Lesson 5: Inequalities (3 Days)
Students will explore the connection between equality and inequality. The behavior of inequalities in the negative number system is explored as well.
Common Core State Standards Addressed:
• A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
• A-CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
• A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
• A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
• A-REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Mathematical Practice Standard(s) Emphasized:
• MP 1: Make sense of problems and persevere in solving them.
• MP 2: Reason abstractly and quantitatively.
• MP 7: Look for and make use of structure.