Math // Counting & Cardinality

One More Each Time

Each successive counting number represents a quantity that is one larger than the previous number

Ages
4 to 6
Type
Concept
Builds on
1 topic
Leads to
3 topics
Standards
2 codes

Quick check

If the learner has 5 stickers and you give them one more, do they know immediately there are now 6 — without needing to count all of them again from one?

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 a set of 5, know that adding one object makes 6
  • Explain that 8 is one more than 7
  • Given a number, identify one more and one less

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
  • How Many in Total?Required

    Counting & Cardinality // Ages 4 to 6

    Understanding 'one more/one less' requires understanding that each number represents a quantity (cardinality)

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One More Each Time

Ages 4 to 6 // Concept

Leads to

3 topics
  • Addition and subtraction strategiesRequired

    Addition & Subtraction // Ages 6 to 7

    Counting on/back relies on understanding that each successive number is one more/less

  • Finding efficient methodsHelpful

    Mathematical Thinking // Ages 5 to 6

    The +1 pattern in counting is the earliest repeated reasoning

  • 10 More or 10 LessHelpful

    Number Representation & Place Value // Ages 6 to 7

    10 more/less generalises the concept of one more/one less to tens

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 4–6 (Reception/Kindergarten to Year 1): the successor principle — each successive counting number names a quantity exactly ONE larger than the one before, and going back one is one less. The aim is to turn the flat count sequence into a structure of +1 / −1 steps, laying the ground for the number line, counting-on and early addition/subtraction. Teach 'one more' and 'one less' together as inverse moves, link the spoken word-step to an actual quantity-step, and build towards counting-on (finding 'one more than 5' as 6 without restarting at 1).

Common misconceptions

  • Recounting from 1 to find 'one more' instead of counting-on (successor not yet linked to cardinality).
  • Knowing 'one more' but not 'one less' — the backward direction lags because the string is learned forward only.
  • Treating 'one more' as merely 'the next word I say' rather than a quantity one larger (fails when the count starts wrong).
  • Not realising every step is exactly one — thinking numbers grow by an inconsistent amount.

Useful representations

  • Number track / number line (steps of one; right = more, left = less).
  • Cube tower / staircase (each step one taller).
  • Ten-frame filled one cell at a time.
  • 'One more / one less' arrow cards or a +1/−1 machine.

Teaching practices

  • Pair the word-step with a quantity-step: add exactly one object as you say the next number, so 'the next number' MEANS 'one more thing'.
  • Teach one-more and one-less as inverse moves on the same model (number track hops right/left), not as two unrelated facts.
  • Make counting-on explicit: from a known total, say the next number WITHOUT restarting at one — this requires cardinality and bridges to addition.
  • Use a staircase / number track so +1 is a single visible step; contrast with a two-step jump (foreshadows skip counting).
  • Ask prediction questions ('if we add one more cube, what number?') before acting, then check — builds the expectation that each step is exactly one.

Activities to try

  1. 1

    One more, one less in lockstep

    Why it works: Each successive counting number is a quantity exactly one larger than the previous one, and one back is exactly one smaller; +1 and −1 are a single step in opposite directions on the same track.

    1. Build a tower with cubes (or fill a ten-frame one cell at a time) and say the count as you go.
    2. Before adding, predict: 'If I add one more cube, what number will it be?' Then add exactly one cube and check that the count moves to the next word.
    3. Add one cube and say the next number in the same beat, so that 'the next number' means 'one more thing'.
    4. Now remove one cube and say the number that is one less, naming it as the mirror move of adding one.
    5. On a number track, hop a marker (or a frog along lily-pads) exactly one place right for 'one more' and one place left for 'one less'.
  2. 2

    Counting on from a hidden total

    Why it works: Once you know how many a set has (its cardinality), finding one more is just naming the next counting word — you do not need to recount from one.

    1. Count a set of objects into a box or under a cover, then agree on how many are inside (e.g. 7).
    2. With the set hidden, drop in exactly one more and answer, without recounting, how many there are now.
    3. Explain how you knew — 'one more than 7 is the next number, 8' — rather than reopening the box.
    4. Try a chain: 'What's one more than 8? And one more than that?' naming each successor without restarting at 1.
    5. Reverse it: 'If I take one back out, how many now?' to practise the predecessor the same way.
  3. 3

    Reading the staircase and retrieval practice

    Why it works: The +1 structure is consistent all along the sequence: every step up is one larger and every step down is one smaller; a fixed staircase can show this structure even though you are not building it yourself.

    1. Study a staircase/number track labelled 1..10 and describe how each step compares to the one before.
    2. Point to where 'one more' and 'one less' live relative to a chosen number.
    3. Answer quick fill-in prompts: 'One more than 6 is ___', 'One less than 6 is ___', and 'What number comes next after 8?'
    4. Contrast a single step (+1) with a two-step jump, noticing that a jump of two is not 'one more' (an early taste of skip counting).

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.CC.4.c
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y1/NPV/3

Math // Counting & Cardinality

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