Third Grade · Math · week 24

Comparing fractions: same numerator

Compare two fractions with the same numerator by reasoning about part size.

When the NUMERATORS are the same, think about part SIZE. 1/3 and 1/6 both have one part — but sixths are smaller pieces than thirds, so 1/3 is the bigger fraction. More cuts make smaller pieces.

This surprises people: a bigger denominator makes a SMALLER fraction (when the numerators match), because the whole is split into more, tinier parts.

📋 For the teacher
Teach it (10–15 min):
  • Cut the SAME whole into thirds and sixths so they see sixths are tinier.
  • Say the counterintuitive rule plainly: bigger bottom = smaller pieces (same top).
  • Contrast with last week so they choose the right reasoning for each case.
  • Use pizza slices — everyone gets that more slices means smaller slices.
Talk about it:
  • With the same numerator, what makes a fraction bigger?
  • Why is 1/8 smaller than 1/4?
  • How is this different from last week?

Mastery looks like: They compare same-numerator fractions by reasoning about part size.

Common stumbles: Assuming the bigger denominator is the bigger fraction; mixing up this rule with the same-denominator rule.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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