Chetek-Weyerhaeuser High School Advanced Math A Units and s Advanced Math A Unit 1 Functions and Math Models (7 days) 10% of grade s 1. I can make connections between the algebraic equation or description for a function, its name, and its graph. 2. I can recognize the shape of a function from its equation, dilate it, translate it, and graph its absolute value. 3. I can use composite functions to prove two functions are inverses. 4. I can create parametric graphs of functions and inverses of functions and use the graph to state the domain and range of an inverse. Unit 2 Trigonometric Functions (8 days) 20% of grade s 1. I can sketch any angle in degrees, minutes, and seconds from standard position, state its reference angle, and find two co-terminal angles for it. 2. I can find the values of the six trigonometric (trig) functions for any point or common angle on the unit circle and apply them to simplify expressions. 3. I can find any angle described by any of the trig functions and its quadrant by utilizing an inverse trig operation and the periodicity of trig functions. 4. I can draw a figure to represent a given problem and use the appropriate right triangle trig to solve for any required angle or side. Unit 3 Applications of Trigonometric and Circular Functions (14 days) 25% of grade s 1. I can write an equation to describe any periodic function using either radians or degrees and sketch any periodic function from an equation. 2. I can state the exact value of any of the six trig functions using degrees and radians for any positive or negative common angle. 3. I can evaluate trigonometric functions for both dependent and independent (x and y) variables using the principal value and knowledge of the periodicity of sine and cosine functions to find other values. 4. I can identify or measure the appropriate values and generate a mathematical model to represent periodic situations in a lab setting or in real-world written problems, and then analyze that function for specific x and y values to test its validity. Unit 4 Properties of the Trigonometric Functions (10 days) 15% of grade s 1. I can prove each of the Pythagorean Properties and solve each of them for a different function. Mrs. Weaver/Mr. Munch 11/28/2017 1
2. I can use reciprocal, quotient, and Pythagorean properties to produce simplified and transformed trig expressions. 3. I can write a general solution to a trig equation using arc notation. 4. I can solve expressions involving inverse functions of another trig function by creating and applying triangle in a coordinate system. Unit 5 Combinations of Trigonometric Functions and Angular Velocity (10 days) 15% of grade s 1. I can use the addition, subtraction, and product formulas to simplify and solve trigonometric equations. 2. I can write equations to describe graphs of the sum and product of trig functions. 3. I can find linear and angular velocities of rotating objects and connected rotating objects. 4. I can identify or measure the appropriate values to calculate the angular and linear velocities of rotating objects in a lab setting or in real-world written problems, and write sinusoidal equations to represent the motion. Unit 6 Triangles and Vectors (10 days) 15% of grade s 1. I can compute the side length or angle measure of a triangle using the law of sines where an angle and opposite side are known. 2. I can apply the law of cosines to solve a triangle given two sides and an included angle or all three sides of the triangle. 3. I can select the appropriate technique and calculate the other side and angle measures of any triangle when given SSS, SAS, ASA, AAS, or SSA, or a right triangle and find the area of the triangle or complex region by breaking it into triangles. 4. I can find the resultant of two vectors by creating a diagram, using triangle trigonometry, and by adding vector components. Unit 1 Identifying Functions Advanced Math B s 1. I can identify linear, quadratic, exponential, and power functions from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. I can identify linear, quadratic, exponential, and power functions from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. 4 Proficient I can identify linear, quadratic, exponential, and power functions from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. 3 Developing I can identify linear, quadratic, and exponential functions from ordered pairs, state the name of the pattern used to come up with the type of function (Add-Add, etc ), and calculate the equation. 2 Basic I can identify linear and quadratic functions from ordered pairs, state the name of the pattern used to come up with the type of function (Add-Add, etc ), and calculate the equation. 1 Minimal I can identify linear functions from ordered pairs, state the name of the pattern used to come up with the type of function (Add-Add, Mrs. Weaver/Mr. Munch 11/28/2017 2
etc ), and calculate the equation. 2. I can apply the logarithm properties to simplify logarithmic expressions and solve logarithmic equations with any base. I can apply the logarithm properties to simplify logarithmic expressions and solve logarithmic equations with any base. 4 Proficient I can apply the logarithm properties to simplify logarithmic expressions and solve logarithmic equations with any base. 3 Developing I can apply the logarithm properties to simplify logarithmic expressions and solve logarithmic equations with base 10. 2 Basic I can use a calculator to find the nth root of a number. 1 Minimal I can use a calculator to raise a number to a power. 3. I can solve equations with variable exponents. I can solve equations with variable exponents. 4 Proficient I can solve equations with variable exponents. 3 Developing I can solve equations with variable expressions as exponents when they appear on both sides of the equation and the bases match. 2 Basic I can solve equations with a single variable expression as an exponent when it appears on only one side of the equation. 1 Minimal I can solve equations with a single variable exponent when it appears on only one side of the equation. 4. I can identify a logarithmic function from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. I can identify a logarithmic function from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. 4 Proficient I can identify a logarithmic function from a table of ordered pairs, state the name of the pattern formed, and hand calculate an equation to fit the data. 3 Developing I can identify a logarithmic function from a Multiply-Add pattern in a data table and use two points to set up a natural logarithmic system of equations. 2 Basic I can correctly identify a Multiply Add pattern as being a logarithmic function. 1 Minimal I can identify the Multiply-Add pattern in a data table. Unit 2 Regression s 1. I can perform linear, exponential, and power regression on a graphing calculator, perform logarithmic regression by hand, use the correlation coefficient to determine which equation is the best fit to the data, and answer questions based on the equation. Mrs. Weaver/Mr. Munch 11/28/2017 3
I can perform linear, exponential, and power regression on a graphing calculator, perform logarithmic regression by hand, use the correlation coefficient to determine which equation is the best fit to the data, and answer questions based on the equation. 4 Proficient I can perform linear, exponential, and power regression on a graphing calculator, perform logarithmic regression by hand, use the correlation coefficient to determine which equation is the best fit data, and answer questions based on the equation. 3 Developing I can utilize the equation of best fit to make predictions for events not observed in the data table. 2 Basic I can choose the best fitting equation for a data set based on the correlation coefficient and explain why it is the best one. 1 Minimal I can utilize the functions on a graphing calculator to run linear, power, and exponential regression on a data table to find the equation of best fit, the correlation coefficient (r), and the coefficient of determination (r 2 ). 2. I can calculate the sum of the square residuals and correlation coefficient, by hand, for linear and logistic functions. I can calculate the sum of the square residuals and correlation coefficient, by hand, for linear and logistic functions. 4 Proficient I can calculate the sum of the square residuals and correlation coefficient, by hand, for linear and logistic functions. 3 Developing I can generate the SS res and SS dev of the points in a data table. 2 Basic I can use the functions of the graphing calculator to enter equations. 1 Minimal I can generate the average of the y values of a data table. 3. I can utilize semi-log and logarithmic graphs to linearize exponential and power function data and use the graph to identify function type. I can utilize semi-log and logarithmic graphs to linearize exponential and power function data and use the graph to identify function type. 4 Proficient I can utilize semi-log and logarithmic graphs to linearize exponential and power function data and use the graph to identify function type. 3 Developing I can utilize semi-log and logarithmic graphs to linearize exponential and power function data. 2 Basic I can draw the data points from a table onto semi-logarithmic or logarithmic graph paper. 1 Minimal I can label the axis on semi-logarithmic and logarithmic graph paper. 4. I can measure and gather data in experiments; then use appropriate techniques to determine the best equation of the data, and answer questions based on the equation I find. I can measure and gather data in experiments; then use appropriate techniques to determine the best equation of the data, and answer questions based on the equation I find. Mrs. Weaver/Mr. Munch 11/28/2017 4
4 Proficient I can measure and gather data in experiments, use appropriate techniques to determine the best equation of the data, and answer questions based on the equation I find. 3 Developing I can generate the possible equations which could fit my data and then use the correlation coefficient to select the equation of best fit. 2 Basic I can utilize the three types of graph paper to demonstrate the pattern formed by my data and use them to make a prediction regarding the type of function I may have discovered. 1 Minimal I can measure and gather data for an experiment. Unit 3 Polynomials and Rational Equations s 1. I can find zeros of a polynomial by factoring, completing the square, using the quadratic formula, and by using a graphing calculator and explain their relevance to the graph of the function. I can find zeros of a polynomial by factoring, completing the square, using the quadratic formula, and by using a graphing calculator and explain their relevance to the graph of the function. 4 Proficient I can find zeros of a polynomial by factoring, completing the square, using the quadratic formula, and by using a graphing calculator and explain their relevance to the graph of the function. 3 Developing I can compute the zeros of a polynomial by completing the square. 2 Basic I can compute the zeros of a polynomial by using a graphing calculator or by using factoring techniques. 1 Minimal I can compute the zeros of a quadratic equation using the quadratic formula. 2. I can relate the degree of a polynomial to the number of roots it will have and find all the real and complex roots of any polynomial. I can relate the degree of a polynomial to the number of roots it will have and find all the real and complex roots of any polynomial. 4 Proficient I can relate the degree of a polynomial to the number of roots it will have and find all the real and complex roots of any polynomial. 3 Developing I can utilize various methods to compute the real and complex roots of a quadratic equation 2 Basic I can recognize the difference between real and complex roots. 1 Minimal I can relate the degree of a polynomial to the number of roots it will have. 3. I can convert the equation of a parabola from standard to vertex form and vice a versa, draw a sketch of the parabola from the information provided by both forms, and label the important parts. I can convert the equation of a parabola from standard to vertex form and vice a versa, draw a sketch of the parabola from the information provided by both forms, and label the important parts. Mrs. Weaver/Mr. Munch 11/28/2017 5
4 Proficient I can convert the equation of a parabola from standard to vertex form and vice a versa, draw a sketch of the parabola from the information provided by both forms, and label the important parts. 3 Developing I can compute the important parts of the graph of a parabola given by the two versions of the equation. 2 Basic I can convert the equation of a parabola from standard form to vertex form. 1 Minimal I can convert the equation of a parabola from vertex form to standard form. 4. I can find removable and non-removable discontinuities of a function and use them to sketch a graph showing and labeling all asymptotes and/ or holes in the graph. I can find removable and non-removable discontinuities of a function and use them to sketch a graph showing and labeling all asymptotes and/ or holes in the graph. 4 Proficient I can find removable and non-removable discontinuities of a function and use them to sketch a graph showing and labeling all asymptotes and/ or holes in the graph. 3 Developing I can draw the sketch of a quadratic function and use the discontinuities to draw in the locations of the asymptotes of the graph. 2 Basic I can find removable and non-removable discontinuities of a function and label them by type. 1 Minimal I can break down a quadratic equation by factoring it into a product of two binomials. Unit 4 Conic Sections s 1. I can identify the equation of a circle given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. I can identify the equation of a circle given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 4 Proficient I can identify the equation of a circle given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 3 Developing I can identify the location of the center and the length of the radius of the circle from the standard form of the equation. 2 Basic I can convert a second-degree polynomial function, for a circle, into standard form. 1 Minimal I can identify the equation of a circle given a second degree polynomial function. 2. I can identify the equation of an ellipse given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. I can identify the equation of an ellipse given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. Mrs. Weaver/Mr. Munch 11/28/2017 6
4 Proficient I can identify the equation of an ellipse given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 3 Developing I can identify the location of the center and the length of the major and minor radii of the ellipse from the standard form of the equation. 2 Basic I can convert a second-degree polynomial function, for an ellipse, into standard form. 1 Minimal I can identify the equation of an ellipse given a second degree polynomial function. 3. I can identify the equation of a hyperbola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. I can identify the equation of a hyperbola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 4 Proficient I can identify the equation of a hyperbola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 3 Developing I can identify the location of the center, determine the direction it opens, and calculate the slopes of the asymptotes of the hyperbola from the standard form of the equation. 2 Basic I can convert a second-degree polynomial function, for a hyperbola, into standard form. 1 Minimal I can identify the equation of a hyperbola given a second degree polynomial function. 4. I can identify the equation of a parabola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. I can identify the equation of a parabola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 4 Proficient I can identify the equation of a parabola given a second-degree polynomial function, convert it to standard form, and construct a sketch of it labeling all critical points. 3 Developing I can identify the location of the vertex and the direction of the opening of the parabola from the standard form of the equation. 2 Basic I can convert a second-degree polynomial function, for a parabola, into standard form. 1 Minimal I can identify the equation of a parabola given a second degree polynomial function. 5. I can generate the equation of a parabola given the focus and directrix, and compute the location of the vertex. I can generate the equation of a parabola given the focus and directrix, and compute the location of the vertex. 4 Proficient I can generate the equation of a parabola given the focus and Mrs. Weaver/Mr. Munch 11/28/2017 7
directrix, and compute the location of the vertex. 3 Developing I can compute the value of a and write the equation of the parabola in proper form. 2 Basic I can utilize the formula for a parabola and fill it in correctly. 1 Minimal I can identify the parts b, c, and d from the given information. 6. I can generate the equation of an ellipse given lengths of axis and center and compute the location of the foci from the equation. I can generate the equation of an ellipse given lengths of axis and center and compute the location of the foci from the equation. 4 Proficient I can generate the equation of an ellipse given lengths of axis and center and compute the location of the foci from the equation. 3 Developing I can write the correct location of the center, in the equation of the ellipse. 2 Basic I can write the correct axis length under the correct variable of the equation given the direction of each axis. 1 Minimal I can calculate the measure of half the major and minor axis of the ellipse. 7. I can use parametric equations to sketch the graph of a conic section. I can use parametric equations to sketch the graph of a conic section. 4 Proficient I can use parametric equations to sketch the graph of a conic section. 3 Developing I can locate the center of a conic section given two parametric equations which will create the conic. 2 Basic I can illustrate a basic sine and cosine function graph in parametric mode. 1 Minimal I can convert my calculator to parametric mode. Unit 5 Matrices and Polar Graphs s 1. I can perform matrix operations of addition, subtraction, scalar multiplication, and multiplication of two matrices. I can perform matrix operations of addition, subtraction, scalar multiplication, and multiplication of two matrices. 4 Proficient I can perform matrix operations of addition, subtraction, scalar multiplication, and multiplication of two matrices. 3 Developing I can perform subtraction with two matrices. 2 Basic I can perform addition with two matrices. 1 Minimal I can perform scalar multiplication on a matrix. Mrs. Weaver/Mr. Munch 11/28/2017 8
2. I can find the inverse of a matrix, prove that two matrices are inverses, and solve a 3 x 3 or larger system by using an inverse matrix on a graphing calculator. I can find the inverse of a matrix, prove that two matrices are inverses, and solve a 3 x 3 or larger system by using an inverse matrix on a graphing calculator. 4 Proficient I can find the inverse of a matrix, prove that two matrices are inverses, and solve a 3 x 3 or larger system by using an inverse matrix on a graphing calculator. 3 Developing I can solve a 2 x 2 system by using an inverse matrix on a graphing calculator. 2 Basic I can prove that two matrices are inverses of each other. 1 Minimal I can use a calculator to find the inverse of a matrix. 3. I can write matrices to dilate, rotate, and iterate figures and use them to draw the resulting figure(s). I can write matrices to dilate, rotate, and iterate figures and use them to draw the resulting figure(s). 4 Proficient I can write matrices to dilate, rotate, and iterate figures and use them to draw the resulting figure(s). 3 Developing I can write a matrix which will rotate a figure. 2 Basic I can write a matrix which will dilate a figure. 1 Minimal I can implement matrices to dilate figures. 4. I can illustrate a polar graph from a table and find the true intersections of two polar equations, using a graphing calculator. I can illustrate a polar graph from a table and find the true intersections of two polar equations, using a graphing calculator. 4 Proficient I can illustrate a polar graph from a table and find the true intersections of two polar equations, using a graphing calculator. 3 Developing I can use my graphing calculator to illustrate all the potential intersection points of two polar equations. 2 Basic I can illustrate a polar graph of a table on special polar graphing paper. 1 Minimal I can convert my graphing calculator into polar mode. Mrs. Weaver/Mr. Munch 11/28/2017 9