Quiz: Grade 4 Fraction Equivalence & Comparison

Multiple Choice Questions

1. In this unit, students compare and order fractions with which of the following denominators?
A) 2, 3, 4, 5, 6, 8, 10, 12, and 100
B) 2, 4, 6, 8, 10, 12, 14, and 16
C) 3, 6, 9, 12, 15, and 18
D) 2, 3, 5, 7, and 11

2. What two benchmark numbers do students use to help reason about the size and location of fractions?
A) 0 and 10
B) 1/2 and 1
C) 1/4 and 2
D) 1 and 100

3. A rectangle is divided into 8 equal parts. If 1 part is shaded, what fraction does the shaded part represent?
A) 1/2
B) 1/4
C) 1/8
D) 8/1

4. On a number line divided into 5 equal parts between 0 and 1, a point sits on the 8th tick mark counting from 0. Which fraction does this point represent?
A) 5/8
B) 8/5
C) 8/8
D) 1/8

5. Which pair of fractions are equivalent, according to the reasoning shown in the resource (partitioning each fifth into 2 equal parts)?
A) 3/5 and 6/10
B) 3/5 and 3/10
C) 3/5 and 5/3
D) 3/5 and 6/5

6. Why is 4/12 equivalent to 1/3, according to the sample reasoning given?
A) Because 4 and 12 are both even numbers
B) Because dividing each third into 4 equal pieces creates twelfths, and 1/3 lands on the 4th tick mark from 0
C) Because 1/3 and 4/12 are both less than 1
D) Because 12 is greater than 3

7. A student says 7/12 is greater than 2/8 just because 7 and 12 are both greater than 2 and 8. What is missing from this reasoning, according to the resource?
A) The student should instead compare the fractions to 0
B) The student is not yet reasoning using benchmarks like 1/2 and 1, or common denominators
C) The student's answer is completely wrong
D) The student should only compare denominators

Short-Answer Questions

8. Explain why 2/4 and 1/2 are equivalent fractions. Use a diagram or words to support your reasoning.

9. A whole rectangle represents 1, divided into 10 equal parts with 7 parts shaded. Explain how you know the shaded part represents 7/10.

10. Explain whether 7/8 is greater than or less than 1/2. Use the benchmark of 1/2 in your explanation.

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Answer Key

1. A — Denominators used in this unit are 2, 3, 4, 5, 6, 8, 10, 12, and 100.
2. B — Students use 1/2 and 1 as benchmarks.
3. C — 1 shaded part out of 8 equal parts is 1/8.
4. B — With 5 equal parts per whole, the 8th tick mark represents 8/5.
5. A — 3/5 is equivalent to 6/10 because each fifth is split into 2 parts, doubling both the number of shaded parts and total parts.
6. B — Dividing each third into 4 equal pieces creates twelfths; 1/3 lines up with the 4th tick mark (4/12).
7. B — The student needs to reason using benchmarks (1/2, 1) or common denominators, not just compare numerators/denominators as "greater than."
8. Sample answer: The shaded portion represents 2/4 because 2 of 4 equal parts are shaded; it also represents 1/2 because the same shaded portion is 1 of 2 equal (larger) parts of the same diagram.
9. Sample answer: The rectangle is broken into 10 equal parts, and since 7 of those equal parts are shaded, the shaded part represents 7/10.
10. Sample answer: 7/8 is greater than 1/2. Half of 8 is 4, so 4/8 would equal 1/2. Since 7/8 has more shaded parts than 4/8, 7/8 is greater than 1/2.