Translating Phrases into Expressions

We ordered these new student whiteboards. They're about a foot by a foot and a half, and blank on one side and have the coordinate plane on the others. I think they'll be great when we get into functions.

I decided to roll them out when the class was exploring the relationship between algebraic expressions and phrases, working in small groups, I started to debrief the homework and then move onto the discussion. "Flipped Learning" is a new thing for some students in my classroom, but basically it's coming prepared to class by taking notes, watching videos or a number of other tasks. The assignment which students had when they walked into class was this:

  1. Read pages 10-11 on algebraic expressions.
  2. Write down synonyms for the following words: Add, Subtract, Multiply, Divide. (A synonym is a word that means the same thing. For example a synonym for "add" would be "plus"
  3. Translate a word phrase of your own into an expression with algebraic language. Example: "Five apples plus 3 oranges = 5a + 3o"
  4. Translate an algebraic expression your own into a word phrase. Example: "4-7y = 4 minus the product of 7 and y"
  5. This assignment is about translating numbers to language. All of you can speak more than one language. What advice would you have to someone that is trying to translate something into a new language?
I like to think that it has more inquiry and analysis leading to higher order thinking skills and creates a better foundational understanding of the principles underlying mathematics that we can use to describe our world.

After discussing this assignment by eliciting notes and sharing our thoughts, we looked at translating phrases and expressions back and forth. They started easy to build confidence and got eventually harder. Some of the examples were:

Translate "3 more than 5" into an expression
Translate "4y + 2" into a phrase
Translate "The quotient of 9 and 'p' times 5" into an expression.

The Quandary of "3 less than 5"
This is deceiving and a question just within or out of a student's zone of proximal development. What's deceiving is that as an expression it becomes "5 - 3" as there are obvious connections to the associative property in mathematics applying to some operations and not the other. I was curious to know whether or not students could identify this misconception.

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