When your students first begin translating phrases and expressions, it’s common for them to feel unsure about what the words really mean. Phrases like “less than,” “sum of,” or “quotient of” can trip them up, especially when the word order doesn’t match how they’d write the math. That’s why it’s so important to slow down and help your students connect key vocabulary to operations step by step. Today, I’ll walk you through how I introduced translating phrases and expressions in my own classroom using visuals, practice examples, and language-focused thinking.
See Translating Phrases and Expressions in Action
In this video, I walk you through how to teach translating phrases and expressions using simple, clear examples. You’ll see how I use a visual reference wheel to connect operation words with math symbols. I’ll also explain how to help your students decide which order to write terms based on the wording of the phrase. This approach is perfect for helping your students connect real-world language to algebraic expressions.
Key Takeaways From the Video
Here’s what to highlight when introducing translating phrases and expressions:
- Vocabulary matters. You want to help your students identify keywords that signal operations. Some keywords are sum, product, difference, quotient, more than, and less than.
- Order isn’t always straightforward. Words like “less than” and “more than” often mean the numbers are written in reverse order of the way they appear in the phrase.
- Use real numbers as examples. Plug in values like 15 less than 35 to help your students visualize what the expression should look like.
Example: “The quotient of a number and 20” should be written as x ÷ 20, not 20 ÷ x. Another example is “15 less than a number,” which should be written as x – 15, not 15 – x. You’re subtracting 15 from something else, not the other way around.
Extra Tips for Translating Phrases and Expressions
A go-to strategy that helped my students with translating phrases and expressions was building a word wheel at the start of the unit. We filled in each section with words that meant addition, subtraction, multiplication, and division. Not only did this become a year-long reference tool, but it also sparked great discussions about which words can be tricky, such as difference, decreased by, times as many.
Try this in your classroom: When your students are unsure about the correct order in a phrase like “15 less than a number,” ask them to replace the variable with a real number. For example, say, “What does 15 less than 30 mean?” Students will likely say 30 – 15. Then, they connect it back to the algebraic form, x – 15. This way, they can see how the structure of the phrase translates into an expression. This quick substitution strategy helps clarify the correct order every time.
I also reinforced that subtraction and division are not commutative. The order does matter. While 5 + x and x + 5 mean the same thing, 25 ÷ x is very different from x ÷ 25.
Additional Resource to Support Translating Phrases and Expressions
If you’re looking for more ways to help your students feel confident with translating phrases and expressions, I have a few favorites to share! These resources are designed to build understanding through visual aids, guided notes, and hands-on practice.
Start with reading Translating Words into Algebraic Expressions to learn more about how I taught this concept to my students.
You can also explore more resources from my TPT store:
- Translating Between Words and Math: Notes, Practice, Exit Tickets
- More Notes and Practice for Translating Between Words and Math
- 6th Grade Interactive Notebook
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