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The Algebra 1 Teacher's guide to the Common Core State Standards for Mathematics.

# Systems of Linear Equations and Inequalities

## Common Core Says...

Standard 1: Make sense of problems and persevere in solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, ?Does this make sense?? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Common Core State Standards - Mathematical Practice #1

## Big Picture Lesson Planning for the Common Core

Making Decisions. I want my students to be able to make decisions in their lives. Choosing the best home, the cheapest cell phone company, the best college, or the best car is difficult and many adults make poor choices for their situation. Students must be able to think through these problems and decide what variables make these the best before they can answer the questions.

#### Week #16Solving Systems by graphing and substitution

• Solve systems of equations by graphing (A.REI.6)
• Solve systems of equations by substitution (A.REI.6)

#### Week #17Elimination

• Solve systems of equations by elimination (A.REI.6)
• Prove elimination (A.REI.5)

## 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.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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.

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