KA-0038Building and counting with unit cubes
3 points, difficulty 1 of 3Level 5–6about 45sA solid block is built from unit cubes and measures 4 by 3 by 2. How many unit cubes does it contain?
Text description of the figure
A rectangular block built from unit cubes, 4 cubes long, 3 cubes deep and 2 cubes tall, drawn so that both layers are visible.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Count one layer, then count the layers.
2The strategy
A solid block is layers of the same size stacked up. Work out how many cubes are in one horizontal layer, then multiply by the number of layers.
3The full solution
One layer is 4 x 3 = 12 cubes and there are 2 layers, so 12 x 2 = 24.
Solution— no shortcut on this one
One horizontal layer is 4 by 3, which is 12 cubes. The block is 2 layers tall, so it holds 12 x 2 = 24 unit cubes. The transferable idea: counting a layer at a time reaches the cubes you cannot see, and it keeps working when the layers are not all the same size.
Why this is on the test: It anchors the layer-by-layer habit before the harder hidden-cube questions where the layers differ in size.