Algebra Scope and Sequence of Instruction. Objectives Lesson Support Description Key Vocabulary

Transcription

1 1 Algebra Scope and Sequence of Instruction UNIT 1: Prerequisite Skills for Algebra (14-16 days) Holt Algebra 1 Textbook Lesson 1-1 to 1-7 Glencoe 1-1 to 1-8, 2-1 Translate Verbal Expressions Into Algebraic Expressions Perform Integer Operations Holt - Lesson 1.1: Create Poster(s) of Words that Mean +,, x, Glencoe 2-1: Create Poster(s) of Words that Mean +,, x, PICTORIAL RESOURCES: Algebraic Expressions Include Integer Tile Activities to build Visual/Concrete Understanding Glencoe Warning!!! No review with operations on integers. You will need to supplement. Use integer tile activities to build visual/concrete understanding Algebraic Expression Evaluate Variable Constant Sum-Difference Product-Quotient More Than/Less Than Consecutive Integers Absolute Value Simplify Powers & Roots PICTORIAL RESOURCES: Integer Addition Use Area Model for explaining and teaching perfect squares. Combine Like Terms Include Algebra Tile Activities to build Visual/Concrete Understanding Glencoe 1-5 Example 3 Combine like terms is only shown here. Intro with algebra tiles and more practice is suggested. See Glencoe 7-3 & 7-4 Algebra Labs - (pgs. 375, ) PICTORIAL RESOURCES: Combine Like Terms , Base Exponent Power Perfect Square Square Root Cube Root Coefficient Variable Like and Unlike Terms 1

2 2 Apply Properties of Real Numbers Simplify using Order of Operations Build understanding of distributive property using Area Model Glencoe 1-5 Algebra Lab (Pg. 27) Algebra Tiles for Distributive Property Glencoe Reading Math (Pg. 38) Do this in preparation for solving equations and justifying steps in unit 2. Commutative Property Associative Property Distributive Property Reciprocal/Multiplicative Inverse Opposite/Additive Inverse Counterexample 2

3 3 UNIT 2: Equations and Inequalities: Solving: (26-30 days) Holt Algebra 1 Chapter 2 Lessons 2-1 to 2-7 Holt Algebra 1 Deductive Reasoning and Equations (Pg 99) Holt Algebra 1 Chapter 3 Lessons 3-1 to 3-7 Holt Algebra 1 Deductive Reasoning and Inequalities (Pg 169) Glencoe 2-2 to 2-8 Glencoe 6-1 to 6-6 Connections: Have students graph the solution to linear and absolute value equations as a point(s) on a number line in preparation for graphing solutions of inequalities. Justify each step in solving equations. (Prep for Geometric Proof) Use concrete representations (algebra tiles, stories, money, pictures, etc.) to build understanding of equations. Use Deductive Reasoning to Justify Solutions Solve 1-Step & 2- Step Equations Glencoe Reading Math (Pg. 38) Refer back to this in preparation for solving equations and justifying steps in solving equations. Glencoe 2-2 Algebra Lab Solve using Algebra Tiles (pg. 77) Equation Solution Properties of Equality Deductive Reasoning Solution Set No Solution Infinite Number of Solutions 3

4 4 Solve Multi-Step Equations Glencoe 2-4 Algebra Lab Solve Multi-Step Equations using Algebra Tiles (pg. 91) Solve with Variables on Both Sides Solve Proportions Solve Equations with Absolute Values Solve Inequalities & Graph on a Number Line Glencoe 6-2 Algebra Lab Solve Inequalities (pg. 300) Ratio Proportion Cross Product Scale Drawing Scale Model Formula Percent Unit Rate Percent of Change Absolute Value Inequality Compound Inequality Union Intersection and/or 4

5 5 UNIT 3: Linear Functions (30-34 days) Holt Algebra 1 Chapter 4 Lessons 4-1 to 4-3, 4-5 Holt Algebra 1 - Inductive Reasoning (Pg 233) Holt Algebra 1 Chapter 5 Lessons 5-1 to 5-3; 5-5 to 5-7 Glencoe 1-9 Glencoe 3-1 to 3-5 Glencoe 4-1 to 4-7 Intro to Functions: Use related vocabulary accurately Plot Points Recognize and Describe Patterns Holt - Inductive Reasoning (Pg 233) & Holt Algebra 1 One- Stop Planner-Exploration 4-5 (Arithmetic Sequences) Have student make predictions about arithmetic sequences. It is suggested NOT to use nth term formula listed here. A stronger connection can be made to slope-intercept form by identifying the initial term as the 0 th term (same as y- intercept) and using the common difference (same as the slope) to extend the pattern. Glencoe 1-9 Intro to Functions & Graphs * Holt - Lesson 4-4 Scatterplots and Trend Lines is not an Algebra 1 standard but does appear on the CAHSEE *Glencoe Lesson 4.6 Statistics: Scatter Plots and Lines of Fit is not an Algebra 1 standard but does appear on the CAHSEE Relation X-Axis Y-Axis Ordered Pair Inductive Reasoning Function Function Notation Domain-Input Range-Output Arithmetic Sequence * Positive Correlation *Negative Correlation *No Correlation *Scatterplot 5

6 6 Graph Lines using a Table Find x- and y- intercepts Find the Slope of a Line Convert Equations from Standard Form to Slope-Intercept Form Graph Equations using Slope- Intercept Form Write Linear Equations with & without a graph Write Linear Equations using Point-Slope Form Algebra Walk (CPM) This in an introductory lesson where students are human points and predictions are made about linear equations. See attached lesson resources. Glencoe 4-3 Graphing Calculator Lab Investigation PICTORIAL RESOURCES (from Pictorial Mathematics by Mendieta) Start writing equations by graphing and transition to non-graphing approaches after a need for algebraic methods is developed. Independent Variable Dependent Variable Linear Equation Linear Function X-Intercept Y-Intercept Rise/Run Slope Rate of Change Vertical Line Undefined Slope Horizontal Line Parallel Lines Perpendicular Lines Standard Form Slope-Intercept Form Point-Slope Form 6

7 7 UNIT 4- Systems of Linear Equations & Inequalities: Solving & Graphing (16-18 days) Holt Algebra 1 Chapter 6 Lesson 6-1 to 6-7 Glencoe 5-1 to 5-5 Glencoe 6-7 to 6-8 (Systems of Linear Inequalities) Connections: Start solving by graphing and transition to non-graphing approaches after a need for algebraic methods is developed. Solve by Graphing Model with Graphing Calculator System of Linear Equations Solution of a System Solve by Substitution Holt - LAB Model Systems of Equations with Algebra Substitution Tiles (Pg. 335) Glencoe 5-2 Algebra Lab Substitution with Algebra Tiles (pg. 260) Solve by Elimination Elimination Apply Systems of Equations Identify Systems with no solutions/many solutions Graph Systems of Linear Inequalities Have students work in pairs to create their own applications of systems. Holt - Lesson 6.4 Work concepts in this section into 6-1to 6-3 Parallel Lines No solution Infinitely many solutions Linear Inequality System of Linear Inequalities 7

8 8 UNIT 5 - Quadratics: Solving & Graphing (36-40 days) Exponent Rules: Holt Algebra 1 Chapter 7 Lesson 7-3, 7-4 Operations with Polynomials: Holt Algebra 1 Chapter 7 Lesson 7-6 to 7-9 Factoring: Holt Algebra 1 Chapter 8 Lesson 8-1 to 8-6 Solving: Holt Algebra 1 Chapter 9 Lesson 9-1 to 9-6 Holt Algebra 1 Chapter 11 Lesson 11-2 (Simplify Square Roots) Solving: Holt Algebra 1 Chapter 9 Lesson 9-7 to 9-9 Exponent Rules: Glencoe 7-1, 7-2 Operations with Polynomials: Glencoe Factoring & Solving 8-1 to 8-6 Graphing Quadratics 9-1 to 9.3 Simplify Radicals 10-1 (example 1 only) Quadratic Formula 9.4 Connections: Make strong connections between numeric solutions and x-intercepts of parabolas. Provide algebra tiles for students to use while factoring and solving. Physical Applications of Quadratics (Projectile Motion) Know and Apply Exponent Rules (products and quotients of powers) Holt - Lesson 7-3 Example #1 (simple applications with variables) Holt - Lesson 7-4 Example #1a (simple applications with variables) 8

9 9 Perform Operations on Polynomials (Add, Subtract, Multiply) Holt - LAB 7-7: Use Algebra Tiles for Polynomial Addition and Subtraction (Pg ) Holt - LAB 7-8: Use Algebra Tiles for Polynomial Multiplication (Pg ) Holt - Lessons 7-8 to 7-9: Use area model Glencoe 7-6 Use area model in addition to FOIL for connection to algebra tile work and preview of factoring. Glencoe 7-3 Algebra Lab Polynomials with Algebra Tiles (pg. 375) Glencoe 7-4 Algebra Lab Combine Like Terms with Algebra Tiles (pg ) Glencoe 7-6 Algebra Lab Multiply Polynomials (pg ) PICTORIAL RESOURCES: Multiplication/Area Model 256,257, 260, 262, 263 Polynomial Standard Form of a Polynomial Degree Constant Monomial Binomial Trinomial Quadratic Area Model F.O.I.L. Simplify Radicals Holt - Section Includes work on simplifying radicals. Radical Expression Square Root Perfect Square Factor using GCF Holt - LAB 8-2: Use Algebra Tiles for Factoring GCF (Page 486) Glencoe 8-2 Algebra Lab Factoring (GCF) with Algebra Tiles (pg. 425) Graph Quadratics and Know that their roots are the x- intercepts. Holt - LAB 9-4: Explore and make predictions about x-intercepts using the graphing calculator (quadratics with integer roots are suggested) Glencoe 9-1 Graphing Calculator Lab Quadratic Functions (pg ) Factor (noun and verb) Prime Factorization Greatest Common Factor Factored Form Parabola Factored Form X-Intercepts Roots Zeros Vertex Axis of Symmetry 9

10 10 Factor Quadratics in the form x 2 +bx+c Holt - LAB 8-3: Use Algebra Tiles for Factoring: x 2 +bx + c (Page 494) Glencoe 8-3 Algebra Lab Factoring x 2 +bx + c with Algebra Tiles (pg ) Glencoe 8-5 Algebra Lab Factoring Difference of Squares (pg. 447) Factored Form Difference of Squares PICTORIAL RESOURCES: Factoring Other Resources: Factor with Algebra Tiles (CPM AP 2 resource page) Factor Quadratics in the form ax 2 +bx+c Factor by Grouping Solve Quadratics using Multiple Methods (Square Root, Factor, Complete the Square, Quadratic Formula) Apply Quadratic Functions Holt - LAB 8-4: Use Algebra Tiles for Factoring: ax 2 +bx + c (Page 504) Glencoe 8-4 When factoring ax 2 +bx + c repeat Algebra Lab 8-3 (pg ) with new problems. Hint: Use Area Model Glencoe 9-3 Use algebra tiles to complete the square Glencoe 9-4 Algebra Lab Applying Quadratics Factored Form Square Root Zero Product Property Quadratic Formula Roots Zeros 10

11 11 UNIT 6: Rational Expressions (16-20 days) Holt Algebra 1 Chapter 7 Lessons 7-1 to 7-5 Holt Algebra 1 Chapter 10 Lessons 10-3 to 10-5, 10-6*, 10.7 Glencoe 11-2 to 11-4, 11-6 to 11-7 Know and Apply Exponent Rules *Holt - Selected problems from Lesson 10-6 may be included with Lesson 10-3 Simplify Rational Expressions Review with students how to reduce fractions by factoring. Numerator Denominator Rational Expression Excluded Value Perform Operations with Rational Expressions Solve Equations with Rational Expressions (Note: Polynomial Long Division and is not an Algebra 1 standards) Extraneous Solution 11