Comparing Fractions Game

Grade 3 | Math | 3.NF.A.3, 3.NF.A.3.d

Objective

Students will compare two fractions and determine whether they are equal, greater than, or less than one another, explaining their reasoning using strategies such as common numerators, common denominators, or comparing to a whole (benchmark of 1).

Materials

• Comparing Fractions Game cards (set without pictures, one set per pair)
• Comparing Fractions Game cards (set with pictures, one set per pair, if available)
• "Less than, equal to, greater than" symbol cards (one set of three symbols per student)
• Scissors (to cut apart symbol cards, if not already cut)
• Paper and pencil for each pair (to record observations)

Warm-up (~5 min)

1. Write two simple fractions on the board, such as 1/2 and 1/4 (or use any pair from the card set).
2. Ask students: "Which fraction is bigger, or are they equal? How do you know?"
3. Take 2–3 quick verbal answers. Remind students that the denominator tells how many equal pieces the whole is cut into, and the numerator tells how many of those pieces we have.
4. Explain that today they will play a partner game comparing fractions using cards.

Main Activity (~25 min)

1. Pair up students. Give each pair one set of fraction cards (with pictures if available) and give each student their own set of the three symbol cards (<, =, >).
2. Explain the game steps (write these on the board for reference):
3. Step 1: The pair selects one card together.
4. Step 2: Each student individually decides whether the two fractions on the card are equal, or which one is greater, and holds up the matching symbol card.
5. Step 3: Partners compare their symbol choices.
6. If they agree, they take turns explaining their reasoning to each other.
7. If they disagree, they discuss until they reach agreement.
8. Step 4: Set the card aside and repeat with a new card.
9. Circulate around the room while pairs play. Listen for and encourage these strategies (do not need to lecture, just prompt with questions if pairs are stuck):
10. Comparing fractions with the same numerator (e.g., thirds are bigger pieces than fifths, so 2/3 > 2/5).
11. Comparing fractions with the same denominator (e.g., 2/3 < 1/3... wait, compare by counting pieces: 2/3 has one more third than 1/3).
12. Using "one whole" as a benchmark (e.g., a fraction less than 1 compared to a fraction greater than 1).
13. Have pairs continue until they complete 10 rounds (10 cards). If a pair finishes early, they may reshuffle and continue with remaining cards.
14. After 10 rounds, instruct each pair to write down on their paper: "What methods did you use to compare the fractions?" Give them a few minutes to jot notes together.

Wrap-up / Exit Ticket (~10 min)

1. Bring the class back together. Ask 2–3 pairs to share one method they used to compare fractions (common numerator, common denominator, or comparing to a whole).
2. Write the shared strategies on the board as a class list.
3. Exit Ticket: Give each student a simple prompt on paper (or have them answer verbally to the sub if no paper is available):
4. "Write down one pair of fractions from the game today. Tell whether one was greater, less than, or equal to the other, and explain how you know."
5. Collect exit tickets as students finish.

If Time Remains

Have pairs pick 3 of their favorite cards from the game and draw a picture (like two equally-sized rectangles or circles, divided and shaded) to show why one fraction is greater than, less than, or equal to the other. This reinforces the idea that equal-sized wholes must be used when comparing fractions visually.