Curriculum Scaffolding for 9-12 Mathematics 9-12 Mathematics Reporting Standards Reporting Standard 1- Linear Function Algebraically solve, graph, interpret & create models of linear relations. Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities, functions & models Reporting Standard 6 - Geometric Structure: Apply attributes & relationships of geometric objects in diverse contexts Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements. Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions. Reporting Standards, Sub-Standards & Sample Problems by Course Reporting Standard 1: Algebraically solve, graph, interpret & create models of linear relations. Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities, functions & models Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements. Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions. 1. Sub-Standard: Applies the order of operations and properties of real numbers to solve multi-step problems. Describes multiple forms of applications of operations and properties of real numbers. Simplifies and evaluates problems that involve exponents. Simplifies and evaluates problems that involve distribution. Simplifies or evaluates problems that involve addition, subtraction, multiplication, and division. 33-5-22+22+33-32 (-3)2 + 4-2(4-9) 3 52 + 4-8
(13)-245(2-14)2+(1-32)-1 30-5 -6(4-9)-2 2(-5-59 - 9) 4-9 36-7 Computer Science Problems var=(math.pow((x/3),- 2)*(4/5))/(math.pow((2- (y/4),2)+math.pow(((x-(3/2)),-1); var=math.pow(3,0)-x*- 6*math.pow((4-9),-z); var=2*(-5-x)/(y- 8); var=x+6; Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical 2. Sub-Standard: Performs arithmetic operations with complex numbers. Justifies the number of complex solutions for any polynomial and solves for them. Solves and explains expressions with complex answers. Solves and rewrites expressions with complex numbers. Uses operations to simplify complex numbers. Determine the number of solutions, types of solutions, and possible turning points for the polynomial: 2x 2-4x + 7 Solve 2x3 + 4x2+ 8x = -16 Solve x 2 +4 = (3 + 2i)(5-4i) 0 = Pre-Calc Sample Problems Find all the zeros of the function. f(x)=2x6+7x5-4x4+91x3-330x2+220x-900 Find all zeros of the Find all zeros of the function function f(x) = x 3-4x 2 +9x-36 f(x) = x2-2x + 5 multiply 6-4i by its conjugate pair Reporting Standard 1: Algebraically solve, graph, interpret & create models of linear relations. Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical Reporting Standard 4 - Exponential and Logarithmic Functions: Analyze and apply exponential and logarithmic Reporting Standard 5 - Trigonometric Relationships: Apply the trig relations to solve & simplify identities, functions & models Reporting Standard 7 - Congruence: Use theorems to prove and apply congruence
Reporting Standard 8 - Similarity: Use theorems to prove and apply similarity Reporting Standard 9 - Measurements: Use geometric tools, theorems & algebra to find measurements. Reporting Standard 10 - Statistics and Probability: Analyze variability in data to make informed decisions. 3. Sub-Standard: Interprets and writes equations and expressions in equivalent forms to solve problems. Compares and contrasts equivalent forms of expressions or equations to interpret the values. Writes an expression or equation in multiple equivalent forms and interprets the resulting values in the expression. Writes an expression or equation in multiple equivalent forms. Writes an expression or equation in an equivalent form. Write the equations for the lines that pass through (½, 7) & (¾,9) and (-⅗,⅕) & ( -25,14). Describe their relationship. Write the equation for the line that passes through (1,3) and (-4,7) in three forms and graph the equation. Write the equation for the line that passes through (- 3, 4) and (5, 1) in slopeintercept form and pointslope form. Write 5x - 2y = 10 in slope intercept form. Prove lines a and b are parallel. Lines a and b are parallel. Solve for x and y. Write an equation and solve to find each missing angle measurement. Write an equation and solve to find each angle measurement. Given that the vertex of a parabola is (2, - 4) and passes through the origin write the equation for the quadratic. Write f(x) = x 2 + 5x + 7 in vertex form and use the equation to graph the parabola. 2 Write f(x) = x + Write the equation for the 5x + 7 in vertex line that passes through (-3, form. 4) and (5, 1) in slopeintercept form and pointslope form. Pre-Calc Sample Problems Advance d Proficien t Developing Beginning
Simplify the expression. Verify that the equation is an identity. Calc Sample Problems Evaluate the following integral 3x2exdx A water tank has the shape of an inverted circular cone with the base radius 3 m and height 4 m. If water is being pumped into the tank at a rate of 2 m3/min., find the rate at which the water level is rising when the water is 2 m deep. Find the volume of the solid that is created by revolving the graph y=3+6xabout the x- axis on the interval [0, 3]. Find the value of dydx. y=cos(3x4+12). 4. Sub-Standard: Performs multiple operations with polynomials and monomials. Reporting Standard 2 - Quadratic Functions: Graphs, solves, interprets & creates models of quadratic Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical Factors and simplifies polynomials and monomials in multiple forms and interprets the results. Factors and simplifies polynomials and monomials in multiple forms. Factors polynomials using two or three steps. Reproduces single step factors. Solve 2x 2 + 13x + 21 and explain what your answers mean. 2 2 Factor 2x - 10x Factor x + 5x + Factor x +12 6 5x 2 +
Solve 2x 3 + 6x 2-8x -24 and draw a sketch of your graph. 2 2 Solve 2x + 13x + 21 and explain Factor 2x - 10x Factor 2x what your answers mean. +12 +8x 2 Reporting Standard 3 - Advanced Functions: Analyze and apply polynomial, rational, and radical 5. Sub-Standard: Solves rational expressions using zeros and identities of polynomials. Distinguishes the most efficient method to solving zeros and explains the the meaning of the zeros in the context of the polynomial and deduces the type of polynomial using multiple identities. Explains the meaning of zeros in the context of the polynomials and determines the type of polynomial. Explains the meaning of zeros and classify the polynomial. Finds the zeros and identify the polynomial. Pre-Calc Sample Problems 6. Sub-Standard: Creates and solves equations, inequalities, and systems. Creates and successfully solves equations, inequalities, and systems from word problems and real world problems using multiple methods. Chooses and justifies the most efficient method to solve equations, inequalities, and systems. Explains the method used for successfully solving equations, inequalities, and systems Solves equations, inequalities, and systems using the prescribed method.
Pre-Calc Sample Problems Calculus Sample Problems 7. Sub-Standard: Constructs and compares linear and exponential Describes characteristics of linear and exponential Produces and contrasts linear and exponential Explains the properties of linear and exponential Identifies the properties of linear and exponential Pre-calc Problems 8. Sub-Standard: Applies the properties of trigonometric
Uses trigonometric properties to solve real world and word problems. Applies the properties of trigonometric functions to solve multiple Uses the sine, cosine, tangent and the inverse trigonometric functions to find missing values. Uses the sine, cosine, and tangent trigonometric functions to find missing values. Pre-calc Sample Problems 9. Sub-Standard: Proves congruence. Advanced Proficient Basic Minimal Proves and justifies congruence using the most efficient method. Proves and justifies congruence using any method. Proves congruence using any method. Proves congruence using the prescribed method. 10. Sub-Standard: Proves similarity. Advanced Proficient Basic Minimal Proves and justifies similarity using the most efficient method. Proves and justifies similarity using any method. Proves similarity using any method. Proves similarity using the prescribed method. 11. Sub-Standard: Applies the properties of two and three dimensional figures. Illustrates the properties of two and three dimensional figures Compares and contrasts the properties of two and three Interprets the properties of two and three dimensional Identifies the properties of two and three
in real world situations. dimensional figures. figures. dimensional figures. 12. Sub-Standard: Applies the theorems of circles to find lengths and areas. Illustrates multiple methods to solve for lengths and areas of circles in real world and word problems. Explains how to solve for lengths and areas of circles using any theorem. Solves lengths and areas of circles. Solves lengths and areas of circles using the prescribed method. 13. Sub-Standard: Summarizes and interprets data using multiple representations. Advanced Proficient Basic Minimal Creates multiple representations to summarize and interpret real world data in order to reach viable conclusions. Interprets and reaches a viable conclusion using multiple representations of the data. Interprets and reaches a conclusion using a representation of the data. Uses prescribed method to create a representation of data. Prob & Stats Sample Problems Algebra 2 Sample Problems
Pre-Calculus Sample Problems Calculus Sample Problems 14. Sub-Standard: Evaluates statistical experiments. Advanced Proficient Basic Minimal Assesses the validity of the conclusions developed through the analysis of statistical experiments. Predicts future values through the analysis of statistical experiments. Explains the meaning of numerical answers from statistical experiments. Finds numerical answers from statistical experiments. Prob & Stats Sample Problems Algebra 1 Sample Problems 15. Sub-Standard: Applies rules of probability to interpret data. Advanced Proficient Basic Minimal Assesses the validity of the conclusions developed through the analysis of the probability of data. Predicts future values through the analysis of the probability of data. Selects the appropriate rule of probability to interpret data. Uses the prescribed rule to interpret data. Probability and Statistics Sample Problems Algebra 1 Sample Problems