Math // Addition & Subtraction

Adding and subtracting

Add and subtract one-digit and two-digit numbers to 20, including zero

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

Quick check

Can the learner work out sums like '14 + 5' or '18 − 6' in their head or on paper, and do they know that adding or taking away zero leaves the number unchanged?

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 14 + 5 = 19
  • Calculate 17 – 3 = 14
  • Add or subtract 0 and explain the result stays the same

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
  • Number bondsRequired

    Addition & Subtraction // Ages 5 to 6

    Adding/subtracting to 20 procedurally requires knowing the number bonds

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Adding and subtracting

Ages 5 to 6 // Method

Leads to

2 topics

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 5-6 (UK Y1), learners add and subtract one-digit and two-digit numbers within 20, including the +0/−0 case, using known number bonds and making-ten rather than counting all. Core aims: fluent within-20 calculation, correct bridging across ten (e.g. 8+7), and understanding that adding or subtracting zero leaves a quantity unchanged. Activities centre on acting out calculations with ten-frames and number lines, with a concrete treatment of the zero case to dispel the belief that every operation must change the number.

Common misconceptions

  • Assuming +0 or −0 must change the number (giving 5+0=6 or 5−0=4).
  • Counting all/counting on in ones across the ten boundary instead of making ten.
  • Errors at the teen boundary (miscounting when crossing 10).
  • Ignoring the operation and just combining the two numbers seen.
  • Reversing subtraction to keep the larger number first without noticing the meaning changes.

Useful representations

  • Ten-frames / rekenrek for within-20 sums and bridging
  • Empty number line for jumps (including a 0 jump that stays put)
  • Part-whole model linking the calculation to bonds
  • Objects demonstrating 'add nothing / take nothing' for the zero case
  • Number track 0-20

Teaching practices

  • Calculate using known bonds and making-ten rather than counting all, so this procedural work reinforces the fact base.
  • Give +0 and −0 explicit, concrete treatment (adding/taking nothing) to establish zero as the additive identity and dispel 'every operation changes the number'.
  • Attend to the teen boundary: bridging-ten cases (8+7, 15−7) need the making-ten strategy, not ones-counting.
  • Record calculations as number sentences and connect to the child's representations to keep meaning attached.
  • Vary which quantity is unknown lightly to connect with missing-number work.

Activities to try

  1. 1

    Drive a ten-frame and number-line calculator

    Why it works: Within-20 sums and differences can be found by using bonds and making ten, not by counting all in ones; bridging reorganises the quantity around ten.

    1. Build the first number on a double ten-frame (two ten-frames, since one frame holds only 10) (e.g. place eight counters on the first frame for 8+7).
    2. Add or subtract the second number by moving counters, and for bridging cases split the second number to fill the frame to ten first (slide two counters over to complete ten, leaving five, to reach 15).
    3. Show the same calculation as a jump on a 0-20 number line.
    4. Write the matching number sentence alongside the action (e.g. 8 + 7 = 15).
    5. Repeat with a non-bridging case (14 + 5) and a take-away (17 − 3).
  2. 2

    Add nothing, take nothing: the zero case

    Why it works: Adding or subtracting 0 leaves a number unchanged (n + 0 = n, n − 0 = n); not every operation changes the quantity.

    1. Build a number on a double ten-frame (e.g. 12: one full frame and 2 on the second frame).
    2. Choose 'add 0' and watch that no counters move and the number stays 12.
    3. Choose 'subtract 0' from another number (e.g. 16) and confirm it stays 16.
    4. Show the same on the number line as a jump of length zero that stays on the spot.
    5. Say or write why the number did not change: adding or taking nothing leaves the quantity exactly as it was.
  3. 3

    Spoken probe: what happens if we add zero?

    Why it works: Being able to state why adding or subtracting zero leaves a number unchanged shows understanding beyond getting the answer.

    1. Discuss: 'What happens to 12 when you add nothing to it?'
    2. Explain in your own words how 17 − 3 is different from 17 − 0.
    3. Predict and justify the answer to a new zero case before checking it with objects.

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/3

Math // Addition & Subtraction

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