Table of Contents. Teacher Resources. Lesson Plans

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1 Table of Contents Teacher Resources Research to Support Algebra Intervention Correlation to the NCTM Standards How to Use This Program Planning Your Intervention Program Algebra Intervention Pacing Plan Differentiation Strategies Data-Driven Instruction Manipulatives Teacher Resource CD Professional Development DVD References Cited Lesson Index Lesson Plans Week Game of the Week: Math Bee Lesson 1: Diagnostic Pre-test Lesson 2: Adding Integers Lesson 3: Multiplying and Dividing Integers Lesson 4: Writing One-Variable Equations Lesson 5: Week 1 Review Week Game of the Week: Who Has? Lesson 6: Collecting Like Terms Lesson 7: Distributing and Collecting Lesson 8: Solving Linear Equations Lesson 9: Solving Linear Equations Lesson 10: Week 2 Review Week Game of the Week: Coordinate Plane Game Lesson 11: Solving Equations Lesson 12: Coordinate Planes Lesson 13: Relations and Functions Lesson 14: Equations as Relations Lesson 15: Week 3 Review Week Game of the Week: Algebra Aces Lesson 16: Slope-Intercept Form Lesson 17: Point-Slope Form Lesson 18: Graphing Linear Equations Lesson 19: Graphing Inequalities Lesson 20: Week 4 Review Week Game of the Week: Algebra Aces Lesson 21: Solving Multistep Inequalities Lesson 22: Compound Inequalities Lesson 23: Absolute Value Inequalities Lesson 24: Graphing Two-Variable Inequalities Lesson 25: Week 5 Review Week Game of the Week: Algebra Aces Lesson 26: Comparing Systems Lesson 27: Substitution Method for Solving Systems Lesson 28: Addition Method for Solving Systems Lesson 29: Systems of Equations Lesson 30: Week 6 Review

2 Table of Contents (cont.) Lesson Plans (cont.) Week Game of the Week: Trash ketball Lesson 31: Proportions Lesson 32: Scientific Notation Lesson 33: Mixed Operations with Monomials Lesson 34: Adding Polynomials Lesson 35: Week 7 Review Week Game of the Week: Factoring MATHO Lesson 36: Factoring the Greatest Common Factor Lesson 37: Factoring Trinomials Lesson 38: Factoring Special Types of Problems Lesson 39: Radical Expressions Lesson 40: Week 8 Review Week Game of the Week: Radicals MATHO Lesson 41: Solving Radical Equations Lesson 42: Parabolas and Quadratic Equations Lesson 43: Quadratic Formula Lesson 44: Rational Expressions and Equations Lesson 45: Diagnostic Post-test Appendices Appendix A: Diagnostic Test Appendix B: Assessments Working with Integers Quiz Mixed Integers Quiz Distributing and Collecting Quiz Writing Equations of Lines Quiz Solving Compound Inequalities Quiz Solving Systems of Equations Quiz Factoring Special Types of Problems Quiz Solving Quadratic Equations Quiz Appendix C: Games Math Bee Cards Who Has? Cards Algebra Aces 1 Cards Algebra Aces 2 Cards Algebra Aces 3 Cards Factoring MATHO Answer Sheet Radicals MATHO Answer Sheet Appendix D: Answer Keys Guided Practice Book Answer Key Assessments Answer Key Transparencies Answer Key Transparencies #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

3 Research to Support Algebra Intervention By Sharon S. Whitehead, Ph.D. Secondary Math Specialist, Mesa, Arizona Teacher Resources High school students study algebra more than any other course in mathematics (Usiskin 1980). Perhaps because of the abstractness of the material, the ages of the students, the pedagogical styles of the teachers, or the complexity of the curriculum, algebra can be very difficult and stressful for many students. However, students will have difficulty in all mathematical courses subsequent to Algebra I if they do not master the material in this pivotal course. And, almost half of the states now require students to pass Algebra I before graduation. So, the question becomes, How can we best help these students who are having difficulty with the concepts presented in Algebra I? The first thing to do is to remind teachers why algebraic thinking is so important. Algebra helps students engage in problem solving and develop rich analytical skills that will serve them throughout their lifetimes. The type of thinking encouraged in an Algebra I course helps students seek solutions, not just memorize procedures; explore patterns, not just memorize formulas; and formulate conjectures, not just do exercises. The National Research Council (1989) encourages this type of thinking to be developed in mathematics courses. Active Algebra: Algebra I Crash Course models all of these practices. The National Council of Teachers of Mathematics (NCTM) (2000) challenges teachers to imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. Algebra I Crash Course is a high-quality, engaging curriculum designed for grades 8 through 12. It can be used for standardized test preparation, credit recovery, Algebra I intervention, and summer school. This program is ideally suited for students having trouble with Algebra I. Not every student learns the same way, and the flexibility of this program allows teachers to engage students in different ways. The program is set up in such a way that it helps students grasp complex algebra concepts with a conceptual understanding that ensures deep procedural knowledge. Conceptual knowledge can be defined as knowledge that involves relations or connections (but not necessarily rich ones) (Star 2005). Star defines deep procedural knowledge as involving comprehension, flexibility, and critical judgment [as] distinct from (but possibly related to) knowledge of concepts (p. 116). Too often, mathematical knowledge is placed only into one category or the other. This eliminates the necessity of the dialogue between both conceptual and procedural knowledge. Crash Course moves students between these two types of knowledge fluidly.

4 Correlation to the NCTM Standards Teacher Resources NCTM Standard Lesson Title and Page Number Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. Adding Integers (pp ) Multiplying and Dividing Integers (pp ) Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency mentally or with paper and pencil in simple cases and using technology in all cases. Writing One-Variable Equations (pp ) Point-Slope Form (pp ) Graphing Inequalities (pp ) Solving Multistep Inequalities (pp ) Compound Inequalities (pp ) Absolute Value Inequalities (pp ) Graphing Two-Variable Inequalities (pp ) Comparing Systems (pp ) Substitution Method for Solving Systems (pp ) Addition Method for Solving Systems (pp ) Systems of Equations (p. 162) Rational Equations (pp ) Develop an initial conceptual understanding of different uses of variables. Collecting Like Terms (pp ) Distributing and Collecting (pp ) Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations. Solving Linear Equations 1 (pp ) Solving Linear Equations 2 (pp ) Solving Equations (pp ) Equations as Relations (pp ) Factoring the Greatest Common Factor (pp ) Factoring Trinomials (pp ) Factoring Special Types of Problems (pp ) Standards are listed with the permission of the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments.

5 Teacher Resources Correlation to the NCTM Standards (cont.) NCTM Standard Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. Lesson Title and Page Number Coordinate Planes (pp ) Make and use coordinate systems to specify locations and to describe paths. Coordinate Planes (pp ) Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. Relations and Functions (pp ) Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. Slope-Intercept Form (pp ) Graphing Linear Equations (pp ) Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation. Scientific Notation (pp ) Understand and use ratios and proportions to represent quantitative relationships. Proportions (pp ) Standards are listed with the permission of the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments. 10 #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

6 Teacher Resources Correlation to the NCTM Standards (cont.) NCTM Standard Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions. Lesson Title and Page Number Mixed Operations with Monomials (pp ) Adding Polynomials (pp ) Radical Expressions (pp ) Solving Radical Equations (pp ) Parabolas and Quadratic Equations (pp ) Quadratic Formula (pp ) Rational Equations (pp ) Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. Solving Radical Equations (pp ) Standards are listed with the permission of the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments. 11

7 Appendix A Name Directions: Solve each equation = A. 11 C. 11 B. 1 D = A. 12 C. 12 B. 3 D = A. 8 C. 8 B. 22 D ( 4)(3) = A. 12 C. 7 B. 9 D = A. 20 C. 6 B. 6 D (6)( 3)( 2) = A. 11 C. 1 B. 36 D. 36 Directions: Read each question and circle the correct answer. 7. Find the expression for the given problem. A chicken sandwich costs $1.50 more than a hamburger. A. h + $1.50 C. $1.50h B. h $1.50 D. $1.50 h Diagnostic Test 8. Find an equation for the given problem. The width of a rectangle is 9 meters. The width is 3 less than twice the length. What is the equation for the length of the rectangle? A. 3 2x = 9 C. 2x 3 = 9 B. 2x + 3 = 9 D x = 9 Directions: Simplify each given expression. 9. 4x 7 + 3x 2 x + 3 x 2 + 7x A. 4x 2 + 8x + 4 C. 2x 2 10x + 4 B. 2x 2 10x + 4 D. 2x x m m m m 2 m A. 4m 2 6m + 2 C. 2m 2 6m + 2 B. 2m 2 + 6m 2 D. 4m 2 + 6m m + 10 (6m + 4) 3 A. 5m + 3 C. 5m + 11 B. 5m + 3 D. 5m x 3(2x + 3) + 7x + 12 A. 3x + 3 C. 3x + 3 B. 3x + 21 D. 3x 21 Directions: Solve for each variable x 5 = 4x + 3 A. x = 8 7 C. x = 8 B. x = 8 D. x = #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

8 Data-Driven Instruction Teacher Resources Standards-based instruction must begin with the goal that all students can reach the standards if given appropriate instruction, materials, and support. Therefore, it is the responsibility of teachers to use various assessment and data-collection strategies to help identify when a student has misconceptions that will affect further learning of mathematical skills and concepts. Frequent formal and informal assessments provide teachers with the data needed to make informed decisions about what to teach and how to teach it. This is the only way that teachers will know who is struggling with various concepts and how to address the difficulties that students are experiencing with the curriculum. Formal Assessments The following formal assessments are included throughout the Algebra I Crash Course program: Diagnostic Test This assessment is given at the beginning of the program and at the end of the program. When students are retested, they should have the same classroom conditions and directions. This assessment is meant to be given within the increments of one school year and not stretched out beyond a single school year of instruction. In this way, the increments between testing are not too stretched out to detect growth. The final post-test use of the assessment becomes the ultimate summative evaluation that measures whether students have mastered what they were taught throughout the whole program. Quizzes The quizzes are integrated into the lessons throughout the program. They measure the learned objectives for a specific lesson or series of lessons. These assessments can be used by teachers to determine whether reteaching is necessary. There are two versions of each quiz. Form A is in the appendix and Form B is only on the Teacher Resource CD. Use both versions at the same time to discourage copying, or use one version as the initial assessment and the other version as the retest. Informal Assessments The following informal assessments are included throughout the program. These allow teachers to frequently watch for markers of comprehension in student responses. Problems in the Lessons Within each lesson, practice problems are provided for modeling. In the lessons, teachers first model the problem while the students watch. Then, the teachers model the problems while the students help. Next, the students model the problems while the teacher helps. Finally, the students model the problems while the teacher watches. Guided Practice Book This student consumable contains activity sheets to be used in correlation with lessons. These activities should be used to practice skills and concepts, and it is recommended that these activities are only given a completion grade versus a formal grade. 27

9 Game of the Week: Radicals MATHO Week 9 Mathematics Game Description The object of the game is to be the first student to have a straight line of answers covered on his or her MATHO card. Materials Transparencies folder Radicals MATHO Problems (trans19.pdf) Appendix C: Games Radicals MATHO Answer Sheet (page 267; radmatho.pdf) Games folder on the CD MATHO cards (mathocrd.pdf) Games folder on the CD MATHO chips (mathochp.pdf) Procedure Step 1 Step 2 Cut the Radicals MATHO Problems transparency into strips with one problem and corresponding letter on each strip. Give each student a MATHO card and a handful of small game markers/chips. Students also need copies of the Radicals MATHO Answer Sheet. Explain the directions to the student: This game is played like Bingo. Put one problem strip at a time on the overhead. Have the students solve each problem. Note: The problem is printed on one end of the strip and the answer on the other for easy location of winning answers. When placing a problem on the overhead, make sure the answer is not visible. It should be hanging off the side. Require all students to play. They should write the problems and answers in an organized manner on notebook paper. If necessary, give students grades for this work. Once students have solved each problem, they should look on their MATHO cards for the answer. If a student s card has the right answer, he or she covers it with a marker. Tell students to call out, MATHO when they get a straight line of covered answers. You can also play for diagonal lines or blackouts (the whole card). Have the winning student(s) call out their answers and check them on the transparency strips that have been played. 207

Lesson 41 Solving Radical Equations Step 1 20 min. Step 2 20 min. Step 1 Lesson Description Understands basic concepts, applications, and solution methods of radical equations.

10 Lesson 41 Solving Radical Equations Step 1 20 min. Step 2 20 min. Step 1 Lesson Description Understands basic concepts, applications, and solution methods of radical equations. Students will understand the Pythagorean theorem and learn how to solve radical equations. Materials PowerPoint folder on the CD Solving Radical Equations (lesson41.ppt) (optional) Guided Practice Book Solving Radical Equations (page 134; page134.pdf) Procedure Step 3 25 min. Step 4 25 min. Present the Notes on the Pythagorean Theorem (pages ). These notes are provided as part of the lesson s PowerPoint slide show on the CD (lesson41.ppt). Discuss the bolded questions with students. You may want to share some of the history of the Pythagorean theorem with students. Notes on the Pythagorean Theorem What is the Pythagorean theorem? a 2 + b 2 = c 2 a 2 c2 What is the hypotenuse? It is represented by the variable c. It is the longest side. It is always the side across from the right angle. What are the legs? They are represented by the variables a and b. When solving for one of the variables, the order of a and b can be switched because of the commutative property. b #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

11 Solving Radical Equations Lesson 41 Notes on the Pythagorean Theorem (cont.) When is the Pythagorean theorem used? It is used to find the length of the third side of a right triangle when the other two sides are known. It is used to determine if a right triangle can be made from three given line segments. How could the Pythagorean theorem help carpenters? Discuss with students how buildings are constructed with right angles. Examples Complete these examples with the students by working out the formula for each triangle. Round the answers to the nearest hundredth. a. 3 5 b. x 24 c. 13 c x x 2 = x 2 = 25 x 2 = 25 9 x 2 = 16 x 2 = 16 x = 4 Teacher Tip x 2 = x 2 = 625 x 2 = x 2 = 49 x 2 = 49 x = 7 If available, you may want students to check their solutions on graphing calculators using the Home Screen method. Store a value for a variable, input the equation, and press enter. The calculator will use Boolean logic to determine if the value stored is true (1) or false (0) = c = c = c = c 2 c

12 Lesson 41 Solving Radical Equations Step 2 Practice Procedure (cont.) Review radical operations. d = 2 6 e. 2 9 = 3 2 f. 3 3( ) = g. ( )( ) = 43 h. (2 6 4)( ) = 8 i. ( 2 5)( 2 + 5) = 3 Step 3 Present the Notes on Solving Radical Equations (pages ). These notes are given as part of the lesson s PowerPoint slide show on the CD (lesson41.ppt). Notes on Solving Radical Equations Examples j. m + 3 = ( m) 2 = (5) 2 m = #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

13 Solving Radical Equations Lesson 41 Notes on Solving Radical Equations (cont.) Examples k. p = ( p 2) 2 = (5) 2 p 2 = p = 27 l. 3y = 5 ø Discuss the principle square root in the above example. Tell students that the symbol represents the principle square root and that it is a positive root. Ask students, Can a principle square root equal a negative value? No; therefore, the answer to the problem is ø. m. y + 3 = y + 1 ( y + 3) 2 = (y + 1) 2 y + 3 = y 2 + 2y + 1 y 3 y 3 0 = y 2 + y 2 0 = (y + 2)(y 1) y + 2 = 0 y 1 = y = 1 Remind students to substitute solutions into the original equation to find the correct answer. 211

14 Lesson 41 Solving Radical Equations Procedure (cont.) Notes on Solving Radical Equations (cont.) n. 3 x 3 = x 3 x = x + 3 ( 3 x ) 2 = (x + 3) 2 3 x = x 2 + 6x = x 2 + 7x = (x + 6)(x + 1) x = 6 x = 1 x = 1 o. 2 a 4 = 2 a = 54 3 p. x = 3 2 x = 18 q. 4n 2 = 8n n = 0, 2 r. 3 2y = 1 y = 2 s. 4z + 6 = 0 z = t. 2y = 6 ø 3 2 Remind students that a principle square root cannot equal a negative value. Step 4 Assignment Assign the Solving Radical Equations activity sheet. 212 #11002 (i2567) Algebra I Crash Course Teacher Created Materials Publishing

15 Radicals MATHO Answer Sheet Appendix C: Games A (5x + 1)(2x + 3) B (7x 2)(x 1) C (x 1)(x 1) D 2(5x 1)(5x + 1) E x(x + 1) N (5x + 1)(2x 1) O (2x + 3)(x + 1) P 2x(2x 3) Q (3x + 1)(x + 2) R (8x 1)(x 1) F 2x 2 y(5 6xy) S (3x 5)(x + 1) G x 2 (x + 10)(x 2) H (1 2x)(1 + 2x) I (4x + 3)(4x 3) J (x + 3)(x 7) K prime L (5x + 1)(5x 1) M (5x + 4)(x 1) T 3x 3 (x 2 + 2) U 2(x + 9)(x + 2) V 5x(x 4)(x + 2) W (x + 3)(x 3) X 2xy 2 (7x 2 4y) Y (3x 1)(x + 1) Z (2x 1)(x + 3) 267

16 Name Solving Radical Equations Directions: Solve. 1. 2x = 7 2. p 10 = y = a + 4 = = 2 6. x 2 = x x = 8 8. a = m + 3 = m 134 #10361 Algebra I Crash Course, Guided Practice Book

17 Appendix D: Answer Keys Standardized Test Practice 7 (cont.) 17. A 18. D 19. D 20. C Dimensions of Rectangles GPB (pages ) 1. (x + 3)(x + 1) A = x 2 + 4x (x 5)(x + 2) A = x 2 3x (2x + 3)(x + 1) A = 2x 2 + 5x (x + 1)(x + 1) A = x 2 + 2x (x + 2)(x 2) A = x (2x + 3)(x + 5) A = 2x x (2x + 1)(x + 2) A = 2x 2 + 5x (x + 5)(x 1) A = x 2 + 4x 5 9. (a + 5)(a 3) 10. (m 7)(m + 7) 11. (3m 5)(2m + 1) 12. (c 6)(c + 6) 13. (a 7b)(a 3b) 14. (3e + 7)(e 3) 15. (2a 3)(a 4) 16. e(e 5) 17. w(w 5) Area and Perimeter with Radicals GPB (pages ) Guided Practice Book Answer Key (cont.) Algebra I Review 8 GPB (pages ) 1. 4 hours people 3. C 4. D 5. C 6. y = 3x m = slope = rise run b = y-intercept 8. 3,4,5; 5,12,13; 7,24,25; 8,15,17; 9,40,41 9. C 10. check graph 11. check graph 12. Perimeter add all sides; 2l + 2w Area length x width 13. D = set of all x s or independent variable or 1 st coordinate R = set of all y s or dependent variables or 2 nd coordinate 14. t = 2s r = 3b b = f + 8 s = 1 3 r 15. n = 2 m = use one variable variable: 4w + 8 = 38 or 2w + 2(w + 4) = 38; 2 variables: 2w + 2l = 38, l = w D 19. A Standardized Test Practice 8 GPB (pages ) 1. B 2. C 3. C 4. A 5. B 6. D 7. A 8. A 9. B 10. D 11. B 12. D 13. C 14. A 15. B 16. A 17. B 18. B 19. D 20. D Solving Radical Equations GPB (page 134) 1. x = p = y = Ø 5. x = x = 4 7. x = a = m = 2, m = 3 Identifying the Axis of Symmetry and the Vertex GPB (page 135) 1. opens downward 2. (2, 64) 3. The x-axis represents time in seconds, and the y-axis represents the position of the ball in feet. 4. It tells us that at the time of two seconds, the ball is at its maximum height of 64 feet. 5. x = 2 Simplifying Rational Expressions GPB (page 136) 1. x + 2 6x 3 2. x 3 3. mn 2 y x (x 3) 2x

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic