2.1 Linear Equations

Lesson Plan 2.1: Linear Equations

Objectives:

• Students should be able to differentiate between equations and expressions.
• Students should be able to recognize solutions to linear equations.
• Students should be able to solve for a variable in a linear equation.
• Students should be able to characterize the solutions to a linear equation.

Suggested Lecture Breaks:

• MWF: You have two days. Get through Problem 4 on the first day.
• MW: You have one day.
• TR: You have 1.5 days. Start Problem 5 on the first day and finish it and the packet on the second.

Suggested Lecture Notes:

• Have students work problems 1 and 2 as a warmup.

Equations

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• Write the definition of an equation on the board (also from the reading):
  • An equation is a statement that two algebraic expressions are equal.
• Ask the class which letters in Problem 1 are equations, and which are expressions. Ask them how they know. Point out that an equation always contains an equality symbol, while an expression does not.
• Write the definition of a linear equation. The following definition is different from the reading, but should be helpful to them.
  • An equation in one variable is linear if it can be rewritten, without multiplying or dividing by x, to match the form Ax+B=C, where A, B, C are real numbers and A is not 0.
• Have them work in their groups on problem 3.

Solving For One Variable

• Pull in the example from the 1.2 lesson: calculating a tip.
  • Recall that last class, we found that an equation representing the tip for a given bill amount, pb=t.
  • What if we we have a bill of $44 and a resulting tip of $8? What was the percentage tipped?
  • Going back to the general formula pb=t, point out how we solve for p (Solving for one variable amongst others).
• Have students work on problem 4 in their groups.

Finding and Classifying Solutions to Linear Equations

• Write the definition of equivalent equations on the board:
  • Equivalent equations are related equations that have the same solutions.
• Provide an example of equivalent equations, such as:
  • 2x+5 = 9 and 3x+4=10. Simultaneously, show how to solve each equation in the set.
• Follow through into more complicated examples of solving equations. Do at least three examples, one each with one solution, infinitely many solutions, or no solutions.
• Use examples to discuss how to know whether an equation has one solution, infinitely many solutions, or none.
  • Good examples from the packet: Problem 5 (d) and (g)
• Have students work on the remainder of the worksheet.