5th Grade Volume of Rectangular Prisms Test Solutions and Scoring (PDF)

1. \(4\times3=12\) cubes
2. \(12\times2=24\) cubic units

Scoring: 1 point for each part.

\(V=9\times4\times3=108\).

\(108\text{ ft}^{3}\)

Scoring: 1 point for a correct method, 1 point for 108 with cubic feet.

\(V=B\times h=35\times6=210\).

\(210\text{ cm}^{3}\)

Scoring: 1 point for multiplying base area by height, 1 point for the answer with units.

Base area: \(8\times7=56\).

\(224\div56=4\).

4 in

Scoring: 1 point for the base area, 1 point for the height.

1. \(6\times4\times3=72\) cubic units
2. \(3\times4\times1=12\) cubic units
3. \(72+12=84\) cubic units

Scoring: 1 point per part.

Cereal: \(8\times2\times12=192\). Juice: \(5\times4\times10=200\).

The juice box is greater by \(8\text{ cm}^{3}\)

Scoring: 1 point for both volumes, 1 point for the comparison and difference.

1. \(24\times12\times10=2{,}880\) cubic inches
2. \(24\times12\times8=2{,}304\) cubic inches
3. \(2{,}880-2{,}304=576\) cubic inches

Scoring: 1 point per part.

Original: \(2\times3\times4=24\). Double the height: \(2\times3\times8=48\), which is 2 times 24. Double all three edges: \(4\times6\times8=192\), which is 8 times 24.

Jamal is correct. Mei is not.

Scoring: 1 point for testing both ideas with numbers, 1 point for the correct conclusion.

1. \(4\times5=20\) cubes per layer, so \(20\times3=60\text{ cm}^{3}\)
2. One more layer needs 20 cubes

Scoring: 1 point for each part.