INTEGRATED ALGEBRA UNIT 1
INTEGRATED ALGEBRA UNIT 1 Unit Title: Foundations of Algebra Enduring Understandings/Big Ideas: The transition from arithmetic to algebraic representation and the introduction of variables sometimes causes difficulty for students It is important to recognize that variables are used in a variety of applications. Grade Level: 9th Unit Length: 9 days Essential Questions: How do you interpret, evaluate and write algebraic expressions that model real-world situations? Common Core Learning Standards: N.Q.1 Use units as a way to understand… and to guide the solution of multi step problems… N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients. A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.2 Use the structure of an expression to identify ways to rewrite it. A.REI.1 Explain each step in solving a simple equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 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. HSA-APR.A.1. Understanding that 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. New York State / Content Standards: A.A.1. Translate a quantitative verbal phrase into an algebraic expression. A.N.1. Identify and apply the properties of real numbers. A.N.6. Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s). Skills (Students will be able to…) Evaluate and simplify expressions Translate between words and algebra Identify and apply the properties of real numbers Classify numbers within the real number system Use the order of operations to simplify expressions Identify patterns formed by points plotted in the coordinate plane Combine like terms Unit Outline – Sequence of learning (AIMs): How do we use the symbol of algebra and how do we evaluate algebraic expressions? How do we add and subtract within the set of signed numbers? How do we multiply and divide signed numbers? How do we evaluate expressions containing exponents? How do we evaluate expressions containing square roots and how do we classify real numbers? How do we use order of operations to simplify expressions? What are the properties of real numbers? Review Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Exit Slips Homework Notebook check quiz Summative Assessment / Performance Task: Unit test Performance Task Key Terms/Vocabulary: Additive inverse, multiplicative inverse, coefficient, constant, coordinate plane, irrational numbers, like terms, origin, rational numbers, variable, reciprocal, power, base, exponents, real numbers, natural numbers, whole numbers, integers, rational numbers, terminating decimals, repeating decimals, order of operations Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 1: Foundations of Algebra (1.1) How do we use the symbol of algebra and how do we evaluate algebraic expressions? HW#1: Handout (1.2) How do we add and subtract within the set of signed numbers? HW#2: Handout (1.3) How do we multiply and divide signed numbers? HW#3: Handout (1.4) How do we evaluate expressions containing exponents? HW#4: Handout (1.5) How do we evaluate expressions containing square roots and how do we classify real numbers? HW#5: p.35-36/ #11-14, 15, 16-23, 28 (1.6) How do we use order of operations to simplify expressions? HW#6: p.43-45/ #26, 28, 36, 41, 42, 49, 50, 54, 55a-f, 72* (1.7) What are the properties of real numbers? HW#7: p.49-50/ #26, 29, 30, 31, 34, 39, 40, 42, 46, 48, 49 Review Test INTEGRATED ALGEBRA UNIT 2 Unit Title: Equations Enduring Understandings/Big Ideas: When solving an equation, you find the number that makes the open sentence true. Equations can also take several forms. Equations can be solved by using inverse operations. Equations are termed conditional equations. If we replace x is a certain number then the equation will be true, and if we replace x with a different number, then the equation will be false Using the distributive property first before applying inverse operations Grade Level: 9th Unit Length: 15 days Essential Questions: What are some different methods for solving linear equations? How can you use properties to justify solutions to equations that involve multiplication and division? How can you use properties to justify solutions to multi-step equations? How can you use properties to justify solutions to equations with variables on both sides? How do you solve literal equations and rewrite formulas? How can you use units to help solve realworld problems? How can you use units to write and solve proportions? Common Core Learning Standards: New York State / Content Standards: A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations…in one variable… A.SSE.2 Use the structure of an expression to identify ways to rewrite it… A.CED.2 Create equations in two or more variables to represent relationships between quantities… A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations… N.Q.1 Use units as a way to understand…and to guide the solution of multi-step problems. A.SSE.1 Interpret expressions that represent a quantity in terms of its context. A.CED.1 Create equations…in one variable and use them to solve problems. A.A.22 Solve all types of linear equations in one variable A.A.23 Solve literal equations for a given variable A.A.24 Solve linear inequalities in one variable A.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable. A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equations A.A.5. Write algebraic equations or inequalities that represent a situation. Skills (Students will be able to…) Solve one-step equations in one variable by using addition and subtraction. Solve one-step equations in one variable by using multiplication and division Solve equations in one variable that contain more than one operation Solve equations in one variable that contain variables on both sides Solve a formula for a given variable Solve an equation in two or more variables for one of the variables Write and use ratios, rates, and unit rates Write and solve proportions Use proportions to solve problems involving geometric figures Use proportions and similar figures to measure objects indirectly Solve problems involving percents Use common applications of percents Estimate with percents Unit Outline: What are equations, and how do we solve them using mental math and tables? How do we solve one-step equations? How do we solve two-step equations? How do we solve multi-step equations? How do we solve equations we variables on both sides? How do we solve literal equations for a variable? How do we use LESCA to solve word problems? How do we use LESCA to solve consecutive integer problems? What are rates, ratios, and proportions? How do we solve proportions? How do we use proportions to geometric and other problems? What are percents, and how do we convert them to fractions and decimals? How do we use percents to solve real life/word problems? How can we apply our skills from Unit 2? Review Test Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Exit Slips Homework Notebook check quiz Summative Assessment / Performance Task: Equation project Unit Test Key Terms/Vocabulary: Equation, formula, identity, indirect measurement, literal equation, percent, percent change, proportion, ratio, unit rate, scale, conversion factor, cross products, scale model, scale drawing, solution of an equation, inverse operations, contradiction, similar, corresponding sides, corresponding angles, scale factor, commission, principal, tip, interest, sales tax, percent change, percent increase, percent decrease, discount, markup Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 2: Equations (2-1) What are equations, and how do we solve them using mental math and tables? HW #8: Handout. (2-2) How do we solve one-step equations? HW #9: Handout. (2-3) How do we solve two-step equations? HW #10: p. 96/ # 2, 5, 7, 11, 14, 17, 20, 47. (2-4) How do we solve multi-step equations? HW #11: p. 96-98 # 8, 23, 28, 31, 34, 50, *76, *77. (2-5) How do we solve equations we variables on both sides? HW #12: p. 103-106/ # 15, 18, 19, 21, 23, 26, 27, 40, 42, *65, *66. (2-6) How do we solve literal equations for a variable? HW #13: p. 109-111/ #10, 11, 12, 15, 17, 19, 48, 49. p. 103/ # 9. (2-7) How do we use LESCA to solve word problems? HW #14: Handout (2-8) How do we use LESCA to solve consecutive integer problems? HW #15: Handout (2-9) What are rates, ratios, and proportions? How do we solve proportions? HW #16: pp. 117-119/ # 2, 5, 8, 11, 14, 17, 31, 41. (2-10) How do we use proportions to geometric and other problems? HW #17: p. 124/ # 3, 4, 5, 6, 7, 22, 30, 31, 32, (no calculators for 30, 31, 32). (2-11) What are percents, and how do we convert them to fractions and decimals? HW #18: p. 130/ # 2, 3, 6, 7, 10, 11, 28, 30, 33, 38, 40, 43. (2-12) How do we apply our skills from Unit 2? HW #19: Handout Review Test INTEGRATED ALGEBRA UNIT 3 Grade Level: 9th Unit Length: 9 days Essential Questions: How can patterns, relations, and functions be used as tools to best describe and help explain real-life relationships? How can situations be modeled as a system of linear inequalities and how to find solutions using all constraints? Unit Title: Inequalities Enduring Understandings/Big Ideas: Patterns and relationships can be represented graphically, numerically, and symbolically. How to use the unknown, constraints and their relationships to model a situation Common Core Learning Standards: New York State / Content Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context A.REI.1 Explain each step in solving a simple inequality as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letter A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable A.A.24 Solve linear inequalities in one variable A.G.6 Graph linear inequalities A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form Skills (Students will be able to…) Write an inequality from a verbal description Write and use inequalities to solve verbal problems Write the inequality of a line parallel to the x- or y-axis Graph linear inequalities on a number line Use set-builder notation to write the solution set of an inequality Solve a compound inequality Determine solutions of compound inequality that make the inequality true Unit Outline: How do we write and graph inequalities? How do we solve one-step inequalities? How do we solve multi-step inequalities? How do we solve inequalities with variables on both sides? How do we solve compound inequalities (Day1)? How do we solve compound inequalities (Day 2)? How do we use set-builder notation and interval notation to write the solution set of an inequality? How do we solve verbal problems with inequalities? Review Test Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Exit Slips Homework Notebook check quiz Summative Assessment / Performance Task: Unit Test Key Terms/Vocabulary: Inequality, Less than, greater than, less than or equal to, greater than or equal to, included, not included, compound inequality, conjunction, intersection, set-builder notation, interval notation, sets, roster form Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 3: Inequalities (3-1) How do we write and graph inequalities? How do we solve one-step inequalities? HW #21: pp. 171-173/ # 6,7, 29-35 pp. 177-179/ # 7-9, 13 – 15, 34 pp. 183-185/ # 23, 24, 30, 32, 67 – 69 (3-2) How do we solve multi-step inequalities? HW #22: pp. 191-193 # 25, 27, 31, 33, 52, 53, 55-59, 78, 79 (3-3) How do we solve inequalities with variables on both sides? HW #23: pp. 197-200/ # 6, 8, 12, 21, 53, 55, 60, 64, 69, 73 . (3-4) How do we solve compound inequalities? (Day 1) HW #24: pp. 206-208/ #3, 6, 11, 14, 28, 30, 32, 59, 62 (3-5) How do we solve compound inequalities? (Day 2) HW #25: pp. 206-208/ # 9, 10, 12, 13, 31, 33, 36, 45, 48, 49, 64 (3-6) How do we use set-builder notation and interval notation to write the solution set of an inequality? HW #26: Handout (3-7) How do we solve verbal problems with inequalities? HW #27: Handout Review Test INTEGRATED ALGEBRA UNIT 4 Unit Title: Intro to Functions Enduring Understandings: What is a function? How do functions relate to mathematics? Grade Level: 9 Unit Length: 9 days Essential Questions: How can patterns, relations, and functions be used as tools to best describe and help explain real-life relationships? Common Core Learning Standards: New York State Standards: A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions A.CED.2 Create equations in two variables to represent relationships between quantities A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letter A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the A.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph A.A.5 Write algebraic equations or inequalities to represents a situation coordinate plane F.LE.2 Construct linear functions given a graph, a description of a relationship, or two input-output pairs F.IF.4 For a function that models a relationship between two quantities, interpret key features if graphs… and sketch graphs showing key features given a verbal description of the relationship Skills: Write an equation from a verbal description Write an inequality from a verbal description Write and use equations to solve verbal problems Graph ordered pairs on a coordinate grid Represent mathematical relationships using graphs Determine if a relation is a function Identify the domain and range of a function Write equations from descriptions and tables Write equations using function notation Use a table of values to graph a function Use a graphing calculator to graph a function Analyze how different transformations affect a graph Unit Outline: How do we use the coordinate plane to graph ordered pairs? How do we use graphs to relate two quantities? What is the difference between a relation and a function? How do we identify the domain and range? How do we write equations of functions from tables or descriptions? What is a parent function? How do we graph functions using the table method? How do we graph functions using a graphing calculator? Review Test Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Homework Notebook check Summative Assessment: Unit test Key Terms/Vocabulary: linear relationships, translate; dependent variable; independent variable; profit; co-ordinate grid; x- and yaxis; quadrants, domain, range, Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 4: Intro to Functions ALL GRAPHS IN THE UNIT MUST BE DONE ON GRAPH PAPER OR YOU WILL NOT RECEIVE CREDIT! YOU WILL NEED A GRAPHING CALCULTOR FOR LESSONS 33 & 34! (4-1) How do we use the coordinate plane to graph ordered pairs? HW #28: p. 57/ #17-20 (Use the same set of axes for 17-20, and label each point.), 21-26, 28, 29, 30. (4-2) How do we use graphs to relate two quantities? HW #29: p. 233-235/ #10, 11, 12, 13, 14, 32, 33. (4-3) What is the difference between a relation and a function? How do we identify the domain and range? HW #30: p. 239-242/ #15, 16, 17, 18, 21, 29, 34, 39. (4-4) How do we write equations of functions from tables or descriptions? HW #31: p. 249-251/ #13, 14, 15, 16, 17, 18, 20, 21, 22, 33, 38, 39. (4-5) What is a parent function? HW#32: p 250-251/#32-35, 43, 44 (4-6) How do we graph functions using the table method? HW #33: p. 256-258/ #13, 14, 18, 19, 24, 37, 39, 40, 41, 68. (4-7) How do we graph functions using a graphing calculator? HW #34: p. 256-258/ 17, 21, 22, 32, 33, 54 p. 284/1, 2, 3, 4, 5, 7 Review Test INTEGRATED ALGEBRA UNIT 5 Unit Title: Linear Functions Enduring Understandings: Patterns and relationships can be represented graphically, numerically, and symbolically. Purpose of intercepts How do changing the m, k and a-values affect the graph? Common Core Learning Standards: 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 N.Q.1 – Use units as a way to understand problems and to guide solutions to multi-step problems;choose and interpret scale and the origin in graphs and data displays. F.IF.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 the domain, then f(x) = denotes the output of f corresponding to the input x. The graph of f is the graph of the equation f(x) = x F.IF.2 – Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.3 – Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. F.IF.4 – For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graph showing key features given a verbal description of the relationship F.IF.5 – Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F.IF.6 – Calculate and interpret the average rate of change of a function (presented symbolically or in a table) over a specified interval. Estimate the rate of change from a graph F.IF.7 – Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F.IF.7a – Graph linear…functions and show intercepts F.BF.1 – Write a function that describes a relationship between two quantities F.LE.2 – Construct linear functions, given a graph, a description of a relationship, or two input-output pairs (include reading a table) F.BF.3 – Identify the effect on the graph of replacing f(x) by f(x) + k and f(x + k) for specific values of k; find the value of k given the graphs F.LE.5 – Interpret the parameters in a linear function in terms of a context Skills: Identify linear functions given a table of values Identify linear functions given its graph Identify linear functions given its equation Grade Level: 9 Unit Length: 10 Days Essential Questions: What is a discrete linear function? How are discrete and continuous linear functions alike and how are they different? What is the slope of a linear function and how can we use it to graph linear functions? How can you represent relationships using linear functions? New York State Standards: A.A.4 Translate verbal sentences into mathematical equations or inequalities A.A.5 Write algebraic equations or inequalities that represent a situation A.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions A.G.5 Investigate and generalize how changing the coefficients of a function affects its graph A.A.32 Explain slope as a rate of change between dependent and independent variables A.A.33 Determine the slope of a line, given the coordinates of two points on the line A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line A.A.35 Write the equation of a line, given the coordinates of two points on the line A.A.36 Write the equation of a line parallel to the xor y-axis A.A.37 Determine the slope of a line, given its equation in any form A.A.38 Determine if two lines are parallel, given their equations in any form A.A.39 Determine whether a given point is on a line, given the equation of the line Determine x and y-intercepts of a given graph Find slope using the slope formula Plot a line given the slope Find the slope of a line, given its equation Write the equation of a line in y=mx + b form Graph a line given its equation Write the equation of a line, given its slope and the coordinates of a point on the line Find slope of a line parallel or perpendicular to a given equation Perform transformations of a linear function Unit Outline: What are linear functions and how do we identify them? What are x-intercepts and y-intercepts and how do we use them to graph functions? What is the slope of the line, and how do we find it from a graph? How do we find slope using the slope formula? How do we write and graph an equation of a line in slope-intercept form? (y = mx + b) How do we write and graph an equation of a line given the slope and a point? How do we use different forms of linear equations? What is the difference between a linear equation and a linear function? How do we find slopes of parallel and perpendicular lines? How do we perform transformations of linear functions? Review Test Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Homework Notebook check quiz Summative Assessment: Unit test Cell Phone Project Key Terms/Vocabulary: Linear function, Rate of change, rise, run, slope, constant function, x-intercept, y-intercept, standard form of a line, direct variation, constant, point slope form, parallel, perpendicular, transformation Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 5: Linear Functions (5.1) What are linear functions, and how do identify them? What are x-intercepts and y-intercepts, and how do we use them to graph functions? HW #35/36: p. 300/ #5, 7, 9-12, 15, 17; p. 306-307/ #2, 4, 6, 11, 30 (5.2) What is the slope of a line, and how do we find it from a graph? HW #37: pp. 314-317/# 2, 4, 5, 8-11, 25, 36-38, 41 (5.3) How do we find slope using the slope formula? HW #38: pp. 323-325/# 1, 3, 5, 6, 8-10, 21, 26, 27, 29, 32, 34 (5.4) How do we write and graph an equation of a line in slope-intercept form? HW #39: pp. 338-340/# 1, 4-8, 10, 11, 20, 24, 25, 50, 53 (5.5) How do we write and graph an equation of a line given the slope and a point? HW #40: pp. 345-347/# 4-6, 13-15, 51, 54, 59 (5.6) How do we use different forms of linear equations? What is the difference between a linear equation and a linear function? HW #41: Worksheet (5.7) How do we find slopes of parallel and perpendicular lines? HW #42: pp. 353-355/# 9, 10, 13, 15, 18, 19, 21, 23, 26, 33, 46, 47 (5.8) How do we perform transformations of linear functions? HW #43: pp. 361-363/# 3, 6, 8, 10, 12, 13, 19, 55, 57, 58, 60 Review Test INTEGRATED ALGEBRA UNIT 6 Unit Title: Systems of Equations and Inequalities Enduring Understandings/Big Ideas: How to graph systems of equations Which algebraic method is most useful Translating word problems Graph linear equations Graph linear inequalities Common Core Learning Standards: A.REI.4 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. A.REI.5 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.REI.6 Solve systems of linear equations…approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. AREI.12 Graph the solutions to a linear inequality in two variables as half-place (excluding the boundary in the case of a strict inequality)… .N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently…. N.Q.2 Define appropriate quantities for the purpose of descriptive modeling. * A.CED.2 Create equations in two or more variables to represent relationships between quantities… Grade Level: 9 Unit Length: 9 days Essential Questions: What does it mean to be the solution of a system of equations? How do we graph linear equations? How can we determine if a value/point is in the solution set? Look at the graphs of the two equations. Does the linear system have exactly one solution? How do you know? How do we graph linear inequalities? How can we determine if a value/point is in the solution set? New York State / Content Standards: A.A.21 Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable A.G.7 Graph and solve systems of linear equations and inequalities with rational coefficients in two variables A.G.6 Graph linear inequalities A.A.40 Determine whether a given point is in the solution set of a system of linear inequalities Skills: Graph linear equations Solve systems of equations by substitution Solve systems of equations by elimination Solve systems of equations from word problems Graph linear inequalities Identify the solution set of linear inequalities Solve systems of linear inequalities Unit Outline: What are systems of equations? How do we solve systems of linear equations by graphing? How do we solve systems of linear equations by Substitution? How do we solve systems of linear equations by Elimination? What are special systems? How do we solve verbal problems leading to solving a system of linear equations algebraically? How do we graph and solve linear inequality in two variables? How do we graph and solve systems of linear inequalities in two variables? Review Test Formative Assessments: Quizzes Do Now responses Teacher/student exchange Questioning during class discussions Homework Notebook check quiz Summative Assessment / Performance Task: Unit test Performance Task, National Treasure Key Terms/Vocabulary: intersection, systems of equations, linear, solution set, substitution Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 6: Systems of Equations and Inequalities ALL GRAPHS MUST BE DONE ON GRAPH PAPER (6.1) What are systems of equations? How do we solve systems of linear equations by graphing? HW #44 : pp. 386-388 /# 1-8, 34, 36, 37, 41 (6.2) How do we solve systems of linear equations by Substitution? HW #45: pp. 394-396 /# 1-7, 38, 39, 46 (6.3) How do we solve systems of linear equations by Elimination? HW #46: pp. 401-403 /# 11, 12, 14, 15, 18-20, 24, 25, 39, 44, 45 (6.4) What are special systems? HW #47: pp. 409-411 /# 12, 14, 16, 20-22, 26, 29, 42-44 (6.5) How do we solve verbal problems leading to solving a system of linear equations algebraically? HW #48: Worksheet (6.6) How do we graph and solve linear inequality in two variables? HW #49: pp. 418-420 /#12-14, 16, 18, 20-22, 27, 42 (6.7) How do we graph and solve systems of linear inequalities in two variables? HW #50: pp. 424-426 /# 6, 10, 12, 14, 29, 35-37, 41, 54-57 Review Test INTGRATED ALGEBRA UNIT 7 Unit Title: Exponents and Exponential Functions Enduring Understandings/Big Ideas: How to multiply and divide monomials What parts of a polynomial represent terms, factors and coefficients How do exponential functions operate? Common Core Learning Standards: A.APR.1 Understand that polynomials form a system of analogous to the integers, namely, they are closed under the operations of addition, subtraction and multiplication; add, subtract, and multiply polynomials Grade Level: 9th Unit Length: 8 days Essential Questions: What are like terms? When we multiply monomials what do we do with the exponents? When we divide monomials what do we do with the exponents? New York State / Content Standards: A.A.12 Multiply and divide monomial expressions with a common base, using the properties of exponents A.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no A.APR.6 Rewrite simple rational expressions in remainder different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), A.N.3 Perform the four arithmetic operations using where a(x), b(x), q(x), and r(x) are polynomials with like and unlike radical terms and express the the degree of r(x) less than the degree of b(x), using result in simplest form inspection, long division, or, for the more complicated examples, a computer algebra system. A.N.4 Understand and use scientific notation to N.RN.1 Explain how the definition of the compute products and quotients of meaning of rational exponents follows from the numbers greater than 100% extending properties of integer exponents to those A.N.6 Evaluate expressions involving factorial(s), values, allowing for a notation for radicals in absolute value(s), and exponential terms of rational exponents expression(s) N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients Skills: Combine like terms Simplify expressions with exponents (integer and rational) Evaluate expressions with rational exponents Multiply monomials Divide monomials Distribute Evaluate growth and decay problems Evaluate compound interest Unit Outline: How do we evaluate and simplify numeric expressions with integer exponents? How can we write and evaluate an nth root of a number? How do we use multiplication properties of exponents to simplify expressions? How do we use division properties of exponents to simplify expressions? How do we solve problems involving exponential growth and decay? How do we compute compound interest? Review Test Formative Assessments: Homework assignments Quizzes Exit Tickets Summative Assessment / Performance Task: Unit test Key Terms/Vocabulary: Like terms, Coefficient, Constant, Rational exponent, Expression, Variable, Exponent, Monomial, Exponential growth/decay, compound interest, principal Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Algebra 1 Textbook – Holt Algebra 1 MES21 Unit 7: Exponents and Exponential Functions (7.1) How do we evaluate and simplify numeric expressions with integer exponents? HW #51 : pp. 449-451 /#1-6, 41, 42, 68, 70, 86-88, 107, 109, 113 (7.2) How can we write and evaluate an nth root of a number? HW #52: Handout (7.3) How can we use multiplication properties of exponents to simplify expressions? HW #53: pp. 464-466 /#2, 4, 7, 10, 11, 21, 36, 39, 41, 48, 77-79 (7.4) How do we use division properties of exponents to simplify expressions? HW #54: pp. 471-473 /#1, 2, 5, 11, 14, 15, 46, 50, 52, 57, 64, 66 (7.5) How do we solve problems involving exponential growth and decay? HW #55: pp. 785-786 /#10, 11, 13, 21-24, 29, 34 (7.6) How do we compute compound interest? HW #56: pp. 785-786 /#14, 15, 17, 30-32, 36, 54 (copy chart) Review Test INTGRATED ALGEBRA UNIT 8 Unit Title: Patterns and Sequences Enduring Understandings/Big Ideas: Connecting knowledge of linear and exponential functions to sequences and patterns Grade Level: 9th Unit Length: 8 days Essential Questions: How can you use a geometric of arithmetic sequence to describe a pattern? How can you define a sequence recursively? Common Core Learning Standards: IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs New York State / Content Standards: A.PS.3 Observe and explain patterns to formulate generalizations and conjectures A2.A.29 Identify an arithmetic or geometric sequence and find the formula for its nth term A2.A.30 Determine the common difference in an arithmetic sequence A2.A.31 Determine the common difference in a geometric sequence A2.A.32 Determine a specified term of an arithmetic or geometric sequence A2.A.33 Specify terms of a sequence, given its recursive definition Skills: Determining whether a sequence is geometric, arithmetic or neither Find an nth term of a given sequence Creating an explicit formula for a given sequence Creating a recursive formula for a given sequence Converting between recursive and explicit rules Unit Outline: What is an arithmetic sequence? How do we solve arithmetic sequences problems? What are geometric sequences? How do we solve geometric sequences problems? How do we define sequences using recursive formula? Practice with Patterns Review Test Formative Assessments: Homework assignments Quizzes Exit Tickets Summative Assessment / Performance Task: Unit test Pattern Task Sequence Project Key Terms/Vocabulary: Common difference, Common ratio, Explicit formula, Recursive formula, Arithmetic sequence, Geometric sequence, Term, Sequence Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Big Ideas – Algebra 1 Textbook Algebra 1 MES21 Unit 8: Patterns and Sequences (8.1) What is an arithmetic sequence? HW #57 : pp. 275 /#2-5, 16-18, 22-25, 28-31 (8.2) How do we solve arithmetic sequence problems? HW #58: pp. 275-276 /#15, 33, 39, 40 (8.3) What are geometric sequences? HW #59: pp. 769-770 /#8-13, 17-22, 26-28, 34-36 (8.4) How do we solve geometric sequence problems? HW #60: pp. 769-770 /#32, 33, 37-39, 42, 43 (8.5) How do we define sequences using a recursive formula? HW #61: Handout (8.5) Practice with Sequences HW #62: Handout Review Test INTEGRATED ALGEBRA UNIT 9 Unit Title: Polynomials and Factoring Grade Level: 9th Unit Length: 12 days Enduring Understandings/Big Ideas: Essential Questions: How do perform operations on polynomial How can you find the GCF of monomials? functions When factoring what numbers do we need to find? How to factor different types of Can you factor expressions with more than expressions one variable? Common Core Learning Standards: A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entry A.SSE.2 Use the structure of an expression to identify ways to rewrite it A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression A.APR.1 Understand that polynomials form a system of analogous to the integers, namely, they are closed under the operations of addition, subtraction and multiplication; add, subtract, and multiply polynomials New York State / Content Standards: A.A.13 Add, subtract, and multiply monomials and polynomials A.A.19 Identify and factor the difference of two perfect squares A.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) Skills (Students will be able to…) Add/subtract polynomials Multiply polynomials Use prime factorization Identify GCF Factor quadratic trinomials Apply multiple types of factoring Unit Outline – Sequence of learning (AIMs): What are polynomials and how do we classify them? How do we add and subtract polynomials? How do we multiply polynomials? What are special products of polynomials? What is prime factorization? How do we factor polynomials? How do we factor trinomials? How do we factor trinomials where a ¹ 1? How do we factor using special products? How do we factor polynomials completely? How do we factor polynomials completely? (Day 2) Review Test Formative Assessments: Homework assignments Quizzes Exit Tickets Summative Assessment / Performance Task: Hanger project Unit 9 Test Key Terms/Vocabulary: Binomial, trinomial, polynomial, quadratic, standard form, leading coefficient, FOIL, difference of two squares, GCF, prime factorization, expression, factor, factoring, perfect-square trinomial, Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Big Ideas Textbook Algebra 1 MES22 Unit 9: Polynomials and Factoring (9.1) What are polynomials and how do we classify them? HW #1: pp. 362-364/ #5 – 12, 13 – 20 (9.2) How do we add and subtract polynomials? HW #2: pp. 362 – 364/ #23 – 40 (evens), 55, 57 (9.3) How do we multiply polynomials? HW #3: pp. 369 – 371/ #21 – 30, 35 – 40 (9.4) What are special products of polynomials? HW #4: pp. 375 /# 3 – 10, 11, 13, 15 – 19, 31, 39, 40 (9.5) What is prime factorization? How do we factor polynomials using the GCF? HW #5: pp. 381 – 383/ #25 – 30, 49 – 52 (9.6) How do we factor trinomials? HW #6: pp. 389 – 391 / #3 – 5, 11 – 14, 20 – 24 (9.7) How do we factor trinomials where a ¹ 1? HW #7: pp. 395 – 397/ #3, 5, 7, 11, 14, 16, 18, 20, 24, 37, 38 (9.8) How do we factor using special products? HW #8: pp. 401 – 403/ #2, 3 – 5, 15 – 21, 23, 25*, 43 (9.9) How do we factor polynomials completely? HW #9: pp. 407 – 409/ #1, 11 – 22 (evens), 37, 39 (9.10) How do we factor polynomials completely (Day 2) HW #10: pp. 407 – 409/ #2, 11 – 22 (odds), 35a, 40 Review Test INTEGRATED ALGEBRA UNIT 10 Unit Title: Graphing Quadratic Functions Enduring Understandings/Big Ideas: What are characteristics of quadratic functions? Transformations on the standard quadratic function Grade Level: 9th Unit Length: 8 days Essential Questions: How do different transformations affect the parabola? When is each type of form of a quadratic equation necessary? Can we compare growth rates of each type of function we have studied? New York State / Content Standards: A.R.8 Use mathematics to show and understand mathematical phenomena Common Core Learning Standards: CED.A.2 Graph equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales A.G.4 Identify and graph, linear, quadratic, absolute SSE.B.3a Factor a quadratic to reveal the zeros of value and exponential functions the function it defines APR.B.3 Identify zeros of polynomials when A.G.5 Investigate and generalize how changing the suitable factorizations are available, and use the coefficients of a function affects its graph zeros to construct a rough graph of the function defined by the polynomial A.G.10 Determine the vertex and axis of symmetry IF.B.4 For a function that models a relationship of a parabola, given its graph between two quantities, interpret key features of graphs in terms of the quantities, and sketch A.A.41 Determine the vertex and axis of symmetry graphs showing key features given a verbal of a parabola, given its equation description of the relationship IF.C.7a Graph... quadratic functions and show A2.S.51 Determine the domain and range of a intercepts, maxima, and minima function from its graph IF.B.3 Identify the effect on the graph of replacing f(x) by kf(x), f(x)+k, f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology IF.C.8a Use the process of factoring in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret in terms of a context IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically…) IF.B.6 Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph. LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as a polynomial function Skills (Students will be able to…) Identify characteristics of a quadratic function Graph quadratic equations from standard form Determine how the value of a coefficient affects a quadratic function Find the vertex of a quadratic function Graph quadratic equations from vertex form Unit Outline – Sequence of learning (AIMs): What are the characteristics of quadratic functions? How do we graph quadratic functions? How does the value of c affect the graph of a quadratic function? How can we find the vertex of the graph of f (x) = ax 2 + bx + c ? How can we describe the graph of a quadratic in vertex form? What are characteristics of the graph f (x) = (x - p)(x - q)? How can we compare the growth rates of linear, exponential, and quadratic functions? Review Test Formative Assessments: Homework assignments Quizzes Exit Tickets Summative Assessment / Performance Task: Unit 10 Test Revolution K12 Key Terms/Vocabulary: Quadratic function, vertex, axis of symmetry, parabola, standard form, vertex form, zeros, translation, maximum, minimum, intercept form, average rate of change Differentiation: choice of homework problems, choice on exit ticket, heterogeneous grouping Higher Achieving - Challenge and bonus questions, accelerate pacing SWD – small group instruction, modified assessments, skeleton – note handouts, mnemonic strategies, computer assisted instruction, peer mediation ELL – use of dictionaries, translated assessments, translated handouts, visuals/graphic organizer that reinforce spoken word Resources: Explorations in CORE Math for Common Core Big Ideas Textbook Algebra 1 MES22 Unit 10: Graphing Quadratic Functions ALL GRAPHS MUST BE ON GRAPH PAPER (10.1) What are the characteristics of quadratic functions? How do we graph quadratic functions? HW #11: pp. 423 #1 – 4, 5, 9, 21 – 23, 33, 34 (10.2) How does the value of c affect the graph of a quadratic function? HW #12: pp. 429 #3, 5, 7, 9, 11, 18 (10.3) How can we find the vertex of the graph of f (x) = ax 2 + bx + c ? HW #13: pp. 436 #3, 5, 7, 9, 13, 14, 19, 21, 22 (10.4) How can we describe the graph of a quadratic in vertex form? HW #14: pp. 446 #31 – 34, 35 – 38, 39, 41 (10.5) What are characteristics of the graph f (x) = (x - p)(x - q)? HW #15: pp. 455 #7, 9, 11, 21, 22, 31 – 36 (10.6) How can we compare the growth rates of linear, exponential, and quadratic functions? HW #16: pp. 465 #4, 9 – 11, 15 – 18, 23, 24, 36 Review Test
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