CH04-05 lesson

Comparing Fractions with Same Numerator or Denominator Learning Activity

A focused Grade 3 learning session for Comparing Fractions with Same Numerator or Denominator using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will compare fractions with the same numerator or denominator and justify the comparison.

Student goal: I can compare fractions with the same numerator or denominator.

Helpful first: Equivalence of Fractions Generating Simple Equivalent Fractions
concept

Learn the Idea

Comparing Fractions with Same Numerator or Denominator means using equal parts, number lines, and clear fraction language to describe parts of a whole.

  • Identify the whole before naming a fraction.
  • Make sure each part is equal in size.
  • Use a number line or model to show where the fraction belongs.
  • Explain whether two fractions have the same size or different sizes.
visual model

See the Math

Visual Model 1

Question: Compare \(\frac{2}{3}\) and \(\frac{2}{4}\). Which is true?

Grade 3 Comparing Fractions with Same Numerator or Denominator figure 1

  • A. \(\frac{2}{3}<\frac{2}{4}\) (bigger denominator = bigger fraction)
  • B. \(\frac{2}{3}=\frac{2}{4}\) (both have numerator 2)
  • C. \(\frac{2}{3}>\frac{2}{4}\)
  • D. \(\frac{2}{4}>\frac{2}{3}\) (4 > 3, so \(\frac{2}{4}\) is larger)

Why it works: Strategy: same numerator (2), so compare denominators. Thirds are bigger pieces than fourths (a whole divided by 3 gives bigger parts than divided by 4). Visual check: the blue bar (2/3) covers more area than the bar would if it were 2/4. Rule: when numerators match, smaller denominator wins.

Answer: \(\frac{2}{3}>\frac{2}{4}\)

worked example

Follow a Worked Example

Example 1

Question: Using the bars, which is true?

Grade 3 Comparing Fractions with Same Numerator or Denominator figure 3

  • A. \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)
  • B. \(\frac{1}{2}<\frac{1}{3}\) (2 < 3)
  • C. \(\frac{1}{2}=\frac{1}{3}\)
  • D. \(\frac{1}{3}>\frac{1}{2}\) (1 out of 3 is more than 1 out of 2)
  1. Same numerator (1): both fractions take 1 piece from their bar.
  2. But the first bar is divided in half (larger piece), the second in thirds (smaller piece).
  3. One half > one third.
  4. Visually: the green shaded area is larger in the first bar.

Answer: \(\frac{1}{2}>\frac{1}{3}\)

Example 2

Question: Compare \(\frac{4}{6}\) and \(\frac{4}{8}\). Which is true?

Grade 3 Comparing Fractions with Same Numerator or Denominator figure 4

  • A. \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)
  • B. \(\frac{4}{6}<\frac{4}{8}\) (8 > 6)
  • C. \(\frac{4}{6}=\frac{4}{8}\)
  • D. \(\frac{4}{8}>\frac{4}{6}\) (more pieces means more amount)
  1. Same numerator (4): sixths are bigger pieces than eighths.
  2. Comparing the shaded areas: 4 sixths covers more than 4 eighths.
  3. The fewer pieces the denominator divides into, the bigger each piece.

Answer: \(\frac{4}{6}>\frac{4}{8}\)

real world

Connect It to a Real Situation

Problem 1

Question: Which comparison is true?

  • A. \(\frac{3}{5}>\frac{3}{4}\)
  • B. \(\frac{3}{5}<\frac{3}{4}\)
  • C. \(\frac{3}{4}<\frac{3}{5}\)
  • D. \(\frac{3}{5}=\frac{3}{4}\)

Why it works: When comparing fractions with the same numerator (3), look at the denominator: fifths are bigger pieces than fourths. So \(\frac{3}{5}\) (3 large pieces) is less than \(\frac{3}{4}\) (3 slightly larger pieces). Key rule: smaller denominator = bigger pieces.

Answer: \(\frac{3}{5}<\frac{3}{4}\)

strategy

Avoid Mistakes and Choose a Strategy

  • Counting unequal parts as if they were equal.
  • Forgetting that the denominator tells how many equal parts make the whole.
  • Comparing fractions without first checking the size of the whole.
  • Placing a fraction on a number line without counting equal intervals.
  • Draw the whole first, then divide it into equal parts.
  • Use number lines when the question asks about order or location.
  • Say the fraction out loud to connect numerator and denominator meanings.
  • Check whether the answer should be closer to 0, 1/2, or 1.
summary

Remember the Key Idea

Comparing Fractions with Same Numerator or Denominator becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Equal parts first, fraction name second.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G3-C04-T05-Q001 About 1 min

Which comparison is true?

  1. A \(\frac{3}{5}>\frac{3}{4}\)
  2. B \(\frac{3}{5}<\frac{3}{4}\)
  3. C \(\frac{3}{4}<\frac{3}{5}\)
  4. D \(\frac{3}{5}=\frac{3}{4}\)
Check answer and explanation

Answer B: \(\frac{3}{5}<\frac{3}{4}\)

When comparing fractions with the same numerator (3), look at the denominator: fifths are bigger pieces than fourths. So \(\frac{3}{5}\) (3 large pieces) is less than \(\frac{3}{4}\) (3 slightly larger pieces). Key rule: smaller denominator = bigger pieces.

G3-C04-T05-Q002 About 1 min

Compare \(\frac{2}{3}\) and \(\frac{2}{4}\). Which is true?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q002
  1. A \(\frac{2}{3}<\frac{2}{4}\) (bigger denominator = bigger fraction)
  2. B \(\frac{2}{3}=\frac{2}{4}\) (both have numerator 2)
  3. C \(\frac{2}{3}>\frac{2}{4}\)
  4. D \(\frac{2}{4}>\frac{2}{3}\) (4 > 3, so \(\frac{2}{4}\) is larger)
Check answer and explanation

Answer C: \(\frac{2}{3}>\frac{2}{4}\)

Strategy: same numerator (2), so compare denominators. Thirds are bigger pieces than fourths (a whole divided by 3 gives bigger parts than divided by 4). Visual check: the blue bar (2/3) covers more area than the bar would if it were 2/4. Rule: when numerators match, smaller denominator wins.

guided

1 question
G3-C04-T05-Q003 About 1 min

The bars show two fractions. Which is larger?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q003
  1. A \(\frac{2}{6}\) (6 > 3)
  2. B \(\frac{2}{3}\) (shaded area is larger)
  3. C They are equal
  4. D Cannot tell from the bars
Check answer and explanation

Answer B: \(\frac{2}{3}\) (shaded area is larger)

Visual reasoning: same numerator (2), so both take 2 pieces. But \(\frac{2}{3}\) divides the whole into 3 parts (each third is large), while \(\frac{2}{6}\) divides into 6 parts (each sixth is small). Comparing shaded amounts: 2 large pieces > 2 small pieces, so \(\frac{2}{3} > \frac{2}{6}\).

practice

5 questions
G3-C04-T05-Q004 About 1 min

Which comparison is true?

  1. A \(\frac{3}{4}<\frac{3}{6}\)
  2. B \(\frac{3}{4}=\frac{3}{6}\)
  3. C \(\frac{3}{4}>\frac{3}{6}\) (same numerator, 4 < 6)
  4. D \(\frac{3}{6}>\frac{3}{4}\) (6 > 4, so sixths are bigger)
Check answer and explanation

Answer C: \(\frac{3}{4}>\frac{3}{6}\) (same numerator, 4 < 6)

Same numerator (3), different denominators: fourths are bigger pieces than sixths (the bar is cut into fewer, larger pieces). Three fourths covers more area than three sixths.

G3-C04-T05-Q005 About 1 min

Using the bars, which is true?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q005
  1. A \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)
  2. B \(\frac{1}{2}<\frac{1}{3}\) (2 < 3)
  3. C \(\frac{1}{2}=\frac{1}{3}\)
  4. D \(\frac{1}{3}>\frac{1}{2}\) (1 out of 3 is more than 1 out of 2)
Check answer and explanation

Answer A: \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)

Same numerator (1): both fractions take 1 piece from their bar. But the first bar is divided in half (larger piece), the second in thirds (smaller piece). One half > one third. Visually: the green shaded area is larger in the first bar.

G3-C04-T05-Q006 About 1 min

Compare \(\frac{4}{6}\) and \(\frac{4}{8}\). Which is true?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q006
  1. A \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)
  2. B \(\frac{4}{6}<\frac{4}{8}\) (8 > 6)
  3. C \(\frac{4}{6}=\frac{4}{8}\)
  4. D \(\frac{4}{8}>\frac{4}{6}\) (more pieces means more amount)
Check answer and explanation

Answer A: \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)

Same numerator (4): sixths are bigger pieces than eighths. Comparing the shaded areas: 4 sixths covers more than 4 eighths. The fewer pieces the denominator divides into, the bigger each piece.

G3-C04-T05-Q007 About 1 min

On the number line, the red dot is at the same position as which label?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q007
  1. A \(\frac{1}{2}\)
  2. B \(\frac{3}{4}\)
  3. C \(\frac{1}{4}\)
  4. D Between \(\frac{1}{2}\) and \(\frac{3}{4}\)
Check answer and explanation

Answer B: \(\frac{3}{4}\)

The dot is positioned at the third quarter mark on the number line, which is \(\frac{3}{4}\). This is greater than \(\frac{1}{2}\).

G3-C04-T05-Q008 About 1 min

Which comparison is true?

  1. A \(\frac{2}{2}<\frac{2}{3}\)
  2. B \(\frac{2}{2}>\frac{2}{3}\) (2/2 = whole, 2/3 < whole)
  3. C \(\frac{2}{3}>\frac{2}{2}\) (3 > 2)
  4. D \(\frac{2}{3}=\frac{2}{2}\)
Check answer and explanation

Answer B: \(\frac{2}{2}>\frac{2}{3}\) (2/2 = whole, 2/3 < whole)

Same numerator (2): two halves = 1 whole, two thirds = part of a whole. Halves are bigger pieces than thirds. Rule: same numerator, smaller denominator (2 < 3) means bigger pieces, so \(\frac{2}{2} > \frac{2}{3}\).

exit

3 questions
G3-C04-T05-Q009 About 1 min

Lily has \(\frac{3}{8}\) of a chocolate bar. Noah has \(\frac{3}{4}\) of the same size chocolate bar. Who has more?

  1. A Lily (8 > 4)
  2. B Noah (3/4 is larger)
  3. C They have the same amount
  4. D Cannot tell without the bar's size
Check answer and explanation

Answer B: Noah (3/4 is larger)

Same numerator (3), different denominators, same chocolate bar: fourths are larger pieces than eighths. So \(\frac{3}{4}\) is more than \(\frac{3}{8}\). Noah has more because he has 3 larger pieces.

G3-C04-T05-Q010 About 1 min

The bars show \(\frac{1}{4}\) of pizza A and \(\frac{1}{6}\) of pizza B. Pizza B is bigger than pizza A. Can you say \(\frac{1}{4}>\frac{1}{6}\)?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q010
  1. A Yes, because fourths are always bigger than sixths
  2. B No, we can only compare when the wholes are the same size
  3. C Yes, the picture shows it
  4. D No, because 6 is bigger than 4
Check answer and explanation

Answer B: No, we can only compare when the wholes are the same size

CRITICAL: Fraction comparisons are ONLY valid when both fractions describe the same-size whole. Since pizza B is bigger than pizza A, \(\frac{1}{4}\) of the smaller pizza may actually be bigger than \(\frac{1}{6}\) of the larger pizza. We cannot compare them. Standard 3.NF.A.3.d requires recognizing that comparisons are valid only when the two fractions refer to the same whole.

G3-C04-T05-Q011 About 1 min

Using the bars, which fraction is larger?

Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q011
  1. A \(\frac{1}{2}\)
  2. B \(\frac{2}{3}\)
  3. C They are equal
  4. D Cannot tell
Check answer and explanation

Answer B: \(\frac{2}{3}\)

Comparing the shaded areas: two thirds covers more of the bar than one half does.

Keep the learning path connected
Previous skillWhole Numbers as Fractions Recommended nextTelling Time to the Nearest Minute Same strandUnit Fractions Same strandFractions on a Number Line
Page UP