Math // Counting & Cardinality

Counting forwards and backwards

Count forwards and backwards in steps of 3 from 0

Ages
6 to 7
Type
Method
Builds on
1 topic
Leads to
0 topics
Standards
1 code

Quick check

Can the learner count in threes — 3, 6, 9, 12, 15 — far enough to reach 30 without losing track or needing to start over?

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.
  • Count 3, 6, 9, 12, 15 … up to at least 30
  • Count backwards in 3s from 30
  • Identify the next number in a sequence of multiples of 3

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
  • Counting in 2sRequired

    Counting & Cardinality // Ages 5 to 7

    Skip counting in 3s builds on the concept of skip counting already established in 2s, 5s, and 10s

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Counting forwards and backwards

Ages 6 to 7 // Method

Leads to

0 topics

Nothing in the catalogue builds on this topic yet. Browse Counting & Cardinality

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 Year 2): count in 3s forwards and backwards from 0, extending equal-groups thinking to a less familiar step size and seeding the 3× table and the idea of 'a third'. The central insight is that multiples of 3 still form a regular pattern — a diagonal pattern of repeating parallel lines on a hundred square — even though they do not line up in neat columns like 2s, 5s and 10s. Each step should be tied to one more group of three, and backward counting and mid-sequence continuation practised as skills in their own right.

Common misconceptions

  • Feeling 3s have 'no pattern' because they don't form neat columns (they form diagonals).
  • Reciting 3s as isolated rote with no link to groups of three or the 3× table.
  • Being able to count forward but not backward in 3s.
  • Losing the step when crossing a decade (…18, 21…) — miscounting the +3 across the ten.

Useful representations

  • Hundred square with multiples of 3 shaded (diagonal stripes).
  • Number line with equal 3-jumps.
  • Arrays / groups of three (bridge to the 3× table and thirds).
  • Backward-count track from 30.

Teaching practices

  • Show 3s as a DIAGONAL pattern on the hundred square so children see 3s are regular even though they don't line up in columns (counters the 'no pattern' feeling).
  • Insist on backward counting from a multiple (30, 27, 24…) — harder and needed for the full table.
  • Tie each step to one more group of three (arrays / repeated addition) and forward to the 3× table and 'a third' (the DfE link).
  • Play spot-the-multiple-of-3 on the hundred square, not only counting up from 0, so multiples are recognised anywhere.

Activities to try

  1. 1

    The diagonal reveal: shading 3s on a hundred square

    Why it works: Multiples of 3 are patterned, not random — the diagonal pattern lets you predict the next multiple and recognise multiples anywhere, countering the feeling that '3s have no pattern'.

    1. Step forward in 3s from 0 (3, 6, 9, 12…), shading or marking each multiple on a hundred square as you say it.
    2. Notice that, unlike the vertical columns 5s and 10s make, the multiples of 3 march down the grid as repeating parallel diagonal lines (a diagonal pattern).
    3. Use the diagonal pattern to predict the next multiple before you reach it, then check.
    4. Play 'spot the multiple of 3' by pointing to multiples anywhere on the grid, not only counting up from 0.
    5. Pay special attention to crossing each decade (…18, 21… and …27, 30…) so the +3 step is not lost across the ten.
  2. 2

    Number-line 3-jumps and groups of three

    Why it works: Each step of 3 is one more group of three; stepping in 3s is the foundation of the 3× table and connects to thirds.

    1. Make equal jumps of 3 along a number line, saying the multiple you land on each time.
    2. For each jump, add one more group of three — show it with an array or counters (three counters per group) alongside the jump.
    3. Connect 'four jumps of 3' to 'four groups of three' (four threes make 12) and to building up the 3× table.
    4. Briefly link three equal groups making a whole to the idea of 'a third'.
  3. 3

    Counting back and entering mid-sequence

    Why it works: Backward counting and continuing from any point are separate skills: the step is always +3 (or −3), so you can add or subtract 3 from the last number rather than restarting.

    1. Count backwards in 3s from a multiple: 30, 27, 24… down to 0, using physical or drawn hops back along a number line.
    2. Practise short backward runs (e.g. 12 → 0) as their own skill, not expecting it to come free with forward counting.
    3. Continue a sequence from the middle: given 12, 15, 18, say the next number (and keep going) without restarting from 3.
    4. Say the number just before a given multiple (e.g. what comes before 12 in the 3s).

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/NPV/1

Math // Counting & Cardinality

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