1.2 Algebraic Expressions and Formulas

Lesson Plan 1.2: Algebraic Expressions and Formulas

Objectives:

• Students should be able to identify variable and coefficient parts of terms.
• Students should be able to combine like terms of an expression.
• Students should be able to evaluate algebraic expressions and formulas.
• Students should be able to solve basic problems using percents.
• Students should be able to apply the percent change formula to basic word problems.

Suggested Lecture Breaks:

• MWF: You have two days. Get through at least problem 3 on the first day.
• MW/TR: You have one day.

Suggested Lecture Notes:

Expressions and Like Terms

• Write the definition of an algebraic expression on the board.
  • An algebraic expression is a combination of variables and numbers along with operation symbols.
• Remind students of the definition of a variable:
  • A variable is a letter used to represent a number.
• Give students a few examples of algebraic expressions. Be sure to include at least two similar to those in Problem 1.
• Explain what it means to be a term in an expression and give the definition of a coefficient. Using these concepts, point out the variable and coefficient parts in the relevant examples you gave.
• Define like terms and what it means to combine like terms. Give 2-3 examples of this process, including one that requires the distributive property.
• Have students work on problems 1-3.

Evaluating Algebraic Expressions and Formulas

• Explain to the class what it means to define a variable and why this is necessary when writing algebraic expressions.
• Example:
  • Ask the class to describe how they would calculate a 20% tip on a restaurant bill of $10, $50, etc. Then lead the class in writing an algebraic expression to represent calculating a 20% tip for any bill amount, B. Illustrate how the expression can be used to calculate the 20% tip on a bill of any amount. Be sure to discuss defining variables.
• Now expand on the above example.
  • If we wanted a formula to calculate the tip for various tip percentages, what would it be? (I.e., how could we model this situation mathematically?)
  • Let the variable p represent the percentage (after converting to a decimal), b the bill amount, and t the tip amount. (Be sure to write out these sentences to be clear for your students). Then we get the formula pb=t.
• Point out that pb=t is an example of a formula. Remind them of the definition of a formula from their reading.

Percents

• Give the definition of a percent:
  • Suppose a represents a partial amount of the whole amount b. Then we have partial amount a / whole amount b = decimal value. The decimal value is then converted to a percent.
• Use the definition and the previous example to explain converting between a decimal and a percent. Be sure to emphasize WHY we do this -- using a percent as is in the previous example results in a nonsensical tip amount.
• Give a few examples using percents. This is a good opportunity to involve your students. Some suggestions are:
  • What percent of the class is from Lincoln?
  • What percent of the class that is from Nebraska is from Lincoln?
• Have students work on problems 5-10.
• Give a brief explanation of percent change, including the formula:
  • percent change = (change in amount / original amount)*100
• Motivate with an example. It's easy to talk about percent increase/decrease using population examples.
• Have students work on problems 11-13.