# ALGEBRA I by 7Ily2Y

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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.

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.

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
Students will design simple experiments or investigations to collect data to answer questions of interest.
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.
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.
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.
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.

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.

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.
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.

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
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.
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
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
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.

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
Students will use spatial relationships to prove basic theorems.
Students will use angle relationships to prove basic theorems.
Students will identify, explain the necessity of, and give examples of definitions, axioms, and theorems.
Students will recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true.
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.

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.
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
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.
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
Students will prove triangles congruent and similar.
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
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.

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
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.
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
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.

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
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.
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
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.,
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.

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
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

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.

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
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
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,
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.

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
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
Students will design simple experiments or investigations to collect data to answer questions of interest.
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.
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,
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

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.

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
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.

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
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.

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.
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

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,

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.
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.

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

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.
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.,

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.

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
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.

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
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

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.

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
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.

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
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.
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
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.

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
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

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.

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
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
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,
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.

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
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

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