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Common Core Content Integrated into All Units in All Courses KY Core Content MA-11-1.2.1 Supporting Students will estimate solutions to problems with real numbers (including very large and very small quantities) in both real world and mathematical situations, and use the estimations to check for reasonable computational results. MA-11-2.2.1 Supporting Students will continue to apply to both real world and mathematical situations U.S. customary and metric systems of measurement. Program of Studies MA-HS-NPO-U-1 Students will understand that numbers, ways of representing numbers, relationships among numbers and number systems are means of representing real-world quantities. MA-HS-NPO-U-2 Students will understand that meanings of and relationships among operations provide tools necessary to solve realistic problems encountered in everyday life and problems encountered in mathematical situations. MA-HS-NPO-U-3 Students will understand that computing fluently and accurately with real numbers and making reasonable estimates increases the ability to solve realistic problems encountered in everyday life. MA-HS-M-U-1 Students will understand that measurable attributes of objects and the units, systems and processes of measurement are powerful tools for making sense of the world around them. MA-HS-NPO-S-E8 Students will establish and apply benchmarks for real numbers in context. MA-HS-NPO-S-NO1 Students will add, subtract, multiply and divide real numbers. MA-HS-NPO-S-E6 Students will use calculators appropriately and regularly make estimations without a calculator to detect potential errors. MA-HS-NPO-S-NO9 Students will solve realistic problems to a specified degree of accuracy. MA-HS-NPO-S-NO12 Students will develop fluency in operations with real numbers and matrices, using mental computation or paper-and-pencil calculations for simple cases and calculators and/or computers for more complicated cases. MA-HS-NPO-S-NO13 Students will use concrete, pictorial and abstract models to develop and/or generalize a procedure. MA-HS-M-S-SM5 Students will compare and contrast the use of US Customary and metric systems of measurement. MA-HS-M-S-MPA1 Students will apply units of measurements of physical quantities correctly in expressions, equations and problem solutions that involve measurement. MA-HS-M-S-SM2 Students will apply to both real world and mathematical situations US Customary and metric systems of measurement. MA-HS-M-S-SM3 Students will make decisions about units and scales that are appropriate for problem solving situations involving measurement. MA-HS-AT-S-VEO4 Students will judge the meaning, utility and reasonableness of the results of symbol manipulations, including those carried out using technology. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. ALGEBRA I Statistics Big Idea: Data Analysis High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. Academic Expectations 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.13 Students understand and appropriately use statistics. POWER STANDARD MA-11-4.1.1 Assessed Students will analyze and make inferences from a set of data with no more than two variables, and will analyze situations for the use and misuse of data representations. (Linear ONLY) DOK – 3 SUPPORTING CORE CONTENT MA-11-4.1.2 Assessed Students will construct data displays for data with no more than two variables. DOK – 2 MA-11-4.2.1 Assessed Students will describe and compare data distributions and make inferences from the data based on the shapes of graphs, measures of center (mean, median, mode) and measures of spread (range). (focus on calculating mean, median, mode and range) DOK – 2 MA-11-4.3.1 Assessed Students will recognize inappropriate strategies for data gathering (e.g., non-random sampling, polling only a specific group of people, using limited or extremely small sample sizes, bias issues) and explain why these strategies can lead to inaccurate inferences. DOK – 2 MA-11-4.3.2 ADP Benchmark Students will design simple experiments or investigations to collect data to answer questions of interest. MA-11-4.3.3 ADP Benchmark Students will explain the differences between randomized experiments and observational studies. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 What mathematical methods provide the “fairest” MA-HS-DAP-S-DR1 Students will understand that quantitative literacy is a rankings? Students will be familiar with the definitions of measurement data necessary tool to be an intelligent consumer and and categorical data, univariate and bivariate data and the term What is average? citizen. variable. How can data lie or mislead? Do people use MA-HS-DAP-U-2 numbers or graphs to mislead others? Should MA-HS-DAP-S-CDS1 Students will understand that data analysis requires they? Students will understand the distinction between a statistic and a developing a plan for collecting, organizing and parameter. analyzing data in order to make decisions. How does what we measure influence how we measure and what we conclude from the results of MA-HS-DAP-S-ES6 our measurements? MA-HS-DAP-U-3 Students will design and conduct simple experiments or Students will understand that graphical and numerical When should we sample? When shouldn’t we? investigations to collect data to answer student-generated questions. techniques can be used to study patterns and analyze How much or many (of a sample) is enough? data. MA-HS-DAP-S-DR3 Students will display the distribution, analyze patterns and describe MA-HS-DAP-U-4 relationships in paired data for univariate measurement data. Students will understand that the choice of data display can affect the visual message communicated. MA-HS-DAP-S-DR5 Students will display and discuss bivariate data where at least one MA-HS-DAP-U-5 variable is categorical. Students will understand that inferences and predictions from data are used to make critical and MA-HS-DAP-S-DR6 informed decisions. Students will organize and display data using appropriate methods (e.g., spreadsheets and graphing calculators) to detect patterns and Students will understand that: departures from patterns. Biases can affect the data and the results. MA-HS-DAP-S-CDS2 An outlier can raise or lower the mean, without Students will describe the shape and select and calculate summary greatly affecting the median. statistics for univariate measurement data, using technological tools A poor choice of graph, scale, or type of statistic can as necessary. be used to mislead people. There are different types of averages (average doesn’t imply mean!) Critical Vocabulary statistical data, mean, median, mode, range, population, histogram, stem-and-leaf plot, bar graph, frequency chart, box-and-whisker plot, scatter plot, dot plot, distribution, quartile Major Topics Collecting and Organizing Data; Bar Graphs and Dot Plots; Graph Misrepresentation; Mean, Median, Mode; Box-and-Whisker Plots; Five Number Summary; Stem-and-Leaf Plots; Frequency Charts and Histograms; Choosing an Appropriate Data Display Equations and Inequalities Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. This becomes the foundation for algebra and working with algebraic symbols. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Algebraic Thinking High school students use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.3.1 Assessed Students will model or solve first degree, single variable equations and inequalities, including absolute value, in real-world situations, and will graph the solutions on a number line. DOK – 2 SUPPORTING CORE CONTENT MA-11-5.3.2 Supporting Students will solve for a specified variable in a multivariable equation. MA-11-1.3.1 Assessed Students will solve real-world problems and mathematical problems to specified accuracy levels by simplifying real number expressions involving addition, subtraction, multiplication, division, and absolute value. DOK – 2 MA-11-1.4.1 Assessed Students will apply ratios, percents, and proportional reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) DOK – 2 MA-11-5.2.1 Assessed Students will apply order of operations, real number properties (identity, inverse, commutative, associative, distributive, closure), and rules of exponents (integer) to simplify algebraic expressions. DOK – 1 MA-11-1.5.1 Supporting Students will identify real number properties (e.g., commutative, associative, distributive, identity and inverse) when used to justify a given step in simplifying an expression or solving an equation. MA-11-1.1.1 Supporting Students will compare real numbers using order relations (less than, greater than, equal to) and represent problems using real numbers. MA-11-1.1.2 Supporting Students will demonstrate the relationships between different subsets of the real number system. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 How are equations (including proportions) MA-HS-NPO-S-PNO1 Students will understand that numbers, ways of and inequalities used to make real-life Students will identify and apply real number properties. representing numbers, relationships among decisions? numbers and number systems are means of MA-HS-NPO-S-PNO4 How can equations help us use patterns? representing real-world quantities. Students will justify the solution steps in simplifying expressions or solving an What is the relationship between expressions, equation. MA-HS-NPO-U-2 equations, and inequalities? How do you Students will understand that meanings of and know? MA-HS-NPO-S-NO4 relationships among operations provide tools Students will apply absolute value, integer exponents, roots and factorials to necessary to solve realistic problems When is the “correct” mathematical answer solve problems not the best solution? encountered in everyday life and problems encountered in mathematical situations. MA-HS-NPO-S-NO13 Students will use concrete, pictorial and abstract models to develop and/or MA-HS-NPO-U-3 generalize a procedure. Students will understand that computing fluently and accurately with real numbers and MA-HS-NPO-S-NS1 making reasonable estimates increases the Students will compare real numbers using order relations. ability to solve realistic problems encountered in everyday life. MA-HS-NPO-S-NS2 Students will locate the position of a real number on the number line, find its MA-HS-NPO-U-4 distance from the origin (absolute value/magnitude) and find the distance Students will understand that problem solving between two numbers on the number line (the absolute value of their difference). and connections with other content areas require a strong sense of number, including MA-HS-NPO-S-NS3 applications of absolute value (magnitude) and Students will determine the relative position on the number line of real numbers, the ordering of numbers. including very large and very small numbers, and the relative magnitude of numbers expressed in fractional form, in decimal form, as roots or in scientific MA-HS-NPO-U-5 notation Students will understand that proportional reasoning is a tool for modeling and solving MA-HS-NPO-S-RP1 problems encountered in everyday situations Students will calculate and apply ratios, proportions, rates and percentages to solve problems. MA-HS-AT-U-3 Students will understand that algebra MA-HS-NPO-S-RP2 represents mathematical situations and Students will translate real-world proportional relationships into mathematical structures for analysis and problem solving. expressions and vice versa. Students will understand that MA-HS-M-S-SM4 real-world situations can be represented using Students will use unit analysis to check measurement computations. mathematical models to analyze quantitative relationships. MA-HS-AT-S-VEO1 Students will write expressions, equations, inequalities and relations in equivalent forms. MA-HS-AT-S-VEO2 Misunderstandings to be clarified: Students will use symbolic algebra to represent and explain mathematical relationships. expressions can be simplified, but not solved. Cross-multiplying is not the same as cross- MA-HS-AT-S-VEO3 canceling Students will use symbolic expressions, including iterative and recursive forms, to represent relationships among various contexts. MA-HS-AT-S-EI1 Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI3 Students will solve one-variable equations and inequalities using manipulatives, symbols, procedures and graphing, including graphing the solution set on a number line. Critical vocabulary rational numbers, irrational numbers, reciprocals, inverse, identity, commutative, associative, distribute, closure, real numbers, matrices, expression, equation, inequality, number line, ratio, proportion, absolute value, percent increase and decrease, order of operations Major Topics Comparing and Ordering Numbers, The Real Number Line, Operations with Integers and Fractions, Matrices, Distributive Property, Number Properties, Variables and Expressions, Order of Operations, Combining Like Terms, Modeling with Expressions, Solving One-step through Multi-step Equations, Equations with no or many solutions, Writing Equations, Ratio and Proportion, Percents, Percent Increase and Decrease, Solving and Graphing inequalities, Solving Absolute Value Equations and Inequalities, Inequality Applications Functions Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear, quadratic, absolute value and exponential functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-1.3.2 Assessed Students will: describe and extend arithmetic and geometric sequences; determine a specific term of a sequence given an explicit formula; determine an explicit rule for the nth term of an arithmetic sequence apply sequences to solve real-world problems. DOK - 3 SUPPORTING CORE CONTENT MA-11-1.3.3 Supporting Students will write an explicit rule for the nth term of a geometric sequence. MA-11-5.1.1 Assessed Students will identify and apply multiple representations (tables, graphs, equations) of functions (linear) to solve real-world or mathematical problems. DOK - 1 MA-11-5.1.3 Supporting Students will demonstrate how equations and graphs are models of the relationship between two real world quantities (e.g., the relationship between degrees Celsius and degrees Fahrenheit) MA-11-5.1.5 Assessed Students will: determine if a relation is a function; determine the domain and range of a function (linear); determine the slope and intercepts of a linear function; evaluate a function written in function notation for a specified rational number. DOK - 2 MA-11-5.3.2 Assessed Students will model or solve first degree, two-variable equations and inequalities in real-world problems, and will graph the solutions on a coordinate plane. DOK - 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 What is the pattern (if one exists)? How do you MA-HS-NPO-S-NO5 Students will understand that numbers, know and how could an equation help us use the Students will determine a specific term of a sequence given an explicit formula. ways of representing numbers, pattern? relationships among numbers and MA-HS-NPO-S-NO6 How do functions represent real-life number systems are means of relationships? How do you know? Students will describe and extend arithmetic and geometric sequences. representing real-world quantities. How can functions be represented and what is the MA-HS-NPO-S-NO7 relationship between the various representations? MA-HS-AT-U-1 Students will determine an explicit rule for the nth term of an arithmetic sequence. How do you know? Why do we need different Students will understand that patterns, representations? relations and functions are tools that MA-HS-G-S-CG6 help explain or predict real-world Students will use Cartesian coordinates and other coordinate systems (e.g., phenomena. navigational, polar, spherical systems) to analyze geometric situations. MA-HS-AT-U-2 MA-HS-G-S-CG7 Students will understand that there are Students will investigate conjectures and solve problems involving two-dimensional relationships between and among figures and three-dimensional objects represented graphically. patterns and functions, their representations and their properties. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures MA-HS-AT-U-3 about slope, midpoints and other geometric ideas that can be expressed using the Students will understand that algebra Cartesian plane represents mathematical situations and structures for analysis and problem MA-HS-AT-S-PRF1 solving. Students will use explicitly defined or recursively defined functions to generalize patterns. MA-HS-AT-U-4 Students will understand that real- MA-HS-AT-S-PRF2 world situations can be represented Students will understand relations and functions and use various representations for using mathematical models to analyze them. quantitative relationships. MA-HS-AT-S-PRF6 MA-HS-AT-U-5 Students will interpret representations of functions of two variables. Students will understand that functions are used to analyze change in various MA-HS-AT-S-PRF9 contexts and model real-world Students will determine whether a relationship given in symbolic or graphical form phenomena. is a function. Students will understand that: MA-HS-AT-S-PRF11 Independent variables relate to domain Students will understand functional notation and evaluate a function at a specified and dependent variables relate to range. point in its domain. Linear functions increase at a constant MA-HS-AT-S-PRF12 rate and exponential functions multiply Students will combine functions by addition, subtraction, multiplication and by a constant factor compositions. Arithmetic sequences are linear and geometric sequences are exponential MA-HS-AT-S-PRF13 Students will graph linear, absolute value, quadratic and exponential functions and identify their key characteristics. MA-HS-AT-S-PRF16 Students will see the patterns in arithmetic and geometric sequences using recursion. MA-HS-AT-S-PRF17 Students will see patterns in other sequences (e.g., quadratic, cubic). MA-HS-AT-S-PRF18 Students will relate the patterns in arithmetic sequences to linear functions. MA-HS-AT-S-PRF19 Students will relate the patterns in geometric sequences to exponential functions. MA-HS-AT-S-EI1 Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI5 Students will solve an equation involving several variables for one variable in terms of the others. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-EI10 Students will graph a linear equation and demonstrate that it has a constant rate of change. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. Critical Vocabulary quadrant, coordinate plane, x- and y-axis, function, relation, domain, range, inverse relation, graphs, equations, tables, coordinate pairs, mapping, formulas, arithmetic sequences, geometric sequences, constant of variation, vertical line test, exponential function, absolute value function, independent and dependent variables, x-intercept, y-intercept, maximum, minimum, function notation Major Topics Coordinate Plane, Scatter Plots, Relations and Inverses, Domain and Range, Functions and Vertical Line Test, Evaluating Formulas, Patterns and Sequences, Arithmetic Sequences, Graphing with a t-chart, solving for y, Geometric Sequences, Exponential Growth and Decay, Graphing Quadratic and Absolute Value Functions with a t-chart Linear Equations Big Idea: Data Analysis High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear and quadratic. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics POWER STANDARD MA-11-4.2.2 Assessed Students will: determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. (linear) DOK – 3 SUPPORTING CORE CONTENT MA-11-1.4.1 Assessed Students will apply and will explain how slope determines a rate of change in linear functions representing real-world problems. DOK – 2 MA-11-5.3.3 Assessed Students will model, solve, and graph first degree, two-variable equations and inequalities in real-world and mathematical problems.. DOK – 2 MA-11-5.3.4 Assessed Students will model and graph systems of linear equations (two equations in two variables) and apply the system to solve and interpret real-world problems. (Introduce algebraic methods, but assess only on graphing method) DOK – 3 MA-11-5.3.5 Supporting Students will write, graph, and solve systems of linear inequalities (two inequalities in two variables) based on real world or mathematical situations and interpret the solution. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How can linear equations help us use MA-HS-NPO-S-RP1 Students will understand that quantitative patterns? Students will calculate and apply ratios, proportions, rates and percentages to literacy is a necessary tool to be an intelligent solve problems. How are linear equations used to make real- consumer and citizen. life decisions? MA-HS-NPO-S-RP2 Students will translate real-world proportional relationships into mathematical MA-HS-AT-U-2 How can linear functions be represented expressions and vice versa. Students will understand that there are and what is the relationship between the relationships between and among patterns and various representations? How do you MA-HS-NPO-S-RP3 functions, their representations and their know? Why do we need different Students will represent slope graphically, numerically and symbolically and properties. representations? relate it to a graph of an equation based on a realistic situation. What types of situations are better suited MA-HS-M-S-MPA8 MA-HS-AT-U-3 for linear inequalities rather than linear Students will explore periodic real-world phenomena, using technology (e.g., Students will understand that algebra represents equations? graphing calculator) as appropriate. mathematical situations and structures for analysis and problem solving. MA-HS-G-S-CG1 Students will express the intuitive concept of the “slant” of a line as slope, use MA-HS-AT-U-4 the coordinates of two points on a line to determine its slope and use slope to Students will understand that real-world express the parallelism and perpendicularity of lines. situations can be represented using mathematical models to analyze quantitative MA-HS-G-S-CG2 relationships. Students will describe a line by a linear equation. MA-HS-G-S-CG6 MA-HS-AT-U-5 Students will use Cartesian coordinates and other coordinate systems (e.g., Students will understand that functions are used navigational, polar, spherical systems) to analyze geometric situations. to analyze change in various contexts and model real-world phenomena. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two- MA-HS-AT-U-6 dimensional figures and three-dimensional objects represented graphically. Students will understand that functions can be MA-HS-G-S-CG8 written in words, in a symbolic sentence or in a Students will use a variety of technological tools to explore and test conjectures table or graph. about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane Students will understand that: MA-HS-AT-S-EI1 Correlation does not mean causation. Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper Slope is a rate of change. and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI5 Students will solve an equation involving several variables for one variable in terms of the others. MA-HS-AT-S-EI6 Students will solve systems of two linear equations in two variables. MA-HS-AT-S-EI9 Students will approximate and interpret rates of change from graphical and numerical data. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-EI10 Students will graph a linear equation and demonstrate that it has a constant rate of change. MA-HS-AT-S-EI11 Students will relate the coefficients of a linear equation and the slope and x- and y-intercepts of its graph. MA-HS-AT-S-EI12 Students will relate a solution of a system of two linear equations in two variables and the graphs of the corresponding lines. MA-HS-AT-S-EI13 Students will graph the solution set of a linear inequality and identify whether the solution set is an open or closed half-plane. MA-HS-AT-S-EI14 Students will graph the solution set of a system of two or three linear inequalities. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. Critical Vocabulary linear equation, linear inequality, coordinate plane, x-intercept, y-intercept, slope, slope-intercept form, point-slope form, standard form, scatterplot, line of best fit, rate of change, system of linear equations and inequalities, parallel, and perpendicular, opposite reciprocal, constant rate, independent and dependent variables Major Topics Graphing Change, Finding Slope, Graphing Equations using slope and y-intercept, Solving for y, Graphing using intercepts, solving systems by graphing, relationships between parallel and perpendicular lines, Solving systems by substitution and elimination (introduction only), Graphing Linear Inequalities, Graphing Systems of Linear Inequalities, Writing Equations given a slope and a point, Writing Equations given two points, Point-Slope and Standard Form (Introduction Only), Line of Best Fit, Predicting using Linear Equations Probability Big Idea: Probability High school students distinguish between combinations and permutations and compare and contrast theoretical and experimental probability. Academic Expectations 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.13 Students understand and appropriately use probability. POWER STANDARD MA-11-4.4.1 Assessed Students will: determine theoretical and experimental (from given data) probabilities; make predictions and draw inferences from probabilities; compare theoretical and experimental probabilities; and determine probabilities involving replacement and non-replacement. DOK - 3 SUPPORTING CORE CONTENT MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube), and factorials. DOK – 2 MA-11-4.4.2 Supporting Students will recognize or identify the differences between combinations and permutations and use them to count discrete quantities. MA-11-4.4.3 Supporting Students will represent probabilities in multiple ways, such as fractions, decimals, percentages, and geometric area models. MA-11-4.4.4 ADP Benchmark Students will explain how the law of large numbers can be applied in simple examples. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-3 How do you determine the best choice in a MA-HS-NPO-S-NO4 Students will understand that computing situation that involves probability? Students will apply absolute value, integer exponents, roots and factorials to fluently and accurately with real numbers solve problems Do people use probability and odds to mislead and making reasonable estimates increases others? Should they? the ability to solve realistic problems MA-HS-DAP-S-P1 encountered in everyday life. Is doing a simulation of an experiment better Students will design and conduct probability simulations and interpret the than doing an actual experiment? When would results. MA-HS-DAP-U-6 you want to actually conduct an experiment Students will understand that probability can and when would you want to simulate an MA-HS-DAP-S-P2 be used to make decisions or predictions or experiment? Students will apply the concepts of sample space and probability distribution to to draw conclusions. construct sample spaces and distributions in simple cases. What are examples of situations when order matters and when it doesn’t? Misunderstandings to be clarified: MA-HS-DAP-S-P3 What are examples of situations when you Students will design simulations to construct empirical probability distributions Theoretical probability differs from would want to use replacement? non- and report/interpret the results. experimental probability. replacement? An experiment can be simulated. MA-HS-DAP-S-P4 Students will compute and interpret the expected value of random variables in Order matters in some situations and not in simple cases. others. Non-replacement changes the outcome of an MA-HS-DAP-S-P5 event. Students will apply the concepts of conditional probability and independent events and be able to compute those probabilities. The probability of two or more independent events occurring simultaneously can not be MA-HS-DAP-S-P6 calculated using simple probability. Students will compute the probability of a compound event. Probability is different from odds. MA-HS-DAP-S-P7 Students will explain how probability quantifies the likelihood that an event occurs in terms of numbers. MA-HS-DAP-S-P8 Students will explain how the relative frequency of a specified outcome of an event can be used to estimate the probability of the outcome. MA-HS-DAP-S-P9 Students will explain how the law of large numbers can be applied in simple examples. MA-HS-DAP-S-P10 Students will determine and compare theoretical and experimental probabilities. MA-HS-DAP-S-P11 Students will determine the probability of an event and the probability of its complement. MA-HS-DAP-S-P12 Students will make predictions and draw inferences from probabilities, and apply probability concepts to practical situations to make informed decisions. MA-HS-DAP-S-P13 Students will determine probabilities involving replacement and non- replacement. MA-HS-DAP-S-P14 Students will recognize and identify the differences between combinations and permutations and use them to count discrete quantities. MA-HS-DAP-S-P15 Students will represent probabilities in multiple ways (e.g., fractions, decimals, percentages, geometric area models). Critical Vocabulary probability, simple probability, compound probability, odds, permutation, combination, sample space, event, outcome, replacement, non-replacement, experimental, theoretical, simulation, and dependent and independent events, Fundamental Counting Principal, Vann Diagram Major Topics Simple Probability, Sample Space, Odds vs. Probability, Compound Events, Venn Diagrams, Dependent and Independent Events, Replacement vs. Non-Replacement, Experimental, Theoretical, and Simulated Probability, Fundamental Principal of Counting, Permutations and Combinations Exponent Properties and Polynomials Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Solving quadratic equations produces a working knowledge of complex numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Algebraic Thinking High school students use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. They factor polynomial expressions and quadratics of the form 1x2+bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.2.3 Assessed Students will: add, subtract, and multiply polynomial expressions; factor polynomial expressions using the greatest common monomial factor; and factor quadratic polynomials of the form ax2+bx+c, when a=1 and b and c are integers. DOK - 1 SUPPORTING CORE CONTENT MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving, integer exponents. DOK – 2 MA-11-1.1.3 Supporting Students will use scientific notation to express very large or very small quantities. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 What is the relationship MA-HS-NPO-S-E7 Students will understand that numbers, ways between polynomials and Students will estimate solutions to problems with real numbers (including very large and very small of representing numbers, relationships among area? How do you know? quantities) in both realistic and mathematical situations. numbers and number systems are means of How do quadratic MA-HS-NPO-S-NO3 representing real-world quantities. equations help us solve Students will multiply and divide numbers expressed in scientific notation. real-life problems? MA-HS-NPO-U-3 MA-HS-NPO-S-NO4 Students will understand that computing Students will apply absolute value, integer exponents, roots and factorials to solve problems fluently and accurately with real numbers and making reasonable estimates increases MA-HS-NPO-S-NO9 Students will solve realistic problems to a specified degree of accuracy. the ability to solve realistic problems encountered in everyday life. MA-HS-NPO-S-NO10 Students will judge the effects of multiplication, division and computing powers and roots on the MA-HS-AT-U-3 magnitudes of quantities. Students will understand that algebra represents mathematical situations and MA-HS-NPO-S-NO13 structures for analysis and problem solving. Students will use concrete, pictorial and abstract models to develop and/or generalize a procedure. MA-HS-AT-S-VEO5 Students will understand that: Students will understand the properties of integer exponents and roots and apply these properties to Polynomials can represent area and perimeter simplify algebraic expressions. Using fraction and radical answers to MA-HS-AT-S-VEO6 represent irrational numbers is sometimes Students will add, subtract and multiply polynomials. better than a decimal approximation because of error in estimation. MA-HS-AT-S-VEO8 Students will factor polynomials by removing the greatest common factor. Exponents help us express extreme quantities MA-HS-AT-S-VEO9 Students will factor quadratic polynomials. MA-HS-AT-S-VEO11 Students will add, subtract, multiply, divide and simplify rational expressions. MA-HS-AT-S-VEO12 Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. MA-HS-AT-S-EI8 Students will solve quadratic equations in one variable. Critical Vocabulary monomial, polynomial, binomial, trinomial, greatest common monomial, factor, grouping, rational expressions, radical expressions, integer exponents, rational exponents, perfect square Major Topics Power of a Power, Product of Powers, Dividing Powers, Negative Powers, Zero Powers, Scientific Notation, Simplifying Radicals using the Product and Quotient Property, Adding and Subtracting Radicals, Solving Quadratic and Radical Equations, Pythagorean Theorem, Distance and Midpoint Formulas, Quadratic Formula, Adding and Subtracting Polynomials, Classifying Polynomials, Multiplying Polynomials, Special Products (introduction only), Solving Polynomials in Factored Form, Factoring x2 + bx + c, factoring special products, factoring common monomial terms, factoring zx2 + bx + c (introduction only), solve factorable quadratic equations (introduction only), factoring using the distributive property, deciding which factoring method to use GEOMETRY Geometric Relationships Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. Big Idea: Geometry High school students expand analysis of two-dimensional figures and three-dimensional objects. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.1.1 Assessed Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines, and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew). DOK – 2 SUPPORTING CORE CONTENT MA-11-3.1.3 Assessed Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding, and alternate interior angles) in real-world or mathematical situations. DOK – 2 MA-11-3.3.1 Assessed Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). DOK - 2 MA-11-3.1.2 ADP Benchmark Students will use spatial relationships to prove basic theorems. MA-11-3.1.4 ADP Benchmark Students will use angle relationships to prove basic theorems. MA-11-3.4.1 ADP Benchmark Students will identify, explain the necessity of, and give examples of definitions, axioms, and theorems. MA-11-3.4.2 ADP Benchmark Students will recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true. MA-11-3.4.3 ADP Benchmark Students will be able to perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line, and the bisector of an angle. MA-11-1.5.2 Supporting Students will use equivalence relations (reflexive, symmetric, transitive) to solve problems using real numbers. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-2 How do you systematically provide MA-HS-NPO-S-PNO2 Students will understand that meanings of and yourself with a mathematical picture or Students will use equivalence relations of real numbers to solve problems. relationships among operations provide tools diagram to represent a problem and solve it MA-HS-M-S-SM5 necessary to solve realistic problems by relating it to algebraic representations? Students will compare and contrast the use of US Customary and metric systems of encountered in everyday life and problems How do you interpret the world in a spatial measurement. encountered in mathematical situations. sense? MA-HS-M-S-MPA1 MA-HS-M-U-1 How do you measure attributes of objects Students will apply units of measurements of physical quantities correctly in Students will understand that measurable in your world? expressions, equations and problem solutions that involve measurement. attributes of objects and the units, systems and How is geometric language different from MA-HS-M-S-SM3 processes of measurement are powerful tools for making sense of the world around them. other mathematical language? Students will make decisions about units and scales that are appropriate for problem solving situations involving measurement. MA-HS-M-U-2 MA-HS-M-S-MPA2 Students will understand that numerical values Students will analyze precision, accuracy and approximate error in measurement associated with measurements of physical situations quantities must be assigned units of measurement or dimensions. MA-HS-G-S-SR1 Students will identify and apply the definitions, properties and theorems about line MA-HS-M-U-3 segments, rays and angles and use them to prove theorems in Euclidean geometry, Students will understand that measurements solve problems and perform basic geometric constructions using a straight edge and are determined by using appropriate a compass. techniques, tools, formulas and degree of MA-HS-G-S-SR2 accuracy needed for the situation. Students will identify and apply properties and theorems about parallel and perpendicular lines and use them to prove theorems and to perform constructions. MA-HS-G-U-1 Students will understand that characteristics MA-HS-G-S-SR3 and properties of two-dimensional figures and Students will analyze and apply angle relationships (e.g., linear pairs, vertical, three-dimensional objects describe the world complementary, supplementary, corresponding and alternate interior angles) in real- and are used to develop mathematical world or mathematical situations. arguments about geometric relationships and MA-HS-G-S-SR6 to evaluate the arguments of others. Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines and planes (e.g., “betweenness” of points, midpoint, MA-HS-G-U-2 segment length, collinear, coplanar, parallel, perpendicular, skew). Students will understand that representational systems, including coordinate geometry, are MA-HS-G-S-FS3 means for specifying locations and describing Students will establish the validity of geometric conjectures using deduction, prove spatial relationships and are organizers for theorems and critique arguments made by others. making sense of the world around them. MA-HS-G-S-SR13 Students will explore geometry to make and test conjectures using geometric tools MA-HS-G-U-5 and technology. Students will understand that visualization, MA-HS-G-S-FS1 spatial reasoning and geometric relationships Students will identify, explain the necessity of and give examples of definitions, model real-world situations. axioms and theorems. MA-HS-G-S-FS2 Students will understand that: Students will explore geometries other than Euclidean geometry, in which the The foundation of Euclidean geometry is the parallel postulate is not true. undefined terms point, line, and plane. MA-HS-G-S-CG3 Specific relationships (among geometric Students will find the distance between two points using their coordinates and the shapes) guide how the world fits together. Pythagorean theorem or the distance formula. MA-HS-G-S-CG5 Students will find the midpoint of a segment when the coordinates of the endpoints are identified. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and three-dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-G-S-FS4 Students will perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line segment and the bisector of an angle. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary Point, line, plane, collinear, coplanar, segment, intersection, ray, angle, vertex, right angles, acute angles, obtuse angles, adjacent angles, linear pair, vertical pair, complementary angles, supplementary angles, corresponding angles, and alternate interior angles, alternate exterior angles, consecutive exterior angles, consecutive interior angles, parallel, perpendicular, transversal, bisector, Postulate, Theorem, coordinate geometry, between, distance, midpoint, slope, reflexive, symmetric, transitive Major Topics Intro to different types of geometries (Euclidean, Hyperbolic, and Elliptic), Euclid’s 5 Axioms, Undefined Terms, Segment Measures and Addition Postulate, Distance Formula, Midpoint Formula, Angle Measures and Addition Postulate, Segment and Angle Bisectors, Angle Pair Relationships, Constructions, Patterns and Inductive Reasoning, Conditional Statements, Definitions and Bi-conditionals, Equivalence Relations, Lines and Transversals, Proving Lines are Parallel, Comparing Slopes and Equations of Parallel and Perpendicular Lines Transformations Big Idea: Geometry High school students expand analysis of two-dimensional figures. They translate figures in a coordinate plane. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.2.1 Assessed Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK – 3 SUPPORTING CORE CONTENT MA-11-3.3.1 Assessed Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). DOK - 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-G-U-2 Where is the mathematics in art? MA-HS-NPO-S-NS4 Students will understand that representational Students will explore vectors and matrices as systems that have some of What patterns exist when examining systems, including coordinate geometry, are means the properties of the real number system. transformations? for specifying locations and describing spatial MA-HS-NPO-S-NO11 relationships and are organizers for making sense of How do you interpret movement Students will develop an understanding of the properties and the world around them. geometrically in the world? representations for the addition and multiplication of vectors and matrices. MA-HS-G-U-3 MA-HS-G-S-FS3 Students will understand that transformations and Students will establish the validity of geometric conjectures using symmetry are used to analyze real-world situations deduction, prove theorems and critique arguments made by others. (e.g., art, nature, construction and scientific MA-HS-G-S-SR13 exploration). Students will explore geometry to make and test conjectures using geometric tools and technology. Students will understand that: Transformations show movement in real-life MA-HS-G-S-CG6 situations. Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. Transformations have been used throughout history to make artistic displays MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two- dimensional figures and three-dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-G-S-TS1 Students will understand and represent transformations within a plane (translations, reflections, rotations and dilations) of figures by using sketches, coordinates, vectors, function notation, matrices and technology. MA-HS-G-S-TS2 Students will use various representations, including electronic displays, to understand the effects of simple transformations within a plane and compositions of transformations. MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary transformation, translation, rotation, reflection, isometry, rigid transformations, coordinate geometry, tessellation Major Topics Rigid Motion in a Plane, Translations, Reflections, Rotations, Composition of Translations, Tessellations Polygon Properties Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. Big Idea: Geometry High school students expand analysis of two-dimensional figures. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.1.4 Assessed Students will solve real-world problems by applying properties of triangles (e.g., Triangle Sum theorem and Isosceles Triangle theorems). DOK – 2 SUPPORTING CORE CONTENT MA-11-3.1.5 Assessed Students will classify and apply properties of two-dimensional geometric figures (e.g., number of sides, vertices, length of sides, sum of interior and exterior angle measures). DOK – 2 MA-11-3.3.1 Assessed Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). DOK – 2 MA-11-3.4.3 ADP Benchmark Students will be able to perform constructions such as a line parallel to a given line through a point not on the line, the perpendicular bisector of a line, and the bisector of an angle. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-M-U-1 How do architects and landscapers MA-HS-M-S-MPA1 Students will understand that measurable use symmetry? Students will apply units of measurements of physical quantities correctly in expressions, attributes of objects and the units, systems equations and problem solutions that involve measurement. Why do we study 2-dimensional and processes of measurement are powerful objects when we study in a 3- MA-HS-M-S-SM3 tools for making sense of the world around dimensional world? Students will make decisions about units and scales that are appropriate for problem them. solving situations involving measurement. Why do we study shapes in the MA-HS-M-U-2 coordinate plane when real-world MA-HS-M-S-MPA2 Students will understand that numerical objects aren’t on a coordinate plane? Students will analyze precision, accuracy and approximate error in measurement values associated with measurements of situations physical quantities must be assigned units of MA-HS-G-S-FS3 measurement or dimensions. Students will establish the validity of geometric conjectures using deduction, prove MA-HS-M-U-3 theorems and critique arguments made by others. Students will understand that measurements MA-HS-G-S-SR13 are determined by using appropriate Students will explore geometry to make and test conjectures using geometric tools and techniques, tools, formulas and degree of technology. accuracy needed for the situation. MA-HS-G-S-CG1 Students will express the intuitive concept of the “slant” of a line as slope, use the MA-HS-G-U-1 coordinates of two points on a line to determine its slope and use slope to express the Students will understand that characteristics parallelism and perpendicularity of lines. and properties of two-dimensional figures and three-dimensional objects describe the MA-HS-G-S-CG3 world and are used to develop mathematical Students will find the distance between two points using their coordinates and the arguments about geometric relationships and Pythagorean theorem or the distance formula. to evaluate the arguments of others. MA-HS-G-S-CG5 Students will find the midpoint of a segment when the coordinates of the endpoints are MA-HS-G-U-2 identified. Students will understand that representational systems, including MA-HS-G-S-CG6 coordinate geometry, are means for Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, specifying locations and describing spatial polar, spherical systems) to analyze geometric situations. relationships and are organizers for making sense of the world around them. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional MA-HS-G-U-5 figures and three-dimensional objects represented graphically. Students will understand that visualization, MA-HS-G-S-CG8 spatial reasoning and geometric relationships Students will use a variety of technological tools to explore and test conjectures about model real-world situations. slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane Students will understand that: Polygons and their angles are useful for MA-HS-G-S-SR12 solving problems in architecture, Students will use geometric models and ideas to gain insights into and answer questions in construction, plumbing, engineering, other areas of mathematics and into other disciplines and areas of interest, such as art and landscaping, etc. architecture. Two-dimensional objects help us to analyze MA-HS-G-S-FS4 various parts of 3-dimensional objects in the Students will perform constructions such as a line parallel to a given line through a point real world. not on the line, the perpendicular bisector of a line segment and the bisector of an angle. A coordinate plane can help us describe the MA-HS-AT-S-EI2 location of objects in the real world in fields Students will draw reasonable conclusions about a situation being modeled. such as computer graphics and mapping. Critical Vocabulary polygons, triangles, isosceles, equilateral, equiangular, quadrilaterals, interior and exterior angles, regular polygons, 2-dimensional, perpendicular bisector, angle bisector, median, altitude, midsegment, concurrency, parallelogram, rhombuses, rectangles, squares, trapezoids, kites Major Topics Perpendiculars and Angle Bisectors or Triangles, Medians and Altitudes of Triangles, Midsegment Theorem, Triangle Inequality, Points of Concurrency, Constructions, Polygons, Polygon Sum, Parallelograms, Proving Quadrilaterals are Parallelograms, Rhombuses, Rectangles, Squares, Trapezoids, Kites, Coordinate Geometry Proofs Congruence and Similarity Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. Big Idea: Geometry High school students expand analysis of two-dimensional figures. They extend work with congruent and similar figures, including proportionality. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.1.12 Assessed Students will apply the concepts of congruence and similarity to solve real-world problems. DOK – 3 SUPPORTING CORE CONTENT MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving, roots (square). DOK – 2 MA-11-1.4.1 Assessed Students will apply ratios, percents, and proportional reasoning to solve real-world problems DOK - 2 MA-11-3.1.13 ADP Benchmark Students will prove triangles congruent and similar. MA-11-3.1.8 ADP Benchmark Students will use the properties of triangles to prove basic theorems. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-3 How do diagrams help us MA-HS-NPO-S-NO4 Students will understand that computing organize information? Students will apply absolute value, integer exponents, roots and factorials to solve problems fluently and accurately with real numbers How can you use ratios and MA-HS-NPO-S-RP1 and making reasonable estimates proportions to connect Students will calculate and apply ratios, proportions, rates and percentages to solve problems. increases the ability to solve realistic mathematical ideas? problems encountered in everyday life. MA-HS-NPO-S-RP2 How do we measure large Students will translate real-world proportional relationships into mathematical expressions and vice MA-HS-NPO-U-5 objects or distances since we versa. Students will understand that proportional cannot measure them directly? MA-HS-NPO-S-RP3 reasoning is a tool for modeling and solving problems encountered in Students will represent slope graphically, numerically and symbolically and relate it to a graph of everyday situations an equation based on a realistic situation. MA-HS-M-S-MPA1 MA-HS-M-U-1 Students will apply units of measurements of physical quantities correctly in expressions, equations Students will understand that measurable and problem solutions that involve measurement. attributes of objects and the units, systems and processes of measurement MA-HS-M-S-SM1 are powerful tools for making sense of Students will convert a measurement using one unit of measurement to another unit of the world around them. measurement given the relationship between the units (e.g., miles per hour to feet per second, °F to °C). MA-HS-M-U-2 MA-HS-M-S-SM3 Students will understand that numerical Students will make decisions about units and scales that are appropriate for problem solving values associated with measurements of situations involving measurement. physical quantities must be assigned units of measurement or dimensions. MA-HS-M-S-MPA2 Students will analyze precision, accuracy and approximate error in measurement situations MA-HS-M-U-3 MA-HS-M-S-SM4 Students will understand that Students will use unit analysis to check measurement computations. measurements are determined by using appropriate techniques, tools, formulas MA-HS-G-S-SR4 and degree of accuracy needed for the Students will use the definitions, properties and theorems about congruent and similar triangles and situation. other figures to prove additional theorems and apply these to solve real-world problems. MA-HS-G-U-1 MA-HS-G-S-FS3 Students will understand that Students will establish the validity of geometric conjectures using deduction, prove theorems and characteristics and properties of two- critique arguments made by others. dimensional figures and three- MA-HS-G-S-SR13 dimensional objects describe the world Students will explore geometry to make and test conjectures using geometric tools and technology. and are used to develop mathematical arguments about geometric relationships MA-HS-G-S-TS1 and to evaluate the arguments of others. Students will understand and represent transformations within a plane (translations, reflections, rotations and dilations) of figures by using sketches, coordinates, vectors, function notation, MA-HS-G-U-4 matrices and technology. Students will understand that similarity of MA-HS-G-S-SR4 figures and scale factors are used to Students will use the definitions, properties and theorems about congruent and similar triangles and analyze and solve problems. other figures to prove additional theorems and apply these to solve real-world problems. MA-HS-G-S-SR12 Students will understand that: Students will use geometric models and ideas to gain insights into and answer questions in other similarity of figures and scale factors are areas of mathematics and into other disciplines and areas of interest, such as art and architecture. used to analyze and solve problems. MA-HS-AT-S-EI2 visualization, spatial reasoning and Students will draw reasonable conclusions about a situation being modeled. geometric relationships model real-world situations. proportional reasoning is a tool for modeling and solving problems encountered in everyday situations. Critical Vocabulary ratio, proportions, congruence, similarity, corresponding parts, transformations, dilations, indirect measurement, scale, right triangle, acute triangle, obtuse triangle, scalene, isosceles, equilateral Major Topics Triangle Classification, Interior and Exterior Angle Sum, Polygon Congruence, SSS, SAS, ASA, AAS, and HL Congruence Theorem and Postulates, Triangle Proofs, Isosceles Triangle Theorem, Using Triangle Congruence, Ratio and Proportion, Similar Figures, Similar Triangles, Proving Similar Triangles, Proportionality Theorems, Dilations, Fractals Right Triangle Properties Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve realistic problems. Big Idea: Geometry High school students expand analysis of two-dimensional figures. Big Idea: Algebraic Thinking High school students combine simple rational expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-2.1.3 Assessed Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. DOK – 3 SUPPORTING CORE CONTENT MA-11-2.1.4 ADP Benchmark Students will apply special right triangles and the converse of the Pythagorean theorem to solve real-world problems. MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving roots (square, cube) DOK - 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-3 How do diagrams help us organize MA-HS-NPO-S-NS4 Students will understand that information? Students will explore vectors and matrices as systems that have some of the properties of computing fluently and accurately the real number system. What are possible methods of with real numbers and making MA-HS-NPO-S-NO4 measurement available to determine reasonable estimates increases the Students will apply absolute value, integer exponents, roots and factorials to solve distances and angles (without using direct ability to solve realistic problems problems measurement e.g. ruler and protractor)? encountered in everyday life. MA-HS-NPO-S-NO11 What is the purpose of right triangles in Students will develop an understanding of the properties and representations for the MA-HS-M-U-1 our world? addition and multiplication of vectors and matrices. Students will understand that MA-HS-M-S-MPA1 measurable attributes of objects and Students will apply units of measurements of physical quantities correctly in expressions, the units, systems and processes of equations and problem solutions that involve measurement. measurement are powerful tools for MA-HS-M-S-SM3 making sense of the world around Students will make decisions about units and scales that are appropriate for problem them. solving situations involving measurement. MA-HS-M-S-MPA2 MA-HS-M-U-2 Students will analyze precision, accuracy and approximate error in measurement Students will understand that situations numerical values associated with MA-HS-M-S-MPA5 measurements of physical quantities Students will explore the relationships between the right triangle trigonometric functions, must be assigned units of measurement using technology (e.g., graphing calculator) as appropriate. or dimensions. MA-HS-M-S-MPA6 Students will apply definitions and properties of right triangle relationships (basic right MA-HS-M-U-3 triangle trigonometry and the Pythagorean theorem) to determine length and angle Students will understand that measures to solve realistic problems measurements are determined by using MA-HS-M-S-MPA7 appropriate techniques, tools, formulas Students will apply special right triangles and the converse of the Pythagorean theorem to and degree of accuracy needed for the solve realistic problems. situation. MA-HS-G-S-FS3 Students will establish the validity of geometric conjectures using deduction, prove theorems and critique arguments made by others. MA-HS-G-S-SR13 Students will explore geometry to make and test conjectures using geometric tools and technology. MA-HS-G-S-CG3 Students will find the distance between two points using their coordinates and the Pythagorean theorem or the distance formula. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and three-dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary Right triangle, Isosceles triangle, Equilateral Triangle, Leg, Hypotenuse, Special Right triangles, Trigonometric ratios, Sine, Cosine, Tangent, Angles of Elevation & Depression, Pythagorean relationships Major Topics Simplifying Radicals, Similar Right Triangles, Pythagorean Theorem, Special Right Triangles, Trigonometric Ratios, Using Ratios to solve for angles and sides of a Right Triangle, Angles of Elevation and Depression, Introduction to Vectors, Applying Right Triangle Trigonometry, Identifying which Right Triangle method is easiest to solve for sides or angles, Indirect Measurement Area and Volume Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use formulas to find surface areas and volumes. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve realistic problems. Big Idea: Geometry High school students expand analysis of two-dimensional figures and three-dimensional objects. They extend work with similar figures, including proportionality. Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They compare and contrast theoretical and experimental probability. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use probability. POWER STANDARD MA-11-2.1.2 Assessed Students will describe how a change in one or more dimensions of a geometric figure affects the perimeter, area, and volume of the figure. DOK – 3 SUPPORTING CORE CONTENT MA-11-2.1.1 Assessed Students will determine the surface area and volume of right rectangular prisms, pyramids, cylinders, cones, and spheres in real-world and mathematical problems. DOK – 2 MA-11-3.1.9 Assessed Students will classify and apply properties of three-dimensional geometric figures (e.g., number of edges, faces, vertices, sum of interior and exterior angle measures). DOK – 2 MA-11-3.1.10 Students will describe the intersection of a plane with a three-dimensional figure MA-11-3.1.11 ADP Benchmark Students will visualize solids and surfaces in three-dimensional space when given two-dimensional representations (e.g., nets, multiple views) and create two-dimensional representations for the surfaces of three-dimensional objects. MA-11-4.4.3 Supporting Students will represent probabilities in multiple ways, such as fractions, decimals, percentages, and geometric area models. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-M-U-1 What life situations might require us MA-HS-M-S-MPA1 Students will understand that measurable attributes of to calculate surface area or volume? Students will apply units of measurements of physical quantities correctly in objects and the units, systems and processes of expressions, equations and problem solutions that involve measurement. How can we break a 3-dimensional measurement are powerful tools for making sense of the object into something we can measure world around them. MA-HS-M-S-MPA4 with 2-dimensional tools? Students will describe how change in one or more dimensions of a geometric MA-HS-M-U-2 What effects does doubling the figure or object affects the perimeter, circumference, area and/or volume of the Students will understand that numerical values dimensions of an object have on the figure or object. associated with measurements of physical quantities surface area and volume? must be assigned units of measurement or dimensions. MA-HS-M-S-SM3 Students will make decisions about units and scales that are appropriate for MA-HS-M-U-3 problem solving situations involving measurement. Students will understand that measurements are determined by using appropriate techniques, tools, MA-HS-M-S-MPA2 formulas and degree of accuracy needed for the Students will analyze precision, accuracy and approximate error in situation. measurement situations MA-HS-G-U-1 MA-HS-M-S-MPA3 Students will understand that characteristics and Students will determine the surface area and volume of right rectangular properties of two-dimensional figures and three- prisms, pyramids, cylinders, cones and spheres in realistic problems. dimensional objects describe the world and are used to develop mathematical arguments about geometric MA-HS-G-S-SR7 relationships and to evaluate the arguments of others. Students will classify, determine attributes of, analyze and apply properties of two-dimensional geometric figures and three-dimensional objects. MA-HS-G-U-5 Students will understand that visualization, spatial MA-HS-G-S-SR8 reasoning and geometric relationships model real-world Students will describe the intersection of lines, planes and solids and visualize situations. three-dimensional objects and spaces from different perspectives and analyze their cross sections. MA-HS-G-S-SR9 Students will classify and apply properties of three-dimensional geometric figures. MA-HS-G-S-SR10 Students will visualize solids and surfaces in three-dimensional space when given two-dimensional representations and create two-dimensional representations for the surfaces of three-dimensional objects. MA-HS-G-S-FS3 Students will establish the validity of geometric conjectures using deduction, prove theorems and critique arguments made by others. MA-HS-G-S-SR13 Students will explore geometry to make and test conjectures using geometric tools and technology. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two- dimensional figures and three dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-G-S-SR11 Students will draw and construct representations of two-dimensional figures and three-dimensional objects using a variety of tools. MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-DAP-S-P15 Students will represent probabilities in multiple ways (e.g., fractions, decimals, percentages, geometric area models). MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary area, perimeter, circumference, arc length, sector, apothem, diameter, radius, pi, surface area, volume, solids, sides, height, slant height, edge, face, vertices, net, ratio, proportion, 2-dimensional, 3-dimensional, polyhedron, rectangular prisms & pyramids, triangular prisms and pyramids, regular polygonal prisms & pyramids, cones, cylinders, and spheres Major Topics Estimating Area of Irregular Shapes, Area of Triangles, Parallelograms, Trapezoids, and Kites, Area of Regular Polygons, Circumference, Arc Length, Area of Circles and Sectors, Applied area problems, geometric probability, polyhedrons, Isometric Drawings, Orthographic Drawings, Net Drawings, Surface area and Lateral area of Prisms and Cylinders, Volume of Prisms and Cylinders, Surface Area and Lateral area of pyramids and cones, volume of pyramids and cones, Area and Volume of Spheres, Proportions with Area, Perimeter and volume of solids Circles Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. Big Idea: Geometry High school students expand analysis of two-dimensional figures. They extend work with congruent and similar figures, including proportionality. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.1.6 ADP Benchmark Students will know the definitions and basic properties of a circle and will use them to prove basic theorems and solve problems Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-M-U-1 How do scientists calculate the MA-HS-M-S-MPA1 Students will understand that measurable attributes of diameters of spatial bodies? (e.g. Students will apply units of measurements of physical quantities correctly in objects and the units, systems and processes of moon, planets) expressions, equations and problem solutions that involve measurement. measurement are powerful tools for making sense of MA-HS-M-S-SM3 How are circles and their the world around them. Students will make decisions about units and scales that are appropriate for problem properties used in landscaping? solving situations involving measurement. MA-HS-M-U-2 MA-HS-M-S-MPA2 Students will understand that numerical values Students will analyze precision, accuracy and approximate error in measurement associated with measurements of physical quantities situations must be assigned units of measurement or dimensions. MA-HS-G-S-SR5 Students will use the definitions and basic properties of a circle (e.g., arcs, chords, MA-HS-M-U-3 central angles, inscribed angles) to prove basic theorems and solve problems. Students will understand that measurements are MA-HS-G-S-FS3 determined by using appropriate techniques, tools, Students will establish the validity of geometric conjectures using deduction, prove formulas and degree of accuracy needed for the theorems and critique arguments made by others. situation. MA-HS-G-S-SR13 Students will explore geometry to make and test conjectures using geometric tools and MA-HS-G-U-1 technology. Students will understand that characteristics and MA-HS-G-S-CG4 properties of two-dimensional figures and three- Students will find the equation of a circle given its center and radius; given the equation dimensional objects describe the world and are used of a circle, find its center and radius. to develop mathematical arguments about geometric relationships and to evaluate the arguments of others. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, Students will understand that: polar, spherical systems) to analyze geometric situations. That pi is the relationship between the circumference MA-HS-G-S-CG7 and diameter of a circle. Students will investigate conjectures and solve problems involving two-dimensional figures and three-dimensional objects represented graphically. Theorems about circles were developed to help early astronomers study spatial bodies. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary circle, inscribed angle, central angle, chord, secant, tangent, arc, area, concentric circles, chord, secant, and tangent theorems Major Topics Circle parts and definitions, tangents of circles, arcs and chords, inscribed angles and intercepted arcs, Angles formed by secants and tangents, segment lengths in circles, equations of circles ALGEBRA II Linear and Piecewise Functions Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear and absolute value functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-4.2.3 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-4.2.4 ADP Benchmark Students will recognize when arguments based on data confuse correlation and causation MA-11-5.1.1 Assessed Students will identify and apply multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) to solve real-world or mathematical problems. DOK - 2 MA-11-5.1.2 Students will identify, relate, and apply representations (graphs, equations, tables) of a piecewise function (such as long distance telephone rates) from mathematical or real world information. MA-11-5.1.5 Assessed Students will: determine if a relation is a function; determine the domain and range of a function (linear and quadratic); determine the slope and intercepts of a linear function; evaluate a function written in function notation for a specified rational number. DOK - 2 MA-11-5.1.6 Supporting Students will find the domain and range for absolute value functions. MA-11-5.1.7 Supporting Students will apply and use direct and inverse variation to solve real world and mathematical problems. MA-11-5.1.8 Assessed Students will identify the changes and explain how changes in parameters affect graphs of functions (linear) (e.g., compare y=x 2, y=2x2, y=(x-4)2, and y=x2+3). DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How do you solve real life problems by Program of Studies Students will understand that quantitative literacy recognizing relationships between cause MA-HS-M-S-MPA8 is a necessary tool to be an intelligent consumer and effect? Students will explore periodic real-world phenomena, using technology (e.g., and citizen. graphing calculator) as appropriate. How do you learn to recognize the pattern MA-HS-DAP-U-3 between cause and effect and represent that MA-HS-G-S-CG6 Students will understand that graphical and pattern? Students will use Cartesian coordinates and other coordinate systems (e.g., numerical techniques can be used to study navigational, polar, spherical systems) to analyze geometric situations. patterns and analyze data. How do you represent multiple solutions and boundaries in real-life situations? MA-HS-G-S-CG7 MA-HS-DAP-U-5 Students will investigate conjectures and solve problems involving two- Students will understand that inferences and dimensional figures and three-dimensional objects represented graphically. predictions from data are used to make critical and informed decisions. MA-HS-G-S-CG8 MA-HS-AT-U-1 Students will use a variety of technological tools to explore and test conjectures Students will understand that patterns, relations about slope, midpoints and other geometric ideas that can be expressed using the and functions are tools that help explain or Cartesian plane predict real-world phenomena MA-HS-AT-S-PRF2 MA-HS-AT-U-2 Students will understand relations and functions and use various representations Students will understand that there are for them. relationships between and among patterns and MA-HS-AT-S-PRF6 functions, their representations and their properties. Students will interpret representations of functions of two variables. MA-HS-AT-U-3 MA-HS-AT-S-PRF9 Students will understand that algebra represents Students will determine whether a relationship given in symbolic or graphical mathematical situations and structures for form is a function. analysis and problem solving. MA-HS-AT-S-PRF11 MA-HS-AT-U-4 Students will understand functional notation and evaluate a function at a specified Students will understand that real-world point in its domain. situations can be represented using mathematical models to analyze quantitative relationships. MA-HS-AT-S-PRF12 Students will combine functions by addition, subtraction, multiplication and MA-HS-AT-U-5 compositions. Students will understand that functions are used to analyze change in various contexts and model MA-HS-AT-S-PRF13 real-world phenomena. Students will graph linear, absolute value, quadratic and exponential functions MA-HS-AT-U-6 and identify their key characteristics. Students will understand that functions can be MA-HS-AT-S-PRF18 written in words, in a symbolic sentence or in a Students will relate the patterns in arithmetic sequences to linear functions. table or graph. MA-HS-AT-S-EI1 Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI5 Students will solve an equation involving several variables for one variable in terms of the others. MA-HS-AT-S-EI9 Students will approximate and interpret rates of change from graphical and numerical data. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non- linear functions. MA-HS-AT-S-PRF20 Students will solve problems that have direct or inverse relationships for any variable. MA-HS-AT-S-EI10 Students will graph a linear equation and demonstrate that it has a constant rate of change. MA-HS-AT-S-EI11 Students will relate the coefficients of a linear equation and the slope and x- and y-intercepts of its graph. MA-HS-AT-S-EI13 Students will graph the solution set of a linear inequality and identify whether the solution set is an open or closed half-plane. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. MA-HS-AT-S-EI19 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically or symbolically non-linear equations (e.g., absolute value, quadratic, exponential equations). MA-HS-AT-S-PRF5 Students will understand and compare the properties of classes of functions (e.g., absolute value, step, exponential, polynomial, rational, logarithmic, periodic). MA-HS-AT-S-PRF7 Students will use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. MA-HS-AT-S-PRF8 Students will identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship. Critical Vocabulary function, relation, domain, range, inverse relation, graphs, equations, tables, coordinate pairs, mapping, formulas, independent and dependent variables, direct and inverse variation, constant of variation, vertical line test, linear equation, linear inequality, piecewise function, absolute value function, x-intercept, y-intercept, slope and rate, slope-intercept form, point-slope form, standard form, line of best fit, rate of change, function notation Major Topics Review of Solving Equations and solving inequalities, Solving absolute value inequalities, functions and relation, vertical line test, function notation, domain and range, review of graphing linear equations, review of parallel and perpendicular lines, review of finding intercepts, review of finding intercepts, review of writing linear equations, correlation, review of graphing inequalities, piecewise functions, graphing absolute value functions, composition of functions, domain and range of functions, inverse functions Systems of Equations and Inequalities Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. They understand large and small numbers and their representations. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.3.4 Assessed Students will model and graph systems of linear equations (two equations in two variables) and apply the system to solve and interpret real-world and mathematical problems. DOK - 3 SUPPORTING CORE CONTENT MA-11-5.3.5 Supporting Students will write, graph, and solve systems of linear inequalities (two inequalities in two variables) based on real world or mathematical situations and interpret the solution. MA-11-4.1.3 Supporting Students will represent real-world data using matrices and will use matrix addition, subtraction, multiplication (with matrices no larger than 2x2), and scalar multiplication to solve real-world problems. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How are systems of equations used in real life? Program of Studies Students will understand that quantitative MA-HS-NPO-S-NS4 How can I represent a real life situation literacy is a necessary tool to be an intelligent Students will explore vectors and matrices as systems that have some of the algebraically? consumer and citizen. properties of the real number system. How do companies maximize profit and MA-HS-DAP-U-3 minimize cost? MA-HS-NPO-S-PNO3 Students will understand that graphical and Students will compare and contrast the number systems according to their numerical techniques can be used to study properties. patterns and analyze data. MA-HS-DAP-U-5 MA-HS-NPO-S-NO11 Students will understand that inferences and Students will develop an understanding of the properties and representations predictions from data are used to make critical for the addition and multiplication of vectors and matrices. and informed decisions. MA-HS-G-S-CG6 MA-HS-NPO-U-1 Students will use Cartesian coordinates and other coordinate systems (e.g., Students will understand that numbers, ways of navigational, polar, spherical systems) to analyze geometric situations. representing numbers, relationships among numbers and number systems are means of MA-HS-G-S-CG7 representing real-world quantities. Students will investigate conjectures and solve problems involving two- MA-HS-AT-U-4 dimensional figures and three-dimensional objects represented graphically. Students will understand that real-world situations can be represented using mathematical MA-HS-AT-S-EI1 models to analyze quantitative relationships. Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with MA-HS-AT-U-5 paper and pencil in simple cases and using technology in all cases. Students will understand that functions are used to analyze change in various contexts and model MA-HS-AT-S-EI2 real-world phenomena. Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-U-6 Students will understand that functions can be MA-HS-AT-S-EI6 written in words, in a symbolic sentence or in a Students will solve systems of two linear equations in two variables. table or graph. MA-HS-AT-S-EI7 Students will understand that: Students will solve systems of three linear equations in three variables. The solutions will be an x and y values that work for both equations and the solutions can be MA-HS-AT-S-EI12 found algebraically and graphically Students will relate a solution of a system of two linear equations in two variables and the graphs of the corresponding lines. Matrices are useful in solving systems of equations MA-HS-AT-S-EI14 Finding limits and boundaries are valuable in Students will graph the solution set of a system of two or three linear business, profit, science, city planning, etc inequalities. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. Students will be able to solve a system of equations using matrices. Students will be able to find the determinant of a matrix. Critical Vocabulary parallel lines, perpendicular lines, system of linear equations and inequalities, substitution, elimination, linear programming, matrix, feasible region, identity matrix, determinant, inverse matrix Major Topics Solving a system of linear equations by graphing, solving a system of linear equations by substitution, solving a system of linear equations by elimination, graphing a system of inequalities, linear programming, adding and subtracting matrices, multiplying matrices by a scalar, naming matrices, multiplying matrices, solving systems using matrices, determinants, Cramer’s Rule Quadratics Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Solving quadratic equations produces a working knowledge of complex numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on quadratic functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. They factor polynomial 2 expressions and quadratics of the form 1x +bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-4.2.3 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-5.3.6 Assessed Students will model, solve, and graph quadratic equations from real world or mathematical situations. DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 What patterns occur when objects are MA-HS-NPO-S-NS5 Students will understand that quantitative thrown or projected? Students will compare and contrast number systems, including complex numbers as literacy is a necessary tool to be an intelligent solutions to quadratic equations that do not have real solutions. How do you determine the most or the consumer and citizen. MA-HS-NPO-S-NO2 least of a given situation? Students will add, subtract and multiply complex numbers. MA-HS-DAP-U-3 What are examples of problems with MA-HS-NPO-S-NO13 Students will understand that graphical and one or more solutions? Students will use concrete, pictorial and abstract models to develop and/or generalize a numerical techniques can be used to study procedure. patterns and analyze data. What relationships exist between a MA-HS-M-S-MPA8 parabola and its equation? Students will explore periodic real-world phenomena, using technology (e.g., graphing MA-HS-AT-U-1 calculator) as appropriate. Students will understand that patterns, MA-HS-G-S-CG6 relations and functions are tools that help Students will use Cartesian coordinates and other coordinate systems (e.g., explain or predict real-world phenomena navigational, polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 MA-HS-AT-U-4 Students will investigate conjectures and solve problems involving two-dimensional Students will understand that real-world figures and three dimensional objects represented graphically. situations can be represented using MA-HS-G-S-CG8 mathematical models to analyze quantitative Students will use a variety of technological tools to explore and test conjectures about relationships. slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-DAP-S-CDS4 Students will determine regression coefficients, regression equations and correlation coefficients for bivariate data using technological tools. MA-HS-DAP-S-CDS5 Students will apply line-of-best fit equations for a set of two-variable data to make predictions. MA-HS-DAP-S-CDS6 Students will collect, organize and display bivariate data and use a curve of best fit as a model to make predictions. MA-HS-DAP-S-CDS7 Students will identify trends in bivariate data and find functions that model the data or transform the data, so that they can be modeled. MA-HS-AT-S-VEO5 Students will understand the properties of integer exponents and roots and apply these properties to simplify algebraic expressions. MA-HS-AT-S-VEO8 Students will factor polynomials by removing the greatest common factor. MA-HS-AT-S-VEO9 Students will factor quadratic polynomials. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI8 Students will solve quadratic equations in one variable. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non-linear functions. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI16 Students will graph a quadratic function and understand the relationship between its real zeros and the x-intercepts of the graph. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. MA-HS-AT-S-EI19 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically or symbolically non-linear equations (e.g., absolute value, quadratic, exponential equations). MA-HS-AT-S-EI20 Students will use graphing technology to explore the meaning of quadratic equations with complex solutions. MA-HS-AT-S-PRF4 Students will transform functions (e.g., arithmetically combining, composing and inverting commonly used functions), using technology on more complicated symbolic expressions. MA-HS-AT-S-PRF5 Students will understand and compare the properties of classes of functions (e.g., absolute value, step, exponential, polynomial, rational, logarithmic, periodic). MA-HS-AT-S-PRF7 Students will use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. MA-HS-AT-S-PRF8 Students will identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship. Critical Vocabulary Minimum, maximum, intercepts, zeros, Discriminant, complex number, factor, standard form, intercept form, vertex form Major Topics Axis of symmetry, Standard form, finding the vertex, using the vertex and y-intercept to find another point, finding the axis of symmetry, using vertex form, graphing, using x- intercept form, changing between forms, finding all parts of the parabola, factoring common term, factoring when a=1, factoring difference of two squares, solving for zeros, factoring when a>1, factor by grouping, reducing radicals, rationalizing denominators, completing the square, quadratic equation, height formula, graphing inequalities, modeling, complex numbers, finding the equation given 2 intercepts and a point, finding the equation given the vertex and a point, finding the equation given 3 points Statistics Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Academic Expectations 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-4.1.1 Assessed Students will analyze and make inferences from a set of data with no more than two variables, and will analyze situations for the use and misuse of data representations. DOK – 3 SUPPORTING CORE CONTENT MA-11-4.1.2 Assessed Students will construct data displays for data with no more than two variables. DOK – 2 MA-11-4.2.1 Assessed Students will describe and compare data distributions and make inferences from the data based on the shapes of graphs, measures of center (mean, median, mode) and measures of spread (range, standard deviation). (focus on spread and applications of mean, median, and mode) DOK – 2 MA-11-4.2.2 ADP Benchmark Students will know the characteristics of the Gaussian normal distribution (bell-shaped curve). MA-11-4.3.1 Assessed Students will recognize potential for bias resulting from the misuse of sampling methods (e.g., non-random sampling, polling only a specific group of people, using limited or extremely small sample sizes, bias issues) and explain why these strategies can lead to inaccurate inferences. DOK – 2 MA-11-4.3.2 ADP Benchmark Students will design simple experiments or investigations to collect data to answer questions of interest. MA-11-4.3.3 ADP Benchmark Students will explain the differences between randomized experiments and observational studies. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 What mathematical methods provide the MA-HS-M-S-MPA8 Students will understand that quantitative “fairest” rankings? Students will explore periodic real-world phenomena, using technology (e.g., graphing literacy is a necessary tool to be an calculator) as appropriate. What is average? intelligent consumer and citizen. MA-HS-DAP-S-CDS12 How can data lie or mislead? Do people Students will evaluate reports based on data published in the media by considering the MA-HS-DAP-U-2 use numbers to mislead others? Should source of the data, the design of the study and the way the data are displayed and Students will understand that data analysis they? analyzed. requires developing a plan for collecting, How does what we measure influence MA-HS-DAP-S-ES1 organizing and analyzing data in order to how we measure and what we conclude Students will understand and explain the differences among various kinds of studies make decisions. from the results of our measurements? (e.g., randomized experiments and observational studies) and which types of inferences can be legitimately be drawn from each. MA-HS-DAP-U-3 When should we sample? When Students will understand that graphical shouldn’t we? How much or many (of a MA-HS-DAP-S-DR1 and numerical techniques can be used to sample) is enough? Students will be familiar with the definitions of measurement data and categorical data, study patterns and analyze data. univariate and bivariate data and the term variable. MA-HS-DAP-S-CDS1 MA-HS-DAP-U-4 Students will understand the distinction between a statistic and a parameter. Students will understand that the choice of MA-HS-DAP-S-ES2 data display can affect the visual message Students will know the characteristics of well-designed studies, including the role of communicated. randomization in surveys and experiments. MA-HS-DAP-S-ES3 MA-HS-DAP-U-5 Students will use simulations to explore the variability of sample statistics from a Students will understand that inferences known population and to construct sampling distributions. and predictions from data are used to make critical and informed decisions. MA-HS-DAP-S-ES4 Students will evaluate published reports that are based on interpretations of data by Students will understand that: examining the design of the study, the appropriateness of the data analysis and the Statistics can be used to make decisions validity of the conclusions. about fairness. MA-HS-DAP-S-ES5 Students will explain the impact of sampling methods, bias and the phrasing of Biases can affect the data and the results. questions asked during data collection and the conclusions that can be justified. An outlier can raise or lower the mean, MA-HS-DAP-S-ES6 without greatly affecting the median. Students will design and conduct simple experiments or investigations to collect data to A poor choice of graph, scale, or type of answer student generated questions. statistic can be used to mislead people. MA-HS-DAP-S-DR3 Students will display the distribution, analyze patterns and describe relationships in There are different types of averages paired data for univariate measurement data. (average doesn’t imply mean!) MA-HS-DAP-S-DR5 Standard deviation describes the spread of Students will display and discuss bivariate data where at least one variable is a set of data. categorical. MA-HS-DAP-S-DR6 Students will organize and display data using appropriate methods (e.g., spreadsheets and graphing calculators) to detect patterns and departures from patterns. MA-HS-DAP-S-CDS2 Students will describe the shape and select and calculate summary statistics for univariate measurement data, using technological tools as necessary. MA-HS-DAP-S-CDS3 Students will recognize how linear transformations of univariate data affect shape, center and spread. MA-HS-DAP-S-CDS4 Students will determine regression coefficients, regression equations and correlation coefficients for bivariate data using technological tools. MA-HS-DAP-S-CDS5 Students will apply line-of-best fit equations for a set of two-variable data to make predictions. MA-HS-DAP-S-DR2 Students will apply histograms, parallel box plots and scatterplots to display data. MA-HS-DAP-S-DR7 Students will identify and explain misleading uses of data displays. MA-HS-DAP-S-CDS8 Students will understand how simple statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference. MA-HS-DAP-S-CDS9 Students will explore how basic statistical techniques monitor process characteristics in the workplace. MA-HS-DAP-S-CDS10 Students will compare data sets using graphs and summary statistics. MA-HS-DAP-S-CDS11 Students will know the characteristics of the Gaussian normal distribution (bell-shaped curve). MA-HS-DAP-S-CDS12 Students will evaluate reports based on data published in the media by considering the source of the data, the design of the study and the way the data are displayed and analyzed. MA-HS-DAP-S-CDS13 Students will identify and explain misleading uses of data. Critical Vocabulary statistical data, standard deviation, spread, correlation, normal curve, mean, median, mode, range, percentiles, population, variance, histogram, stem-and-leaf plot, bar graph, frequency chart, box-and-whisker plot, scatter plot, dot plot, normal distribution, skew, summary statistics, randomized, observation, experiment, bias, random sampling, sample size Major Topics Examine biased/inaccurate study, data gathering, non-random sampling, sample size, bias, standard deviation, center and spread, measures of central tendency, do a class study Probability Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. They understand large and small numbers and their representations. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They distinguish between combinations and permutations and compare and contrast theoretical and experimental probability. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-1.3.2 Assessed Students will: describe and extend arithmetic and geometric sequences; determine a specific term of a sequence given an explicit formula; determine an explicit rule for the nth term of an arithmetic sequence; and apply sequences to solve real-world problems. DOK - 3 SUPPORTING CORE CONTENT MA-11-1.3.3 Supporting Students will write an explicit rule for the nth term of a geometric sequence. MA-11-4.4.2 Supporting Students will recognize or identify the differences between combinations and permutations and use them to count discrete quantities. MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube), and factorials. DOK - 2 MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions and factorials. DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 How do you determine the best choice in a MA-HS-NPO-S-NO5 Students will understand that numbers, ways of situation that involves probability? Students will determine a specific term of a sequence given an explicit representing numbers, relationships among formula. Do people use probability and odds to numbers and number systems are means of mislead others? Should they? representing real-world quantities. MA-HS-NPO-S-NO6 Is doing a simulation of an experiment better Students will describe and extend arithmetic and geometric sequences. MA-HS-NPO-U-3 than doing an actual experiment? When Students will understand that computing fluently would you want to actually conduct an MA-HS-NPO-S-NO7 and accurately with real numbers and making experiment and when would you want to Students will determine an explicit rule for the nth term of an arithmetic reasonable estimates increases the ability to simulate an experiment? sequence. solve realistic problems encountered in everyday What are examples of situations when order life. matters and when it doesn’t? MA-HS-NPO-S-NO4 Students will apply absolute value, integer exponents, roots and factorials to MA-HS-AT-U-1 What are examples of situations when you solve problems Students will understand that patterns, relations would want to use replacement? non- and functions are tools that help explain or replacement? MA-HS-DAP-S-P14 predict real-world phenomena Students will recognize and identify the differences between combinations and permutations and use them to count discrete quantities. MA-HS-AT-U-2 Students will understand that there are MA-HS-AT-S-PRF1 relationships between and among patterns and Students will use explicitly defined or recursively defined functions to functions, their representations and their generalize patterns. properties. MA-HS-AT-S-PRF16 Students will see the patterns in arithmetic and geometric sequences using Students will understand that: recursion. Theoretical probability differs from experimental probability. MA-HS-AT-S-PRF17 An experiment can be simulated. Students will see patterns in other sequences (e.g., quadratic, cubic). The probability of two or more independent MA-HS-AT-S-PRF18 events occurring simultaneously can not be Students will relate the patterns in arithmetic sequences to linear functions. calculated using simple probability. Probability is different from odds. MA-HS-AT-S-PRF19 Students will relate the patterns in geometric sequences to exponential functions. Critical Vocabulary probability, odds, permutation, combination, sample space, event, outcome, replacement, non-replacement, experimental, theoretical, simulation, dependent and independent events, sequences, series, arithmetic, geometric, infinite, finite Major Topics Combinations, Permutations, Pascal’s Triangle, Infinite and finite series, Sigma notation, arithmetic series and sums, geometric series and sums, sum of infinite series Polynomial and Rational Expressions Big Idea: Algebraic Thinking High school students extend analysis and use of functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. They factor polynomial expressions and quadratics of the 2 form 1x +bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.2.5 Assessed Students will add, subtract, multiply, and divide simple rational expressions with monomial first-degree denominators and integer numerators (e.g., 3 4 ; 9 7 ; 3 4 ; 5 9 ), and will express the results in simplified form. 5x 3y 2a 4b 5x 7y 2c 11d DOK – 1 SUPPORTING CORE CONTENT MA-11-5.2.2 ADP Benchmark Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-AT-U-3 How do the basic operations (add, subtract, MA-HS-G-S-CG7 Students will understand that algebra multiply, and divide) with fractions and whole Students will investigate conjectures and solve problems involving two- represents mathematical situations and numbers compare to the basic operations with dimensional figures and three dimensional objects represented graphically. structures for analysis and problem solving. polynomials and rational expressions? MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures Students will understand that: How can rational expressions be used in about slope, midpoints and other geometric ideas that can be expressed using Polynomials and rational expressions operate cooking? the Cartesian plane the same why as fractional whole numbers. MA-HS-AT-S-VEO5 Students will understand the properties of integer exponents and roots and There is a relationship between rational apply these properties to simplify algebraic expressions. numbers and rational expressions MA-HS-AT-S-VEO7 Students will divide a polynomial by a first-degree polynomial. MA-HS-AT-S-VEO10 Students will determine when an expression is undefined. MA-HS-AT-S-VEO11 Students will add, subtract, multiply, divide and simplify rational expressions. MA-HS-AT-S-VEO12 Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. Critical Vocabulary Rational expression, common denominator Major Topics Reducing, multiplying, and dividing rational expressions, adding and subtracting rational expressions, solving rational equations Polynomial Functions Big Idea: Algebraic Thinking High school students extend analysis and use of functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. They factor polynomial expressions and quadratics of the 2 form 1x +bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.2.3 Assessed Students will: add, subtract, and multiply polynomial expressions; factor polynomial expressions using the greatest common monomial factor; and factor quadratic polynomials of the form ax2+bx+c, when a=1 and b and c are integers. DOK - 1 SUPPORTING CORE CONTENT MA-11-5.2.4 Supporting Students will factor quadratic polynomials, such as perfect square trinomials and quadratic polynomials of the form ax2 bx c when a≠1 and b and c are integers. MA-11-5.2.2 ADP Benchmark Students will evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-AT-U-3 What is the relationship between MA-HS-AT-S-VEO6 Students will understand that algebra polynomials and area? How do you Students will add, subtract and multiply polynomials. represents mathematical situations and know? structures for analysis and problem solving. MA-HS-AT-S-VEO12 How can a function have more than Students will evaluate polynomial and rational expressions and expressions containing one maximum or minimum? Students will understand that: radicals and absolute values at specified values of their variables. Polynomials can represent area and perimeter MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-M-S-MPA8 Students will explore periodic real-world phenomena, using technology (e.g., graphing calculator) as appropriate. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and three dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-DAP-S-CDS4 Students will determine regression coefficients, regression equations and correlation coefficients for bivariate data using technological tools. MA-HS-DAP-S-CDS5 Students will apply line-of-best fit equations for a set of two-variable data to make predictions. MA-HS-DAP-S-CDS6 Students will collect, organize and display bivariate data and use a curve of best fit as a model to make predictions. MA-HS-DAP-S-CDS7 Students will identify trends in bivariate data and find functions that model the data or transform the data, so that they can be modeled. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non-linear functions. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI19 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically or symbolically non-linear equations (e.g., absolute value, quadratic, exponential equations). MA-HS-AT-S-PRF4 Students will transform functions (e.g., arithmetically combining, composing and inverting commonly used functions), using technology on more complicated symbolic expressions. MA-HS-AT-S-PRF5 Students will understand and compare the properties of classes of functions (e.g., absolute value, step, exponential, polynomial, rational, logarithmic, periodic). MA-HS-AT-S-PRF7 Students will use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. MA-HS-AT-S-PRF8 Students will identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship. Critical Vocabulary monomial, polynomial, greatest common monomial factor, grouping, difference of squares, perfect square trinomials, rational expressions, radical expressions, integer exponents, rational exponents, perfect square, synthetic division Major Topics Long division of polynomials, synthetic division, finding zeros and factoring using synthetic division, adding functions, subtracting and multiplying polynomials, dividing and reducing polynomials, domain, graphing square root equations, solving radical equations, end behavior, degree, standard form, type, possible number of zeros Functions Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear and absolute value functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-5.1.5 Assessed Students will: determine if a relation is a function; determine the domain and range of a function (linear and quadratic); determine the slope and intercepts of a linear function; evaluate a function written in function notation for a specified rational number. DOK - 2 SUPPORTING CORE CONTENT MA-11-5.1.1 Assessed Students will identify and apply multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) to solve real-world or mathematical problems. DOK - 2 MA-11-5.1.6 Supporting Students will find the domain and range for absolute value functions. MA-11-5.1.7 Supporting Students will apply and use direct and inverse variation to solve real world and mathematical problems. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How do you solve real life problems Program of Studies Students will understand that quantitative by recognizing relationships MA-HS-G-S-TS1 literacy is a necessary tool to be an between cause and effect? Students will understand and represent transformations within a plane (translations, intelligent consumer and citizen. reflections, rotations and dilations) of figures by using sketches, coordinates, vectors, function How do you learn to recognize the MA-HS-DAP-U-3 notation, matrices and technology. pattern between cause and effect and Students will understand that graphical and represent that pattern? MA-HS-G-S-TS2 numerical techniques can be used to study Students will use various representations, including electronic displays, to understand the patterns and analyze data. How do you represent multiple effects of simple transformations within a plane and compositions of transformations. solutions and boundaries in real-life MA-HS-AT-U-1 situations? MA-HS-AT-S-PRF2 Students will understand that patterns, relations and functions are tools that help Students will understand relations and functions and use various representations for them. explain or predict real-world phenomena MA-HS-AT-S-PRF6 MA-HS-AT-U-2 Students will interpret representations of functions of two variables. Students will understand that there are relationships between and among patterns MA-HS-AT-S-PRF9 and functions, their representations and Students will determine whether a relationship given in symbolic or graphical form is a their properties. function. MA-HS-AT-U-3 MA-HS-AT-S-PRF11 Students will understand that algebra Students will understand functional notation and evaluate a function at a specified point in its represents mathematical situations and domain. structures for analysis and problem solving. MA-HS-AT-S-PRF12 MA-HS-AT-U-5 Students will combine functions by addition, subtraction, multiplication and compositions. Students will understand that functions are used to analyze change in various contexts MA-HS-AT-S-PRF13 and model real-world phenomena. Students will graph linear, absolute value, quadratic and exponential functions and identify MA-HS-AT-U-6 their key characteristics. Students will understand that functions can MA-HS-AT-S-EI2 be written in words, in a symbolic sentence Students will draw reasonable conclusions about a situation being modeled. or in a table or graph. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non-linear functions. MA-HS-AT-S-PRF20 Students will solve problems that have direct or inverse relationships for any variable. MA-HS-AT-S-PRF4 Students will transform functions (e.g., arithmetically combining, composing and inverting commonly used functions), using technology on more complicated symbolic expressions. MA-HS-AT-S-PRF8 Students will identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship. Critical Vocabulary function, relation, domain, range, inverse relation, graphs, equations, tables, coordinate pairs, mapping, formulas, independent and dependent variables, direct and inverse variation, constant of variation, vertical line test, linear equation, linear inequality, piecewise function, absolute value function, x-intercept, y-intercept, slope and rate, slope-intercept form, point-slope form, standard form, line of best fit, rate of change, function notation Major Topics Review of Solving Equations and solving inequalities, Solving absolute value inequalities, functions and relation, vertical line test, function notation, domain and range, review of graphing linear equations, review of parallel and perpendicular lines, review of finding intercepts, review of finding intercepts, review of writing linear equations, correlation, review of graphing inequalities, piecewise functions, graphing absolute value functions, composition of functions, domain and range of functions, inverse functions Exponential and Logarithmic Functions Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on exponential functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-4.2.3 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-5.1.1 Assessed Students will identify and apply multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) to solve real-world or mathematical problems. DOK – 1 MA-11-1.3.4 ADP Benchmark Students will recognize and solve problems that can be modeled using a finite geometric series, such as home mortgage problems and other compound interest problems. MA-11-5.1.4 ADP Benchmark Students will recognize and solve problems that can be modeled using an exponential function, such as compound interest problems. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 How do scientists use the Richter Scale to MA-HS-M-S-MPA8 Students will understand that numbers, calculate the strength of an earthquake? Students will explore periodic real-world phenomena, using technology (e.g., ways of representing numbers, relationships graphing calculator) as appropriate. If population growth is exponential, why do we among numbers and number systems are not run out of room on Earth? means of representing real-world quantities. MA-HS-G-S-CG6 Students will use Cartesian coordinates and other coordinate systems (e.g., MA-HS-DAP-U-3 navigational, polar, spherical systems) to analyze geometric situations. Students will understand that graphical and numerical techniques can be used to study MA-HS-G-S-CG7 patterns and analyze data. Students will investigate conjectures and solve problems involving two- dimensional figures and three dimensional objects represented graphically. MA-HS-AT-U-1 Students will understand that patterns, MA-HS-G-S-CG8 relations and functions are tools that help Students will use a variety of technological tools to explore and test conjectures explain or predict real-world phenomena. about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-AT-U-5 Students will understand that functions are MA-HS-DAP-S-CDS4 used to analyze change in various contexts Students will determine regression coefficients, regression equations and and model real-world phenomena. correlation coefficients for bivariate data using technological tools. Students will understand that: MA-HS-DAP-S-CDS5 Many real-life relationships are exponential Students will apply line-of-best fit equations for a set of two-variable data to or logarithmic make predictions. Exponential relationships grow quickly MA-HS-DAP-S-CDS6 over time and logarithmic relationships Students will collect, organize and display bivariate data and use a curve of grow slowly over time best fit as a model to make predictions. Exponential functions and logarithmic functions are inverses MA-HS-DAP-S-CDS7 Students will identify trends in bivariate data and find functions that model the data or transform the data, so that they can be modeled. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non- linear functions. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI19 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically or symbolically non-linear equations (e.g., absolute value, quadratic, exponential equations). MA-HS-AT-S-PRF4 Students will transform functions (e.g., arithmetically combining, composing and inverting commonly used functions), using technology on more complicated symbolic expressions. MA-HS-AT-S-PRF5 Students will understand and compare the properties of classes of functions (e.g., absolute value, step, exponential, polynomial, rational, logarithmic, periodic). MA-HS-AT-S-PRF7 Students will use a variety of symbolic representations, including recursive and parametric equations, for functions and relations. MA-HS-AT-S-PRF8 Students will identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationship. MA-HS-AT-S-PRF19 Students will relate the patterns in geometric sequences to exponential functions. Students will be able to. . . Solve problems that can be modeled using exponential or logarithmic functions Solve problems that can be modeled using a finite geometric series Critical Vocabulary exponential and logarithmic functions, natural log, simple and compound interest, half-life Major Topics Properties of exponents, introduce rational exponents, finding roots, reducing radicals with variables, solving equations with roots, graphing exponential functions, transformations of exponential functions, e, solving equations, logarithmic properties, logarithmic equations, simple and compound interest, concentration word problems APPLIED MATH Geometric Relationships Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. Big Idea: Geometry High school students expand analysis of two-dimensional figures and three-dimensional objects. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-3.1.1 Assessed Students will analyze and apply spatial relationships (not using Cartesian coordinates) among points, lines, and planes (e.g., betweenness of points, midpoint, segment length, collinear, coplanar, parallel, perpendicular, skew). DOK – 2 SUPPORTING CORE CONTENT MA-11-3.1.3 Assessed Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding, and alternate interior angles) in real-world or mathematical situations. DOK – 2 MA-11-3.3.1 Assessed Students will apply algebra or graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, finding midpoints, finding the distance between two points, finding the slope of a segment). DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-M-U-1 How do you systematically MA-HS-M-S-SM5 Students will understand that measurable provide yourself with a Students will compare and contrast the use of US Customary and metric systems of measurement. attributes of objects and the units, systems mathematical picture or diagram and processes of measurement are to represent a problem and solve MA-HS-M-S-MPA1 powerful tools for making sense of the it by relating it to algebraic Students will apply units of measurements of physical quantities correctly in expressions, world around them. representations? equations and problem solutions that involve measurement. How do you interpret the world MA-HS-M-U-2 MA-HS-G-S-SR1 in a spatial sense? Students will understand that numerical Students will identify and apply the definitions, properties and theorems about line segments, rays values associated with measurements of How do you measure attributes and angles and use them to prove theorems in Euclidean geometry, solve problems and perform physical quantities must be assigned units of objects in your world? basic geometric constructions using a straight edge and a compass. of measurement or dimensions. How is geometric language MA-HS-G-S-SR2 different from other MA-HS-M-U-3 Students will identify and apply properties and theorems about parallel and perpendicular lines mathematical language? and use them to prove theorems and to perform constructions. Students will understand that measurements are determined by using appropriate techniques, tools, formulas MA-HS-G-S-SR3 and degree of accuracy needed for the Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, situation. supplementary, corresponding and alternate interior angles) in real-world or mathematical situations. MA-HS-G-U-1 MA-HS-G-S-SR6 Students will understand that Students will analyze and apply spatial relationships (not using Cartesian coordinates) among characteristics and properties of two- points, lines and planes (e.g., “betweenness” of points, midpoint, segment length, collinear, dimensional figures and three-dimensional coplanar, parallel, perpendicular, skew). objects describe the world and are used to develop mathematical arguments about MA-HS-G-S-CG3 geometric relationships and to evaluate Students will find the distance between two points using their coordinates and the Pythagorean the arguments of others. theorem or the distance formula. MA-HS-G-U-2 MA-HS-G-S-CG5 Students will understand that Students will find the midpoint of a segment when the coordinates of the endpoints are identified. representational systems, including coordinate geometry, are means for MA-HS-G-S-CG6 specifying locations and describing spatial Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, relationships and are organizers for spherical systems) to analyze geometric situations. making sense of the world around them. Students will understand that. . . MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and The foundation of Euclidean geometry is three-dimensional objects represented graphically. the undefined terms point, line, and plane. Unknown angle and segment MA-HS-G-S-CG8 measurements can be found through Students will use a variety of technological tools to explore and test conjectures about slope, geometric relationships. midpoints and other geometric ideas that can be expressed using the Cartesian plane Specific relationships (among geometric MA-HS-G-S-SR12 shapes) guide how the world fits together. Students will use geometric models and ideas to gain insights into and answer questions in other areas of mathematics and into other disciplines and areas of interest, such as art and architecture. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary Point, line, plane, collinear, coplanar, segment, intersection, ray, angle, vertex, right angles, acute angles, obtuse angles, adjacent angles, linear pair, vertical pair, complementary angles, supplementary angles, corresponding angles, and alternate interior angles, alternate exterior angles, Consecutive Exterior Angles, Consecutive Interior Angles, parallel, perpendicular, transversal, bisector, coordinate geometry, between, distance, midpoint, slope Major Topics Degrees in a triangle, triangle inequality, parallel lines and transversals, angle pair relationships Linear Equations Big Idea: Data Analysis High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear and quadratic. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics POWER STANDARD MA-11-4.2.3 Assessed Students will: determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. (linear) DOK – 3 SUPPORTING CORE CONTENT MA-11-5.3.1 Assessed Students will model or solve first degree, single variable equations and inequalities, including absolute value, based in real-world and mathematical problems, and will graph the solutions on a number line. DOK – 2 MA-11-5.3.2 Supporting Students will solve for a specified variable in a multivariable equation. MA-11-1.4.1 Assessed Students will and will explain how slope determines a rate of change in linear functions representing real-world problems. DOK – 2 MA-11-5.3.3 Assessed Students will model, solve, and graph first-degree, two-variable equations and inequalities in real-world and mathematical problems. DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How can linear equations help us use MA-HS-NPO-S-NO13 Students will understand that quantitative patterns? Students will use concrete, pictorial and abstract models to develop and/or literacy is a necessary tool to be an intelligent generalize a procedure. How are linear equations used to make consumer and citizen. real-life decisions? MA-HS-NPO-S-RP2 Students will translate real-world proportional relationships into mathematical MA-HS-DAP-U-3 How can linear functions be represented expressions and vice versa. Students will understand that graphical and and what is the relationship between the numerical techniques can be used to study various representations? How do you MA-HS-NPO-S-RP3 patterns and analyze data. know? Why do we need different Students will represent slope graphically, numerically and symbolically and representations? relate it to a graph of an equation based on a realistic situation. What types of situations are better suited MA-HS-M-S-MPA8 MA-HS-AT-U-2 for linear inequalities rather than linear Students will explore periodic real-world phenomena, using technology (e.g., Students will understand that there are equations? graphing calculator) as appropriate. relationships between and among patterns and functions, their representations and their MA-HS-G-S-CG1 properties. Students will express the intuitive concept of the “slant” of a line as slope, use the coordinates of two points on a line to determine its slope and use slope to MA-HS-AT-U-3 express the parallelism and perpendicularity of lines. Students will understand that algebra represents mathematical situations and structures for MA-HS-G-S-CG2 analysis and problem solving. Students will describe a line by a linear equation. MA-HS-G-S-CG6 MA-HS-AT-U-4 Students will use Cartesian coordinates and other coordinate systems (e.g., Students will understand that real-world navigational, polar, spherical systems) to analyze geometric situations. situations can be represented using mathematical models to analyze quantitative MA-HS-G-S-CG7 relationships. Students will investigate conjectures and solve problems involving two- dimensional figures and three-dimensional objects represented graphically. MA-HS-AT-U-5 MA-HS-G-S-CG8 Students will understand that functions are used Students will use a variety of technological tools to explore and test conjectures to analyze change in various contexts and about slope, midpoints and other geometric ideas that can be expressed using the model real-world phenomena. Cartesian plane MA-HS-AT-U-6 MA-HS-AT-S-EI1 Students will understand that functions can be Students will write equivalent forms of equations, inequalities and systems of written in words, in a symbolic sentence or in a equations and inequalities and solve them with fluency - mentally or with paper table or graph. and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will understand that: Students will draw reasonable conclusions about a situation being modeled. Correlation does not mean causation. MA-HS-AT-S-EI5 Slope is a rate of change. Students will solve an equation involving several variables for one variable in terms of the others. MA-HS-AT-S-EI9 Students will approximate and interpret rates of change from graphical and numerical data. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-EI10 Students will graph a linear equation and demonstrate that it has a constant rate of change. MA-HS-AT-S-EI11 Students will relate the coefficients of a linear equation and the slope and x- and y-intercepts of its graph. MA-HS-AT-S-EI13 Students will graph the solution set of a linear inequality and identify whether the solution set is an open or closed half-plane. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. Critical Vocabulary linear equation, coordinate plane, x-intercept, y-intercept, slope, slope-intercept form, scatterplot, line of best fit, rate of change, independent, dependent, domain, range Major Topics Quadrants, graphing points, graph lines using t-chart, x-y intercepts, graph vertical and horizontal lines, graph line given slope and point, graph using y=mx+b Radical and Exponent Properties Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Solving quadratic equations produces a working knowledge of complex numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Algebraic Thinking High school students use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. 2 They factor polynomial expressions and quadratics of the form 1x +bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving addition, subtraction, multiplication, division, absolute value, integer exponents, roots (square, cube) DOK – 2 SUPPORTING CORE CONTENT MA-11-1.1.3 Supporting Students will use scientific notation to express very large or very small quantities. MA-11-5.2.1 Assessed Students will apply order of operations, real number properties (identity, inverse, commutative, associative, distributive, closure), and rules of exponents (integer) to simplify algebraic expressions. DOK – 1 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 How could estimating answer MA-HS-NPO-S-E7 Students will understand that numbers, involving a radical or a Students will estimate solutions to problems with real numbers (including very large and very small ways of representing numbers, fraction cause a problem? quantities) in both realistic and mathematical situations. relationships among numbers and number systems are means of MA-HS-NPO-S-NO3 representing real-world quantities. Students will multiply and divide numbers expressed in scientific notation MA-HS-NPO-U-3 MA-HS-NPO-S-NO4 Students will understand that computing Students will apply absolute value, integer exponents, roots and factorials to solve problems fluently and accurately with real numbers and making reasonable MA-HS-NPO-S-NO9 estimates increases the ability to solve Students will solve realistic problems to a specified degree of accuracy. realistic problems encountered in everyday life. Students will understand that: Estimation can has caused large errors in fields such as space exploration when repeated numerous times throughout a large problem. Radicals have many of the same properties as variables. Exponents helps us express extreme quantities Critical Vocabulary rational numbers, irrational numbers, real numbers, expression, monomial, polynomial, rational expressions, radical expressions, integer exponents, rational exponents, perfect square Major Topics Reduce radicals, multiply radicals, add/subtract radicals, multiply monomials, divide monomials, negative exponents, multiply polynomials, find zeros of polynomials, difference of two squares, factor with a>1 Right Triangle Properties Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve realistic problems. Big Idea: Geometry High school students expand analysis of two-dimensional figures. Big Idea: Algebraic Thinking High school students combine simple rational expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-2.1.3 Assessed Students will apply definitions and properties of right triangle relationships (right triangle trigonometry and the Pythagorean theorem) to determine length and angle measures to solve real-world and mathematical problems. DOK – 3 SUPPORTING CORE CONTENT MA-11-2.1.4 ADP Benchmark Students will apply special right triangles and the converse of the Pythagorean theorem to solve real-world problems. MA-11-1.3.1 Assessed Students will solve real-world problems to specified accuracy levels by simplifying real number expressions involving roots (square, cube) DOK - 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-3 How do diagrams help us organize MA-HS-NPO-S-NS4 Students will understand that computing information? Students will explore vectors and matrices as systems that have some of the properties fluently and accurately with real of the real number system. What are possible methods of measurement numbers and making reasonable available to determine distances and angles estimates increases the ability to solve MA-HS-NPO-S-NO4 (without using direct measurement e.g. realistic problems encountered in Students will apply absolute value, integer exponents, roots and factorials to solve ruler and protractor)? everyday life. problems What is the purpose of right triangles in our MA-HS-M-U-1 world? MA-HS-NPO-S-NO11 Students will understand that measurable Students will develop an understanding of the properties and representations for the attributes of objects and the units, addition and multiplication of vectors and matrices. systems and processes of measurement are powerful tools for making sense of MA-HS-M-S-MPA5 the world around them. Students will explore the relationships between the right triangle trigonometric functions, using technology (e.g., graphing calculator) as appropriate. MA-HS-M-U-2 Students will understand that numerical MA-HS-M-S-MPA6 values associated with measurements of Students will apply definitions and properties of right triangle relationships (basic right physical quantities must be assigned triangle trigonometry and the Pythagorean theorem) to determine length and angle units of measurement or dimensions. measures to solve realistic problems MA-HS-M-U-3 MA-HS-M-S-MPA7 Students will understand that Students will apply special right triangles and the converse of the Pythagorean theorem measurements are determined by using to solve realistic problems. appropriate techniques, tools, formulas MA-HS-G-S-CG6 and degree of accuracy needed for the Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, situation. polar, spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and three-dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary Right triangle, Isosceles triangle, Equilateral Triangle, Leg, Hypotenuse, Special Right triangles, Trigonometric ratios, Sine, Cosine, Tangent, Angles of Elevation & Depression Major topics Pythagorean Theorem word problems, solving side of a right triangle using trig ratios, angles of elevation and depression INTERMEDIATE MATH Linear Equations Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear and absolute value functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-4.2.3 Assessed Students will: determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. (linear) DOK – 3 SUPPORTING CORE CONTENT MA-11-5.3.1 Assessed Students will model, solve, and graph first degree, single variable equations and inequalities, including absolute value, in real-world and mathematical problems, and will graph the solutions on a number line. DOK – 2 MA-11-5.3.2 Supporting Students will solve for a specified variable in a multivariable equation. MA-11-1.4.1 Assessed Students will apply proportional reasoning to solve real-world problems (e.g., those involving slope and rate) and will explain how slope determines a rate of change in linear functions representing real-world problems. DOK – 2 MA-11-5.3.3 Assessed Students will model, solve, and graph first degree, two-variable equations and inequalities in real-world and mathematical problems. DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 How can linear equations help us use MA-HS-NPO-S-RP2 Students will understand that patterns? Students will translate real-world proportional relationships into mathematical expressions quantitative literacy is a necessary tool and vice versa. How are linear equations used to make to be an intelligent consumer and citizen. real-life decisions? MA-HS-NPO-S-RP3 Students will represent slope graphically, numerically and symbolically and relate it to a How can linear functions be represented MA-HS-DAP-U-3 graph of an equation based on a realistic situation. and what is the relationship between the Students will understand that graphical various representations? How do you and numerical techniques can be used MA-HS-M-S-MPA8 know? Why do we need different to study patterns and analyze data. Students will explore periodic real-world phenomena, using technology (e.g., graphing representations? calculator) as appropriate. What types of situations are better suited MA-HS-AT-U-2 for linear inequalities rather than linear MA-HS-G-S-CG1 Students will understand that there are equations? Students will express the intuitive concept of the “slant” of a line as slope, use the relationships between and among coordinates of two points on a line to determine its slope and use slope to express the patterns and functions, their parallelism and perpendicularity of lines. representations and their properties. MA-HS-G-S-CG2 MA-HS-AT-U-3 Students will describe a line by a linear equation. Students will understand that algebra represents mathematical situations and MA-HS-G-S-CG6 structures for analysis and problem Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, solving. polar, spherical systems) to analyze geometric situations. MA-HS-AT-U-4 MA-HS-G-S-CG7 Students will understand that real- Students will investigate conjectures and solve problems involving two-dimensional world situations can be represented figures and three-dimensional objects represented graphically. using mathematical models to analyze quantitative relationships. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about MA-HS-AT-U-5 slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane Students will understand that functions are used to analyze change in various MA-HS-AT-S-EI1 contexts and model real-world Students will write equivalent forms of equations, inequalities and systems of equations phenomena. and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases. MA-HS-AT-U-6 Students will understand that functions MA-HS-AT-S-EI2 can be written in words, in a symbolic Students will draw reasonable conclusions about a situation being modeled. sentence or in a table or graph. MA-HS-AT-S-EI5 Students will understand that: Students will solve an equation involving several variables for one variable in terms of the Correlation does not mean causation. others. Slope is a rate of change. MA-HS-AT-S-EI9 Students will approximate and interpret rates of change from graphical and numerical data. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF10 Students will determine the domain of a function represented in either symbolic or graphical form. MA-HS-AT-S-PRF20 Students will solve problems that have direct or inverse relationships for any variable. MA-HS-AT-S-EI10 Students will graph a linear equation and demonstrate that it has a constant rate of change. MA-HS-AT-S-EI11 Students will relate the coefficients of a linear equation and the slope and x- and y- intercepts of its graph. MA-HS-AT-S-EI13 Students will graph the solution set of a linear inequality and identify whether the solution set is an open or closed half-plane. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. Critical Vocabulary function, relation, domain, range, inverse relation, graphs, equations, tables, coordinate pairs, mapping, formulas, independent and dependent variables, direct and inverse variation, constant of variation, vertical line test, linear equation, linear inequality, piecewise function, absolute value function, x-intercept, y-intercept, slope and rate, slope- intercept form, point-slope form, standard form, line of best fit, rate of change, function notation Major Topics Review of Solving Equations and solving inequalities, Solving absolute value inequalities, functions and relation, vertical line test, function notation, domain and range, review of graphing linear equations, review of parallel and perpendicular lines, review of finding intercepts, review of finding intercepts, review of writing linear equations, correlation, review of graphing inequalities, piecewise functions, graphing absolute value functions, composition of functions, domain and range of functions, inverse functions Systems of Equations and Inequalities Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. They understand large and small numbers and their representations. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on linear functions. They use rules and properties to simplify algebraic expressions. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. POWER STANDARD MA-11-5.3.4 Assessed Students will model and graph systems of linear equations (two equations in two variables) in real-world and mathematical problems. DOK - 3 SUPPORTING CORE CONTENT MA-11-5.3.5 Supporting Students will write, graph, and solve systems of linear inequalities (two inequalities in two variables) based on real world or mathematical situations and interpret the solution. MA-11-4.1.3 Supporting Students will represent real-world data using matrices and will use matrix addition, subtraction, multiplication (with matrices no larger than 2x2), and scalar multiplication to solve real-world problems. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-NPO-U-1 How are systems of equations used in real MA-HS-NPO-S-NS4 Students will understand that numbers, life? Students will explore vectors and matrices as systems that have some of the properties ways of representing numbers, of the real number system. How can I represent a real life situation relationships among numbers and number algebraically? MA-HS-NPO-S-NS5 systems are means of representing real- Students will compare and contrast number systems, including complex numbers as world quantities. How do companies maximize profit and solutions to quadratic equations that do not have real solutions. minimize cost? MA-HS-AT-U-6 MA-HS-NPO-S-PNO3 Students will understand that functions can Students will compare and contrast the number systems according to their properties. be written in words, in a symbolic sentence MA-HS-NPO-S-NO11 or in a table or graph. Students will develop an understanding of the properties and representations for the addition and multiplication of vectors and matrices. Students will understand that: Linear programming can be used to MA-HS-G-S-CG6 maximize profit or minimize cost Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, spherical systems) to analyze geometric situations. Matrices are useful in solving systems of equations MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional Finding limits and boundaries are valuable figures and three-dimensional objects represented graphically. in business, science, city planning, etc MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-AT-S-EI1 Students will write equivalent forms of equations, inequalities and systems of equations and inequalities and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI6 Students will solve systems of two linear equations in two variables. MA-HS-AT-S-EI7 Students will solve systems of three linear equations in three variables. MA-HS-AT-S-EI12 Students will relate a solution of a system of two linear equations in two variables and the graphs of the corresponding lines. MA-HS-AT-S-EI14 Students will graph the solution set of a system of two or three linear inequalities. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI17 Students will write and solve linear sentences, describing real-world situations by using and relating formulas, tables, graphs and equations. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. Critical Vocabulary parallel lines, perpendicular lines, system of linear equations and inequalities, substitution, elimination, linear programming, matrix, feasible region, identity matrix, determinant, inverse matrix Major Topics Solving a system of linear equations by graphing, solving a system of linear equations by substitution, solving a system of linear equations by elimination, graphing a system of inequalities, linear programming, adding and subtracting matrices, multiplying matrices by a scalar, naming matrices, multiplying matrices, solving systems using matrices Quadratics Big Idea: Number Properties and Operations High school students should enter high school with a strong background in rational numbers and numerical operations and expand this to real numbers. Solving quadratic equations produces a working knowledge of complex numbers. This becomes the foundation for algebra and working with algebraic symbols. They understand large and small numbers and their representations, powers and roots. They compare and contrast properties of numbers and number systems and develop strategies to estimate the results of operations on real numbers. Students will use and understand the limitations of, graphing calculators and computer spreadsheets appropriately as learning tools. Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They relate curve-of-best-fit with two-variable data and determine a line-of-best-fit for a given set of data. Big Idea: Algebraic Thinking High school students extend analysis and use of functions and focus on quadratic functions. They explore parametric changes on graphs of functions. They use rules and properties to simplify algebraic expressions. They combine simple rational expressions and simple polynomial expressions. They factor polynomial 2 expressions and quadratics of the form 1x +bx+c. Academic Expectations 2.7 Students understand number concepts and use numbers appropriately and accurately. 2.8 Students understand various mathematical procedures and use them appropriately and accurately. 2.11 Students understand mathematical change concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use statistics and probability. POWER STANDARD MA-11-4.2.3 Assessed Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data; and apply line of best fit equations to make predictions within and beyond a given set of data. DOK – 3 SUPPORTING CORE CONTENT MA-11-5.3.6 Assessed Students will model, solve, and graph quadratic equations in real-world and mathematical problems. DOK – 2 Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-DAP-U-1 What patterns occur when objects are MA-HS-NPO-S-NS5 Students will understand that quantitative thrown or projected? Students will compare and contrast number systems, including complex numbers as literacy is a necessary tool to be an solutions to quadratic equations that do not have real solutions. How do you determine the most or the intelligent consumer and citizen. least of a given situation? MA-HS-NPO-S-NO5 Students will determine a specific term of a sequence given an explicit formula. MA-HS-DAP-U-3 What are examples of problems with one Students will understand that graphical and or more solutions? MA-HS-NPO-S-NO2 numerical techniques can be used to study Students will add, subtract and multiply complex numbers. patterns and analyze data. What relationships exist between a parabola and its equation? MA-HS-NPO-S-NO13 Students will use concrete, pictorial and abstract models to develop and/or generalize a MA-HS-AT-U-1 procedure. Students will understand that patterns, relations and functions are tools that help MA-HS-M-S-MPA8 explain or predict real-world phenomena Students will explore periodic real-world phenomena, using technology (e.g., graphing calculator) as appropriate. MA-HS-AT-U-4 Students will understand that real-world MA-HS-G-S-CG6 situations can be represented using Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, mathematical models to analyze polar, spherical systems) to analyze geometric situations. quantitative relationships. MA-HS-G-S-CG7 Students will investigate conjectures and solve problems involving two-dimensional figures and three-dimensional objects represented graphically. MA-HS-G-S-CG8 Students will use a variety of technological tools to explore and test conjectures about slope, midpoints and other geometric ideas that can be expressed using the Cartesian plane MA-HS-AT-S-VEO5 Students will understand the properties of integer exponents and roots and apply these properties to simplify algebraic expressions. MA-HS-AT-S-VEO6 Students will add, subtract and multiply polynomials. MA-HS-AT-S-VEO7 Students will divide a polynomial by a first-degree polynomial. MA-HS-AT-S-VEO8 Students will factor polynomials by removing the greatest common factor. MA-HS-AT-S-VEO9 Students will factor quadratic polynomials. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. MA-HS-AT-S-EI8 Students will solve quadratic equations in one variable. MA-HS-AT-S-PRF14 Students will recognize and solve problems that can be modeled using linear, absolute value, quadratic or exponential functions. MA-HS-AT-S-PRF3 Students will analyze functions by investigating rates of change, intercepts, zeros, asymptotes and local and global behavior. MA-HS-AT-S-PRF15 Students will extend the ideas of transformations and parametric changes of linear function, such as vertical and horizontal shifts, to transformations of non-linear functions. MA-HS-AT-S-EI15 Students will read information and draw conclusions from graphs and identify properties of a graph that provide useful information about the original problem. MA-HS-AT-S-EI16 Students will graph a quadratic function and understand the relationship between its real zeros and the x-intercepts of the graph. MA-HS-AT-S-EI18 Students will recognize and solve problems that can be modeled using a linear equation in one variable, a quadratic equation or a system of linear equations. MA-HS-AT-S-EI19 Students will use the skills learned to solve linear equations and inequalities to solve numerically, graphically or symbolically non-linear equations (e.g., absolute value, quadratic, exponential equations). MA-HS-AT-S-EI20 Students will use graphing technology to explore the meaning of quadratic equations with complex solutions. Critical Vocabulary Minimum, maximum, intercepts, zeros, Discriminant, complex number, factor, standard form, intercept form, vertex form Major Topics Axis of symmetry, Standard form, finding the vertex, using the vertex and y-intercept to find another point, finding the axis of symmetry, using vertex form, graphing, using x- intercept form, changing between forms, finding all parts of the parabola, factoring common term, factoring when a=1, factoring difference of two squares, solving for zeros, factoring when a>1, factor by grouping, reducing radicals, rationalizing denominators, completing the square, quadratic equation, height formula, graphing inequalities, modeling, complex numbers, finding the equation given 2 intercepts and a point, finding the equation given the vertex and a point, finding the equation given 3 points Area and Volume Big Idea: Measurement High school students continue to measure and estimate measurements including fractions and decimals. They use formulas to find surface areas and volumes. They use US Customary and metric units of measurement. They use the Pythagorean theorem and other right triangle relationships to solve realistic problems. Big Idea: Geometry High school students expand analysis of two-dimensional figures and three-dimensional objects. They extend work with similar figures, including proportionality. Big Idea: Data Analysis and Probability High school students extend data representations, interpretations and conclusions. They describe data distributions in multiple ways and connect data gathering issues with data interpretation issues. They compare and contrast theoretical and experimental probability. Academic Expectations 2.9 Students understand space and dimensionality concepts and use them appropriately and accurately. 2.10 Students understand measurement concepts and use them appropriately and accurately. 2.12 Students understand mathematical structure concepts including the properties and logic of various mathematical systems. 2.13 Students understand and appropriately use probability. POWER STANDARD MA-11-2.1.1 Assessed Students will determine the surface area and volume of right rectangular prisms, pyramids, cylinders, cones, and spheres in real-world and mathematical problems. (strong emphasis on application problems) DOK – 2 SUPPORTING CORE CONTENT MA-11-2.1.2 Assessed Students will describe how a change in one or more dimensions of a geometric figure affects the perimeter, area, and volume of the figure. DOK – 3 MA-11-3.1.5 Assessed Students will classify and apply properties of three-dimensional geometric figures (e.g., number of edges, faces, vertices, sum of interior and exterior angle measures). DOK – 2 MA-11-3.1.10 Students will describe the intersection of a plane with a three-dimensional figure MA-11-3.1.11 ADP Benchmark Students will visualize solids and surfaces in three-dimensional space when given two-dimensional representations (e.g., nets, multiple views) and create two-dimensional representations for the surfaces of three-dimensional objects. MA-11-4.4.3 Supporting Students will represent probabilities in multiple ways, such as fractions, decimals, percentages, and geometric area models. Understandings/ Big Ideas Essential Questions Knowledge and Skills/ Learning Targets MA-HS-M-U-1 What life situations might require us MA-HS-M-S-MPA1 Students will understand that to calculate surface area or volume? Students will apply units of measurements of physical quantities correctly in expressions, measurable attributes of objects and equations and problem solutions that involve measurement. How can we break a 3-dimensional the units, systems and processes of MA-HS-M-S-MPA4 object into something we can measure measurement are powerful tools for Students will describe how change in one or more dimensions of a geometric figure or object with 2-dimensional tools? making sense of the world around affects the perimeter, circumference, area and/or volume of the figure or object. them. What effects does doubling the MA-HS-M-S-SM3 dimensions of an object have on the Students will make decisions about units and scales that are appropriate for problem solving MA-HS-M-U-2 surface area and volume? situations involving measurement. Students will understand that MA-HS-M-S-MPA2 numerical values associated with Students will analyze precision, accuracy and approximate error in measurement situations measurements of physical quantities MA-HS-M-S-MPA3 must be assigned units of Students will determine the surface area and volume of right rectangular prisms, pyramids, measurement or dimensions. cylinders, cones and spheres in realistic problems. MA-HS-G-S-SR10 MA-HS-M-U-3 Students will visualize solids and surfaces in three-dimensional space when given two- Students will understand that dimensional representations and create two-dimensional representations for the surfaces of three- measurements are determined by dimensional objects. using appropriate techniques, tools, MA-HS-G-S-CG6 formulas and degree of accuracy Students will use Cartesian coordinates and other coordinate systems (e.g., navigational, polar, needed for the situation. spherical systems) to analyze geometric situations. MA-HS-G-S-CG7 MA-HS-G-U-1 Students will investigate conjectures and solve problems involving two-dimensional figures and Students will understand that three-dimensional objects represented graphically. characteristics and properties of two- MA-HS-G-S-CG8 dimensional figures and three- Students will use a variety of technological tools to explore and test conjectures about slope, dimensional objects describe the midpoints and other geometric ideas that can be expressed using the Cartesian plane world and are used to develop MA-HS-G-S-SR11 mathematical arguments about Students will draw and construct representations of two-dimensional figures and three- geometric relationships and to dimensional objects using a variety of tools. evaluate the arguments of others. MA-HS-G-S-SR12 Students will use geometric models and ideas to gain insights into and answer questions in other MA-HS-G-U-5 areas of mathematics and into other disciplines and areas of interest, such as art and architecture. Students will understand that MA-HS-DAP-S-P15 visualization, spatial reasoning and Students will represent probabilities in multiple ways (e.g., fractions, decimals, percentages, geometric relationships model real- geometric area models). world situations. MA-HS-AT-S-EI2 Students will draw reasonable conclusions about a situation being modeled. Critical Vocabulary area, perimeter, circumference, arc length, sector, apothem, diameter, radius, pi, surface area, volume, solids, sides, height, slant height, edge, face, vertices, net, ratio, proportion, 2-dimensional, 3-dimensional, polyhedron, rectangular prisms & pyramids, triangular prisms and pyramids, regular polygonal prisms & pyramids, cones, cylinders, and spheres Major Topics Estimating Area of Irregular Shapes, Area of Triangles, Parallelograms, Trapezoids, and Kites, Area of Regular Polygons, Circumference, Arc Length, Area of Circles and Sectors, Applied area problems, geometric probability, polyhedrons, Isometric Drawings, Orthographic Drawings, Net Drawings, Surface area and Lateral area of Prisms and Cylinders, Volume of Prisms and Cylinders, Surface Area and Lateral area of pyramids and cones, volume of pyramids and cones, Area and Volume of Spheres, Proportions with Area, Perimeter and volume of solids