In this lesson, students will learn how to translate words to expressions. Students will begin by translating phrases into one-step expressions. Then, students will review clue words that help them determine operations before moving on to writing two-step expressions from a description. As an additional challenge, an expression with parentheses is included as a final example. You can expect this lesson with additional practice to take one `45`-minute class period.
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Students should review what they already know about writing algebraic expressions. Give students a few minutes to write each expression and check them with a partner.
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Students should identify the key words from the phrases that helped them identify the operation needed to help translate to an expression. If needed, consider asking students what they would do if they knew the variable was `5` (or any other number they want to use) to help them identify the operation.
Work with different forms of subtraction and division. Talk about how “`5` subtracted from `n`” is different from “`n` subtracted from `5`”. This is especially confusing when you compare “`n` minus `5`” with “`n` subtracted from `5`”. Students think of these as the same expression.
There is a difference of opinion about “difference”. Typically, in elementary school students are taught that “difference of `7` and `5`” means `7-5`. Difference is related to subtraction; however it means the distance between two numbers and should always be positive.
Students should already have some prior knowledge and ideas of what clue words might be used. The key words from the warm up are already added to the table. Encourage your students to add as many clue words as they can to the table. They do not have to be limited to the number of rows shown!
Although not an exhaustive list, here are some words students may come up with.
If students miss any from this list, bring up the word and ask students which operation it would represent before adding it to the correct column of the list. Give students time to copy down the clue words in their notebook before moving forward.
Students need to be exposed to examples where there is more than one operation. For each of the next four examples, give students an opportunity to translate to an expression. They can compare their answer with a partner.
Telling a story: When reviewing each example with students, be sure to ask students what operations they used and how they determined the order of the operations. Typically, I would explain this as we start with `x`. Then it is multiplied by `5`. and then we add `10` more. Thinking of this as a story resonates with students.
Although translating expressions with parentheses is less common, it’s still important that students can differentiate between the descriptions.
List down what is same and what is different about these two expressions. Some students might say that they are the same expression while some others might believe that the we need to add a parentheses. Write down `8 + 1/2 n` and ask them if we followed the order of operations, what would we do first. Then ask them what we want to do first in sum of `n` and `8`. Talk about how we need to use parentheses to force addition to be done first.
After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of mild, medium, spicy practice problems for translating words to expressions. Check out the online practice and assign to your students for classwork and/or homework!
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