Comparing Fractions by Size
A 45-minute Grade 3 lesson on comparing fractions by reasoning about their size, and on the rule that makes the whole thing work: you can only compare parts of the same whole.
Comparing Fractions by Size is a free 45-minute Grade 3 maths lesson plan for Common Core standard 3.NF.A.3 — recognise equivalent fractions and compare fractions. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.
- Grade:
- Grade 3
- Length:
- 45 minutes
- Standard:
- 3.NF.A.3
Grade 3 · Number & Operations — Fractions
3.NF.A.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Objective
Students will be able to compare two fractions with the same numerator or the same denominator, and recognise simple equivalent fractions.
Students are successful when they can
- Compares fractions with the same denominator by the numerator.
- Compares fractions with the same numerator and explains why more parts means smaller parts.
- Says why comparing fractions of different wholes is meaningless.
What you need
- Fraction strips, all cut from the same length
- Two paper strips of obviously different lengths for the counterexample
- Number lines
- The printable practice sheet linked at the end of this plan
The lesson
Warm-up — which is more?
5 min- Compare 3/8 and 5/8 using fraction strips. Straightforward.
- Then compare 1/3 and 1/8. Take the votes without settling it.
Teach — two easy cases and one warning
14 min- Same denominator: 3/8 against 5/8. The parts are the same size, so counting them decides it.
- Same numerator: 1/3 against 1/8. Lay the strips side by side. The eighth is smaller because the whole was cut into more pieces.
- Say it plainly: more parts, smaller each. That is the opposite of what the numbers look like, which is why it needs the strips.
- Now the warning. Hold up a third of a long strip and a half of a short one. The third is physically bigger.
- Ask whether 1/3 is greater than 1/2. It is not — the comparison was never valid, because the wholes were different.
- Finish with equivalence: 1/2 and 2/4 lie on top of each other. Same point on the line, two names.
“Fractions can only be compared when they are parts of the same whole. Half of a bus is more than all of a biscuit, and that tells you nothing about a half and a whole.”
Guided practice — reason, then check
12 min- Pairs compare fraction cards, saying which case it is — same numerator, same denominator — and reasoning before checking with strips.
- They record each comparison with the correct symbol.
- Then they find two equivalent fractions using the strips.
Independent practice
11 min- Students complete a comparing fractions page.
- Same-numerator comparisons are the diagnostic. Same-denominator ones can be answered by whole number reasoning that happens to work.
Close
3 min- Ask whether 1/4 or 1/6 is greater, and why.
- 'Six pieces are smaller than four pieces' is the sentence to end on.
What goes wrong, and why
Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.
Says 1/8 is greater than 1/3 because 8 is greater than 3.
Why: Whole number order is being applied to the denominator. Everything the pupil knows about numbers says eight beats three.
Fix: Fraction strips cut from the same whole, laid on top of each other. The eighth is visibly shorter, and the reason — more people sharing — connects to fairness.
Compares 1/3 of one whole with 1/2 of a different whole and concludes 1/3 is bigger.
Why: The physical pieces really are different sizes, and the wholes were not checked because nothing has said they must match.
Fix: Do it deliberately with two obviously different strips and ask what went wrong. The rule is easier to accept after it has been broken on purpose.
Compares 2/3 and 3/4 by subtracting: both are 'one away from the whole' so they are equal.
Why: A pattern has been spotted and generalised. It is a genuinely thoughtful observation and it happens to be wrong.
Fix: Put both on a number line. One away from the whole is a different distance when the parts are different sizes, and the line shows it.
If they are not there yet
- Work with same-denominator pairs first, then same-numerator, keeping the two cases separate.
- Keep the fraction strips on the desk. The comparison is a matter of looking until the reasoning is secure.
If they finish early
- Compare a fraction with 1/2 as a benchmark: is 5/8 more or less than half?
- Find three fractions equivalent to 2/3.
- Order four fractions with different denominators.
Exit ticket
Which is greater, 1/5 or 1/9? Explain. Then: is 3/6 the same as 1/2?
What to look for: 1/5, with a reason about the size of the parts, and yes. '1/9 because 9 is bigger' is the whole number misconception and needs strips, not correction.
Printable practice for 3.NF.A.3
Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.
- Equivalent Fractions — HalvesFill in the missing number.
- Equivalent Fractions — DoublingFill in the missing number.
Questions about Comparing Fractions by Size
How long does the Comparing Fractions by Size lesson take?
45 minutes, split across 5 timed sections: warm-up 5 min, teach 14 min, guided practice 12 min, independent practice 11 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.
Which standard does Comparing Fractions by Size teach?
CCSS.MATH.CONTENT.3.NF.A.3 — 3.NF.A.3, Number & Operations — Fractions for Grade 3: “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.” In plain terms, recognise equivalent fractions and compare fractions.
What do I need to teach this lesson?
Fraction strips, all cut from the same length, two paper strips of obviously different lengths for the counterexample, number lines and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.
What mistakes should I expect in this lesson?
Three, each a reasoning error rather than carelessness: says 1/8 is greater than 1/3 because 8 is greater than 3; compares 1/3 of one whole with 1/2 of a different whole and concludes 1/3 is bigger and compares 2/3 and 3/4 by subtracting: both are 'one away from the whole' so they are equal. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.
How do I know whether the lesson worked?
The exit ticket asks: “Which is greater, 1/5 or 1/9? Explain. Then: is 3/6 the same as 1/2?.” 1/5, with a reason about the size of the parts, and yes. '1/9 because 9 is bigger' is the whole number misconception and needs strips, not correction. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.
Is there a worksheet to go with Comparing Fractions by Size?
Yes — 2 printable 3.NF.A.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.
Is Comparing Fractions by Size free to use?
Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.
Last reviewed 2026-09-05. Aligned to 3.NF.A.3 of the Common Core State Standards for mathematics.