • Rekenrek for shifting beads to make ten
  • Empty number line with a jump to 10 then beyond
  • Part-whole model decomposing the second addend (6 = 2 + 4)
  • Bead string of 20 partitioned at the ten

Teaching practices

  • Teach making-ten physically on two ten-frames/a rekenrek: children MOVE counters to complete the first ten, seeing why 8+6 becomes 10+4.
  • For subtraction bridging ten, model decomposing to land on ten first (13−4 = 13−3−1), so ten is the landmark in both directions.
  • Frame ten as a 'friendly number' and connect making-ten to the bonds-to-10 facts children already know.
  • Encourage strategy flexibility — near-doubles, known facts and making-ten — and discuss which is efficient for a given calculation.
  • Use the empty number line to record bridging jumps (+2 to 10, then +4), linking strategy to a spatial model that scales to larger numbers.

Activities to try

  1. 1

    Make ten by moving counters on a double ten-frame

    Why it works: Making ten is a MOVE: reorganising an awkward fact around the friendly ten (8+6 becomes 10+4) shows WHY the strategy works, not just that it gives 14.

    1. Set out 8 counters in the first ten-frame (two cells empty) and 6 in the second to add 8 + 6.
    2. Move 2 counters from the 6 across to fill the first frame to 10, and notice the 6 has broken into 2 and 4.
    3. Read the result as 10 + 4 = 14, and say aloud which part you moved and why.
    4. Record the same move on an empty number line as a jump of +2 to reach 10, then +4 to reach 14.
    5. Repeat with other bridging facts (e.g. 7+5, 9+6), each time completing the first ten first.
  2. 2

    Bridge down to ten for subtraction

    Why it works: Ten is a landmark in BOTH directions: decomposing the number being subtracted so you land on ten first keeps the calculation accurate across the boundary.

    1. To work out 13 − 4, start at 13 and first subtract enough to land on 10: 13 − 3 = 10.
    2. Then subtract the rest: the 4 was split into 3 and 1, so take the remaining 1, giving 10 − 1 = 9.
    3. Show both jumps back on a number line — back to 10, then one more past it.
    4. Check you have subtracted the whole amount (3 + 1 = 4), not just part of it.
    5. Try more subtractions that cross ten (12−5, 15−7), each time stepping onto ten first.
  3. 3

    Explain and compare strategies aloud

    Why it works: Because this is a reasoning strategy, explaining and comparing methods builds flexibility — children learn to choose making-ten, a near-double or a known fact according to the calculation, and to see addition and subtraction as related.

    1. Talk through how you worked out 8 + 6, step by step: which number did you split, and what did that make?
    2. Answer probing questions: 'Why did you take 2 across to the 8 — what does that make?' and 'For 13 − 4, why break the 4 into 3 and 1?'
    3. Offer a second method for 8 + 6 (e.g. treat it as a near-double: move 1 from the 8 to the 6 to make the double 7 + 7 = 14, or use 6 + 6 + 2, or a known fact) and say which felt quicker.
    4. Use a known addition fact to derive a subtraction: if 8 + 4 = 12, explain how that gives 12 − 8 = 4.
    5. Describe how a ten-frame shows what is happening in your method.

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.6

Math // Addition & Subtraction

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