Fraction Classroom · 2.3.0 · Student pages

Count a solid by complete layers of unit cubes

Connect unit-cube packing to the area of one layer and the number of identical layers in a rectangular prism.

Anonymous group code: __________ Date: __________

Top-view plans of two complete layers. Each outlined cell marks one unit cube, so the two 12-cube layers contain 24 cubes in all.

Build the idea

Build or draw one complete base layer. Four cubes along the length and three along the width make twelve cube positions.
Place one cube in every position. The layer must be full; gaps would mean that a rectangular-prism formula no longer describes the actual packing.
Stack a second identical layer with no overlap or gap. The height of two cubes counts two complete layers of twelve.
Record 4 × 3 × 2 = 24 cubic units. Distinguish the base's area in square units from the solid's volume in cubic units.

Worked example: 24 unit cubes, so its volume is 24 cubic units. Each complete layer contains 4 × 3 = 12 cubes, and two layers contain 12 × 2.

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.