Lesson 1 Lesson Plan Title: Linear Equations, Linear Inequalities, and Linear Functions in Context Concept / Topic To Teach: I. Using algebra to analyze and solve problems in context, otherwise known as word problems Standards Addressed: I. identify and implement the steps necessary to use algebra to analyze and solve problems in context. II. define one or more variables that represent quantities in context, and write expressions, equations, inequalities, and/or functions that represent the relationships described in the context. III. solve equations and interpret their solutions in terms of the context. IV. recognize that different questions could be asked about the same context. General Goal(s): I. Understand the terminology common to Algebraic equations II. Practice with problems a. Interpreting linear functions b. Linear equations word problems c. Linear inequality word problems d. Linear function word problems III. Develop a step process to solving a problem Required Materials: Handouts Example problems Anticipatory Set (Lead-In): Go through the terms and ask students to define them Step-By-Step Procedures: Outline for students notes: Students will have this as a handout in their folder I. Define the terms a. Variable b. Linear c. Expression d. Function e. Equation f. Inequality g. Independent and dependent variable II. For each of the following examples do the following: a. b. What a variable is, and how to define a variable. How to write an expression. Lesson 1 c. How to substitute-in a value for a variable. d. How to create a function for a given situation/context. e. How to solve an equation/inequality. f. How to interpret a solution. III. Example Problem 1: At the beginning of an experiment, the concentration of a solution was 25mmol/dL. Three seconds later the concentration was 54 mmol/dL. Find the rate at which the concentration is changing, given that the rate of change is linear. Use these results to predict what the concentration would be after 12 seconds. IV. Example Problem 2: In the previous example, you had a concentration of 25 mmol/dL. Immediately after the experiment, the concentration is increasing by the value you calculated in problem 1. At this rate, if t is the number of seconds after the experiment starts, which of the following functions f gives the concentration there will be in the solution? (Assume that the reaction continues uninterrupted. ) A. f(t) = 54 + 25t mmol/dL B. f(t) = 25 + 54t mmol/dL C. f(t) = 25 + 9.7t mmol/dL D. f(t) = 9.7 + 25t mmol/dL V. Example Problem 3: In the previous example, you had a concentration of 25 mmol/dL. Immediately after the experiment, the concentration is increasing by the value you calculated in problem 1. At this rate, how many seconds will the concentration be at least 5 times the initial. VI. Example Problem 4: To tutor UB students, Mr. Vasquez charges $50 for the first 2 hours and $20 per hour after the first 2 hours. Which of the following expresses the amount, C, in dollars, Mr. Vasquez charges if it takes him x hours to tutor a student who has NOT paid attention in class, where x > 2? A. C = 20x B. C = 20x + 10 C. C = 20x + 50 D. C = 20x + 90 Plan For Independent Practice: Closure (Reflect Anticipatory Set): Assessment Based On Objectives: Example 4 Adaptations (For Students With Learning Disabilities): Extensions (For Gifted Students): Possible Connections To Other Subjects: This lesson can be tied to students taking chemistry although no chemistry concepts are needed to understand the problem.