Small cubes are stacked in a corner as shown. Some are hidden from view. How many small cubes are there altogether?
Text description of the figure
A stack of unit cubes in a corner, three layers tall. The bottom layer is a 3 by 3 square of 9 cubes, the middle layer is a 2 by 2 square of 4 cubes sitting on one corner of it, and the top layer is a single cube.
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Count one layer at a time, from the bottom.
2The strategy
Work out how many cubes are in each horizontal layer separately, including the ones hidden behind the front. Then add the layers.
3The full solution
Bottom layer 3 by 3 = 9 cubes, middle layer 2 by 2 = 4 cubes, top layer 1 cube. Total 9 + 4 + 1 = 14.
Solution— no shortcut on this one
Count by layer rather than by what you can see. The bottom layer is a full 3 by 3 square, which is 9 cubes. The middle layer is 2 by 2, which is 4. The top is a single cube. Adding gives 9 + 4 + 1 = 14. The transferable idea: layers reach the cubes the drawing hides.
Why this is on the test: Hidden cubes are one of the most common Kangaroo figures, and the only reliable method is layer by layer, not face by face.