Math // Counting & Cardinality

Counting forwards and backwards (age 6+)

Count forwards and backwards in tens from any number (not just multiples of 10)

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

Quick check

If the learner starts at 37 and you ask them to count up in tens, can they say 37, 47, 57, 67 — crossing over into the next hundred without getting stuck?

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 7, 17, 27, 37 … from a non-multiple starting point
  • Count backwards in tens from 83
  • Explain the pattern of adding/subtracting 10

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
  • Counting in 2sRequired

    Counting & Cardinality // Ages 5 to 7

    Counting in tens from any number builds on skip counting in tens from 0

  • The two digits of a two-digit numberRequired

    Number Representation & Place Value // Ages 6 to 7

    Counting in tens from non-multiples requires understanding that adding 10 changes the tens digit

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Counting forwards and backwards (age 6+)

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 (Year 2): counting in tens from ANY number, not just multiples of ten (e.g. 7, 17, 27, 37…). The core place-value insight is that adding or subtracting 10 keeps the ones digit the same while the tens digit changes by one — and at a hundred boundary such as 96 → 106 the tens roll from 9 to 0 and a new hundred appears (backwards, 106 → 96, they roll from 0 to 9), while the ones digit still does not move. This is the foundation for mental +10/−10 and later column place value. It is best made visible as a vertical move on a hundred square (on a standard square numbered from 1 at the top, straight down = +10 and straight up = −10; check the direction on squares numbered from the bottom), with concrete support from base-ten blocks (add/remove a ten-rod, ones untouched). Practise forwards and backwards from non-multiples and say the rule aloud.

Common misconceptions

  • Changing the ones digit too (e.g. 27 → 38) — not isolating the +10 to the tens.
  • Only able to add 10 to multiples of 10 (can't start from 7 or 23).
  • Treating +10 as 'just add a 0' — which fails for non-round numbers (27 ≠ 270).
  • Losing the column on the hundred square (drifting sideways instead of straight down).

Useful representations

  • Hundred square (vertical move = ±10; ones digit fixed down a column).
  • Base-ten blocks / Dienes (add or remove a ten-rod).
  • Place-value chart (tens column changes, ones column unchanged).
  • Number line with 10-jumps from a non-round start.

Teaching practices

  • Teach it as a VERTICAL move on the hundred square (down = +10, up = −10) so the tens-digit change and the fixed ones-digit are seen.
  • Use base-ten blocks: add one ten-rod while the ones pile is untouched — the concrete 'why' behind the digit rule.
  • Say the rule aloud — 'the ones stay the same, the tens go up by one' — and test it from many non-multiple starts.
  • Practise backward (−10) from any number; connect to mental 10-more / 10-less.

Activities to try

  1. 1

    Down a column, ones frozen — the +10/−10 move on the hundred square

    Why it works: Adding or subtracting ten never touches the ones digit; it is the same single downward (or upward) step on the hundred square whatever number you start from. '+10' is not 'add a zero' — it is 'one row down'.

    1. Start on a non-multiple, e.g. 27, on a hundred square.
    2. Make a +10 move by dropping straight DOWN one row: 27 → 37 → 47 → 57, saying each number aloud.
    3. Each step of this 27 → 57 run, point to the ones digit (the 7) and say 'the ones stay the same'; point to the tens digit and say 'the tens go up by one' (true while you stay inside a hundred).
    4. Reverse it: make −10 moves by going straight UP one row: 83 → 73 → 63 → 53, saying what stays (the ones) and what changes (the tens).
    5. Watch for drifting sideways — keep the move strictly vertical so you stay in the same ones-digit column.
  2. 2

    Concrete why: add a ten-rod with base-ten blocks

    Why it works: Physically, +10 is just one extra ten-rod; the ones stay as they are. This is the concrete reason the ones digit never changes.

    1. Build a two-digit number with base-ten blocks, e.g. 23 as two ten-rods and three ones.
    2. To add 10, bring in ONE more ten-rod and leave the ones pile untouched; read the new number (33).
    3. To subtract 10, take one ten-rod away and leave the ones pile untouched; read the new number.
    4. Say the rule as you go: 'one more ten, the ones don't change'.
    5. Link each action to its numeral and, if available, to the hundred-square move.
  3. 3

    Say-it and spot-the-slip practice

    Why it works: Fluent +10/−10 from any starting number, with the ability to notice when the ones digit has wrongly moved.

    1. Answer quick questions: 'What is 10 more than 47?' and 'What is 10 less than 47?'
    2. Fill in a tens sequence from a non-multiple, e.g. 4, 14, __, __, 44.
    3. Look at a wrong sequence (e.g. 7, 17, 28, 38) and say which digit changed that shouldn't have.
    4. Count aloud forwards from a non-multiple and backwards from a two-digit number, stating each step is +10 or −10.

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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