Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: EQUATIONS Grade: 8 Algebra 1 Chapter 1 Unit Length: 8 days Essential Question(s) Vocabulary How do you solve linear equations in one variable? How can you solve a multi-step equation? How can you check the reasonableness of your solution? How can you use a formula for one measurement to write a formula for a different measurement? Absolute value equation Literal equation NJSLS Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
8.EE.7. Solve linear equations in one variable. 8.EE.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Learning Expectations WAL To/That WALT solve linear equations in one variable with rational number coefficients that might require expanding expressions using the distributive property and/or combining like terms, including examples with one solution, infinite solutions, or no solution. WALT solve mathematical and realworld problems involving addition, subtraction, multiplication, and Activities Resources Formative Assessments Modifications 1.2 Solving Multi-Step Equations Day 1: 1.2 Lesson Activity and Cornell Notes pg. 10-15 1.3: Solving Equations with Variables on Both Sides pg. 18-25 Day 2: Lesson Activity pg. 18-19 Day 3 & 4: Formal Lesson (Cornell Notes and Practice) pg. 20-25 Day 5: Practice of 1.1-1.3 Day 6: Review 8th Grade Big Ideas Math Textbook 1.1-1.5 1 Mini Assessment Collected: TBD by 1.1-1.5 Homework Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 1.1-1.3 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com
division of rational numbers. Day 7: Test James Rahn website Summative Assessment Task Chapter Test Algebra Tiles
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: GRAPHING AND WRITING LINEAR EQUATIONS Grade: 8 Algebra 1 Chapter 2 Unit Length: 16 days Essential Question(s) Vocabulary How can you recognize a linear equation? How can you Linear equation draw its graph? Solution of a linear equation How can the slope of a line be used to describe the line? How can you describe the graph of the equation y = mx + b How can you describe the graph of the equation ax + by = c Slope Rise Run Perpendicular lines How can you write the equation of a line when given the slope and y-intercept of the line? How can you write an equation of a line when you are given the slope and a point on the line? How can you use a linear equation in two variables to model and solve a real-life problem? x-intercept y-intercept slop-intercept form standard form point-slope form
NJSLS Standards for Mathematical Practice The Standards for Mathematical Practice (MP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 8.F.A.2 Compare properties (e.g., rate of change, intercepts, domain and range) of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Learning Expectations WAL To/That WALT recognize a linear equation and draw its graph WALT describe the slope of a line WALT describe the graph of the equation y = mx + b (slopeintercept form) WALT describe the graph of standard form of a linear equation Activities Resources Formative Assessments Modifications Day 1: 2.1 Lesson Activity 1 & 2 p. 42-43 Day 2: 2.2 Activity pg. 42-49 Day 3: Formal Lesson Practice) pg. 50-53 Day 4: 2.2 Ext. Slops of Parallel and Perpendicular Lines Formal Lesson (Cornell Notes and Practice) pg. 56-57 Day 5: 2.3 Formal Lesson (Cornell Notes and Practice) pg. 58-63 Day 6: 2.4 Lesson Activity pg. 64-65 Day 7: (Cornell Notes and Practice) pg. 66-69 Day 8: Quiz 2.1-2.4 8th Grade Big Ideas Math Textbook 2.1-2.4 2 Mini Assessment Collected: TBD by 2.1-2.4 Homework OEQ to be determined by the Quiz Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 2.1-2.4 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program WALT write the equation of a line when given the slope and y- Day 9: 2.5 Lesson Activity pg. 72-73 Day 10: Formal Lesson 8th Grade Big Ideas Math Textbook 2 Mini Assessment Collected: TBD by
intercept WALT write the equation of a line when given the slope and point on a line WALT use a linear equation in two variable to model and solve real-life problem Chapter Test Practice) pg. 74-77 Day 11: 2.6 Lesson Activity pg. 78-79 Day 12: (Cornell Notes and Practice) pg. 80-83 2.6 Ext. Writing Equations of Parallel & Perpendicular Lines pgs. 84-85 Day 13: 2.7(Cornell Notes and Practice) pg. 84-85; Lesson Activity pg. 86-87 Day 14: 2.7 (Cornell Notes and Practice) pg. 88-91 Day 15: Review for Test Day 16: Test 2.5 2.7 Summative Assessment Task 2.5 2.7 Homework OEQ to be determined by the Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 2.5 2.7 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com Smart Board program
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: SOLVING LINEAR INEQUALITIES Grade: 8 Algebra 1 Chapter 3 Unit Length: 11 days Essential Question(s) How can you use an inequality to describe a real-life situation/statement? How can we use addition, subtraction, multiplication, or division to solve an inequality? Vocabulary Inequality Solution of an inequality Solution set How can you use an inequality to describe the area and perimeter of a composite figure? Graph of an inequality Compound inequality How can you use a coordinate plane to solve problems involving linear inequalities? Absolute value inequality Linear inequality in two variables Solution of a linear inequality Graph of a linear inequality Half-planes NJSLS Standards for Mathematical Practice Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problem HSA-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Learning Expectations WAL To/That WALT translate inequalities from word to symbols and check to see if a vale is a solution of the inequality. WALT use the Addition and Subtraction Properties of Inequality of solve inequalities. Activities Resources Formative Assessments Modifications Day 1: 3.1 Lesson Activity 1 & 3 p. 104-105 Day 2: Formal Lesson Practice) p. 106-108 Day 3: 3.2 Lesson Activity pg. 110-111 Day 4: Formal Lesson Practice) pg. 112-115 8th Grade Big Ideas Math Textbook 3.1-3.4 1 Mini Assessment Collected: TBD by 3.1-3.2 Homework OEQ to be determined by the Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B
WALT use the Multiplication and Division Properties of Inequality to solve inequalities. WALT solve and graph multi-step inequalities Day 5: 3.3 Lesson Activity pg. 116-117 Day 6: Formal Lesson Practice) pg. 118-123 Day 7: OEQ 3.1-3.3 Day 8: 3.4 Lesson Activity pg. 126-127 Day 9: Formal Lesson Practice) pg. 78-81 Day 10: Teacher Activity determined by Day 11: Review for Test Day 12: Test Puzzle Time worksheet 3.1-3.2 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program Khan Academy Chapter Test Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: SOLVING SYSTEMS OF LINEAR EQUATIONS Grade: 8 Algebra 1 Chapter 4 Unit Length: 11 days Essential Question(s) Vocabulary How can you solve a system of linear equations How can you use substitution to solve a system of linear equations? How can you use elimination to solve a system of linear equations? Can a system of linear equations have no solution? Can a system of linear equations have many solutions? How can you sketch the graph of a system of linear inequalities? NJSLS System of linear equations Solution of a system of linear equations System of linear inequalities Solution of a system of linear inequalities Graph of a system of linear inequalities Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision.
7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection of their graphs, because points of intersection satisfy both equations simultaneously 8.EE.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8.EE.8c Solve real-world and mathematical problems leading to two linear equations A.CED.3 Represent constraints by equations of inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. A.REI.6 Solve systems of linear equations exactly and approximately (w/graphs), focusing on pairs of linear equations in two variables A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions (ELIMINATION) A.REI.12 Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes Learning Expectations WAL To/That WALT solve a system of linear equations by graphing WALT use substitution to solve a system of Activities Resources Formative Assessments Modifications Day 1: 4.1 Lesson Activity and Cornell Notes Day 2: 4.2 Lesson Activity p. Day 3: Formal Lesson 8th Grade Big Ideas Math Textbook 4.1-4.5 1 Mini Assessment Collected: TBD by 4.1-4.5 Homework Fair Game Review Skills Review Handbook
linear equations WALT use elimination to solve a system of linear equations WALT systems of equations can have one solution, no solution, and infinite solutions WALT sketch the graph of a system of linear inequalities Summative Assessment Task Chapter Test Practice) p. Day 4: 4.3 Day 5: Formal Lesson Practice) Day 6: QUIZ Day 7: 4.4 Day 8: 4.5 Day 9: Review Day 10: Test (one day less than recommendation) Lesson Tutorials Practice A and B Puzzle Time worksheet Enrichment and Extension wksht. Game Closet at BigIdeasMath.com
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: LINEAR FUNCTIONS Grade: 8 Algebra 1 Chapter 5 Unit Length: 16 days Essential Question(s) How can you find the domain and range of a function? How can you decide whether the domain of a function is discrete or continuous? How can you use a linear function to describe a linear pattern? How can you use function notation to represent a function? How can you recognize when a pattern in real life is linear or nonlinear? How are arithmetic sequences used to describe patterns? Vocabulary Function Domain Range Independent variable Dependent variable Relation Vertical line test Discrete domain Linear function Function notation Piecewise function Step function Absolute value function Nonlinear function Sequence Term Arithmetic sequence Common difference NJSLS HSF-IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x). HSF-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT determine and describe whether a Activities Resources Formative Assessments Modifications Day 1: 5.1Lesson Activity pg. 202-203 8th Grade Big Ideas Math Textbook 2 Mini Assessment Collected: TBD by Graph paper
relation is a function WALT identify and describe the domain and range of a function from a graph and table of values WALT graph functions and determine whether the domain is discrete or continuous WALT write linear functions by recognizing patterns in graphical and tabular information WALT use function notation to evaluate functions, graph functions, and vertically shift the graphs of functions Day 2: Formal Lesson Practice) p. 204-207 Day 3: 5.1 extension; Lesson and Activity 208-209 Day 4: 5.2 Lesson Activity p. 210-211 Day 5: Formal Lesson Practice) p. 212-215 Day 6: 5.3 Activity and Formal Lesson (Cornell Notes and Practice) pg. 216-221 Day 7: Quiz/OEQ Day 8: 5.4 Lesson Activity pg. 224-225 Day 9: Formal Lesson Practice) pg. 226-231 Day 10 & 11: Practice pg. 226-231 Day 12: 5.5 Lesson Activity pg. 236-237 Day 13: Formal Lesson Practice) pg. 238-241 Day 14: Review/OEQ 5.1-5.3 Virtualnerd.com Parcc.pearson.com 8th Grade Big Ideas Math Textbook 5.1-5.3 Homework OEQ to be determined by the Learning Upgrade 2 Mini Assessment Collected: TBD by 5.4-5.5Homework Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 5.1-5.3 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com Smart Board program Khanacademy.org Graph paper Fair Game Review
WALT compare and contrast linear and nonlinear functions Day 15: Test (one day less than recommendation) 5.4-5.5 OEQ to be determined by the Learning Upgrade Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 5.4-5.5Enrichment and Extension wksht. Game Closet at BigIdeasMath.com Smart Board program Khanacademy.org Chapter Test Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: EXPONENTIAL EQUATIONS AND FUNCTIONS Grade: 8 Algebra 1 Chapter 6 Unit Length: 18 days Essential Question(s) Vocabulary How can you multiply and divide square roots? Closed How can you use inductive reasoning to observe patterns Nth root and write general rules involving properties of Exponential function exponents? Exponential growth How can you write and evaluate an nth root of a Exponential growth function number? Compound interest What are the characteristics of an exponential function? Exponential decay What are the characteristics of exponential growth? Exponential decay function What are the characteristics of exponential decay? Geometric sequence How are geometric sequences used to describe patterns? Common ratio Recursive rule NJSLS HSN-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational HSN-RN.A2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT use properties of square roots to simplify and evaluate expression involving square roots WALT explore closure for rational and irrational numbers WALT use properties of exponents to simplify expressions Activities Resources Formative Assessments Modifications 6.1 Properties of Square Roots: pgs. 260-265 Day 1: Lesson Activity pg. 260-261 Day 2: Formal Lesson Practice) pg. 262-265 6.1 Ext. Relations & Functions: 266-267 Day 3: Lesson and Activity 266-267 8th Grade Big Ideas Math Textbook 6.1-6.2 2 Mini Assessment Collected: TBD by 6.1-6.2 Homework OEQ to be determined by the Learning Upgrade Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 6.2 Properties of Exponents: pgs. 268-275 Day 4: Lesson Activity 6.1-6.2Enrichment and Extension wksht. Game Closet at
WALT use growth pattern of a set of data to determine whether the data represents a linear or an exponential function. WALT write and evaluate exponential growth functions WALT write and evaluate exponential decay functions pg. 268-269 Day 5: Formal Lesson Practice) pg. 270-275 Day 6: Quiz/OEQ 6.4 Exponential Functions: pgs. 284-293 Day 6: Lesson Activity pg. 284-285 Day 7 & 8: Formal Lesson (Cornell Notes and Practice) pg. 286-293 6.5 Exponential Growth pgs. 294-299 Day 9: Lesson Activity pg. 294-295 Day 10: Formal Lesson Practice) pg. 296-299 6.6 Exponential Decay pgs. 300-305 Day 11: Lesson Activity & Practice pg. 300-305 6.6 Geometric 8th Grade Big Ideas Math Textbook 6.4-6.7 3 Mini Assessment Collected: TBD by 6.4-6.7 Homework OEQ to be determined by the Learning Upgrade BigIdeasMath.com www.learningupgrade.com Smart Board program Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 6.4-6.7 Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program
Sequences pgs. 306-315 Day 12: Lesson Activity pg. 306-307 Day 13: Formal Lesson Practice) pg. 308-315 Khanacademy.org Chapter Test Day 14: Review/OEQ Day 15: Test (3 day less than recommendation) Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: POLYNOMIAL EQUATIONS AND FACTORING Grade: 8 Algebra 1 Chapter 7 Unit Length: 18 days Essential Question(s) How can you use algebra tiles to model and classify polynomials? How can you add and subtract polynomials? How can you multiply two binomials? What are the patterns in the special products (a+b)(a-b), (a+b)^2, and (a-b)^2? How can you solve a polynomial equation that is written in factored form? How can you use common factors to write a polynomial in factored form? How can you factor the trinomial x^2 + bx + c into the product of two binomials? How can you factor the trinomial ax^2 + bx + c into the product of two binomials? How can you recognize and factor special products? NJSLS Vocabulary Monomial Degree of a monomial Polynomial Binomial Trinomial Degree of a polynomial FOIL method Factored form Zero-Product Property Root Factoring by grouping Prime polynomial Factored completely A.SSE.1a Interpret parts of an expression, such as terms, factors, coefficients A.APR.1 Understand the polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex
solutions [and write them as a +/- bi for real numbers a and b] A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines A.SSE.2 Use the structure of an expression to identify ways to rewrite it Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT identify different types of polynomials and the degree of a polynomial WALT add and subtract polynomials WALT multiply and divide polynomials Activities Resources Formative Assessments Modifications Day 1: 7.1 Classifying Polynomials: p. 328-333;Lesson Activity p. 328 & Formal Lesson Practice) p. 330-333 Day 2: 7.2 Lesson and Activity p. 334-339 Day 3: 7.3 Activity and Lesson p. 340-347 Day 4: 7.4 Lesson 8th Grade Big Ideas Math Textbook 7.1-7.2 2 Mini Assessment Collected: TBD by 7.1-7.4 Homework OEQ to be determined by the Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B
WALT find patterns in special binomial products WALT solve a polynomial equation written in factored form WALT factor using the GCF WALT factor trinomials into the product of two binomials when a =1 WALT factor trinomials into the product of two binomials when a > 1 WALT factor special products Activity p.348-353 Day 5: Reflection & additional practice (Cornell Notes) Day 6: Quiz/OEQ Day 7: 7.5 Activity p. 356-361 Day 8: Formal Lesson Practice) p. 358-361 Day 9: 7.6 Activity & formal lesson p.362-367 Day 10: 7.7 Formal Lesson (Cornell Notes and Practice) p. 364-375 Day 11: 7.8 Lesson Activity & Practice pg. 378-381 Day 12: 7.9 Lesson & Activity p. 382-387 Day 13: Reflection & additional practice/ QUIZ 7.5-7.9 Day 14: Review/OEQ Khan Academy 8th Grade Big Ideas Math Textbook 3 Mini Assessment Collected: TBD by 7.5-7.9 Homework OEQ to be determined by the Puzzle Time worksheet 7.1-7.2Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet Enrichment and Extension wksht.
Day 15: Test (3 day cushion) Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program Khanacademy.org Chapter Test Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: SOLVING QUADRATIC EQUATIONS Grade: 8 Algebra 1 Chapter 9 Unit Length: 13 days Essential Question(s) How can you use a graph to solve a quadratic equation in one variable? How can you determine the number of solutions of a quadratic equation of the form ax^2 + c = 0? How can you use completing the square to solve a quadratic equation? How can you use the discriminant to determine the number of solutions of a quadratic equation? How can you solve a system of two equations when one is linear and the other is a quadratic? NJSLS Vocabulary Quadratic equation Completing the square Quadratic formula Discriminant A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions [and write them as a +/- bi for real numbers a and b] A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., use technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear (polynomial, rational, absolute value) and exponential. A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context A.REI.7 Solve a simple system consisting of linear equation and a quadratic equation in two variables algebraically and graphically Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT use a graph to solve a quadratic equation WALT determine the number of solutions of a quadratic equation WALT solve a Activities Resources Formative Assessments Day 1: 9.1 Activities, Formal Lesson (Cornell Notes & Practice p. 454-461 Day 2: 9.2 Activities, Formal Lesson (Cornell Notes & Practice) p. 462-467 Day 3: 9.3 Activities, 8th Grade Big Ideas Math Textbook Peardeck.com 2 Mini Assessment Collected: TBD by Homework OEQ to be determined by the Modifications Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials
quadratic equation by completing the square Formal Lesson (Cornell Notes and Practice) p. 468-473 Day 4: QUIZ/ OEQ Learning Upgrade Practice A and B Puzzle Time worksheet WALT solve quadratic equations using the quadratic formula WALT solve systems of linear and quadratic equations Day 5 & 6: 9.4 Activities, Formal Lesson (Cornell Notes and Practice) p. 476-483 Day 7: Extension 9.4 Choosing a method p. 484-486 Day 8: 9.5 Activities, Formal Lesson (Cornell Notes and Practice) p 487-491 Day 9: Quiz/OEQ/Additional practice Day 10: Review/ OEQ Day 11 : Test (2 days less than recommended length) 8th Grade Big Ideas Math Textbook Khanacademy Virtualnerd http://parcc.pearson.com/practicetests/math/ 3 Mini Assessment Collected: TBD by Homework OEQ to be determined by the Enrichment and Extension wksht. Game Closet at BigIdeasMath.com Smart Board program Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet 6.4-6.7 Enrichment and Extension wksht.
Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program Khanacademy.org Chapter Test Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: Square Root Functions and Geometry Grade: 8 Algebra 1 Chapter 10 Unit Length: 11 days Essential Question(s) Vocabulary Square root function How can you sketch the graph of a square root function? Simplest form of a radical expression How can you solve an equation that contains square Rationalizing the denominator roots? Conjugates How are the lengths of the sides of a right triangle Square root equation related? Extraneous solution In what other ways can you use the Pythagorean Theorem Theorem? Legs Hypotenuse Pythagorean Theorem Distance formula NJSLS F.IF.4 For a function that models the relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features: intercepts, maximum and minimum, intervals where the function is increasing, decreasing, positive, or negative, symmetries. F.IF.7b Graph square root, [cube root], and piecewise-defined functions, including step functions and absolute value functions N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents 8.G.6 Explain a proof of the Pythagorean Theorem and its converse 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system
Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT sketch the graph of a square root function WALT rationalize the denominator WALT solve square root equations Activities Resources Formative Assessments Day 1: 10.1 Activities, Formal Lesson (Cornell Notes and Practice)p. 502-507 Day 2: Extension 10.1 p. 508-509 Day 3: 10.2 Activity, Formal Lesson Practice) p. 510-517 Day 4: QUIZ 8th Grade Big Ideas Math Textbook Virtualnerd khanacademy http://parcc.pearson.com/practicetests/math/ 8th Grade Big Ideas Math Textbook 2 Mini Assessment Collected: TBD by 6.1-6.2 Homework OEQ to be determined by the Learning Upgrade Modifications Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet
WALT the lengths of the sides of right triangles are related WALT use the Pythagorean Theorem Day 5: 10.3 Activities, Formal Lesson (Cornell Notes and Practice) p.520-525 Day 6: 10.4 Activities, Formal Lesson (Cornell Notes and Practice) p. 526-531 Day 7: QUIZ Day 8: Review/OEQ Day 9: Test Peardeck.com 2 Mini Assessment Collected: TBD by Homework OEQ to be determined by the 6.1-6.2Enrichment and Extension wksht. Game Closet at BigIdeasMath.com www.learningupgrade.com Smart Board program Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet Enrichment and Extension wksht. Game Closet at BigIdeasMath.com
www.learningupgrade.com Smart Board program Khanacademy.org Chapter Test Summative Assessment Task
Red Bank Borough Schools Mathematics Curriculum Unit Plan Unit Title/Theme: RATIONAL EQUATIONS AND FUNCTIONS Grade: 8 Algebra 1 Chapter 11 Unit Length: 14 days Essential Question(s) Vocabulary Direct variation How can you recognize when two variables vary directly? Inverse variation How can you recognize when they vary inversely? Rational function What are the characteristics of the graph of a rational Excluded value function? Asymptote How can you simplify a rational expression? What are the Inverse relation excluded values of a rational expression? Inverse function How can you multiply and divide rational expressions? Rational expression How can you divide one polynomial by another Simplest form of a rational expression polynomial? Least common denominator of rational expressions How can you add and subtract rational expressions? Rational equation How can you solve a rational equation? NJSLS A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) A.SSE.2 Use the structure of an expression to identify ways to rewrite it F.BF.4A Solve an equation in the form f(x) = c for a simple function f that has an inverse and write and expression for the inverse A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Standards for Mathematical Practice The Standards for Mathematical Practice (SMP) describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Expectations WAL To/That WALT recognize when two variable vary directly and inversely WALT identify the characteristics of the graph of a rational function WALT simplify rational expressions WALT multiply and divide rational Activities Resources Formative Assessments Modifications Day 1: 11.1 Lesson Activity p. 542-543 Day 2: Formal Lesson Practice) p. 544-549 Day 3: 11.2 Activities p. 550-551 Day 4: Formal Lesson Practice) p.552-557 Day 5 & 6: 11.3 Activities, Formal Lesson Practice) p. 560-565 Day 7: Quiz/OEQ Day 8: 11.4 Lesson Activity p. 568-569 Day 9: Formal Lesson 8th Grade Big Ideas Math Textbook 2 Mini Assessment Collected: TBD by Homework OEQ to be determined by the Learning Upgrade Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet Enrichment and Extension wksht. Game Closet at BigIdeasMath.com
expressions WALT divide polynomials WALT adding and subtracting rational expressions Practice) p. 570-573 Day 10 & 11: 11.5 Lesson Activity, Formal Lesson (Cornell Notes and Practice) p. 574-579 Day 11 & 12: 11.6 p. 580-587 Day 13: 11.7 Lesson Activity & Practice p. 588-593 Day 14: Quiz/Rview Day 15: Test (one day over recommendation) 8th Grade Big Ideas Math Textbook Virutalnerd.com Khanacademy 2 Mini Assessment Collected: TBD by Homework OEQ to be determined by the Smart Board program Graph paper Fair Game Review Skills Review Handbook Lesson Tutorials Practice A and B Puzzle Time worksheet Enrichment and Extension wksht. Game Closet at BigIdeasMath.com Smart Board program Khanacademy.org
Chapter Test Summative Assessment Task