1. Students will learn to create 2-variable expressions from a given situation
2. Students will evaluate 2-variable expressions for various values of each variable
3. Students will develop an appreciation for the notion that one must have a value for both
variables in order to evaluate an expression
Attached "Writing 2-Variable Expressions" worksheet
This lesson is an introduction to the concept of 2-variable expressions (leading to 2-variable equations). The teacher should begin with a review of the concept of algebraic expressions, highlighting the difference between expressions and equations (namely that expressions have different evaluations for different variable values). Review several examples of single-variable expressions on the board and ensure that the class is sufficiently comfortable with the concept before proceeding.
Now ask why there only has to be one variable in these expressions. Is it possible to have more than one? What would that mean? Lead a brief discussion on what having 2 different variables in a single expression would mean, highlighting the fact that everywhere a certain type of variable occurs, it must represent the same quantity
. Put several examples on the board (e.g. 2x + 4y ; 3z - 2q ;
etc.). Have students practice evaluating several of these expressions individually for different values for the given variables.
Next, remind students of the skill of translating real-world situations into "Mathspeak" -- i.e. into Algebraic notation. Give them the following example to remind them of this skill from 1-variable Algebra:
John makes $150 less than three times what Mary makes: John = 3m
where 3m - 150
is an Algebraic expression representing what John makes.
Introduce the analagous skill for 2-variable expressions, highlighting that each variable must stand for a different kind
of quantity, and not simply a different number. Example:
I spent a lot of money at the fair! I bought a number of hotdogs and a number of hamburgers. The hotdogs cost $1.20 each and the hamburgers cost $3.40 each. Write an expression to represent the amount of money I spent using this information, and make sure to define your variables:
x = # of hotdogs , y = # of hamburgers
1.20x + 3.40y
Ask student to find how much money I spent if I bought 10 hotdogs and 10 hamburgers, 20 of each, and 50 of each. Then highlight the fact that it is impossible to say how much money was spent if I only tell you how many hotdogs I ate and not how many hamburgers.
Break students up into small groups and have them complete the attached worksheet together.