First Nine Weeks Sequence Standard Description Resources Assessment Week 1 - 2 (Q1) 8/24/15 - 9/2/15 Unit 1: Constructing Graphs and Multiple in the Real World 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. Define appropriate quantities for the purpose of descriptive modeling. Calculator: Neutral Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. Calculator: Neutral Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes Textbook: Sections 1-1, 1-2, 1-7, 1-8, 1-9, 4-2, 4-6, CPALMS Lessons: Key Vocabulary: Domain, Range, independent variable, dependent variable, discrete, continuous, scale, symbolic representation, numerical representation, concrete representation, verbal representation, graphical representation, equivalent representation, function Conceptual Knowledge: and Intervals of Graphs *Domain and Range *Independent and Dependent Variables *Discrete and Continuous Data *Multiple Representations *Distributive Property Skills: ~Using data to construct graphs with varying intervals and determine which is appropriate. ~Distinguish between independent and
Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. Standards of Mathematical Practices SMP 1 Make sense of problem and preserve in solving them SMP 4 Model with mathematics SMP 5 Use appropriate tools strategically SMP 6 Attend to precision SMP 8 Look for and express regularity in repeated reasoning. Week 2 - 4(Q1) 9/3/15 - 9/16/15 Unit 2: Functions Calculator: Neutral Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. Calculator: Neutral Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes Textbook: 4-1, 4-3, 4-4, 4-6, 4-7 CPALMS Lessons: 912.F-IF.1.1 - Key Vocabulary: Function, function notation, input, output, independent variable, dependent variable, recursive definition, sequence, term Conceptual Knowledge: *Functional Relationships
with labels and scales. Calculator: Neutral Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Calculator: Neutral 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 to the input x. The graph of f is the graph of the equation y=f(x). Calculator: Neutral Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Calculator: Neutral Recognize that sequences are functions, sometimes defined recursively, domain is a subset of the integers. *Function Notation *Independent Variables *Dependent Variables Skills: ~Evaluate functions using order of operations. ~Construct tables and graphs of linear functions ~Compare and contrast functional and nonfunctional relationships ~Distinguish between independent and dependent variables
engines in a factory, then the positive integers would be an appropriate domain for the function. Calculator: No Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables or by verbal descriptions). example, given a graph of one quadratic function and on algebraic expression for another, say which has the larger maximum. Standards of Mathematical Practices SMP 3 Construct viable arguments and critique the reasoning of others SMP 6 Attend to precision Week 4 - 5 (Q1) 9/17/15 - 9/24/15 Unit 3: Exploring Rate of Change in Motion Problems Use units as a way to and to guide the of Textbook: 5-1, CPALMS Lessons: Key Vocabulary: Rate of change, speed, steepness, horizontal, vertical Conceptual Knowledge: *Rate of change *Constant Rates *Motion Graphs Skills: under
Use units as a way to and to guide the of and units in and the scale and the origin in and data Calculator: No 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 of change, direct variation, constant of proportionality Conceptual Knowledge: *Rate of change *Direct Variation *Identify different of functions Skills: ~Calculate rates of change using first differences. ~Identify proportional relationships and key features of direct variation. ~Classify functions based on their rates of change. graph step
change of a function (presented symbolically or as a over a specified interval. Estimate the rate of change from a graph. Calculator: Neutral Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima. Calculator: Neutral Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Combine standard function types using arithmetic operations. Calculator: Neutral Identify the effect on the graph of replacing f(x) by standard form, point-slope form Conceptual Knowledge: *Slope *x and y intercepts *Slope intercept form *standard form *point slope form Skills: ~Calculate and interpret slope in a given situation ~Identify as parallel and perpendicular according to their slope. ~Identify and interpret x and y intercepts in a situation. ~Find and use the equations of lines in slope intercept form, standard form and point-slope form
End of First Nine Weeks Exam Professional Day Second Nine Weeks Sequence Standard Description Resources Assessment Week 1 - 2 (Q2) 10/26/15 - 11/5/15 Unit 6: Solving Linear Equations and Inequalities Calculator: Neutral Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. Calculator: Neutral Create equations in two or more variables to represent relationships between quantities; equations on coordinate axes with labels and scales. Calculator: Neutral 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. Calculator: Neutral Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Textbook: 2-2, 2-4, 2-5, 3-1, 3-2, 3-3, 3-4, CB 5-5, 6-5, CPALMS Lessons: Key Vocabulary: Linear inequality in one, Linear inequality in two, variables, equality, equations, inverse functions, inverse Conceptual Knowledge: *Solving linear equations and inequalities *Inverse functions
Week 2 - 3 (Q2) 11/6/15 - 11/13/15 Unit 7: Systems of Linear Equations and Inequalities Calculator: Neutral Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Calculator: Neutral Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Calculator: Neutral Graph the solutions to a linear inequality in two variables as a 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. Standards of Mathematical Practice: SMP 1 Make sense of problem and preserve in solving them. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. Textbook: 6-1, 6-6 CPALMS Lessons: Key Vocabulary: System of equations and inequalities, system of linear equations and inequalities in two variables, solution, satisy the equation and inequality, no solution Conceptual Knowledge: *Systems of Equation *Systems of Inequalities * Solution to Systems Skills: ~Write a system of equations and inequalities to model a situation a system of equations by a table or a graph ~Solve a system of inequality by graphing and finding the intersection ~Check and interpret solutions of systems MFAS:
Week 4 (Q2) 11/16/15 - 11/20/15 Unit 8: Other Methods for Solving Systems Calculator: Neutral Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or options in a modeling context. Calculator: Neutral 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. Calculator: Neutral Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Calculator: Neutral the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to system of linear inequalities in two variables as the intersection of the corresponding half-planes. Standards of Mathematical Practice: SMP 1 Make sense of problem and preserve in solving them. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. Textbook: 6-2, Key Vocabulary: System of equations in two variables, substitution, linear combination, dependent equations, independent equations, consistent equations, inconsistent equations Conceptual Knowledge: *Solving systems using substitution *Solving systems using linear combination method Skills: ~Solving systems of equations algebraically ~Checking and justifying solutions to systems of equations ~Identifying which method is most effective in a given situation
Week 5-7 (Q2) 11/23/15 - 12/7/15 Unit 9: Creating Linear models for Data 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. Define appropriate quantities for the purpose of descriptive modeling. Choose a of accuracy appropriate to limitations on measurement when reporting quantities. Calculator: Neutral Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including functions and absolute value functions. c. polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are Textbook: 5-7, Key Vocabulary: Positive correlation, negative correlation, tend line, parent function, transformation, line of best fit, regression, Conceptual Knowledge: *Write equations of a trend line from data *Assess whether data is approximately linear *Explain transformations from the parent function *Use technology to determine the line of best fit. Skills: ~Write equations of a trend line from data ~Assess whether data is approximately linear ~Explain transformations from the parent function ~Use technology to determine the line of best fit
Third Nine Weeks Sequence Standard Description Resources Assessment Week 1 - 3 (Q3) 1/5/16 - 1/22/15 Unit 11: Exponential Functions and Equations Calculator: No Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of 5 because we want = to hold, so must equal 5. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Calculator: Neutral Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic function and simple rational, absolute, and exponential functions. Calculator: Neutral Create equations in two or more variables to Textbook: 7-1, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8 CPALMS Lessons: Key Vocabulary: Linear function, exponential function, constant rate of change, rational exponent, exponents Conceptual Knowledge: *Exponential Functions *Exponential Growth *Exponential Decay *Rational Expressions *Exponents Skills: ~Recognize exponential patterns and represent them algebraically ~Represent and analyze situations involving exponential growth and decay. MFAS:
labels and scales. Calculator: Neutral Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. and and and *Quadratic parent function *Domain and Range of a quadratic function *y=ax2+c Skills: ~Identify and sketch the quadratic parent function ~Determine the domain and range that make sense in given situations ~Describe effects of changes of a & on a
Week 5 - 7(Q3) 2/3/16 - 2/19/16 Unit 13: Operations of Polynomials Calculator: Neutral Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an such as terms, factors, and b. by viewing one or more of their parts as a single entity. Neutral Use the structure of an to identify ways to rewrite it. Calculator: Neutral Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Textbook: 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8 CPALMS Lessons: Key Vocabulary: Polynomial, monomial, binomial, trinomial, coefficient, degree, distributive property, of squares Conceptual Knowledge: *Type and degree of polynomials. *Operations on polynomials. *Factoring *Simplify radical expressions Skills: ~Classify polynomials by type and degree ~Multiply monomials and binomials ~Using the undoing process to apply factoring ~Add, Subtract and multiply rational expressions MFAS:
SMP 4 Model with mathematics. SMP 7 Look for and make use of structure. Week 7 - 9 (Q3) 2/22/16 - 3/8/16 Unit 14: Modeling with Quadratic Functions Calculator: Neutral Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Calculator: Neutral Choose and produce an Textbook: 9-1, CPALMS Lessons: Key Vocabulary: Quadratic function, parabola, vertex, axis of symmetry Conceptual Knowledge: *Analyze graphs of quadratic functions *General form of quadratic functions *Convert a quadratic from general to vertex form MFAS:
equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. the square in a to reveal the or of the it c. Use the of to for Calculator: No 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. Skills: ~Explain how a, h, & k affect the shape of the parabola ~Describe shifts on a graph ~Identify the vertex using a table ~Completing the
Fourth Nine Weeks Sequence Standard Description Resources Assessment Week 1 - 3 (Q4) 3/21/16 - 4/1/16 Unit 15: Solving Quadratic Equations Calculator:Neutral Create equations and inequalities in one variable and use them to problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. Calculator: Neutral Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a Textbook: 9-3, 9-5, 9-6, CPALMS Lessons: Key Vocabulary: Roots, solutions, x-intercepts, zeros Conceptual Knowledge: *Quadratic functions *Solutions to quadratic functions Skills: ~Solve by graphing, factoring and completing the square ~Identify and make connections among factors, roots, zeros and x-intercepts as solutions to quadratic functions MFAS:
Week 3 - 4 (Q4) 4/6/16 - 4/12/16 Unit 16:The Quadratic Formula Calculator: No 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. Solve quadratic equations in variable. a. Use the method of the square to any equation in into an equation of the form (x – p)² = that has the same Derive the formula from this form. b.Solve by (e.g., for x² = 49), taking Textbook: CPALMS Lessons: Key Vocabulary: Whole number, integer, rational number, irrational number, complex number, real number, roots, solutions, zerod Conceptual Knowledge: *Quadratic functions *Solutions to quadratic functions *Real Numbers *Identify the components of the quadratic formula Skills: ~Solving the quadratic formula ~Identify and make connections among factors, roots, zeros, and x-intercepts as solutions to quadratic functions ~Classify numbers as natural, whole, integer, rational, and irrational ~Use discriminant to tell how many solutions MFAS: