Problem
The symbol is a rule, not an operation: a ⊙ b becomes (a + b) x (a - b), so just substitute.
A fifth grader can write a calculation as an expression; the strange symbol is just shorthand for 'add, then multiply by the gap.'
5.OA.A.2Solve An Easier Related ProblemThe inner 7 ⊙ 5 sits in parentheses, so do it first: 12 x 2 = 24.
Parentheses tell us which little piece to finish first, so the messy expression turns into a single tidy number, 24.
5.OA.A.1Identify SubproblemsThe inner part 7 ⊙ 5 works out to 24.
The symbol is not a fixed sign but a recipe we were handed, so 7 ⊙ 5 may be rewritten as (7 + 5) x (7 - 5).
A rule that defines a symbol says the two sides always stand for the same number, so either one may be written in place of the other.
That leaves 12 x 2, which counts twelve taken two times and comes to 24.
Now the expression 32 ⊙ (7 ⊙ 5) becomes 32 ⊙ 24, because we just found that the parenthesized part equals 24.
Swapping the inside for its value keeps the meaning the same but leaves only one easy step to go.
5.OA.A.1Identify SubproblemsUse the same rule once more. Add 32 and 24 to get the sum, subtract to get the difference, then multiply the two results.
It is exactly the same 'add, subtract, multiply' move we already practiced on the small case, now with bigger numbers.
5.NBT.B.5Identify SubproblemsA new symbol is just a recipe in disguise: finish the part inside the parentheses first, then follow the same steps again.