The question came up on a homeschool math forum:
“My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’
“He wrote down 10 – 2 × 3 + 1.
“When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.
“How can I help him understand order of operations?”
[If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]
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 b…
The question came up on a homeschool math forum:
“My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’
“He wrote down 10 – 2 × 3 + 1.
“When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.
“How can I help him understand order of operations?”
[If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]
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
If you’re old enough to understand the rules for order of operations, can you explain why we need such seemingly arbitrary rules?
Can you explain how the rules aren’t quite as arbitrary as they seem at first glance? Why might it have made sense to mathematicians to pick these particular rules?
Or do you think there are other rules that would have worked better?
* * *
“Musings: Math is Communication” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © inarik / Depositphotos.
Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my free email newsletter.
This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.