Brainstorming Algebraic Expressions

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Objective

SWBAT model real life situations with variables. SWBAT make sense of expressions written with variables. SWBAT determine when an expression does not have meaning.

Big Idea

Does this expression mean anything? Students create algebraic expressions from a given a table of variables and their definitions.

Opening

10 minutes

I begin class by handing out Serving Up Symbols. This resource includes a table with all of the variables and their meanings.  We read through the opening paragraph and task as a class. I tell students that using these letters, it is possible to write many algebraic expressions.  I let my students know that today they will be working in small groups to generate as many meaningful expressions from the list as they can. Essentially, we do the second part of the task first.

Next, I open up discussion to consider what a "meaningful expression" might be.  I ask for examples. If necessary, I give students an example of one meaningful expression and an example of an expression that has no meaning. For example, I scribe the expression B*W on the board. I tell students they can multiply the number of boys that each lunch each day by the number of food servers per line. Then I ask, does this expression give them any useful information.  In other words, BW doesn't have much meaning in the context of the cafeteria lunch.

Next, I tell students that, of course, many other expressions do have a meaning.  For example, the expression C*P, the number of classes per lunch period times the number of lunch periods per day represents the total number of classes for lunch each day.  In the context of cafeteria lunch, the expression C*P does have meaning.

Finally, I establish a protocol with my students for writing expressions. I show them that when they write an expression, I want them to write the variables and the operation(s) they use on the left side of the equals sign and then the meaning (in words) of the expression on the right side.  I clarify with them that the expression C*P can be written you would want them to write C*P = the number of classes that have lunch each day.

Investigation

30 minutes

Now, I let my students get to work on Serving Up Symbols! I usually set up the small groups ahead of time. As I circulate I watch for the following:

• If students have difficulty getting started, I may give them an example of an expression and ask them to generate the meaning. For example, I might ask them what B + G would represent. Students should see that B + G would add the number of boys and girls that buy lunch each day and they could write that it equals the total number of students that buy lunch each day.
• Another way to get students thinking is to ask them to come up with some questions that they think the table might be able to answer.  For example, they might be able to generate an expression that answers the question: What expression represents the total cost of an entree, side dish, and beverage?

For many students, this task may represent a shift in approach to modeling situations with expressions. I find that this is usually the case for my students, so I give them plenty of time to think, reason, and (if necessary) persevere.

Discussion + Closing

20 minutes

Serving Up Symbols is a fun task to have students share out toward the end of class. Going around the room, I ask each group to share out an expression and its meaning with the class.  If it will work given the mood in the room, I make it a challenge activity and ask the other groups to either verify or challenge the expression based on whether or not it has meaning.  This is a great opportunity for students to practice Critiquing the Reasoning of Others You can keep a record of all the expression on the board and continue around the room until they have all been shared.

Before closing, I ask my students to do a reflection:

What makes an expression meaningful?

If time allows, I will have some students share their responses. If not, I will collect the responses as an Exit Ticket and type up some of their responses to share with the whole class at the beginning of the next lesson.

Citations

Serving Up Symbols is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

http://www.mathematicsvisionproject.org/secondary-1-mathematics.html