Comparison is the mathematics of relative size. A child must learn not only which number is larger, but why, how much larger, what “fewer” refers to, and how symbols such as >, < and = record those relationships.
This laboratory extends Mathematical Language, More, Fewer, Difference and Comparison, Comparison Chains, Ordering, Inequalities and Relative Magnitude, and the Number Line Laboratory.
The comparison sign should record a relationship the learner already understands, not replace that understanding.
Session 1 | Compare Concrete Quantities
Place 8 counters beside 5 counters. Ask which group has more, which has fewer, and how many more. Pair the counters one-to-one. Five pairs match, leaving three unmatched counters in the larger group.
This gives three linked statements: 8 is greater than 5; 5 is less than 8; the difference is 3.
Worked Example 1 | More and Fewer
Mei has 11 stickers and Kai has 7. Mei has more. Kai has fewer. Mei has 4 more than Kai because 11 − 7 = 4.
Session 2 | Read Greater Than and Less Than
Introduce 8 > 5 only after the quantities are clear. Read it as “eight is greater than five”. Reverse the order: 5 < 8, “five is less than eight”.
Do not depend only on an alligator-mouth mnemonic. The learner should be able to say which value is greater before choosing a symbol.
Worked Example 2 | Reverse the Relationship
If 14 > 9 is true, then 9 < 14 is also true. Reversing the number order reverses the inequality direction.
Session 3 | Equal Means Same Value
Compare 6 + 4 with 7 + 3. Both have value 10, so 6 + 4 = 7 + 3. Equality belongs inside the comparison system: the values are neither greater nor less; they are the same.
This connects comparison with the Equation Balance Laboratory.
Worked Example 3 | Same Value, Different Form
12 = 9 + 3 because both sides have value 12. The forms differ, but the values are equal.
Session 4 | Compare Two-Digit Numbers by Place Value
Compare 47 and 52. Five tens are greater than four tens, so 52 is greater even though 7 ones is greater than 2 ones. Tens are checked before ones because they represent a larger place value.
When tens are equal, compare ones. Between 43 and 48, both have four tens, so compare 3 and 8 ones. Therefore 48 > 43.
Worked Example 4 | Same Tens, Different Ones
65 and 62 both contain six tens. Five ones are greater than two ones, so 65 > 62.
Session 5 | Order Three or More Numbers
Order 38, 42, 35 and 40 from smallest to largest. The numbers with three tens come first: 35, 38. Then the four-tens numbers: 40, 42. The final order is 35, 38, 40, 42.
Ask the learner to justify the order using tens and ones or a number line. Avoid sorting by the final digit alone.
Comparison Chains
If 28 < 31 and 31 < 36, then 28 < 36. A chain of ordered relationships can be used to infer another comparison.
At Primary 1, keep the chain concrete and readable. The deeper habit is transitive reasoning: if one value is smaller than a second, and the second is smaller than a third, the first must be smaller than the third.
Session 6 | Difference as Comparison Distance
Comparison asks not only which is larger but sometimes how far apart the values are. On a number line, 15 and 11 are four units apart. Therefore their difference is 4.
Aligned bars show the same idea: match 11 units, leaving an unmatched segment of 4 on the longer bar.
Worked Example 5 | How Many More?
One basket has 17 apples and another has 12. The first basket has 5 more because 17 − 12 = 5.
“More Than” and “Less Than” Need a Reference
“Mei has 4 more than Kai” does not tell Mei’s amount unless Kai’s amount is known. The phrase describes a relationship between two quantities.
If Kai has 9, then Mei has 13. If Mei has 13 and she has 4 more than Kai, then Kai has 9. The operation depends on which quantity is unknown.
Worked Example 6 | Find the Smaller Quantity
Mei has 16 beads, which is 5 more than Kai. Kai has 11 because 16 − 5 = 11.
Compare Measurements, Money and Data
The same comparison structure transfers across contexts: 12 cm is 4 cm longer than 8 cm; 70 cents is 20 cents more than 50 cents; a graph category with 9 votes has 3 more votes than one with 6.
The numbers are compared in the same way, but the answer unit changes with context.
Impossible Comparison Claims
If a learner writes 42 > 57, ask them to build or decompose the numbers. Four tens cannot be greater than five tens when both numbers are positive two-digit quantities within this range.
A contradiction between the symbol and the place-value evidence should be repaired explicitly.
Common Comparison Errors
| Error | Likely weak link |
|---|---|
| chooses symbol before deciding which is greater | notation replacing meaning |
| compares ones before tens | place-value hierarchy weak |
| adds quantities in a “how many more?” problem | difference structure not recognised |
| uses “more” as an automatic addition cue | reference quantity not identified |
| orders 38, 42, 35 by ones digit | whole-number magnitude weak |
| gives difference without unit | comparison detached from context |
Twenty Practice Questions
- Which is greater: 8 or 5?
- Which is less: 12 or 17?
- Choose the sign: 9 __ 6.
- Choose the sign: 4 __ 11.
- Choose the sign: 8 + 2 __ 7 + 3.
- Compare 47 and 52.
- Compare 65 and 62.
- Order 38, 42, 35, 40 from smallest to largest.
- Order 71, 68, 73 from largest to smallest.
- How much greater is 15 than 9?
- How much less is 12 than 18?
- Mei has 14 stickers and Kai has 9. How many more does Mei have?
- Mei has 16 beads, 5 more than Kai. How many does Kai have?
- Kai has 7 marbles. Mei has 4 more. How many does Mei have?
- True or false: 28 < 31 < 36.
- If 28 < 31 and 31 < 36, compare 28 and 36.
- Which is longer: 12 cm or 8 cm? By how much?
- Which is more: 70 cents or 50 cents? By how much?
- A graph shows 9 votes and 6 votes. Find the difference.
- Create one true comparison using 43 and 48.
Explained Answers
1. 8. 2. 12. 3. >. 4. <. 5. =. Both sides equal 10. 6. 52 > 47. Five tens are greater than four tens.
7. 65 > 62. Tens are equal, so compare ones. 8. 35, 38, 40, 42. 9. 73, 71, 68. 10. 6. 11. 6.
12. 5 stickers. 13. 11 beads. 14. 11 marbles. 15. True. 16. 28 < 36. 17. 12 cm is longer by 4 cm. 18. 70 cents is more by 20 cents. 19. 3 votes. 20. Example: 43 < 48.
A Strong Practice Progression
- Pair concrete sets.
- Use more, fewer and equal.
- Introduce >, < and = after meaning is secure.
- Compare two-digit numbers by tens and ones.
- Order multiple values.
- Build comparison chains.
- Find differences with bars or number lines.
- Move the unknown between larger, smaller and difference quantities.
- Transfer comparison to measurement, money and data.
- Remove supports and justify mentally.
What Adults Can Ask
- “Which quantity is larger before you choose the sign?”
- “Which place value decides this comparison?”
- “What does ‘more than’ refer to?”
- “Are we finding a total or a difference?”
- “What unit should the difference have?”
- “Can a number line or aligned bars check your claim?”
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