Problem
First evaluate the bare expression using order of operations: do the multiply and divide first, then add and subtract left to right.
Knowing the baseline value of 81 tells us what any parenthesis placement has to beat.
5.OA.A.1Look For A PatternWhatever is folded inside the parentheses gets multiplied by 10 too, so 8 + 5 makes it 13.
Adding inside the parentheses before multiplying lets the +5 ride along with the times-10, which is far more powerful than adding 5 on its own.
5.OA.A.2Look For A PatternPutting the parentheses around 8 + 5 makes the result as large as it can be.
Grouping 8 + 5 hands the multiplier 10 a bigger amount to copy, and the 5 that was worth only 5 on its own becomes worth 50 inside the multiplication.
Ten groups of (8 and 5) is ten groups of 8 plus ten groups of 5, so anything pulled inside the parentheses gets multiplied by ten as well.
No other placement does better, because every other grouping makes the amount that 10 multiplies smaller instead of larger.
The expression is these pieces put together and taken away in turn, so shrinking the piece that 10 multiplies shrinks the whole result.
With the parentheses around 8 + 5, finish the rest of the expression: still divide 16 by 4 first, then subtract.
This single placement lifts the answer from 81 all the way to 126.
5.OA.A.1Guess And CheckEvery other grouping gives 90, a non-whole 77.25, or leaves 81, so none of them beats it.
Listing every meaningful placement confirms that 126 is truly the largest whole-number result, not just a lucky guess.
5.OA.A.1Make A Systematic ListPut the parentheses where they help the times-10 work harder: 10 x (8 + 5) - 16 / 4 = 126.