Math // Number Representation & Place Value

Comparing and ordering numbers

Compare and order two-digit numbers using the symbols >, =, and <, based on place value understanding

Ages
6 to 7
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
2 codes

Quick check

If you show the learner the numbers 34, 67, and 21, can they put them in order from smallest to largest — and use the symbols > or < correctly?

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.
  • Correctly place > or < between 34 and 43
  • Order a set of two-digit numbers from smallest to largest
  • Explain a comparison by referring to the tens digit first, then ones

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

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Comparing and ordering numbers

Ages 6 to 7 // Method

Leads to

3 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

Ages 6-7 (Y2) compare and order two-digit numbers using >, =, < grounded in place value: compare the tens first, and only if the tens are equal compare the ones. Establish quantity/position meaning of 'greater' and 'less' with base-ten blocks and a 0-100 number line before attaching symbols, deliberately use same-tens pairs to force attention onto the ones, and progress from comparing pairs to ordering a set in both directions.

Common misconceptions

  • Using the crocodile/Pac-Man mouth as a rote trick with no sense of which number is actually bigger, so the symbol is placed by guess.
  • Comparing by digit count of the numeral or by the ONES first (34 vs 38: choosing by 4 vs 8 alone is fine here, but 52 vs 48 wrongly judged by 2 vs 8) — ignoring the leading (tens) digit.
  • Reversing the symbol — knowing which is bigger but writing > where < belongs.
  • Thinking = can only sit between identical-looking expressions, not that it asserts equal value.
  • For same-tens pairs, defaulting to 'they're the same' because the tens match, instead of moving to the ones.

Useful representations

  • Two sets of base-ten blocks placed side by side (more tens = taller/greater)
  • 0-100 number line where the number further right is greater
  • Tens|ones place-value chart aligning two numbers column by column
  • The <, >, = symbols with the 'points to the smaller / opens to the larger' orientation, grounded in quantity
  • Ordered track or 'washing line' for pegging a set of numbers smallest to largest

Teaching practices

  • Compare quantities and positions FIRST (blocks side by side, points on a 0-100 line) so 'greater' means visibly more, then attach the symbol — symbol before meaning breeds the crocodile-mouth-without-understanding error.
  • Teach the leading-digit strategy explicitly: look at the tens; the number with more tens is greater; only if the tens are equal do you compare the ones.
  • Read the statement both ways — 34 < 43 as 'thirty-four is less than forty-three' AND 43 > 34 — so the child sees the relation is the same fact stated from either end.
  • Use same-tens pairs (34 vs 38) deliberately to force attention onto the ones once tens are equal, defeating 'just compare the first digit'.
  • Move from pairwise comparison to ordering a set, recording with symbols, so comparison becomes a tool for organising numbers, not an isolated trick.

Activities to try

  1. 1

    Comparison bench: build, see, and place the symbol

    Why it works: 'Greater' and 'less' name a real difference in quantity/position, and the symbol records that relation — the same fact can be read from either end.

    1. Build or show two two-digit numbers in two forms at once: base-ten block piles and dots/markers on a shared 0-100 number line.
    2. Decide which is greater by looking at the quantity/position first (more tens rods and more blocks in total, further right on the line), then say it aloud: e.g. 'forty-three is greater than thirty-four'.
    3. Place the correct symbol (<, >, or =) into the gap between the two numbers.
    4. Read the completed statement both ways: 34 < 43 ('thirty-four is less than forty-three') and 43 > 34 ('forty-three is greater than thirty-four').
    5. State the rule used: compare the tens first; the number with more tens is greater, and if the tens are equal, compare the ones.
  2. 2

    Tens-tie rounds: when the first digit can't decide

    Why it works: Comparing only the first digit you see is not enough: compare the tens first, and only when the tens are equal does the ones digit decide. = asserts equal value, not merely identical-looking symbols.

    1. Compare same-tens pairs such as 34 and 38, where the tens columns are identical.
    2. Notice that the tens no longer settle it, then compare the ones to decide which is greater.
    3. Place the correct symbol and justify: 'the tens are the same, so I looked at the ones'.
    4. Try a 'crossed-decade' pair such as 52 and 48, and check: 52 has more tens, so it is greater even though its ones digit (2) is smaller than 8.
    5. Also handle an equal pair such as 60 and 60, choosing = and explaining that both show the same value.
  3. 3

    Order a scrambled set onto a washing line

    Why it works: Comparison is a tool for organising numbers: ordering a set applies the tens-then-ones rule repeatedly, not as an isolated trick.

    1. Take a mixed set of two-digit numbers, e.g. 19, 27, 51, 72, and arrange them smallest to largest.
    2. Repeat, ordering the same set largest to smallest.
    3. Include a set containing a same-tens tie so ordering requires the ones to break it.
    4. Check the finished order left to right and record the relations with symbols where appropriate.
    5. Explain how you decided the order: tens first across the set, ones to break ties.

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
1.NBT.3
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y2/NPV/4

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