High School Mathematics Algebra I Part II Unit 6
Subject: Mathematics
Course: Algebra I Part II
Timeline: Days
Unit 6 Title: Systems of Linear Equations and Inequalities
Unit Overview:
This unit introduces and formalizes systems of linear equations and inequalities, beginning with recognizing the types of problem contexts that can be modeled by a linear system. Students will work with a variety of contexts to model and interpret solutions. This unit allows students to discover through guided exploration the methods of solving a system of linear equations: by using a table, graphing, substitution and elimination. Students will also learn to identify which method is the most efficient when solving a particular system. Students will then learn to graph and shade a linear inequality on a coordinate grid and find multiple solutions that make the inequality true and other solutions that make the inequality false. Finally, students will graph a system of linear inequalities and use shading to determine an appropriate solution set. Students will be consistently called on to explain their own strategies and procedures using appropriate mathematical vocabulary as well as analyze the solution methods of others.
Unit Objectives:
By the end of Unit 6 all students will be able to:
- identify and define systems of equations and inequalities;
- make a model of a problem context involving linear systems;
- write and solve linear systems using a table, graph, substitution and/ or elimination;
- decide and defend when one method is more efficient to use than another;
- describe what no solution, one solution, and infinitely many solutions means in a given context;
- graph a linear inequality on a coordinate grid and find multiple solutions that make the inequality true;
- graph a system of linear inequalities on a coordinate grid and find multiple solutions to make the system of inequalites true;
- interpret solutions to problems in the context of the problem situation.
Focus Standards:
PA.CCSS.Math.Eligible Content.A1.1.2.2.1 Write and/ or solve a system of linear equations (including problem situation) using graphing, substitution, and/ or elimination.
PA.CCSS.Math.Eligible Content.A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (limit system to two linear equations only).
PA.CCSS.Math.Eligible Content.A1.1.3.2.1 Write and/ or solve a system of linear inequalities using graphing.
PA.CCSS.Math.Eligible Content.A1.1.3.2.4 Interpret solutions to problems in the context of the problem situation (limit system to two linear inequalities only).
Mathematical Practice Standards:
#5 Model with mathematics.
#6 Attend to precision.
#7 Look for and make use of structure.
Assessments:
- Formative Assessments within Lessons
- Unit 6 Assessment
Differentiation:
This unit has accommodation suggestions included throughout.