3rd Grade Equivalent and Comparing Fractions Test Solutions and Scoring (PDF)

1. Four of the eight parts are shaded.
2. \(\frac{1}{2}\) = \(\frac{4}{8}\)

Scoring: 1 point for shading exactly 4 eighths. 1 point for the missing numerator 4.

1. The mark is at the sixth eighths tick.
2. \(\frac{6}{8}\)
3. \(\frac{4}{8}\)

Scoring: 1 point per part. In (a) the mark must line up with the dashed line.

1. 7
2. \(\frac{6}{3}\)
3. 1

Scoring: 1 point per part. In (b), 2 wholes of 3 thirds each is 6 thirds.

1. \(\frac{5}{8} < \frac{7}{8}\)
2. \(\frac{4}{6} > \frac{2}{6}\)

Scoring: 1 point per correct symbol.

1. The top bar: \(\frac{2}{3}\); bottom bar: \(\frac{2}{6}\).
2. \(\frac{2}{3} > \frac{2}{6}\)
3. Thirds are bigger parts because the whole is cut into fewer pieces.

Scoring: 1 point for both fractions correct, 1 point for the comparison, 1 point for a reason about part size.

Each fourth is 2 eighths, so 3 fourths are 6 eighths.

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

Scoring: 1 point for circling only \(\frac{6}{8}\).

1. Priya. Sixths are bigger than eighths.
2. \(\frac{5}{6} > \frac{5}{8}\)

Scoring: 1 point per part.

When the numerators match, the bigger denominator means smaller parts. Sixths are smaller than thirds.

Correct: \(\frac{2}{6} < \frac{2}{3}\)

Scoring: 1 point for a correct explanation about part size, 1 point for the correct symbol.

1. Ten halves: \(\frac{10}{2}\) = 5 feet.
2. Six thirds: \(\frac{6}{3}\) = 2 feet.

Scoring: 1 point per part. Give the point if the fraction is shown and the whole number is correct.