Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.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 exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (A) linear equations (B) linear inequalities (G) absolute value equations (H) absolute value inequalities 5. Use appropriate tools strategically. I will solve problems by creating equations and inequalities in one variable. Section 1.2-1.9 Section 2.3-2.7 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Inequality
Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's Law V=IR to highlight resistance R. [Limit to formulas that are linear in the variable of interest or formulas involving squared variables.] 5. Use appropriate tools strategically. 7. Look for and make use of structure. I will rearrange formulas to solve for a specified variable. Section 1.6 Review this standard with the different types of equations (linear, exponential, and quadratic). Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Formula Laws of Equality
Quarter 1 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.A.REI.3 * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Include simple exponential equations that rely only on application of the laws of exponents such as 5 x =125 or 2 x = ] (A) linear and literal equations (B) linear inequalities 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. I will solve linear equations and inequalities, including coefficients represent by letters. Section 1.1 Lab Section 1.2 Section 1.4 Lab Section 1.6-1.9 Section 2.1 2.7 Section 2.6 Lab Section 5.1 Lab Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Exponent
Quarter 1 In what ways can the choice of units, quantities, and levels of accuracy impact a solution? Number - Quantities AI.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 in formulas; choose and interpret the scale and the origin in graphs and data displays. (A) units (B) scale and origin 5. Use appropriate tools strategically. 6. Attend to precision. Algebra I Supporting I will use units to understand problems and to interpret solutions. Section 1.1 Section 1.6 Section 1.8-1.9 Section 3.5 Modeling: Having Kittens A19 Leaky Faucet A24 Yogurt Formula Literal equation Origin Scale
Quarter 1 How does the knowledge of integers help when working with rational and irrational numbers? Number The Real Number System AI.N.RN.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. [Connect to physical situations, e.g., finding the perimeter of a square of area 2.] 3. Construct viable arguments and critique the reasoning of others. Algebra I Additional I will understand the properties of adding and multiplying rational and irrational numbers. Section 6.5 Extension Equations of Circles 2 Rational and Irrational Numbers 1 Rational and Irrational Numbers 2 N01 The Real Number System Closure Element Set Subset
Quarter 1 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.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). [Focus on linear and exponential equations.] (A) linear equations I will understand that a graph represents all possible solutions to a two variable function. Section 3.4 Section 4.1 Section 8.1 Section 8.10 Extension Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Linear function Linear equation
Quarter 1 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.A.REI.12 * Graph the solutions to a linear inequality in two variables as half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (A) linear inequality (B) system of linear inequalities 5. Use appropriate tools strategically. I will graph linear inequalities and systems of linear inequalities. Section 5.5 5.6 Section 5.6 Lab Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Boundary Half plane Strict inequality
Quarter 1 How can the relationship between quantities best be represented? Functions Interpreting Functions AI.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. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] a*. Graph linear and quadratic functions and show intercepts, maxima, and minima. (A) linear functions 5. Use appropriate tools strategically. 6. Attend to precision. Algebra I Supporting I will graph functions by hand or using technology. Section 3.4 Section 4.1 4.2 Section 4.5 4.7 Section 4.7 Lab Section 4.9 4.10 Section 4.10 Extension Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Linear equation Linear function x intercept y intercept
Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (A) linear equations 5. Use appropriate tools strategically. I will represent relationships between quantities by creating equations in two or more variables. Section 4.1-4.2 Section 4.5-4.7 Section 5.1 Section 5.4 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Axis Direct variation Slope Constant of variation Quadratic equations Slope intercept form Coordinate plane Scale
Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. [Limit to linear equations and inequalities.] (A) linear equations (B) linear inequalities 5. Use appropriate tools strategically. I will understand constraints as they apply to real world problems. Section 3.3 Section 4.2 Section 4.5-4.7 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Constraint Non-viable Viable
Quarter 1 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. [Limit to linear equations and inequalities.] (C) system of linear equations (D) system of linear inequalities 5. Use appropriate tools strategically. I will understand constraints as they apply to real world problems. Section 5.1-5.6 Section 8.7 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Constraint Non-viable Viable
Quarter 1 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.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. [Include systems of equations that yield infinitely many solutions and no solutions.] 3. Construct viable arguments and critique the reasoning of others. Algebra I Additional I will prove the elimination method of solving a system of equations is valid. Section 5.3 Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Elimination method Infinitely many solutions No solution System of equations
Quarter 1 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.A.REI.6 Solve systems of linear. equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 2. Reason abstractly and quantitatively 6. Attend to precision. 7. Look for and make use of structure. 5. Use appropriate tools strategically 8. Look for and express regularity in repeated reasoning. Algebra I Additional I will solve systems of linear equations in a variety of methods. Section 5.1-5.4 Section 5.1 Lab Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Substitution method
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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 its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of y=f(x). [Focus on linear and exponential functions] I will understand the meaning of a function. Section 3.2 3.4 Section 3.2 Lab Section 3.4 Lab Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Domain Function Range
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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. [Focus on linear and exponential functions] I will use function notation to evaluate functions for a given domain. I will identify independent and dependent variables. I will write an equation in function notation. I will interpret functions in context. Section 3.3-3.4 Section 4.2 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Dependent variable Function rule Inputs Function notation Independent variable Outputs
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f (0) = f (1) = 1, f (n+1) = f (n) + f (n-1) for n is greater than or equal to 1. [Emphasize arithmetic and geometric sequences as examples of linear and exponential functions.] 8. Look for and express regularity in repeated reasoning. I will recognize that sequences are functions. Section 3.6 Section 9.1 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Arithmetic sequence Geometric sequence Range Common difference Negative correlation Relation Common ratio No correlation Sequence Correlation Positive correlation Term Domain
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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 graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (A) linear functions 5. Use appropriate tools strategically. 6. Attend to precision. I will interpret the key features of a function graph. Section 3.1 Section 4.2 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Decreasing Maximum Vertex End behavior Minimum Zeros Increasing Symmetry
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (A) linear functions 6. Attend to precision. I will relate the domain of a function to its graph and apply appropriate constants. Section 3.2 3.4 Section 4.1 4.2 Section 4.5 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Constraints
Quarter 1 How can the relationship between quantities best be represented? Functions Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (A) linear functions 5. Use appropriate tools strategically. I will calculate and interpret the average rate of change for a function. I will compare rates of change from a graph. Section 4.3 4.4 Section 4.3 Lab Section 4.6 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Average rate of change Slope
Quarter 1 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (A) linear functions 6. Attend to precision. 7. Look for and make use of structure. Algebra I Supporting I will compare the properties of two functions when they are represented different ways, for instance comparing graphs to tables or to equations. Section 4.1 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Average rate of change
Quarter 1 In what ways can functions be built? Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (A) linear functions Mathematical Practices : 5. Use appropriate tools strategically. 7. Look for and make use of structure. Algebra I Additional I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when a linear equation is changed. I will find the value of k given the graphs. Section 4.10 Section 4.9 Lab Section 4.10 Extension Ferris Wheel Medical Testing Modeling: Rolling Cups Generalizing Patterns: Table Tiles Modeling Conditional Probabilities 2 Representing Polynomials Dilation Horizontal stretch Vertical compression Horizontal compression Parameter Vertical shift Horizontal shift Reflection Vertical stretch
Quarter 2 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.3 * Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. [Include quadratic and exponential expressions] (B) exponential expressions c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 (1/12) ) (12t) = 1.012 (12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 1. Make sense of problems and persevere in solving them. Algebra I Supporting I will use properties of exponents to transform expression s for exponential functions. Section 9.2 Supplement CLAROOM CHALLENGE ACTIVITES: map.mathshell.org Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials A04 Circle Pattern N02 Seeing Structure in Expressions Exponential function August 2014 Quarter 2 Page 1 of 18
Quarter 2 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (B) exponential expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r) n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (B) exponential expressions 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure. I will interpret expressions that represent a quantity. Section 6.3 Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials A04 Circle Pattern N02 Seeing Structure in Expressions Coefficients Factors Square Cube roots Quadratic expressions Terms August 2014 Quarter 2 Page 2 of 18
Quarter 2 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.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 exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (E) exponential equations (F) exponential inequalities 5. Use appropriate tools strategically. I will create exponential equations and inequalities. Section 9.2 Supplement Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Exponential function August 2014 Quarter 2 Page 3 of 18
Quarter 2 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (B) exponential equations 5. Use appropriate tools strategically. I will create exponential system of equations. Section 9.2 Supplement Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Exponential function August 2014 Quarter 2 Page 4 of 18
Quarter 2 When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.1 * Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 3. Construct viable arguments and critique the reasoning of others. 8. Look for and express regularity in repeated reasoning. Algebra I Supporting I will distinguish between situations which can be modeled with linear and exponential functions. Section 9.2 Section 9.4 Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens E11 Table Tiling N08 Linear and Exponential Models Equal differences Equal intervals Exponential functions Exponential growth Geometric sequences August 2014 Quarter 2 Page 5 of 18
Quarter 2 When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.2 * Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (A) linear functions (B) exponential functions 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Algebra I Supporting I will construct linear and exponential functions from arithmetic and geometric sequences given: Graph Description of a relationship Two input outputs pairs. Section 3.6 Section 4.5 4.7 Section 9.3 9.4 Section 4.1 4.2 Section 9.1 Section 9.3 Lab - Extension Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens E11 Table Tiling N08 Linear and Exponential Models Arithmetic sequence Exponential function Sequence Constant of variation Geometric sequence Term August 2014 Quarter 2 Page 6 of 18
Quarter 2 When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.3 * Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [Include comparison between linear and exponential models as well as compare linear and exponential growth to quadratic growth.] (A) compare linear and exponential models (B) compare linear and exponential growth to quadratic growth 8. Look for and express regularity in repeated reasoning. Algebra I Supporting I will observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically and as a polynomial function using tables and graphs. Section 9.5 Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens E11 Table Tiling N08 Linear and Exponential Models Average rate of change Exponential models Polynomial function Exponential growth Linear models Quadratic growth August 2014 Quarter 2 Page 7 of 18
Quarter 2 When does a function best model a situation? Functions - Linear and Exponential Models AI.F.LE.5 * Interpret the parameters in a linear or exponential function in terms of a context. [Limit exponential functions to those of the form f(x) =b x +k.] (A) linear functions (B) exponential functions Algebra I Supporting I will interpret the parameters of a function in terms of a context. Section 4.6 Comparing Investments Foundations and Everyday Situations Modeling: Having Kittens E11 Table Tiling N08 Linear and Exponential Models Slope intercept form August 2014 Quarter 2 Page 8 of 18
Quarter 2 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.A.REI.3 * Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Include simple exponential equations that rely only on application of the laws of exponents such as 5 x =125 or 2 x = ] (C) exponential equations 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. I will solve exponential equations and inequalities. Supplement Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities August 2014 Quarter 2 Page 9 of 18
Quarter 2 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.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). [Focus on linear and exponential equations.] (B) exponential equations I will understand that a graph represents all possible solutions to a two variable function. Section 9.2 Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Exponential function Exponential graph August 2014 Quarter 2 Page 10 of 18
Quarter 2 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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 graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (B) exponential functions 5. Use appropriate tools strategically. 6. Attend to precision. I will interpret the key features of an exponential function graph. Section 9.4 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Decreasing Maximum Symmetry End behavior Minimum Vertex Increasing August 2014 Quarter 2 Page 11 of 18
Quarter 2 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (B) exponential functions 6. Attend to precision. I will relate the domain of a function to its graph and the quantative relationship. Section 9.4 9.5 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Domain Exponential functions Function Quantative relationship August 2014 Quarter 2 Page 12 of 18
Quarter 2 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (B) exponential functions 5. Use appropriate tools strategically. I will calculate and interpret average rate of change (slope) of a function. I will compare rates of change from a graph. Section 8.2 8.3 Section 9.4 Extension Section 9.5 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Exponential function Rate of change Run Linear function Rise Slope Quadratic function August 2014 Quarter 2 Page 13 of 18
Quarter 2 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (B) exponential functions 6. Attend to precision. 7. Look for and make use of structure. Algebra I Supporting I will compare properties of two functions each represented in a different way. Section 9.5 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Average rate of change August 2014 Quarter 2 Page 14 of 18
Quarter 2 In what ways can functions be built? Functions - Building Functions AI.F.BF.3 * Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Focus on vertical translations of graphs of linear, exponential, quadratic, and absolute value functions. Relate the vertical translation of a linear function to its y-intercept.] (B) exponential functions 5. Use appropriate tools strategically. 7. Look for and make use of structure. Algebra I Additional I will identify the effect that parameter changes will have on a function graph. I will identify the effect on the graph when the quadratic and exponential equation is changed. I will find the value of k given the graphs. Section 8.3 Lab Section 8.4 Ferris Wheel Medical Testing Modeling: Rolling Cups Generalizing Patterns: Table Tiles Modeling Conditional Probabilities 2 Representing Polynomials A02 Patchwork A12 Printing Tickets E11 Table Tiling A06 Sidewalk Patterns E07 Skeleton Tower E13 Sidewalk Stones Quadratic functions Translation Vertical intercept Vertical transformation August 2014 Quarter 2 Page 15 of 18
Quarter 2 In what ways can functions be built? Functions - Building Functions AI.F.BF.1 * Write a function that describes a relationship between two quantities. [Focus on linear, exponential, and quadratic functions.] a*. Determine an explicit expression, a recursive process, or steps for calculation from a context. (A) linear functions (B) exponential functions 1. Make sense of problems and persevere in solving them. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 5. Use appropriate tools strategically. Algebra I Supporting I will write a function describing the relationship between two quantities. Section 8.4 Section 8.7 Section 9.3 9.4 Section 9.3 Extension Ferris Wheel Medical Testing Modeling: Rolling Cups Generalizing Patterns: Table Tiles Modeling Conditional Probabilities 2 Representing Polynomials A02 Patchwork A12 Printing Tickets E11 Table Tiling A06 Sidewalk Patterns E07 Skeleton Tower E13 Sidewalk Stones Compound interest Exponential growth Half life Dependent variable Function notation Independent variable Exponential decay Function rule August 2014 Quarter 2 Page 16 of 18
Quarter 2 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (A) linear expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r) n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (A) linear expressions 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure. I will understand the parts of an expression, such as terms, factors and coefficients. Section 1.1 Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials A04 Circle Pattern N02 Seeing Structure in Expressions Coefficients Factors Equations Linear expressions August 2014 Quarter 2 Page 17 of 18
Quarter 2 How can the properties of the real number system be useful when working with polynomials and rational expressions? Algebra - Arithmetic with Polynomials and Rational Expressions AI.A.APR.1 * Understand 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. [Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x.] (A) addition and subtraction (B) multiplication 8. Look for and express regularity in repeated reasoning. I will understand that polynomials represent quantities and therefore can be added, subtracted and multiplied. Section 6.4 6.6 Section 6.3-6.4 Lab Section 6.5 Extension Interpreting Algebraic Expressions Manipulating Polynomials Representing Polynomials N03 Arithmetic with Polynomials and Rational Expressions Polynomial August 2014 Quarter 2 Page 18 of 18
Quarter 3 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.1 * Interpret expressions that represent a quantity in terms of its context. [Focus on linear, exponential, and quadratic expressions] a*. Interpret parts of an expression, such as terms, factors, and coefficients. (C) quadratic expressions b*. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P (1+r) n as a product of P and a factor not depending on P. [Include integer and rational exponents with focus on those that represent square or cube roots.] (C) quadratic expressions 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure. I will interpret expressions that represent a quantity. Section 6.3 Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials Coefficients Factors Square Cube roots Quadratic expressions Terms Page 1 of 82
Quarter 3 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 - y 4 as (x 2 ) 2 - (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 - y 2 ) (x 2 + y 2 ). 7. Look for and make use of structure. I will write equivalent expressions. Section 7.2 7.4 Section 7.1 and 7.2 Lab Section 7.5 7.6 Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials o A04 Circle Pattern N02 Seeing Structure in Expressions Exponents Factor Squares Page 2 of 82
Quarter 3 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.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. [Tasks are limited to quadratic equations.] 3. Construct viable arguments and critique the reasoning of others. I will solve one step equations by using addition and subtraction. I will solve one step equations by using multiplication and division. I will solve equations with variables on both sides. Section 1.1 and 1.4 Lab Section 1.2-1.5 Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Solving Quadratic Equations: Cutting Corners Boomerangs A17 Cubic Graphs N05 Reasoning with Equations and Inequalities Linear function Linear equation Page 3 of 82
Quarter 3 In what ways can the problem be solved, and why should one method be chosen over another? Algebra Reasoning with Equations and Inequalities AI.A.REI.4 * Solve quadratic equations in one variable. a*. 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) process of completing the square (B) derive quadratic formula b*. 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. [Include existence of complex number system, but do not solve quadratics with complex solutions until Algebra 2.] (A) real roots (B) quadratic formula yields complex roots 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. I will solve quadratic equations by completing the square. I will solve quadratic equations by the quadratic formula. I will derive the quadratic formula. I will recognize the types of roots from quadratic equation including real and complex roots. Section 8.6-8.9 Defining Regions Using Inequalities Solving Linear Equations in Two Variables Sorting Equations and Identities Optimization Problems: Boomerangs Solving Quadratic Equations: Cutting Corners Complex roots Quadratic equations Quadratic formula Real roots Page 4 of 82
Quarter 3 Why structure expressions in different ways? Algebra- Seeing Structure in Expressions AI.A.SSE.3 * Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. [Include quadratic and exponential expressions] (A) quadratic expressions a*. Factor a quadratic expression to reveal the zeros of the function it defines. (A) factor a quadratic expression (B) reveal the zeros by factoring b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 1. Make sense of problems and persevere in solving them. Algebra I Supporting I will factor an expression and find the zeros of the function. Section 7.3 7.6 Section 7.4 Section 8.5 Lab Comparing Investments Manipulating Polynomials Sectors of Circles Forming Quadratics Modeling Conditional Probabilities 2 Sorting Equations and Identities Interpreting Algebraic Expressions Representing Polynomials Factor Zero Page 5 of 82
Quarter 3 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.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 exponential functions. [In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (C) quadratic equations (D) quadratic inequalities 5. Use appropriate tools strategically. I will create quadratic equations and inequalities to solve problems. Section 8.6-8.9 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Quadratic functions Quadratic inequalities Page 6 of 82
Quarter 3 How can algebra describe the relationship between sets of numbers? Algebra Creating Equations AI.A.CED.2 * Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Limit to linear, exponential equations, and quadratic equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.] (C) quadratic equations 5. Use appropriate tools strategically. I will represent relationships between quantities by creating equations in two or more variables. Section 8.6-8.9 Section 9.4 Equations of Circles 1 Inscribing and Circumscribing Right Triangles Solving Linear Equations in Two Variables Equations of Circles 2 Optimization Problems: Boomerangs A07 Functions E07 Skeleton Tower E14 Best Buy Tickets A12 Printing Tickets E08 Pythagorean Triples N04 Creating Equations E05 Fearless Frames E09 Triangular Frameworks Axis Quadratic equations Slope Coordinate plane Scale Slope intercept form Direct variation Page 7 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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 graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior. [Focus on linear, exponential, and quadratic functions.] (C) quadratic functions 5. Use appropriate tools strategically. 6. Attend to precision. I will match graphs to their verbal descriptions. I will recognize key features of a quadratic function. Section 8.2 8.3 Section 8.5 Section 8.10 Extension Forming Quadratics Functions and Everyday Situations Representing Polynomials Continuous graph Discrete graph Page 8 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.5 * Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. [Focus on linear, exponential, and quadratic functions.] (C) quadratic functions 6. Attend to precision. I will graph functions given a limited domain. I will graph functions given the domain of all real numbers. Section 8.4 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Domain Page 9 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.6 * Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Focus on linear, exponential, and quadratic functions] (C) quadratic functions 5. Use appropriate tools strategically. I will calculate and interpret average rate of change (slope) of a function. I will compare rates of change from a graph. Section 8.2 8.3 Section 9.4 Extension Section 9.5 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Exponential function Rate of change Run Linear function Rise Slope Quadratic function Page 10 of 82
Quarter 3 How can the properties of the real number system be useful when working with polynomials and rational expressions? Algebra - Arithmetic with Polynomials and Rational Expressions AI.A.APR.3* Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (A) quadratic polynomials 5. Use appropriate tools strategically. Algebra I Supporting I will identify zeros of polynomials by factoring. I will use the zeros to construct a rough graph of the function. Section 8.6 Interpreting Algebraic Expressions Manipulating Polynomials Representing Polynomials N03 Arithmetic with Polynomials and Rational Expressions Page 11 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.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. [Include linear, exponential, quadratic, absolute value, step, piece-wise defined functions.] a*. Graph linear and quadratic functions and show intercepts, maxima, and minima. (B) quadratic functions 5. Use appropriate tools strategically. 6. Attend to precision. Algebra I Supporting I will identify quadratic functions and determine whether they have minimums or maximums. I will graph functions and give the domain and range. Section 8.1 8.5 Section 8.1-8.3 Lab Section 8.10 Extension Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Minimum Maximum Parabola Quadratic function Page 12 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.8 * Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. 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. 7. Look for and make use of structure. Algebra I Supporting I will find the zeros of a quadratic function. I will find the axis of symmetry and vertex. Section 8.1-8.3 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Axis of symmetry Zeros of a function Page 13 of 82
Quarter 3 How can the relationship between quantities best be represented? Functions - Interpreting Functions AI.F.IF.9 * Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [Focus on linear, exponential, and quadratic functions] (C) quadratic functions 6. Attend to precision. 7. Look for and make use of structure. Algebra I Supporting I will compare functions in different representations. Section 8.2 8.3 Forming Quadratics Functions and Everyday Situations Representing Polynomials A16 Sorting Functions N06 Interpreting Functions Average rate of change Page 14 of 82