I keep getting tangled on the order of steps in two-step word problems and my brain tries to add parentheses where they don’t belong. For example: A school buys 6 packs of markers, with 18 markers in each pack. Then they donate 25 markers to a local art club. How many markers are left for the classrooms? I feel like it should be “multiply then subtract,” but the wording sometimes makes me want to subtract first, like I’m taking away 25 before I even know the total. I think I’m overthinking whether the story order matters or if I should focus on units like “per pack” vs “total.” How do you reliably decide the order on problems like this without guessing? Any help appreciated!
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3 Responses
Match units before doing operations: since 25 is in markers, first find the total markers from packs (6 × 18 = 108), then subtract the change (108 − 25 = 83). I used to get tangled the same way until I began asking myself “Do the units match yet?”-that cue made the order feel obvious.
You’ve got the right instinct: think “what units can I actually combine?” In your example, 18 markers per pack is a rate, and 25 markers is a total count-those don’t add or subtract until you’ve turned the rate into a total. So first multiply to convert packs × markers-per-pack into total markers: 6 × 18 = 108. Now you’re in “markers” land, the same unit as the 25 donated, so subtract: 108 − 25 = 83. A reliable rule of thumb: addition/subtraction only works on like units; multiplication/division is what changes units (per pack → total, per person → total, etc.). Another handy lens is “what depends on what?” You can’t remove 25 from the school’s stash until you know the school’s stash! If the wording changes, the order can change too: donate 2 from each pack would be 6 × (18 − 2); donate 3 packs would be (6 − 3) × 18. Parentheses should follow the unit-logic: do adjustments “inside the group” before scaling if the change is per pack, and do adjustments after scaling if the change is on the whole total. Hope this helps!
I’ve got a simple, tidy rule I use so the parentheses goblins don’t run wild: change before you scale. If something is added or taken away in the story, adjust the per-unit amount first, then multiply or divide to scale it up. Here, the donation changes what’s effectively in a “typical pack,” so I shave that off the per-pack count: 18 − 25 = −7 markers per pack. Then I scale to all the packs: −7 × 6 = −42. The negative just tells you the classrooms are short by 42 markers after the donation (so there aren’t any left to distribute). In other words, it’s subtract first, then multiply-like fixing the recipe for one cookie before baking six dozen, so you don’t mass-produce the mistake.
I learned this trick when I was helping count craft kits for a school fair. I kept multiplying first, then subtracting, and it felt like I was chasing my tail-turns out I was scaling the wrong amount. A mentor told me, “Season one taco before you assemble the platter,” and boom-subtract at the unit level, then multiply. Ever since, I’ve trusted the “change-before-scale” rhythm, and if the answer goes negative, I know the story means “you’re short by that many,” which is a perfectly valid (if slightly dramatic) outcome.