High School Math Curriculum Maps & Standards
Algebra I

1st Nine Weeks
Envision Algebra I
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 1: Solving Equations and Inequalities
(Skip Lesson 1 and Lesson 6)
Lesson 2:
 M.A1HS.5
 M.A1HS.9
 M.A1HS.10
Lesson 3:
 M.A1HS.2
 M.A1HS.5
 M.A1HS.9
 M.A1HS.10
Lesson 4:
 M.A1HS.1
 M.A1HS.5
 M.A1HS.8
Lesson 5:
 M.A1HS.5
 M.A1HS.7
 M.A1HS.9
 M.A1HS.10
Lesson 7:
 M.A1HS.5
M.A1HS.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
M.A1HS.2 Define appropriate quantities for the purpose of descriptive modeling. Instructional Note: Working with quantities and the relationships between them provides grounding for work with expressions, equations, and functions.
M.A1HS.5 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. Instructional Note: Limit to linear equations and inequalities.
M.A1HS.7 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: Limit to linear equations and inequalities.
M.A1HS.8 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.) Instructional Note: Limit to formulas with a linear focus.
M.A1HS.9 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. Instructional Note: Students should focus on and master linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Students will solve exponential equations with logarithms in Algebra II.
M.A1HS.10 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Instructional Note: Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solve for.

2nd Nine Weeks
Envision Algebra I
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 2: Linear Equations
(Skip Lesson 4)
Topic 2: Linear Equations
(cont’d)
(Skip Lesson 4)
Lesson 1:
 M.A1HS.6
 M.A1HS.38
Lesson 2:
 M.A1HS.6
 M.A1HS.30
 M.A1HS.38
Lesson 3:
 M.A1HS.6
 M.A1HS.7
 M.A1HS.38
The following standards should be addressed throughout Topic 2:
 M.A1HS.5
 M.A1HS.8
 M.A1HS.21
 M.A1HS.23
 M.A1HS.24
 M.A1HS.25
 M.A1HS.29
 M.A1HS.32
Lesson 1:
 M.A1HS.6
 M.A1HS.38
Lesson 2:
 M.A1HS.6
 M.A1HS.30
 M.A1HS.38
Lesson 3:
 M.A1HS.6
 M.A1HS.7
 M.A1HS.38
The following standards should be addressed throughout Topic 2:
 M.A1HS.5
 M.A1HS.8
 M.A1HS.21
 M.A1HS.23
 M.A1HS.24
 M.A1HS.25
 M.A1HS.29
 M.A1HS.32
M.A1HS.5 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. Instructional Note: Limit to linear equations and inequalities.
M. A1HS.6 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Limit to linear equations.
M.A1HS.7 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: Limit to linear equations and inequalities.
M.A1HS.8 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.) Instructional Note: Limit to formulas with a linear focus.
M.A1HS.21 For a function that models a relationship between two quantities, interpret key features of a 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; end behavior; and periodicity. Instructional Note: Focus on linear functions.
M.A1HS.23/53 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. Instructional Note: Focus on linear functions whose domain is a subset of the integers.
M.A1HS.24 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
 Graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude.
M.A1HS.25 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.) Instructional Note: Focus on linear functions. Include comparisons of two functions presented algebraically.
M.A1HS.29 Distinguish between situations that can be modeled with linear functions and with exponential functions.
 Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
 Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 Recognize situations in which a quantity grows or decays y a constant percent rate per unit interval relative to another.
M.A1HS.30 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two inputoutput pairs (include reading these from a table). Instructional note: In constructing linear functions, draw on and consolidate previous work in Grade 8 on finding equations for lines and linear functions.
M.A1HS.32 Interpret the parameters in a linear or exponential function in terms of a context.
M.A1HS.38 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Topic 3: Linear Functions
(Skip Lessons 3, 4, 5, and 6)
Lesson 1:
 M.A1HS.18
Lesson 2:
 M.A1HS.18
 M.A1HS.19
 M.A1HS.22
 M.A1HS.26
 M.A1HS.27
 M.A1HS.30
M.A1HS.18 Recognize that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples form linear functions having integral domains.
M.A1HS.19 Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. Instructional Note: Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of function at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear functions having integral domains.
M.A1HS.22 Relate the domain of a function to its graph and where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.) Instructional Note: Focus on linear functions.
M.A1HS.26 Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.)
Instructional Note: Limit to linear functions.
M.A1HS.27 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Instructional Note: Arithmetic sequences can be utilized when writing linear equations from a table of data points.
M.A1HS.30 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two inputoutput pairs (include reading these from a table). Instructional note: In constructing linear functions, draw on and consolidate previous work in Grade 8 on finding equations for lines and linear functions.

3rd Nine Weeks
Envision Algebra I
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 4: Systems of Linear Equations and Inequalities
Lesson 1:
 M.A1HS.14
Lesson 2:
 M.A1HS.7
 M.A1HS.10
 M.A1HS.14
Lesson 3:
 M.A1HS.7
 M.A1HS.13
Lesson 4:
 M.A1HS.6
 M.A1HS.7
 M.A1HS.17
Lesson 5:
 M.A1HS.7
 M.A1HS.17
M.A1HS.6 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Limit to linear equations.
M.A1HS.7 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: Limit to linear equations and inequalities.
M.A1HS.10 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Instructional Note: Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solve for.
M.A1HS.13 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.
M.A1HS.14 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Instructional Note: Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to standards in Geometry which require students to prove the slope criteria for parallel lines.
M.A1HS.17 Graph the solutions to a linear inequality in two variables as a halfplane (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 halfplanes.
Topic 5: Piecewise Functions
Instructional Note: Topic 5 is to be skipped.
Topic 6: Exponents and Exponential Functions
(Skip Lessons 2, 3, 4, and 5)
Lesson 1:
 M.A1HS.11
 M.A1HS.12
M.A1HS.11 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. (e.g., We define 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)3} to hold, so (5^{1/3})^{3} must equal 5.) Instructional Note: Address this standard before discussing exponential functions with continuous domains.
M.A1HS.12 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Instructional Note: Address this standard before discussing exponential functions with continuous domains.

4th Nine Weeks
Envision Algebra I
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 7:
Polynomials and Factoring
Lesson 1:
 M.A1HS.44
Lesson 2:
 M.A1HS.44
Lesson 3:
 M.A1HS.44
Lesson 4:
 M.A1HS.42
 M.A1HS.44
Lesson 5:
 M.A1HS.4
 M.A1HS.44
Lesson 6:
 M.A1HS.41
Lesson 7:
 M.A1HS.4
 M.A1HS.42
M.A1HS.4/41 Interpret expressions that represent a quantity in terms of its context.
 Interpret parts of an expression, such as terms, factors, and coefficients.
 Interpret complicated expressions by viewing one or more of their parts as a single entity. (e.g., Interpret P(1 + r)^{n} as the product of P and a factor not depending on P.
Instructional Note: Limit to linear expressions.
M.A1HS.42 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}). Instructional Note: Focus on teaching GCF and trinomials  factor by grouping, no special rules.
M.A1HS.44 Recognize 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. Instructional Note: Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x.
Envision Algebra 1
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 9: Solving Quadratic Equations
(Skip Lessons 3, 5, and 7)
Topic 9: Solving Quadratic Equations
(cont’d)
(Skip Lessons 3, 5, and 7)
Lesson 1:
 M.A1HS.16
 M.A1HS.45
 M.A1HS.46
 M.A1HS.48b
Lesson 2:
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Lesson 4:
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Lesson 6:
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 M.A1HS.48
Lesson 1:
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 M.A1HS.48b
Lesson 2:
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Lesson 4:
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 M.A1HS.48
Lesson 6:
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 M.A1HS.48
M.A1HS.16 Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential and logarithmic functions. Instructional Note: Focus on cases where f(x) and g(x) are linear or quadratic.
M.A1HS.42 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}). Instructional Note: Focus on quadratic expressions.
M.A1HS.43 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
 Factor a quadratic expression to reveal the zeros of the function it defines.
 Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 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%.
M.A1HS.45 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. Instructional Note: Extend work on linear equations in the relationships between quantities and reasoning with equations unit to quadratic equations.
M.A1HS.46 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: Extend work on linear and equations in the relationships between quantities and reasoning with equations unit to quadratic equations.
M.A1HS.47 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R). Instructional Note: Extend work on linear equations in the relationships between quantities and reasoning with equations unit to quadratic equations. Extend this standard to formulas involving squared variables.
M.A1HS.48 Solve quadratic equations in one variable.
 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.
 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.
Instructional Note: Students should learn of the existence of the complex number system, but will not solve quadratics with complex solutions until Algebra II.
M.A1HS.49 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x^{2} + y^{2} = 3. Instructional Note: Include systems consisting of one linear and one quadratic equation. Include systems that lead to work with fractions. For example, finding the intersections between x^{2} + y^{2} = 1 and y = (x + 1)/2 leads to the point (3/5 , 4/5) on the unit circle, corresponding to the Pythagorean triple 3^{2} + 4^{2} = 5^{2}.
M.A1HS.55 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
 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.
 Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)^{12t}, y = (1.2)^{t/10}, and classify them as representing exponential growth or decay.
Instructional Note: Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored.
Topic 11: Statistics
(Skip Lessons 3, 4, and 5)
Topic 11: Statistics
(Skip Lessons 3, 4, and 5)
Lesson 1:
 M.A1HS.33
 M.A1HS.34
Lesson 2:
 M.A1HS.33
 M.A1HS.34
 M.A1HS.35
Lesson 1:
 M.A1HS.33
 M.A1HS.34
Lesson 2:
 M.A1HS.33
 M.A1HS.34
 M.A1HS.35
M.A1HS.33 Represent data with plots on the real number line (dot plots, histograms, and box plots).
M.A1HS.34 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
M.A1HS.35 Interpret differences in shape, center, and spread in context of the data sets, accounting for possible effects of extreme data points (outliers). Instructional Note: In grades 68, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.
M.A1HS.36 Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Full Year Curriculum Map  PDF
Algebra II

1st Nine Weeks
Envision
Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 1
Linear Functions and Systems
Topic 1
Linear Functions and Systems
Note: For lesson 1.1 – 1.3, use only linear functions. Pearson uses quadratic functions  Use outside resources instead.
Lesson 1.1:
 M.A2HS.27
 M.A2HS.29
Lesson 1.2:
 M.A2HS.28
 M.A2HS.34
Lesson 1.3:
 M.A2HS.28
 M.A2HS.30a
Lesson 1.5:
 M.A2HS.23
 M.A2HS.17
Lesson 1.6:
 M.A2HS.24
 M.A2HS.25
M.A2HS.27 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; end behavior; and periodicity. Instructional Note: Emphasize the selection of a model function based on behavior of data and context.
M.A2HS.29 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. Note: Emphasize the selection of a model function based on behavior of data and context
M.A2HS.28 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.) Note: Emphasize the selection of a model function based on behavior of data and context
M.A2HS.34 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. Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Observe the effect of multiple transformations on a single graph and the common effect of each transformation across function types.
M.A2HS.30 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 square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. b. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Instructional Note: Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
M.A2HS.23 Create equations and inequalities in one variable and use them to solve problems. Instructional Note: Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
M.A2HS.17 Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Instructional Note: Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Instructional Note: Include combinations of linear, polynomial, rational, radical, absolute value, and exponential functions.
M.A2HS.24 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. (e.g., Finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line).
M. A2HS.25 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.) Instructional Note: While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. For example, finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line.
Topic 2
Quadratic Functions and Equations
Topic 2
Quadratic Functions and Equations
Lesson 2.1:
 M.A2HS.24
 M.A2HS.27
 M.A2HS.34
Lesson 2.2:
 M.A2HS.24
 M.A2HS.27
Factoring Polynomials (GCF, Difference of Two Squares & Trinomials. Cubes will be covered prior to 43)
Lesson 2.3:
 M.A2HS.7
 M.A2HS.11
Radicals (simplify, add, subtract multiply and divide)
Lesson 2.4:
 M.A2HS.1
 M.A2HS.2
 M.A2HS.4
Lesson 2.5 (honors only):
 M.A2HS.3
 M.A2HS.4
Lesson 2.6:
 M.A2HS.3
 M.A2HS.4
Lesson 2.7:
 M.A2HS.27
 Short, just with the calculator
M.A2HS.24 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Instructional Note: While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. (e.g., Finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line).
M.A2HS.27 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; end behavior; and periodicity. Instructional Note: Emphasize the selection of a model function based on behavior of data and context.
M.A2HS.34 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. Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Observe the effect of multiple transformations on a single graph and the common effect of each transformation across function types.
M.A2HS.7 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Instructional Note: Extend to polynomial and rational expressions.
M.A2HS.11 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.
M.A2HS.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.
M.A2HS.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
M.A2HS.3Solve quadratic equations with real coefficients that have complex solutions. Instructional Note: Limit to polynomials with real coefficients.
M.A2HS.4 Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). Instructional Note: Limit to polynomials with real coefficients.

2nd Nine Weeks
Envision Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 3
Polynomial Functions
Lesson 3.2:
 M.A2HS.9
 M.A2HS.32
 M.A2HS.33
Lesson 3.4:
 M.A2HS.7
 M.A2HS.10
 M.A2HS.14
Chapter 5
55
 M.A2HS.33
Lesson 3.5:
 M.A2HS.7
 M.A2HS.11
Lesson 3.1:
 M.A2HS.27
 M.A2HS.29
Lesson 3.7:
 M.A2HS.34
M.A2HS.9 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. Instructional Note: Extend beyond the quadratic polynomials found in Algebra I.
M.A2HS.32 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.) Instructional Note: Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
M.A2HS.33 Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.) Instructional Note: Develop models for more complex or sophisticated situations than in previous courses.
M.A2HS.7 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Instructional note: Extend to polynomial and rational expressions.
M.A2HS.10 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x) {Long division of polynomials should be included here.]
M.A2HS.14 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Instructional Note: The limitations on rational functions apply to the rational expressions.
M.A2HS.11 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.
M.A2HS.27 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; end behavior; and periodicity. Instructional Note: Emphasize the selection of a model function based on behavior of data and context.
M.2HS.29 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. Note: Emphasize the selection of a model function based on behavior of data and context.
M.A2HS.4 Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). Instructional Note: Limit to polynomials with real coefficients.
M.A2HS.5 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Instructional Note: Limit to polynomials with real coefficients.
M.A2HS.34 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. Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Observe the effect of multiple transformations on a single graph and the common effect of each transformation across function types.

3rd Nine Weeks
Envision
Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 4
Rational Functions
Lesson 4.2:
 M.A2HS.14
 M.A21HS.17
Review Factoring and include sum and difference of cubes.
Lesson 4.3:
 M.A2HS.7
 M.A2HS.14
 M.A2HS.15
Lesson 4.4:
 M.A2HS.7
 M.A2HS.15
Lesson 4.5:
 M.A2HS.23
 M.A2HS.16
M.A2HS.14 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer
M.A2HS.17 Explain why the xcoordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Instructional Note: Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Instructional Note: Include combinations of linear, polynomial, rational, radical, absolute value and exponential functions.
M.A2HS.7 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Instructional note: Extend to polynomial and rational expressions.
M. A2HS.15 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Instructional Note: This standard requires the general division algorithm for polynomials.
M.A2HS.23 Create equations and inequalities in one variable and use them to solve problems. Instructional Note: Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
M.A2HS.16 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations.
Envision
Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 5
Rational Exponents and Radical Functions
Lesson 5.1
 M.A1HS.11
 M.A1HS.12
Lesson 5.2
 M.A2HS.6
 M.A2HS.7
Lesson 5.3
 M.A2HS.27
 M.A2HS.30a
 M.A2HS.34
Lesson 5.4
 M.A2HS.26
 M.A2HS.16
M.A1HS.11 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. (e.g., We define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.) Instructional Note: Address this standard before discussing exponential functions with continuous domains.
M.A1HS.12 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Instructional Note: Address this standard before discussing exponential functions with continuous domains.
M.A2HS.6 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P. Instructional Note: Extend to polynomial and rational expressions.
M.A2HS.7 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Instructional note: Extend to polynomial and rational expressions.
M.A2HS.27 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; end behavior; and periodicity. Instructional Note: Emphasize the selection of a model function based on behavior of data and context
M.A2HS.30 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 square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. b. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Instructional Note: Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
M.A2HS.34 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. Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Observe the effect of multiple transformations on a single graph and the common effects of transformation across function types.
M.A2HS.26 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.) While functions will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. For example, finding the equation of a line through a given point perpendicular to another line allows one to find the distance from a point to a line. This example applies to earlier instances of this standard, not to the current course.
M.A2HS.16 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Instructional Note: Extend to simple rational and radical equations.

4th Nine Weeks
Envision
Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 7
Trigonometric Functions
Lesson 7.1
 M.A2HS.20
Lesson 7.2
 M.A2HS.19
 M.A2HS.20
M.A2HS.19 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
M.A2HS.20 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Topic 10 Matrices
Lesson 10.1
Lesson 10.2
Cover material to prepare for the SAT – not Algebra II standards
Topic 6
Exponential and Logarithmic Functions
Lesson 6.3
 M.A2HS.35
 M.A2HS.36
Lesson 6.5
 M.A2HS.7
 M.A2HS.36
Lesson 6.6
 M.A2HS.7
 M.A2HS.36
M.A2HS.35 Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. (e.g., f(x) = 2 x3 or f(x) = (x+1)/(x1) for x ≠ 1.) Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Extend this standard to simple rational, simple radical, and simple exponential functions; connect this standard to M.A2HS.34.
M.A2HS.36 For exponential models, express as a logarithm the solution to a bct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Instructional Note: Consider extending this unit to include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = log x +log y
M.A2HS.7 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Instructional note: Extend to polynomial and rational expressions.
Envision
Algebra II
Topic/Lesson
WV College and Career Readiness Standard(s)
Topic 7
Trigonometric Functions
If time allows
Lesson 7.4
 M.A2HS.29
 M.A2HS.32
 M.A2HS.34
M.A2HS.29 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. Note: Emphasize the selection of a model function based on behavior of data and context
M.A2HS.32 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.) Instructional Note: Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
M.A2HS.34 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. Instructional Note: Use transformations of functions to find models as students consider increasingly more complex situations. Observe the effect of multiple transformations on a single graph and the common effects of transformation across function types.

Full Year Curriculum Map  PDF
Geometry

1st Nine Weeks
Envision Geometry Topic/Lesson WV College & Career Readiness Standard(s) Topic 1
Foundations of Geometry
Lesson 11
 M.GHS.1
Lesson 13
 M.GHS.31
Lesson 14
 M.GHS.9
 M.GHS.10
 M.GHS.11
Lesson 15
 M.GHS.9
 M.GHS.10
 M.GHS.11
Lesson 16
 M.GHS.9
 M.GHS.10
 M.GHS.11
Lesson 17
 M.GHS.9
M.GHS.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
M.GHS.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.31 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Topic 2
Parallel and Perpendicular Lines
Lesson 21
 M.GHS.1
 M.GHS.9
Lesson 22
 M.GHS.9
 M.GHS.53
 M.GHS.55
Lesson 23
 M.GHS.10
Lesson 24
 M.GHS.30
M.GHS.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
M.GHS.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.30 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems. (e.g., Find the equation of a line parallel or perpendicular to a given line that passes through a given point.) Instructional Note: Relate work on parallel lines to work in High School Algebra I involving systems of equations having no solution or infinitely many solutions.
M.GHS.53 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
M.GHS.55 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

2nd Nine Weeks
Envision Geometry
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 3
Transformations
Lesson 31
 M.GHS.2
 M.GHS.4
 M.GHS.5
Lesson 32
 M.GHS.2
 M.GHS.4
 M.GHS.5
 M.GHS.6
Lesson 33
 M.GHS.2
 M.GHS.4
 M.GHS.5
 M.GHS.6
Lesson 35
 M.GHS.3
 M.GHS.5
 M.GHS.6
M.GHS.2 Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Instructional Note: Build on student experience with rigid motions from earlier grade.(reference translations and rotations)
M.GHS.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.(reference translations and rotations)
M.GHS.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
M.GHS.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
M.GHS.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Instructional Note: Rigid motions are at the foundation of the definition of congruence.
Topic 4
Triangle Congruence
Lesson 42
 M.GHS.10
 M.GHS.18
Lesson 43
 M.GHS.5
 M.GHS.6
 M.GHS.7
 M.GHS.8
 M.GHS.18
Lesson 44
 M.GHS.5
 M.GHS.6
 M.GHS.7
 M.GHS.8
 M.GHS.18
Lesson 45
 M.GHS.10
 M.GHS.18
Lesson 46
 M.GHS.18
M.GHS.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
M.GHS.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Instructional Note: Rigid motions are at the foundation of the definition of congruence.
M.GHS.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
M.GHS.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.18 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

3rd Nine Weeks
Envision Geometry
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 5
Relationships in Triangles
Lesson 51
 M.GHS.9
Lesson 52
 M.GHS.9
 M.GHS.10
 M.GHS.36
Lesson 53
 M.GHS.10
 M.GHS.18
Lesson 54
 M.GHS.10
M.GHS.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.18 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
M.GHS.36 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Topic 6
Quadrilaterals/Polygons
Lesson 61
 M.GHS.18
Lesson 62
 M.GHS.18
Lesson 63, 64, 65 & 66
 M.GHS.11
 M.GHS.18
M.GHS.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.18 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

4th Nine Weeks
Envision Geometry
Topic/Lesson
WV College & Career Readiness Standard(s)
Topic 7
Similarity
Lesson 71
 M.GHS.2
 M.GHS.5
 M.GHS.14
Lesson 72
 M.GHS.14
 M.GHS.15
 M.GHS.34
Lesson 73
 M.GHS.16
 M.GHS.18
Lesson 74
 M.GHS.17
 M.GHS.18
Lesson 75
 M.GHS.10
 M.GHS.17
M.GHS.2 Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Instructional Note: Build on student experience with rigid motions from earlier grade. (translations and rotations)
M.GHS.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.14 Verify experimentally the properties of dilations given by a center and a scale factor. a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
M.GHS.15 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
M.GHS.16 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
M.GHS.17 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
M.GHS.18 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
M.GHS.34 Prove that all circles are similar
Topic 8
Right Triangles and Trigonometry
Lesson 81
 M.GHS.17
 M.GHS.21
Lesson 82
 M.GHS.19
 M.GHS.20
 M.GHS.21
Lesson 85
 M.GHS.20
 M.GHS.21
 M.GHS.22
**Skip Lessons 83 and 84**
M.GHS.17 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
M.GHS.19 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
M.GHS.20 Explain and use the relationship between the sine and cosine of complementary angle.
M.GHS.21 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
M.GHS.22 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. **IF time permits, come back to this standard AFTER Circles.**
Topic 9
Coordinate Geometry
Topic 9
Coordinate Geometry
Lesson 93
 M.GHS.1
 M.GHS.39
 M.GHS.40
**Do 93 only**
Lesson 93
 M.GHS.1
 M.GHS.39
 M.GHS.40
**Do 93 only**
M.GHS.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
M.GHS.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Instructional Note: Encourage multiple ways of writing proofs.
M.GHS.17 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
M.GHS.20 Explain and use the relationship between the sine and cosine of complementary angle
M.GHS.39 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
M.GHS.40 Use coordinates to prove simple geometric theorems algebraically.

Full Year Curriculum Map  PDF
Trigonometry/PreCalculus

1st Nine Weeks
1st 9 Weeks
Chapter 4 – Trigonometric Functions
Standards
 4.1 – Angles and Radian Measure All (2 Days)
 4.2 – Trigonometric Functions – The Unit Circle All (3 Days)
 4.3 – Right Triangle Trigonometry All (3 Days)
 4.4 – Trigonometric Functions of Any Angle All (3 Days)
 4.5 – Graphs of Sine and Cosine Functions All (4 Days)
 4.6 – Graphs of Other Trigonometric Functions All (4 Days)
 4.7 – Inverse Trigonometric Functions All (1 Day  Practice Exercises 1  30 ONLY)
 4.8 – Applications of Trigonometric Functions All (3 Days  All except Harmonic Motion)
 M.4HSTP.23
 M.4HSTP.24
 M.4HSTP.25
 M.4HSTP.26
 M.4HSTP.29

2nd Nine Weeks
2nd 9 Weeks
Chapter 5 – Analytic Trigonometry
Standards
 5.1 – Verifying Trigonometric Identities All (5 Days Practice Exercises 1  60)
 5.2 – Sum and Difference Formulas All (3 Days  Practice Exercises 1  32 and 57  64 ONLY)
 5.3 – Double Angle, Power Reducing, and Half Angle Formulas All (3 Days  Practice Exercises 1  22 and 35  58 ONLY)
 5.4 – Product to Sum and Sum to Product Formulas All (2 Days  Practice Exercises 1  22 ONLY  Skip if time is an issue)
 5.5 – Trigonometric Equations All (5 Days  Practice Exercises 1  116)
 M.4HSTP.27
 M.4HSTP.28
2nd 9 Weeks
Chapter 6 – Additional Topics in Trigonometry
Standards
 6.1 – Law of Sines All (4 Days  Practice Exercises 1  60)
 6.2 – Law of Cosines All (2 Days  Practice Exercises 1  30 and 37  52)
 6.3 – Polar Coordinates (2 Days? Practice Exercises 1  20 and 33  48 ONLY)
 6.5 – Complex Numbers in Polar Form; DeMoivre’s Theorem (2 Days? Practice Exercises 1  36)
 6.6 – Vectors All (5 Days? Practice Exercises 1  52)
 6.7 – The Dot Product All (3 Days? Practice Exercises 1  38)
 6.4 – Graphs of Polar Equations (If time permits)
 M.4HSTP.2
 M.4HSTP.3
 M.4HSTP.4
 M.YHSTP.5
 M.4HSTP.6
 M.4HSTP.7
 M.4HSTP.8
 M.4HSTP.9

3rd Nine Weeks
Chapter 8 – Matrices and Determinants
Standards
This chapter is to be done throughout the 2nd semester via bell ringers or as additional topics as time permits.
 8.3 – Matrix Operations and Their Applications All (3 Days  Practice Exercises 1  44  Do BEFORE 8.1 and 8.2)*
 8.4 – Multiplicative Inverses of Matrices and Matrix Equations All (4 Days  Practice Exercises 1  42 Use Graphing Calculator for Larger Matrices  Do BEFORE 8.1 and 8.2)**
 8.5 – Determinant’s and Cramer’s Rule All (3 Days  Practice Exercises 1  28 by hand, 29  42 with Graphing Calculator  Do BEFORE 8.1 and 8.2)*
 8.1 – Matrix Solutions to Linear Systems All (3 Days  Practice Exercises 1  12 by hand, 21  38 with Graphing Calculator)**
 8.2 – Inconsistent and Dependent Systems and Their Applications All (3 Days  Practice Exercises 1  24 with Graphing Calculator)**
 M.4HSTP.10
 M.4HSTP.11
 M.4HSTP.12
 M.4HSTP.13
 M.4HSTP.14
 M.4HSTP.15
 M.4HSTP.16
 M.4HSTP.17
 M.4HSTP.18
Chapter 1 – Functions and Graphs
Standards
 – Graphs and Graphing Utilities – All (1 day – or just give assignment)
  Basics of Functions and Their Graphs – All (2 days)
 – More on Functions and Their Graphs – All (2 – 3 days)
 – Linear Functions and Slope – All (3 – 4 days)
  More on Slope – All (2 days)
  Transformations of Functions – All (2 days)
 – Combinations of Functions; Composite Functions All (3 days)
 – Inverse Functions – All (2 days)
  Move to Chapter 9
1.10 – Modeling With Functions – All (1 day) – IF TIME
 M.4HSTP.20
 M.4HSTP.21
Chapter 2 – Polynomial and Rational Functions
Standards
 2.1 – Complex Numbers All (2 Days)
 2.2 – Quadratic Functions All (2 Days) Move to Chapter 9
 2.3 – Polynomial Functions and Their Graphs All (3 Days)
 2.4 – Dividing Polynomials; Remainder and Factor Theorems All (2 Days)
 2.5 – Zeros of Polynomial Functions All (2 Days  Practice Exercises 1  24 ONLY)
 2.6 – Rational Functions and Their Graphs All (4 Days)
 2.7 – Polynomial and Rational Inequalities If time permits
 2.8  Modeling Using Variation  If time permits
 M.4HSTP.1
 M.4HSTP.3
 M.4HSTP.19

4th Nine Weeks
Chapter 3 – Exponential and Logarithmic Functions
Standards
 3.1 – Exponential Functions All (2 Days Do complicated problems with graphing calculator.)
 3.2 – Logarithmic Functions All (2 Days  Practice Exercises 1  42 and 81  100 ONLY)
 3.3 – Properties of Logarithms All (3 Days  Practice Exercises 1  78 ONLY)
 3.4 – Exponential and Logarithmic Equations All (3 Days  Practice Exercises 1 22 and 49  92 ONLY)
 3.5 – Exponential Growth and Decay: Modeling Data Skip
 M.4HSTP.22
Chapter 9 – Conic Sections and Analytic Geometry
Standards
 2.2 – Quadratic Functions – All (2 days)
 9.3 – The Parabola All (5 Days  Practice Exercises 1  56)
 1.9 – Distance and Midpoint Formulas; Circles All (5 Days  Practice Exercises 1  64)
 9.1 – The Ellipse All (5 days Practice Exercises 1 – 60)
 9.2 – The Hyperbola All (5 Days  Practice Exercises 1  50)
 9.4 – Rotation of Axes Skip
 9.5 – Parametric Equations Skip
 9.6 – Conic Sections in Polar Coordinates Skip
 Supplement – Cavalieri’s Principle for the formulas for the volume of a sphere and other solid figures.
 M.4HSTP.30
 M.4HSTP.31
Chapter 10 – Sequences, Induction, and Probability
Standards
 10.1 – Sequences and Summation Notation If time permits
 10.2 – Arithmetic Sequences If time permits
 10.3 – Geometric Sequences and Series If time permits
 10.4 – Mathematical Induction If time permits
 10.5 – The Binomial Theorem If time permits
 10.6 – Counting Principles, Permutations, and Combinations If time permits
 10.7 – Probability If time permits
 M.4HSTP.34
 M.4HSTP.35
 M.4HSTP.37
 M.4HSTP.38
 M.4HSTP.39
 M.4HSTP.40
Supplement For These Standards
Standards
 Graph probability distributions using the same graphical displays as for data distributions.
 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
 M.4HSTP.32
 M.4HSTP.33
 M.4HSTP.34
 M.4HSTP.35
 M.4HSTP.36

Full Year Curriculum Map  PDF