Maria has 3 bags with 6 apples each. She gives 7 apples to her friends. How many does she have left? A student writes 6 − 7 = −1 as their first step. What went wrong?
AThe student used the wrong numbers from the problem
BThe student should have divided instead of subtracted
CThe student subtracted before multiplying, skipping the necessary first step of finding the total apples before any can be given away
DThe student got the correct answer; negative numbers are valid here
This problem requires two steps in a specific order: first, find the total apples (3 × 6 = 18), then subtract the ones given away (18 − 7 = 11). The subtraction step depends on the multiplication result — you cannot subtract from a quantity you haven't yet calculated. Performing the subtraction first uses a partial number (just 6, one bag's worth) instead of the full total, producing a nonsensical result. The order of steps is dictated by logic, not choice.
Question 2 Multiple Choice
When beginning a multi-step word problem, what should you do first?
AIdentify the largest numbers in the problem and work with those first
BWrite a number sentence immediately so you can start calculating
CRead the question carefully to identify what the final answer must be, then determine what intermediate steps are needed to get there
DFind all the addition in the problem before looking for multiplication or division
The final question is your destination. Identifying it first lets you work backward to determine what intermediate results you need. Without this step, students often grab nearby numbers and apply a familiar operation rather than thinking through the logical sequence. In a multi-step problem, the question at the end of the paragraph determines which calculations are necessary — and in what order.
Question 3 True / False
In a multi-step word problem, you can solve the steps in any order and still arrive at the correct final answer.
TTrue
FFalse
Answer: False
Steps must follow a logical sequence because later steps depend on the results of earlier ones. If a problem requires finding a total before subtracting from it, performing the subtraction first uses the wrong number. The order of operations in word problems is determined by the dependencies between quantities — some results must exist before others can be computed.
Question 4 True / False
Drawing a picture or diagram before calculating is a useful strategy for any student solving a multi-step word problem, not just students who struggle with arithmetic.
TTrue
FFalse
Answer: True
Diagrams and pictures make the problem's structure visible — they show what quantities are known, what is unknown, and how the pieces relate. This planning step helps all students, including strong ones, by ensuring they understand the problem before committing to calculations. Writing equations with labeled unknowns (□ or a letter) also keeps thinking visible and makes errors easier to find. The diagram is not a crutch; it is part of correct problem-solving process.
Question 5 Short Answer
After solving a multi-step word problem, why is it important to check whether your answer makes sense within the context of the story?
Think about your answer, then reveal below.
Model answer: The context sets boundaries on what is reasonable. If a problem says there are 25 students in a class and your answer is that 40 students received something, the story itself tells you that is impossible — your check caught an error before it was accepted as correct. Arithmetic can be executed correctly step by step and still produce a contextually impossible answer if the wrong operations were applied or the wrong numbers were used. Checking the answer against the story verifies that the plan was correct, not just the calculations.
This check is sometimes called a 'reasonableness check' and is distinct from checking the arithmetic. A student can recheck 4 × 8 = 32 and 32 − 9 = 23 perfectly and still have the wrong answer if they used the wrong operation at the first step. Only asking 'does this make sense in the story?' catches that kind of structural error.