Problem 8 worked answer
The Ore Cart Graph
Designed for Grade 3 · Uses Middle Grade 3 math · About 2.5–7 minutes
At a glance
- Part 1: The graph represents 40 ore blocks altogether.
- Part 2: After the move, iron has 16 blocks and gold has 12 blocks, so iron has 4 more blocks than gold.
Key idea
Each cart symbol represents 4 blocks. The graph begins with 3 coal symbols, 5 iron symbols, and 2 gold symbols.
1. Find the total represented
There are cart symbols in all. Scale the symbol count using the key:
.
Therefore the three rows represent 40 ore blocks altogether.
The row-by-row calculation gives the same result: coal is , iron is , and gold is ; then .
2. Compare iron and gold after the move
One cart symbol’s worth is 4 blocks. Moving that amount from iron to gold changes the piles to
iron blocks
and
gold blocks.
Now compare them: . Iron has 4 more blocks than gold.
Check
Moving blocks does not change the total. After the move, , matching Part 1. Iron lost exactly the same 4 blocks that gold gained.
Technical fit and rating
Data and probability · Number and operations
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