Algebra 1 Unit 1 – Variables, Function Patterns, and Graphs Content Outcomes Essential Questions Key Concepts Standards Addressed Students will understand the use of variables. How are phrases in English written as algebraic expressions? How are situations modeled with equations? Modeling relationships with variables. Modeling relationships with equations. California: CA 17 Common Core: 6.EE-2 Students will learn about exponents and order of operations. How is order of operations used to simplify expressions? How is substitution used to evaluate expressions? Simplifying expressions using order of operations PEMDAS: Parentheses, Exponents, Multiplication or Division, Addition or Subtraction. Evaluating expressions using substitution. California: CA 17 Common Core: Students will learn about real numbers. How are real numbers classified? How are real numbers compared? Classifying real numbers. California: CA 17 Common Core: 8.NS-1 Students will learn about patterns and functions. How are dependent and independent quantities identified? How are relationships written as functions? Writing Function Rules. Understanding dependent and independent quantities. California: CA 17 Common Core: 6.EE-9
Algebra 1 Unit 4 – Solving Inequalities Content Outcomes Essential Questions Key Concepts Standards Addressed Students will learn about inequalities and their graphs. How are solutions of inequalities identified? How are solutions of inequalities graphed? Identifying solutions of inequalities using substitution. Graphing inequalities. California: CA 3 - 5 Common Core: Students will understand how to solve inequalities using addition and subtraction. How are inequalities solved using addition? How are inequalities solved using subtraction? Using addition to solve inequalities. Using subtraction to solve inequalities. California: CA 3 - 5 Common Core: A-REI-3 Students will understand how to solve inequalities using multiplication and division. How are inequalities solved using multiplication? How are inequalities solved using division? Using multiplication to solve inequalities. Using division to solve inequalities. California: CA 3 - 5 Common Core: A-REI-3 Students will understand how to solve multi-step inequalities. How are multi-step inequalities with variables on one side solved? How are multi-step inequalities with variables on both sides solved? Solving multi-step inequalities with variables on one side. Solving multi-step inequalities with variables on both sides. California: CA 3 - 5 Common Core: A-REI-3 Students will understand how to solve compound inequalities. How are inequalities containing “and” solved and graphed? How are inequalities containing “or” solved and graphed? Solving and graphing inequalities containing “and”. Solving and graphing inequalities containing “or”. California: CA 3 - 5 Common Core: A-REI-3 Students will understand how to solve absolute value equations and inequalities. How are equations that involve absolute value solved? How are inequalities that involve absolute value solved? Solving equations that involve absolute value. Solving inequalities that involve absolute value. California: Common Core:
Algebra 1 Unit 5 – Solving Inequalities Content Outcomes Essential Questions Key Concepts Standards Addressed Students will learn about relations and functions. What is a function? How are relations and functions identified? How are functions evaluated? Identifying relations and functions. Evaluating functions. California: CA 16, 17 Common Core: F-IF-1 Students will understand how to use function rules, tables, and graphs. How are functions modeled using rules, tables, and graphs? Modeling functions using rules, tables, and graphs. California: CA 16, 17 Common Core: Students will understand how to write a function rule. How is a function rule written given a table or situation? Writing a function rule given a table or real-world situation. California: CA 16, 17 Common Core: Students will learn about direct variation. How is a direct variation equation written? How are ratios and proportions used with direct variations? Writing an equation of a direct variation. Using ratios and proportions with direct variations. California: CA 16, 17 Common Core: Students will learn about inverse variation. How are inverse variations solved? How do direct variations and inverse variations compare? Solving inverse variations. Comparing direct and inverse variation. California: CA 16, 17 Common Core:
Unit 10 – Quadratic Equations and Functions Content Outcomes Essential Questions Key Concepts Standards Addressed Students will learn about quadratic graphs. How are quadratic functions of the form y=ax2 and y = ax2 + c graphed? Graphing quadratic functions of the form y=ax2 and y = ax2 + c using tables. California: CA 14, 19 -22 Common Core: F-IF-7a Students will learn about quadratic functions. What is a quadratic function? How are quadratic functions of the form y = ax2 + bx + c graphed? How are quadratic inequalities graphed? Graphing quadratic functions of the form y = ax2 + bx + c using x = . Graphing quadratic inequalities. California: CA 14, 19 -22 Common Core: F-IF-7a Students will understand how to solve a quadratic equation. How is a quadratic equation solved by graphing? How is a quadratic equation solved using square roots? Solving quadratic equations by graphing. Solving quadratic equations using square roots. California: CA 14, 19 -22 Common Core: A-REI-4b Students will understand how to solve a quadratic equation using factoring. How is a quadratic equation solved by factoring? Solving quadratic equations by factoring. California: CA 14, 19 -22 Common Core: A-SSE-3a; A-REI-4b Students will understand how to solve a quadratic equation by completing the square. How is a quadratic equation solved by completing the square? Solving quadratic equations by completing the square. California: CA 14, 19 -22 Common Core: A-REI-4b Students will learn about the quadratic formula. How is the quadratic formula used to solve quadratic equations? Using the quadratic formula, x = , to solve quadratic equations. California: CA 14, 19 -22 Common Core: A-REI-4b Students will learn about the discriminant. What is a discriminant? How is the number of solutions of a quadratic equation found? Finding the number of solutions of a quadratic equation using the discriminant: b2 – 4ac. California: CA 14, 19 -22 Common Core: Algebra 1
Content Outcomes Essential Questions Key Concepts Standards Addressed Students will learn about the Pythagorean Theorem. How are real-world problems solved using the Pythagorean Theorem? How are right triangles identified? Pythagorean Theorem: a2 + b2 = c2 California: Common Core: Students will understand how to use the distance formula. How is the distance formula used to find the distance between two points? Distance formula: d = California: Common Core: 8.G-8 : Students will understand how to use the midpoint formula. How is the midpoint formula used to find the midpoint of a line segment? Midpoint formula: M = . California: Common Core: Students will learn about trigonometric ratios. How are trigonometric ratios found? Finding trigonometric ratios using SOHCAHTOA. California: Common Core: Students will learn about angles of elevation and angles of depression. How are trigonometric ratios used? Solving problems using trigonometric ratios. California: Common Core: Algebra 1 Unit 12 – Rational Explanations and Functions