Problem 3 worked answer
Steve’s Big Dig
Designed for Grade 5 · Uses Middle Grade 5 math · About 2.5–6.5 minutes
At a glance
- Part 1: Steve removes 125 blocks.
- Part 2: He should expect 12.5 blocks, or coal blocks, on average.
Key idea
The cube-shaped hole can be viewed as 5 equal horizontal layers. Each layer is a 5-by-5 square. First find the number of blocks in one layer, then multiply by the number of layers.
1. Count all removed blocks
One horizontal layer contains
blocks.
There are 5 such layers, so the whole hole contains
blocks.
Equivalently, multiply all three dimensions: . Steve removes 125 blocks.
2. Find the expected amount of coal
On average, 1 out of every 10 removed blocks contains coal. One tenth of 125 is
.
Steve should therefore expect coal blocks on average. This is an expected value across many similar holes. A single actual hole cannot contain half a block; its coal count will be a whole number and may be above or below .
Check
Five layers of 25 blocks give . Ten groups averaging 12.5 coal blocks would correspond to total blocks, so the one-in-ten calculation is consistent.
Technical fit and rating
Geometry · Measurement · Number and operations · Data and probability
How the rating works →mathjewels.com/answers/problems/3/