Solving systems of equations Solving systems of inequalities by graphing Systems of equations with three variables Focus Standards Addressed in this Unit: CC.2.2.HS.D.10 – Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically Important Standards Addressed in this Unit: N/A Misconceptions: Common mistakes with creating a graph from a linear equation Confusing “greater than” and “less than” Difficulty creating a math problem from the information in a real life situation Concepts/Content: System of equations Break-even point Consistent Inconsistent Independent Dependent Substitution method Elimination method Ordered triple Competencies/Skills: Solve systems of linear equations graphically Solve systems of linear equations algebraically Solve systems of inequalities by graphing Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities Solve systems of linear equations in three variables Solve real-world problems using systems of equations and inequalities Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test Interdisciplinary Connections: Additional Resources:
Interdisciplinary Connections: N/A Additional Resources: Glencoe Algebra 2 textbook USA TestPrep Subject: Mathematics Course: Algebra II Suggested Timeline: 4 to 5 weeks Unit Title: Radical Functions Unit Overview/Essential Understanding: In Unit 5, students will simplify various radical expressions as well as apply operations to radical expressions. They will also determine solutions of radical equations using algebraic methods. Unit Objectives: At the end of this unit, students will have a strong understanding of and be able to independently work with: Simplifying radicals nth roots Operations with radical expressions Rational exponents Solving radical equations Focus Standards Addressed in this Unit: CC.2.2.HS.D.2 – Write expressions in equivalent forms to solve problems CC.2.1.HS.F.1 – Apply and extend the properties of exponents to solve problems with rational exponents
Important Standards Addressed in this Unit: N/A Misconceptions: Difficulties with graphing quadratic equations Confusion with choosing the correct factoring method when solving quadratic equations Basic arithmetic errors when using completing the square or the quadratic formula Concepts/Content: Quadratic Parabola Axis of symmetry Vertex Standard form Root Zero Factored form FOIL Imaginary unit Complex number Complex conjugates Completing the square Quadratic formula Discriminant Competencies/Skills: Graph quadratic functions Find and interpret the maximum and minimum values of a quadratic function Solve quadratic equations by graphing Estimate solutions of quadratic equations by graphing Solve quadratic equations by factoring Perform operations with pure imaginary numbers Perform operations with complex numbers Solve quadratic equations by using the square root property Solve quadratic equations by completing the square Solve quadratic equations by using the quadratic formula Use the discriminant to determine the number and type of roots of a quadratic equation Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test