Math // Multiplication & Division

Odd and even numbers

Recognise odd and even numbers

Ages
6 to 7
Type
Concept
Builds on
2 topics
Leads to
0 topics
Standards
1 code

Quick check

If you give the learner a number like 37 or 84, can they quickly tell you whether it's odd or even — and explain how they know?

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.
  • Identify whether a given number is odd or even
  • Explain that even numbers can be divided into 2 equal groups
  • Spot the pattern: even numbers end in 0, 2, 4, 6, or 8

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
  • Division as equal sharingRequired

    Multiplication & Division // Ages 4 to 6

    Odd/even is about whether a number can be divided into 2 equal groups

  • Counting in 2sHelpful

    Counting & Cardinality // Ages 5 to 7

    Even numbers connect to counting in 2s

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Odd and even numbers

Ages 6 to 7 // Concept

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Multiplication & Division

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 (UK Y2 / US Grade 2), teach odd and even as a structural property of number: even means a count can be split fully into pairs (or two equal groups) with none left over (= 2×something); odd leaves exactly one unpaired. Build the meaning by pairing physical or on-screen counters, connect it to the 2s table and the ones-digit pattern (ends in 0,2,4,6,8), and make clear that 0 is even and that odd/even has nothing to do with a number's size.

Common misconceptions

  • Thinking odd/even is about a number's SIZE rather than divisibility by 2.
  • Forgetting that 0 is even.
  • Judging by the first (leading) digit instead of the ones digit.
  • Believing a number could be both odd and even, or neither.
  • Not connecting even numbers to the 2s table / '2×n' — treating the ending rule as unrelated to multiplication.

Useful representations

  • Pairing counters into twos (leftover = odd)
  • Two equal rows / the 2s array (even = two equal groups)
  • Ten-frame (full pairs vs one lonely counter)
  • Hundred square with even numbers shaded (alternating columns)

Teaching practices

  • Define odd/even by pairing objects (or making two equal rows), not by memorised endings first — even means everything pairs up with none left over; odd leaves exactly one.
  • Connect even numbers to the 2s multiplication table and to '2 × something' / two equal addends, so odd/even is understood as a multiplicative/divisibility property, not an arbitrary label.
  • Derive the ones-digit rule (ends in 0,2,4,6,8) from the pairing pattern rather than teaching it as a bare fact, and apply it to larger numbers.
  • Explicitly address that 0 is even (zero objects pair perfectly — none left over) and that odd/even has nothing to do with how big a number is.
  • Use the hundred square to see even/odd as alternating columns, reinforcing the pattern visually (links to the 2s skip-count pattern).

Activities to try

  1. 1

    Pairing machine: pair the counters and spot the leftover

    Why it works: Even means everything pairs up with none left over (two equal groups / 2×n); odd means exactly one is left unpaired. The ones-digit rule and the 2s table both come from this pairing structure, not from an arbitrary ending.

    1. Choose a quantity of counters (start with numbers to 10, then extend to 20).
    2. Pair the counters up into twos — physically with real counters, or by tapping a 'pair up' control if using a screen model.
    3. Optionally lay the counters on a ten-frame to see full pairs versus one lonely counter.
    4. Decide: if every counter has a partner, the number is EVEN; if exactly one counter is left on its own, the number is ODD.
    5. Test number after number and watch the result build on a hundred square (even numbers shaded) so the alternating-column / ends-in-0,2,4,6,8 pattern appears.
  2. 2

    Introduce with a paired vs leftover picture

    Why it works: A set that pairs up completely is even; a set with one left over is odd — and even numbers fall in a regular pattern.

    1. Look at a picture that contrasts a set whose objects all pair up (even) with a set that has one object left over (odd).
    2. Tap or point to an even set to reveal its neat pairs; tap an odd set to reveal the single leftover.
    3. Look at a hundred square with even numbers shaded to see the alternating pattern.
  3. 3

    Sort numbers and check the edge cases

    Why it works: The classification holds for every whole number, including0. In base ten, each ten can be paired fully, so the ones digit determines whether a counter remains unpaired; a number’s size or leading digit does not decide its parity.

    1. Sort a mix of numbers (including 0 and two-digit numbers to 20) into 'odd' and 'even' boxes.
    2. Answer: is 0 odd or even? Explain why.
    3. Find the number that breaks a stated rule, and resist a distractor that judges by the leading (first) digit instead of the ones digit.

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/Y2/MD/1

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