I’m practicing two-step word problems and my brain keeps trying to put its shoes on before its socks. Here’s the puzzle: I bought some bundles of pencils. Each bundle has 4 pencils. I also bought 3 extra single pencils. Altogether I ended up with 27 pencils. How many bundles did I buy?
I’m stuck on which operation should go first. Do I deal with the extra singles before I think about the bundles, or do I jump straight to dividing by 4 and then figure out the leftovers? I keep flip-flopping and end up with crumbly fractions that feel wrong.
It’s like making a sandwich: if I spread jelly before I remember the peanut butter, everything slides around. How do you read a problem like this and decide the correct two steps and their order? For this exact pencil situation, what are the two operations you’d do, and in which order, so it makes clean sense?
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3 Responses
Subtract the 3 singles first to isolate the pencils that must come in groups of 4 (27 − 3 = 24), then divide by 4 to get the number of bundles (24 ÷ 4 = 6), since only after removing the extras is the total a clean multiple of 4. Does writing it as 4b + 3 = 27 and then “undoing” +3 and ×4 help make the order feel natural?
Write it as 4b + 3 = 27 and “undo” in reverse order: subtract the 3 singles, then divide by 4, so (27 − 3) ÷ 4 = 6 bundles (equivalently, 27 ÷ 4 = 6 with remainder 3 matching the singles). I used to mix this up until a teacher told me to undo addition before undoing multiplication-this short refresher helps: https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations/v/two-step-equations.
Peel off what was added last: subtract the 3 singles first (27−3=24), then divide by 4 to get 6 bundles-I used to do 27÷4 and freak out at 6.75 bundles until my teacher laughed and said the “.75” is just the 3 loose pencils hiding in decimal clothes.
If you do divide first, the remainder 3 is exactly those singles, which is cute but always made me overthink it.