MILLIS PUBLIC SCHOOLS Curriculum Guide High School Math The Millis Public Schools Curriculum Guide highlights the Power Standards for each grade level, Grade 9 through Grade 12 for the Math department. Power standards are a prioritized set of learning expectations that Millis has determined to be the most essential for students to learn. While other standards from the Massachusetts Curriculum Frameworks are taught, power standards are those that have endurance (knowledge and skills are relevant throughout a student's lifetime); leverage (knowledge and skills are used across multiple content areas) and essentiality (knowledge and skills are necessary for success in future courses or grade levels). The standards are from the most recent Massachusetts Curriculum Frameworks in the following areas: http://www.doe.mass.edu/frameworks/math/0311.pdf Joan Lynn Curriculum Director Millis Public Schools jlynn@millisps.org revised September 2015
MILLIS PUBLIC SCHOOLS Curriculum Guide High School Algebra I Demonstrate the ability to apply the order of operations to simplify expressions. Demonstrate the ability to use the distributive property and the ability to combine like terms to simplify expressions. Apply the properties of equality to solve linear equations. Apply the properties of inequalities to solve linear inequalities. Expand the use of solving linear equations and inequalities to real world problems by transforming problems into mathematical sentences. Identify a function if shown a graph or a table of values. Graph and label points in the coordinate plane. Graph linear equations using slope-intercept form or standard form. Find the slope of a line using a graph or given two points. Find the equation of a line using slope-intercept form. Develop the linear equation of a set of data using the line of best fit. Demonstrate the ability to solve compound inequalities as well as absolute value equations. Solve a linear system of equations using graphing, substitution or addition methods Identify a polynomial and to apply their understanding of like terms and the distributive properties to simplify polynomial expressions using addition, subtraction or multiplication. Distinguish the correct values needed to factor a simple quadratic expression. Identify a simple quadratic equation and solve by Algebra II Solve linear equations and inequalities including applications. Graph linear equations and inequalities. Solve systems of equations. Solve and graph absolute value equations and inequalities. Solve quadratic functions by factoring, quadratic formula, completing the square, and graph quadratic functions by various forms: vertex, standard and intercept. Perform the operations of complex numbers. Use properties of exponents. Evaluate, graph and apply properties for polynomial functions. Add, subtract, multiply and factor polynomials. Evaluate nth roots and apply properties of rational exponents. Inverse functions and radical equations. Perform Function Operations and Compositions Exponential functions (growth, decay and modeling). Simplify rational expressions and solve rational equations. Evaluate, graph, and apply properties for logarithmic functions.
Geometry Interpret and apply proper use of geometric terminology. Utilize inductive and deductive reasoning to compose a proof (two-column proof and coordinate proof). Identify appropriate properties of angles formed by intersecting lines. Recognize a variety of triangles, and to compute angle measures and side lengths (the Pythagorean Theorem). Prove triangles congruent using a variety of postulates and theorems (SSS, SAS, ASA, AAS and HL). Differentiate between special quadrilaterals, utilize properties and calculate angles. Identify similar polygons and use ratios and solve proportions. Calculate the circumference/perimeter and area of two-dimensional geometric figures. Calculate the surface area and volume of common solid figures. Find the trigonometric ratios of an acute angle of a right triangle. Interpret and reproduce a variety of transformations (reflections, rotations, dilations). Apply properties of circles to calculate: arcs, sectors, chords, tangents, and inscribed polygon dimensions. Compose geometric formulas together for complex 2D and 3D geometric figures. Write multi-variable equations requiring a system to solve, applied to geometric figures. Algebra and Trigonometry Solve linear equations using the fundamental operations of addition, subtraction, multiplication, and division. Understand concepts such as opposite, reciprocal, absolute value, exponents, inequalities, radicals, and logarithms. Solve linear, quadratic, exponential, and polynomial equations graphically and algebraically. Solve quadratic equations using various methods, such as completing the square, factoring, and the quadratic formula. Evaluate nth roots and rational exponents. Execute and explain the six trigonometric rations used to solve right triangle problems. Create and solve various problems involving right triangles using the six different trigonometric functions and the Pythagorean Theorem. Solve for unknown sides and angles in obtuse and acute triangles using the laws of sine and cosine. Examine different probability techniques, such as permutations and combinations.
Intro to Calculus and Statistics Use the methods of substitution, elimination, and graphing to solve systems of equations in equations in two and three variables; model and solve real-life problems. Calculate different matrix operations, including addition, subtraction, scalar multiplication, and multiplication. Use these skills to prove and solve for inverses. Evaluate summation notation and factorials. Recognize, write, and find the nth terms of arithmetic and geometric sequences. Find nth partial sums of arithmetic and geometric sequences. Use arithmetic and geometric sequences to model and solve real-life problems. Use the Binomial Theorem to calculate binomial coefficients and write binomial expansions. Apply the Fundamental Counting Principle, permutations, and combinations to solve more complicated counting problems. Find probabilities of events, mutually exclusive events, and independent events. Understand the limit concept and use the definition of a limit to estimate limits. Determine whether limits exist and then use the properties of limits to evaluate. Evaluate and calculate derivatives. Evaluate various measures of center and spread, such as, the five number summary, box and whisker plots, and outliers. Explore standard deviation and solve real world problems relating to it. Precalculus Student will: Demonstrate the understanding of the necessary mathematics to begin the study of Pre Calculus; a review of key Algebra II topics. Examine graphically the main characteristics of functions and apply these to the ten basic functions. Create functions using the composition of functions with application to real world problems. Evaluate functions to determine graphical translations and transformations. Apply the understanding of functions to model real world problems. Demonstrate an understanding of power functions by application to problems. Examine polynomial functions and find all the zeros of the polynomial equations (real and complex) using the fundamental theorem of algebra. Examine the graphs of rational functions and solve rational equations. Demonstrate an understanding of the exponential and logistic functions and apply the functions to real world problems. Examine the properties of logarithms and recognize their use in solving equations. Compare degrees to radians and how the trigonometric functions work as circular functions; evaluating all the special angles. *Examine a trigonometric equation in for its graphical characteristics and graph. Apply the basic trigonometric identities to simplifying and proving identities. Apply the law of sines, law of cosines, and area formulas to real world problems. *Examine the equations and graphs of the conic sections. *Vectors in two or three dimensions.
Calculus Interpret the connections between the four ways of representing a function (verbally, numerically, visually, algebraically). Calculate finite and infinite limits using algebra by manipulation and graphical examination. Recognize how limits arise by attempting to find the tangent to a curve or the velocity of an object. Explore the end behavior of functions and the concept of continuity. Demonstrate the concept of the derivative as a function of a tangent line. Evaluate and calculate derivatives of polynomial, rational, algebraic, exponential and logarithmic, trigonometric and inverse trigonometric functions, using various computation rules. Explore how to analyze the behavior of the families of functions, how to solve related rates problems, and how to find the maximum or minimum value of a quantity using derivatives. Connect the concepts between integral calculus and differential calculus, using the Fundamental Theorem of Calculus. Compare the exact area under the curve to approximation techniques using rectangles or trapezoidal methods. Explore applications of the definite integral by computing areas between curves, volumes of solids, and average value of functions. Explore differential equations in various situations, such as, exponential growth and decay, compound interest, and applications with slope fields. Use technology to graph various functions, find zeros to aid with solving equations numerically, calculate derivatives and integrals. Topics of Math in the Real World Apply basic mathematical principles and problem solving strategies to problem solving. Demonstrate and understanding of set notation and perform set operations that apply to solving real world problems. Demonstrate the use Venn diagrams with sets in real world applications. Represent logic statements symbolically using the appropriate connectives. Create truth tables and analyze the results to determine statements equivalency. Compute truth tables for conditionals and bi-conditionals using the different forms of conditionals. Recognize and write the forms of valid and invalid statements using symbols and Euler diagrams. Apply the use of graph theory to model relationships between objects in order to solve real world problems. Apply counting techniques and the fundamental counting principle to solve problems. Apply theory of permutations and combinations to real problems. Understand the relationship between probability and odds and apply the various probability techniques to solving problems. Use a variety of methods to represent data visually and apply measures of central tendency and dispersion to compare data. Apply the use of interest, annuities, loans, mortgages and evaluate how money and debt work within the every day world.