Depth · one concept from first principles · step 2 of 4
There are red marbles. There are more green marbles than red marbles. The number of yellow marbles is fewer than times the number of green marbles. How many yellow marbles are there?
Green is 3 more than the 12 red marbles, so add 3 to 12.
"3 more than" is a simple addition a fifth grader can write straight from the words.
5.OA.A.2Identify SubproblemsYellow is 4 fewer than 2 times the green count. Double 15, then subtract 4.
"2 times" means multiply and "4 fewer" means subtract, so the order multiply-then-subtract matches the words.
5.OA.A.2Identify SubproblemsSwapping 15 for (12 + 3) folds everything into one expression: 2 x (12 + 3) - 4.
Seeing the same 15 appear in both steps lets us nest one part inside the other; parentheses tell us to add before multiplying.
5.OA.A.1Look For A PatternWriting (12 + 3) in place of the green count turns the work into the single expression 2 x (12 + 3) - 4, and it still comes to 26.
15 and (12 + 3) are two names for the very same number, so swapping one for the other cannot change what the expression comes to.
The parentheses have to stay, because doubling is meant to act on the whole green count, not on the 12 alone.
Two times the green count means two equal groups of everything green, and everything green is the 12 and the 3 together.
Solve each part in order, then nest the parts inside one expression with parentheses so the whole story fits in a single calculation.
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Branching State Enumeration, Small-Domain Constrained Search. Why the shapes repeat →