Linear Equations and Inequalities

Unit 5

Common Core Says...

Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example,?p?+ 0.05p?is the sum of the simpler expressions?p?and 0.05p. Viewing an expression as the result of operation on simpler expressions can sometimes clarify its underlying structure.

Mathematics ? High School: Algebra ? Introduction

Big Picture Lesson Planning for the Common Core

 

 

Week #14 Solve and Justify Literal Equations

• Solve literal equations for a variable A.CED.4, A.REI.3
• Justify solving equations A.REI.1, A.CED.1

Week #15 Solve and Graph Inequalities

• Solve complex one variable equations A.REI.3, A.CED.1
• Graph one variable inequalities A.CED.1
• Graph two variable inequalities A.REI.12

Lesson Ideas

All of these resources and more can be found in the livebinder below.

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Common Core Standards

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.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*

A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm?s law V = IR to highlight resistance R.

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. Construct a viable argument to justify a solution method.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* (Emphasize linear, absolute value, and exponential functions) Video Explaination

A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F.BF.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) = (x + 1)/(x -?- 1) for x ? 1.

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