3rd Grade Understanding Fractions Test Solutions and Scoring (PDF)

3rd Grade math test solutions: Understanding Fractions – Maths PDF

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This fractions test answers for 3rd Grade covers understanding fractions (Common Core 3.NF.A.1, 3.NF.A.2), with a free PDF to print.

Use these solutions to score the test out of 20. Each question lists how its points are earned. Give credit for correct reasoning even when the wording is different, but the fraction itself must be correct.

Grade 3 · Common Core State Standards: 3.NF.A.1, 3.NF.A.2

Fractions test answers: worked solutions

Question 1 – Read the model [3 pts]

\(\frac{5}{8}\)
\(\frac{3}{8}\)
\(\frac{1}{8}\)

Scoring: 1 point for each correct fraction. In part (b), 3 of the 8 parts are not shaded.

Question 2 – Shade the circle [2 pts]

Four parts shaded.

Any 4 of the 6 parts are shaded.
4 copies.

Scoring: 1 point for shading exactly 4 parts, 1 point for the answer 4.

Question 3 – Equal parts [2 pts]

Rectangle A.
Rectangle B has only 3 parts, and they are not the same size.

Scoring: 1 point for A. 1 point for a reason that says the parts are not equal (or that B has 3 parts).

Question 4 – Copies of a unit fraction [2 pts]

\(\frac{1}{8}\)
\(\frac{3}{4}\)

Scoring: 1 point per correct answer.

Question 5 – Points on a number line [3 pts]

Point C is one length from 0.

\(\frac{2}{6}\)
\(\frac{5}{6}\)
C is at the first tick mark after 0.

Scoring: 1 point for each part. For (c) the point must be at the first tick mark.

Question 6 – Garden sections [2 pts]

\(\frac{3}{8}\)
3 + 4 = 7 sections: \(\frac{7}{8}\)

Scoring: 1 point per part.

Question 7 – Find the mistake [2 pts]

He swapped the numbers. The denominator must be the number of equal parts in the whole (4), and the numerator is the shaded parts (3).

Correct fraction: \(\frac{3}{4}\)

Scoring: 1 point for the explanation, 1 point for the correct fraction.

Question 8 – Steps on a number line [2 pts]

Mei lands 3 lengths from 0.

The third tick mark after 0.
\(\frac{3}{6}\)

Scoring: 1 point for the mark at the third tick, 1 point for the fraction.

Question 9 – Rope pieces [2 pts]

1 + 2 + 2 = 5 pieces: \(\frac{5}{6}\)
6 – 5 = 1 piece: \(\frac{1}{6}\)

Scoring: 1 point per part.

Total score

Total

20 points

Key facts behind this fractions test answers

Key facts

A fraction describes equal parts of one whole.
The denominator (bottom) counts the equal parts in the whole; the numerator (top) counts the parts named.
A unit fraction has numerator 1 and shows one equal part, such as 1/8.
The fraction a/b is a copies of the unit fraction 1/b.
On a number line from 0 to 1, a/b is the point reached after a hops of length 1/b.

How to use this fractions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 3 chapters: Grade 3 math.

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