Comparing Fractions Game — Quiz

Multiple Choice

1. In the Comparing Fractions Game, students work in what kind of groups?
A. Groups of four
B. Individually
C. Pairs
D. Whole class teams

2. After selecting a card, what does each student do first?
A. Immediately tell their partner the answer
B. Individually decide whether the fractions are equal, or which is greater
C. Draw a picture before looking at the card
D. Skip to the next card

3. What happens if the two partners disagree about a card?
A. They ask the teacher for the answer
B. They each keep their own answer
C. They discuss until they reach a consensus
D. They discard the card

4. How many rounds do students complete before recording their observations?
A. 5
B. 10
C. 15
D. 20

5. When comparing fractions with the same numerator, such as 2/3 and 2/5, which is true?
A. 2/5 is greater because 5 is a bigger number
B. 2/3 is greater because thirds are bigger pieces than fifths
C. They are always equal
D. It cannot be determined

6. When comparing fractions with the same denominator, such as 1/3 and 2/3, how do we know which is greater?
A. Compare the denominators only
B. The fraction with more of the equal-sized pieces (larger numerator) is greater
C. The smaller numerator is always greater
D. They must be equivalent

7. Which strategy uses the number 1 (a whole) to compare fractions like 1/3 and 3/2?
A. Common numerator strategy
B. Common denominator strategy
C. Benchmark strategy
D. Picture-only strategy

8. According to the resource, what must be true about the wholes shown in fraction pictures for a comparison to be valid?
A. They can be different sizes
B. They must be equally sized
C. They must be different shapes
D. They are not important

Short Answer

9. Explain why 1/2 and 2/4 are equivalent fractions, using the reasoning described in the resource about shaded squares.

10. Describe one method (other than drawing a picture) that students can use to compare two fractions, and explain how it works.

11. Why is it appropriate for third graders to use "1 whole" as a benchmark when comparing fractions, according to the commentary?

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Answer Key

1. C
2. B
3. C
4. B
5. B
6. B
7. C
8. B
9. Both squares (equal-sized wholes) show the same amount shaded — 1/2 shows one of two equal parts shaded, and 2/4 shows two of four equal parts shaded, but the shaded area covers the same total amount of the whole in each case.
10. Accept either: Common numerator — if two fractions have the same numerator, the one with the smaller denominator is greater because the whole is divided into fewer, larger pieces; Common denominator — if two fractions have the same denominator, the one with the larger numerator is greater because it has more of the same-sized pieces.
11. Because understanding the meaning of "a whole" is fundamental to understanding a fraction, so using 1 as a benchmark fits within third-grade understanding of fractions.