Order of operations doesn’t matter in this instance. What matters is communication.The mother didn’t know how to read what her son wrote.He could help her understand by putting parentheses around the part he wanted her to read first.
He doesn’t need to know abstract rules for arbitrary calculations, or all the different ways we might possibly misunderstand each other. He just needs to know how to say what is in his mind.
What the Son Was Thinking
“Ten minus all of this stuff.”
10 – (2 × 3 + 1) = 3
How the Mom Interpreted It
“Ten minus this chunk, and then add one.”
(10 – 2 × 3) + 1 = 5
A Math Journaling Prompt
Write a multi-step equation. See how many values you can make, just by adding parentheses in different places.
For example…
(10 – 2) × (3 + 1) = 32
[(10 – 2) × 3] + 1 = 25
10 – [2 × (3 + 1)] = 2
Did I miss any?
For Older Students
Could you explain why we need such seemingly arbitrary rules if you are old enough to comprehend the order of operations?
Could you elaborate on how the rules aren’t as arbitrary as they initially appear to be? Why may mathematicians have chosen these specific rules?
Or do you believe that other regulations would have been more effective?
“Musings: Communication in Math” Denise Gaskins, copyright © 2025. Copyright © Inarik/Depositphotos for the image at the top of the post.
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