High School Math Curriculum
Algebra 1
Algebra 1 Pacing and Units of Study
How can Algebra help us beyond school? As we explore situations, what do we notice? Are there patterns of interest? If there are, how can we describe these patterns and how can they help us make predictions and decisions? What language and mathematical ideas do we use to increase our precision? As new topics are introduced, students will work with informal descriptions of contextual data and generalize what they see. It is important to allow the students time to describe the patterns without the burden of using formal symbols or vocabulary. The formalization of these ideas is developed as students generalize concepts through the exploration of specific functions. This generalization leads towards proficiency with abstract symbolic manipulation. Students will complete the course with conceptual understanding and procedural skills for success in continued study of advanced mathematics.
Quarter 1
Unit 1: Using the Data Cycle with Bivariate Data
While exploring patterns, students will use the data cycle to structure their process. Relationships in bivariate data will be the basis of formulating investigative questions and collecting or acquiring data. Tables and scatterplots will provide representations of the data for students to begin making observations and communicating inferences about the patterns and relationships.
Standards Covered: A.EO.1, A.F.2, A.ST.1
Unit 2: Linear Functions in Context
The focus of Unit 2 will be on generalized linear relationships; recognizing there is a constant rate of change (slope) and a starting point (y-intercept). Students will also recognize limitations (domain and range) of the model in the context of real-world data sets and make predictions using the model (finding values of a function). This unit serves a conceptual transition from the open-ended exploration of bivariate data in Unit 1 and a more formal, rigorous approach to linear equations and inequalities in Unit 3.
Standards Covered: A.EO.1, A.ST.1, A.F.1
Assessment Window: September 9 - September 13, 2024
Unit 3: Linear Functions
Students will build upon contextual and generalized concepts as they represent linear equations and inequalities algebraically. This will include comparison of various forms of linear functions (slope-intercept, standard, point-slope) to explore the benefits of each approach. Students will formalize their understanding of linear functions by interpreting various forms of a linear model with and without context.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A.F.2
Standards Covered: A.F.1, A.ST.1, A.F.1
Assessment Window: October 14 - October 18, 2024
Begin Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1
Quarter 2
Continue Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1
Assessment Window: November 25 - November 29, 2024
Unit 5: Non-Linear Expressions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Standards Covered: A.EO.1, A.EO.3, A.EO.4
Assessment Window: December 16 - December 20, 2024
Begin Unit 6: Exponential Functions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Standards Covered: A.F.2, A.ST.1, A.F.2
Quarter 3
Unit 6: Exponential Functions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Standards Covered: A.F.2, A.ST.1, A.F.2
Assessment Window: February 3 – 7, 2025
Unit 7: Operations with Polynomials
Students will expand their analytical skills to include polynomial operations such as sums, differences, products, quotients, and factoring. Emphasis will be placed on using concrete objects, along with pictorial and symbolic models, as well as applying the distributive property and area models to visualize the relationship between multiplication and factoring. Students will demonstrate the equality of quadratic expressions in multiple forms.
Standards Covered: A.EO.2
Assessment Window: March 10 – 14, 2025
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, x-intercepts, y-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations.
Standards Covered: A.EI.3, A.F.2, A.ST.1
Quarter 4
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, 𝑥-intercepts, 𝑦-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations.
Standards Covered: A.EI.3, A.F.2, A.ST.1
Assessment Window: Week of April 7-11, 2025
Unit 9: Function Synthesis
This final unit solidifies the connections and distinctions between the types of functions studied throughout the course. Students will refine their understanding of transformational graphing for quadratic and exponential functions in the forms 𝑓(𝑥) + 𝑘 and 𝑘𝑓(𝑥). They will now compare and contrast the characteristics of graphs across all three function types: linear, quadratic, and exponential. Additionally, the unit revisits the data patterns introduced in Unit 1, as students analyze data sets and scatterplots to identify whether a linear or quadratic model provides the best fit.
Standards Covered: A.F.2, A.ST.1, A.F.2, A.ST.1
Assessment Window: Week of April 28 – May 2, 2025
Advanced Algebra 1
Advanced Algebra 1 Pacing and Units of Study
How can Algebra help us beyond school? As we explore situations, what do we notice? Are there patterns of interest? If there are, how can we describe these patterns and how can they help us make predictions and decisions? What language and mathematical ideas do we use to increase our precision? As new topics are introduced, students will work with informal descriptions of contextual data and generalize what they see. It is important to allow the students time to describe the patterns without the burden of using formal symbols or vocabulary. The formalization of these ideas is developed as students generalize concepts through the exploration of specific functions. This generalization leads towards proficiency with abstract symbolic manipulation. Students will complete the course with the conceptual understanding and procedural skills for success in continued study of advanced mathematics.
Quarter 1
Unit 1: Using the Data Cycle with Bivariate Data
While exploring patterns, students will use the data cycle to structure their process. Relationships in bivariate data will be the basis of formulating investigative questions and collecting or acquiring data. Tables and scatterplots will provide representations of the data for students to begin making observations and communicating inferences about the patterns and relationships.
Standards Covered: A.EO.1, A.F.2, A.ST.1
Unit 2: Linear Functions in Context
The focus of Unit 2 will be on generalized linear relationships; recognizing there is a constant rate of change (slope) and a starting point (y-intercept). Students will also recognize the limitations (domain and range) of the model in the context of real-world data sets and make predictions using the model (finding values of a function). This unit serves a conceptual transition from the open-ended exploration of bivariate data in Unit 1 and a more formal, rigorous approach to linear equations and inequalities in Unit 3.
Standards Covered: A.EO.1, A.ST.1, A.F.1
Assessment Window: September 9 - September 13, 2024
Unit 3: Linear Functions
Students will build upon contextual and generalized concepts as they represent linear equations and inequalities algebraically. This will include a comparison of various forms of linear functions (slope-intercept, standard, point-slope) to explore the benefits of each approach. Students will formalize their understanding of linear functions by interpreting various forms of a linear model with and without context.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A.F.2, A.F.1
Assessment Window: October 14 - October 18, 2024
Begin Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine their understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A2.EI.1
Quarter 2
Continue Unit 4: Solving Linear Equations, Inequalities, and Systems
The abstraction of algebra continues in this unit as students expand their ability to algebraically and graphically represent, solve, explain, and interpret solutions to linear equations and inequalities (including systems). Students refine understanding of equality within algebraic situations, and the preservation of the relationship between expressions when operating on equations and inequalities.
Standards Covered: A.EO.1, A.EI.1, A.EI.2, A.ST.1, A2.EI.1
Assessment Window: November 25 - November 29, 2024
Unit 5: Non-Linear Expressions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Standards Covered: A.EO.1, A.EO.3, A.EO.4, A2.EO.2
Assessment Window: January 6 - January 31, 2025
Begin Unit 6: Exponential Functions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given placement values.
Standards Covered: A.F.2, A.ST.1, A.F.2
Quarter 3
Unit 6: Exponential Functions
Students will move from contextualized situations in units 2 - 4 to abstract symbolic manipulation. Translating between verbal and algebraic expressions will direct students’ need to simplify expressions with radicals and exponents, including rational exponents. Students will continue to develop the idea of equivalence by deriving and applying the laws of exponents. This idea of equivalence will continue as students learn to simplify and perform operations on radical expressions. Formalized rules will then be utilized as students evaluate algebraic expressions for given replacement values.
Standards Covered: A.F.2, A.ST.1, A.F.2
Assessment Window: February 3 – 7, 2025
Unit 7: Operations with Polynomials
Students will expand their analytical skills to include polynomial operations such as sums, differences, products, quotients, and factoring. Emphasis will be placed on using concrete objects, along with pictorial and symbolic models, as well as applying the distributive property and area models to visualize the relationship between multiplication and factoring. Students will demonstrate the equality of quadratic expressions in multiple forms.
Standards Covered: A.EO.2, A2.EO.3
Assessment Window: March 10 – 14, 2025
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, x-intercepts, y-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations
Standards Covered: A.EI.3, A.F.2, A.ST.1
Quarter 4
Unit 8: Quadratic Functions
This unit will build on the procedural fluency developed in Unit 7 by linking factoring to the graphical representation of solutions. Students will then progress to solving quadratic equations that cannot be factored and will explore whether a quadratic function has one, two, or no real solutions. Additionally, students will investigate other key characteristics of quadratic function graphs—such as the vertex, 𝑥-intercepts, 𝑦-intercept, domain, and range—and will practice evaluating these functions. Finally, students will apply their skills to connect quadratic models to contextual situations.
Standards Covered: A.EI.3, A.F.2, A.ST.1
Assessment Window: Week of April 7-11, 2025
Unit 9: Function Synthesis
This final unit solidifies the connections and distinctions between the types of functions studied throughout the course. Students will refine their understanding of transformational graphing for quadratic and exponential functions in the forms 𝑓(𝑥) + 𝑘 and 𝑘𝑓(𝑥). They will now compare and contrast the characteristics of graphs across all three function types: linear, quadratic, and exponential. Additionally, the unit revisits the data patterns introduced in Unit 1, as students analyze data sets and scatterplots to identify whether a linear or quadratic model provides the best fit.
Standards Covered: A.F.2, A.ST.1, A.F.2, A.ST.1
Assessment Window: Week of April 28 – May 2, 2025
Geometry
Geometry Pacing and Units of Study
Geometry allows us to understand and make connections to the physical world around us. In this course, students will analyze physical relationships through the development of conjecture and proof using transformational, coordinate, algebraic methods, and logical means. Students will develop efficient strategies for the proof and classification of two- and three-dimensional objects and the use of properties to solve problems.
Quarter 1
Unit 1: Venn Diagrams and Introduction to Logic
Unit story: Venn diagrams and logic provide vehicles through which we can understand and model relationships and categorizations, including geometric relationships. These key components to geometrical thinking are revisited throughout the year when working with theorems, postulates, definitions, and examples.
Standards Covered: G.RLT.1
Assessment Window: September 9 - September 13, 2024
Unit 2: Parallel Lines
The angle relationships formed when parallel lines are cut by a transversal are foundational to the study of geometry. In this unit, students will explore, analyze, and use those relationships to prove conjectures, solve problems, and apply to contextual situations.
Standards Covered: G.RLT.2, G.RLT.1
Assessment Window: September 23 - September 27, 2024
Unit 3: Symmetry and Transformations
Students have been working with symmetry and transformations since elementary school in both geometric and algebraic contexts. This unit provides an opportunity to formalize these ideas and use this knowledge to justify similarity and congruence in geometric figures.
Standards Covered: G.RLT.3, G.RLT.1
Assessment Window: October 14 - October 18, 2024
Unit 4: Triangle Properties
Students use spatial reasoning to form conjectures about whether three given lengths can form a triangle. Exploration is used to determine the relationship between the sides and angles of a triangle. Contextual situations allow for students to see the relevance of these concepts.
Standards Covered: G.TR.1
Targeted Review: G.RLT.1
Assessment Window: October 28 - November 1, 2024
Quarter 2
Unit 5: Similarity and Congruence
Students have been working with similar and congruent figures in various contexts since elementary school. This course provides for a formalized definition of congruent and similar figures. Through exploration, students discover some postulates about congruent and similar figures that allow for some shortcuts to prove whether two figures are congruent or similar. These concepts are used to solve abstract and contextual problems.
Standards Covered: G.TR.2, G.TR.3, G.RLT.1, G.RLT.2
Assessment Window: December 9 - December 13, 2024
Begin Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Quarter 3
Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Standards Covered: G.TR.4, G.TR.2, G.RLT.1, G.TR.1, G.TR.2, G.TR.3
Assessment Window: January 27-31, 2025
Unit 7: Quadrilaterals & Polygons
Exploring the unique characteristics of quadrilaterals and polygons enables us to prove their existence and unlock further insights. Once we establish the fundamental properties, we can confidently apply them to analyze and understand these geometric shapes
Standards Covered: G.PC.1, G.PC.2, G.RLT.1, G.RLT.2, G.TR.1, G.TR.1
Assessment Window: February 24-28, 2025
Unit 8: Three-Dimensional Figures
Students begin with nets of solid figures and use these to develop formulas for surface area and lateral area. This thinking allows students to calculate surface area and volume of composite figures. Students further expand on this thinking to determine the effect changing one or more dimensions of a figure has on any derived measures of the new figure. Proportional reasoning comes into play when comparing surface area and volume of similar three-dimensional figures.
Standards Covered: G.DF.1, G.DF.2, G.RLT.1
Assessment Window: March 17-21, 2025
Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, G.RLT.1
Quarter 4
Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, G.RLT.1
Assessment Window: Week of April 28 – May 2, 2025
Advanced Geometry
Advanced Geometry Pacing and Units of Study
Geometry allows us to understand and make connections to the physical world around us. In this course, students will analyze physical relationships through the development of conjecture and proof using transformational, coordinate, algebraic methods, and logical means. Students will develop efficient strategies for the proof and classification of two- and three-dimensional objects and the use of properties to solve problems.
Quarter 1
Unit 1: Venn Diagrams and Introduction to Logic
Unit story: Venn diagrams and logic provide vehicles through which we can understand and model relationships and categorizations, including geometric relationships. These key components to geometrical thinking are revisited throughout the year when working with theorems, postulates, definitions, and examples.
Standards Covered: G.RLT.1
Unit 2: Parallel Lines
The angle relationships formed when parallel lines are cut by a transversal are foundational to the study of geometry. In this unit, students will explore, analyze, and use those relationships to prove conjectures, solve problems, and apply to contextual situations.
Standards Covered: G.RLT.2, G.RLT.1
Unit 3: Symmetry and Transformations
Students have been working with symmetry and transformations since elementary school in both geometric and algebraic contexts. This unit provides an opportunity to formalize these ideas and use this knowledge to justify similarity and congruence in geometric figures.
Standards Covered: G.RLT.3, G.RLT.1
Unit 4: Triangle Properties
Students use spatial reasoning to form conjectures about whether three given lengths can form a triangle. Exploration is used to determine the relationship between the sides and angles of a triangle. Contextual situations allow for students to see the relevance of these concepts.
Standards Covered: G.TR.1, G.RLT.1
Quarter 2
Unit 5: Similarity and Congruence
Students have been working with similar and congruent figures in various contexts since elementary school. This course provides for a formalized definition of congruent and similar figures. Through exploration, students discover some postulates about congruent and similar figures that allow for some shortcuts to prove whether two figures are congruent or similar. These concepts are used to solve abstract and contextual problems.
Standards Covered: G.TR.2, G.TR.3, G.RLT.1, G.RLT.2
Begin Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Standards Covered: G.TR.4, G.TR.2, G.RLT.1, G.TR.1, G.TR.2, G.TR.3
Quarter 3
Unit 6: Similarity and Right Triangle Ratios
Having worked with similar triangles, students narrow their focus to similar right triangles. Beginning with special right triangles, students apply geometric concepts to determine relationships between the legs and hypotenuse. Expanding to all right triangles allows for the introduction of trigonometric functions. These ratios are used to solve problems.
Standards Covered: G.TR.4, G.TR.2, T.CT.2, G.RLT.1, G.TR.1, G.TR.2, G.TR.3
Unit 7: Quadrilaterals & Polygons
Exploring the unique characteristics of quadrilaterals and polygons enables us to prove their existence and unlock further insights. Once we establish the fundamental properties, we can confidently apply them to analyze and understand these geometric shapes.
Standards Covered: G.PC.1, G.PC.2, G.RLT.1, G.RLT.2, G.TR.1, G.TR.2
Unit 8: Three-Dimensional Figures
Students begin with nets of solid figures and use these to develop formulas for surface area and lateral area. This thinking allows students to calculate surface area and volume of composite figures. Students further expand on this thinking to determine the effect changing one or more dimensions of a figure has on any derived measures of the new figure. Proportional reasoning comes into play when comparing surface area and volume of similar three-dimensional figures.
Standards Covered: G.DF.1, G.DF.2, G.RLT.1
Begin Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, T.CT.1 T, G.RLT.1
Quarter 4
Unit 9: Circles
Students move their thinking from polygons to circles in the final unit. Students apply coordinate geometry when working with the equation of the circle. Circles are also considered outside of the coordinate plane when looking at the proportional relationships that exist between parts of the circle and the entire circle.
Standards Covered: G.PC.3, G.PC.4, T.CT.1, G.RLT.1
Algebra Functions & Data Analysis (AFDA)
Algebra Functions & Data Analysis (AFDA) Pacing and Units of Study
Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and analysis of data. Data will be generated through practical applications arising from science, business, and finance. Students will solve problems that require the formulation of linear, quadratic, exponential, or piecewise-defined equations or a system of equations.
Quarter 1
Unit 1: The Data Cycle
Unit 1 is an introduction to the iterative steps of the data cycle. Students will start with formulating questions that require them to collect or acquire bivariate, quantitative data. They will use this data to create scatterplots that represent the data and determine if the data they have will answer their questions. They will describe how their variables are related and explore making predictions and decisions with their representations to answer contextual questions. In later units, students will apply what they have learned to create equations of their data and design and implement experiments or studies.
Standards Covered: AFDA.DA.1, AFDA.DA.2
Unit 2: Linear Programming
Unit 2 focuses on using real-world applications and identifying optimal solutions. As teachers and students get to know one another, data collection and analysis serve as a vehicle for community building within the classroom. As students review solving systems of inequalities, they will learn to determine the feasible region solution areas. They will use vertices from the feasible region to determine maximum and minimum values in an optimization function. They will learn how optimization affects business decisions that impact their daily lives. Students should have the opportunity to collect/acquire, display, and discuss data related to themselves and their interests.
Standards Covered: AFDA.AF.3
Assessment Window: September 30 - October 4, 2024
Unit 3: Characteristics of Functions
In Unit 3, the focus will be to review and extend students’ knowledge of various functions to include linear, quadratic, exponential, and piecewisedefined function families. Characteristics will include domain and range, intervals on which a function is increasing, decreasing or constant, end behaviors, absolute maxima and minima, zeros, intercepts, and vertical and horizontal asymptotes. Students will also determine the values of a function and describe and relate the characteristics of the graphs to contextual situations.
Standards Covered: AFDA.AF.2
Assessment Window: October 21 - October 25, 2024
Begin Unit: 4 Transformation of Functions
Students will use a transformational approach for linear, quadratic, and exponential functions that include translations, reflections, and dilations based on the graph of the parent function. Given a graph, they will use their knowledge of transformations to make connections between and among multiple representations of a function.
Standards Covered: AFDA.AF.1
Assessment Window: December 2 - December 6, 2024
Quarter 2
Continue Unit: 4 Transformation of Functions
Students will use a transformational approach for linear, quadratic, and exponential functions that include translations, reflections, and dilations based on the graph of the parent function. Given a graph, they will use their knowledge of transformations to make connections between and among multiple representations of a function.
Assessment Window: December 2 - December 6, 2024
Unit 5: Regressions
Regression is a powerful statistical tool used to understand and predict relationships between variables. In its simplest form, regression involves fitting a line or curve to a set of data points on a graph, allowing one to model and analyze how changes in one variable can impact another. For students, linear regression is a key concept, where a straight line is used to represent the best fit for data that shows a linear relationship. By
learning how to calculate and interpret this line, students can make informed predictions and gain deeper insights into patterns within their data. This foundational skill not only enhances mathematical understanding but also applies to real-world scenarios, from economics to science and beyond.
Standards Covered: AFDA.DA.1
Assessment Window: January 6 - January 10, 2025
Begin Unit 6: Probability
This unit focuses on understanding and applying concepts related to probability. Students will explore theoretical probability, conditional probabilities, and the relationships between different types of events, including complementary, dependent, independent, and mutually exclusive events. They will also learn to represent probabilities using various models and to calculate permutations and combinations in a variety of
contexts.
Standards Covered: AFDA.DA.3
Assessment Window: February 17 - February 21, 2025
Quarter 3
Unit 6: Probability
This unit focuses on understanding and applying concepts related to probability. Students will explore theoretical probability, conditional probabilities, and the relationships between different types of events, including complementary, dependent, independent, and mutually exclusive events. They will also learn to represent probabilities using various models and to calculate permutations and combinations in a variety of contexts.
Standards Covered: AFDA.DA.3
Assessment Window: February 17-21, 2025
Unit 7: Normal Distribution
Normal distribution is a fundamental concept in statistics that helps us understand patterns in data. Often called the “bell curve,” it shows how data tend to cluster around a central value, with fewer occurrences as you move further from the center. In this unit, students will explore how the mean and standard deviation shape the curve and learn how to use 𝑍-scores to compare individual data points. They will also calculate probabilities by representing areas under the curve using tools like Standard Normal Probability Tables and statistical software. By the end of the unit, students will be able to determine when the normal distribution is the best model for a data set and apply it to contextual situations such as analyzing heights, test scores, and financial data.
Standards Covered: AFDA.DA.4
Assessment Window: March 24-28, 2025
Quarter 4
Unit 8: Sampling and Experiments
Sampling and experiments help us understand information about a group without studying every person or item in it. In this unit, students will learn to collect data samples fairly and accurately. They will explore a variety of sampling techniques and learn how each method can affect the results. Students will also learn the difference between observing data and conducting experiments to test ideas. Activities will include creating surveys, collecting data, and looking at results to see how they can vary. By the end of the unit, students will know how to choose the best sampling technique, detect biased samples, and determine whether the results of an experiment are reliable. They will use these skills to understand contextual situations, such as voting polls, product testing, and scientific experiments.
Standards Covered: AFDA.DA.2
Assessment Window: Week of May 5-9, 2025
Algebra 2
Algebra Functions & Data Analysis (AFDA) Pacing and Units of Study
Within the context of mathematical modeling and data analysis, students will study functions and their behaviors, systems of inequalities, probability, experimental design and implementation, and analysis of data. Data will be generated through practical applications arising from science, business, and finance. Students will solve problems that require the formulation of linear, quadratic, exponential, or piecewise-defined equations or a system of equations.
Quarter 1
Unit 1: The Data Cycle
Unit 1 is an introduction to the iterative steps of the data cycle. Students will start with formulating questions that require them to collect or acquire bivariate, quantitative data. They will use this data to create scatterplots that represent the data and determine if the data they have will answer their questions. They will describe how their variables are related and explore making predictions and decisions with their representations to answer contextual questions. In later units, students will apply what they have learned to create equations of their data and design and implement experiments or studies.
Standards Covered: AFDA.DA.1, AFDA.DA.2
Unit 2: Linear Programming
Unit 2 focuses on using real-world applications and identifying optimal solutions. As teachers and students get to know one another, data collection and analysis serve as a vehicle for community building within the classroom. As students review solving systems of inequalities, they will learn to determine the feasible region solution areas. They will use vertices from the feasible region to determine maximum and minimum values in an optimization function. They will learn how optimization affects business decisions that impact their daily lives. Students should have the opportunity to collect/acquire, display, and discuss data related to themselves and their interests.
Standards Covered: AFDA.AF.3
Assessment Window: September 30 - October 4, 2024
Unit 3: Characteristics of Functions
In Unit 3, the focus will be to review and extend students’ knowledge of various functions to include linear, quadratic, exponential, and piecewisedefined function families. Characteristics will include domain and range, intervals on which a function is increasing, decreasing or constant, end behaviors, absolute maxima and minima, zeros, intercepts, and vertical and horizontal asymptotes. Students will also determine the values of a function and describe and relate the characteristics of the graphs to contextual situations.
Standards Covered: AFDA.AF.2
Assessment Window: October 21 - October 25, 2024
Begin Unit: 4 Transformation of Functions
Students will use a transformational approach for linear, quadratic, and exponential functions that include translations, reflections, and dilations based on the graph of the parent function. Given a graph, they will use their knowledge of transformations to make connections between and among multiple representations of a function.
Standards Covered: AFDA.AF.1
Assessment Window: December 2 - December 6, 2024
Quarter 2
Continue Unit: 4 Transformation of Functions
Students will use a transformational approach for linear, quadratic, and exponential functions that include translations, reflections, and dilations based on the graph of the parent function. Given a graph, they will use their knowledge of transformations to make connections between and among multiple representations of a function.
Assessment Window: December 2 - December 6, 2024
Unit 5: Regressions
Regression is a powerful statistical tool used to understand and predict relationships between variables. In its simplest form, regression involves fitting a line or curve to a set of data points on a graph, allowing one to model and analyze how changes in one variable can impact another. For students, linear regression is a key concept, where a straight line is used to represent the best fit for data that shows a linear relationship. By
learning how to calculate and interpret this line, students can make informed predictions and gain deeper insights into patterns within their data. This foundational skill not only enhances mathematical understanding but also applies to real-world scenarios, from economics to science and beyond.
Standards Covered: AFDA.DA.1
Assessment Window: January 6 - January 10, 2025
Begin Unit 6: Probability
This unit focuses on understanding and applying concepts related to probability. Students will explore theoretical probability, conditional probabilities, and the relationships between different types of events, including complementary, dependent, independent, and mutually exclusive events. They will also learn to represent probabilities using various models and to calculate permutations and combinations in a variety of
contexts.
Standards Covered: AFDA.DA.3
Assessment Window: February 17 - February 21, 2025
Quarter 3
Unit 6: Probability
This unit focuses on understanding and applying concepts related to probability. Students will explore theoretical probability, conditional probabilities, and the relationships between different types of events, including complementary, dependent, independent, and mutually exclusive events. They will also learn to represent probabilities using various models and to calculate permutations and combinations in a variety of contexts.
Standards Covered: AFDA.DA.3
Assessment Window: February 17-21, 2025
Unit 7: Normal Distribution
Normal distribution is a fundamental concept in statistics that helps us understand patterns in data. Often called the “bell curve,” it shows how data tend to cluster around a central value, with fewer occurrences as you move further from the center. In this unit, students will explore how the mean and standard deviation shape the curve and learn how to use 𝑍-scores to compare individual data points. They will also calculate probabilities by representing areas under the curve using tools like Standard Normal Probability Tables and statistical software. By the end of the unit, students will be able to determine when the normal distribution is the best model for a data set and apply it to contextual situations such as analyzing heights, test scores, and financial data.
Standards Covered: AFDA.DA.4
Assessment Window: March 24-28, 2025
Quarter 4
Unit 10: Exploring Univariate Data Distributions through The Data Cycle
In this unit, students will study how univariate data can be examined in a variety of ways, including analyzing the shape of the distribution and using measures of center and spread. They will explore how the normal distribution can be used to compare data sets and identify various data points relationship to the mean. In previous mathematics courses, students have collected, plotted, and analyzed a set of data collected from a sample. Algebra 2 provides the first opportunity for students to use the sample to hypothesize what the distribution of the full population would look like. Students fit a histogram with a smooth curve, which is a normal curve for unimodal symmetric distributions. Students use this idealized curve to analyze and make predictions about the population. Additionally, students will use data to determine appropriate linear, quadratic, and exponential best-fit curves that model the data.
Standards Covered: A2.ST.1
Unit 11: Permutations and Combinations
In this unit, students consider the number of ways that events can occur to discover the Fundamental Counting Principle, the foundational concept of permutations and combinations. Students distinguish between permutations and combinations, and apply appropriate formulas in these situations. Students use technology to verify their answers.
Standards Covered: A2.ST.3
Advanced Algebra 2
Advanced Algebra 2 Pacing and Units of Study
Advanced Algebra 2 is about functions and their associated equations. By the end of the course, students should be able to sketch the general shape and name identifying characteristics of absolute value, quadratic and other polynomial, radical, rational, exponential, and logarithmic functions. They should recognize how
equivalent forms of expressions and equations illuminate different characteristics and provide opportunities to solve equations, and they should be able to use technology (i.e. graphing utilities) to verify algebraic solutions as well as solve any equation involving those functions. Unit 1 provides a foundation in using bivariate data to drive the need to describe situations with functions. In Unit 2, we establish the vocabulary that will be used to describe the functions. In Units 3-9 students examine each function family in turn, following a similar pattern of looking at data, identifying key characteristics of functions, exploring various forms of the function expressions, and solving equations involving that function. Unit 10 provides a synthesis of all the function types, with opportunities to compare and contrast function characteristics as well as to create new functions through composition and combining them into piecewise functions. Units 11 and 12 are not directly linked to the function concepts but provide a foundation for students to study statistics at a higher level.
Quarter 1
Unit 1: Building a Mathematical Community Through the Data Cycle with Bivariate Data and Functions
Unit 1 provides a foundation in using bivariate data to drive the need to describe situations with functions. As teachers and students get to know one another, data collection and analysis serve as a vehicle for community building within the classroom. Students should have the opportunity to collect/acquire, display, and discuss data related to themselves and their interests.
Standards Covered: A2.ST.2
Assessment Window: August 26 - August 30, 2024
Unit 2: Analyzing and Describing Graphs of Functions
In Unit 1, students explored bivariate data that can be modeled by a function. In Unit 2, we will focus on describing key features of functions from their equations and their graphs. Students will identify certain characteristics of a function (common vocabulary such as: domain, range, zeros, max/min, end behaviors) to help them be able to analyze and make conclusions. This unit is not focused on memorizing the characteristics of each of the function families; rather, this unit is designed to be an introductory unit for the skills and vocabulary needed in future units when exploring specific types of functions.
Standards Covered: A2.F.1, A2.F.2, T.GT.1
Assessment Window: September 16 - September 20, 2024
Unit 3: Solving Absolute Value Equations and Inequalities
Students will represent, solve, and interpret absolute value equations and inequalities. The standards do not require students to know about absolute value functions, but connecting the solutions to equations and inequalities to the graphs of the related functions provides an opportunity to apply the function vocabulary and notation introduced in unit 2. Note: This unit could be swapped with Unit 2 or moved later in the year.
Standards Covered: A2.F.1, A2.EI.1, T.IE.3
Assessment Window: September 30 - October 4, 2024
Unit 4: Quadratic Models
Students will continue to use data as a foundation for a deeper exploration of quadratic models. We will consider the contextual meaning of key characteristics of the graphs (e.g. vertex, x-intercepts). Students will review factoring techniques from Algebra 1 and extend to rewriting quadratic expressions in different forms to illuminate the key characteristics. Solving quadratic equations includes addressing functions that do not have real roots, establishing the need for an introduction to complex numbers. This introduction to complex numbers will be further developed by performing operations. Finally, systems of equations will be presented in a manner that includes at least one quadratic function.
Standards Covered: A2.EO.3, A2.EO.4, A2.F.1, A2.F.2, A2.EI.2, A2.EI.3, MA.AG.1
Assessment Window: October 28 - November 1, 2024
Quarter 2
Unit 5: Polynomial Models
Building on the function behaviors and algebraic techniques in Unit 4, students will extend their understanding of polynomial models to degrees beyond 2. Key features to highlight in this unit are increasing/decreasing intervals and relative/absolute extremes. Students will continue to make
connections between the factored form of the polynomial function and the total number of roots as well as the number of x-intercepts (i.e. real roots).
Standards Covered: A2.EO.3, A2.F.1, A2.F.2, A2.EO.4, A2.EI.6, A2.F.2, T.TT.1
Assessment Window: November 18 - November 22, 2024
Unit 6 Radical Functions Models:
In this unit, students expand their understanding of functions by exploring radical functions. They learn about inverse functions through the analysis of square root and cube root functions, comparing their graphs to those of parent quadratic and cubic functions. Key topics include understanding
domain restrictions (not all real numbers are valid) and identifying extraneous solutions when solving radical equations. This builds on their existing knowledge and enhances their problem-solving skills with new techniques related to radical functions.
Standards Covered: A2.F.1, A2.F.2, A2.EO.2, A2.EI.5
Assessment Window: December 9 - December 13, 2024
Begin Unit 7: Rational Function Models
Standards Covered: A2.F.1, A2.F.2, A2.EO.1, A2.EO.3, A2.EI.4
Assessment Window: January 13 - January 17, 2025
Quarter 3
Unit 8: Exponential and Logarithmic Function Models
Algebra 2 students progress into studying exponential and logarithmic functions, which are the final families they explore in-depth. By connecting the equation of the exponential function to its graph, students can note where and why the asymptotes occur. Exponential and logarithmic functions are defined as inverses of each other, providing an opportunity to reinforce the conceptual understanding of inverses and their importance. Contextual data serves as an application for exponential functions, allowing students to see their relevance in various contexts.
Standards Covered: A2.F.1, A2.F.2, A2.ST.2, MA.FR.2
Assessment Window: February 3 – 7, 2025
Unit 9: Trigonometric Function Models
Students will develop the foundation of Trigonometry by building their understanding of the Unit Circle and applying it to the six functions: sine, cosine, tangent, cosecant, secant, and cotangent. Student will begin expanding their knowledge of the three functions by examining the graphs of three of the periodic functions. Students will apply their knowledge and skills of functions to explore three of the periodic functions (sine, cosine, and tangent) and the associated graphs. These periodic functions model real-world phenomena such as the rise and fall of tides, the oscillation of pendulum, the distance from the ground of a rider on a Ferris wheel. The study of the trigonometric circular functions will continue from Advanced Geometry and prepare students for further study of this topic in the Pre-Calculus courses for both AP Calculus AB and AP Calculus BC.
Standards Covered: T.TT.1, T.CT.2
Assessment Window: February 17-21, 2025
Unit 10: Modeling with Functions
In this unit, students are asked to synthesize and demonstrate mastery of all they have learned about function behavior and specific function families. Piecewise-defined functions and function composition are two ways that students may build new functions from basic parent functions. Integrated in this unit are select Math Analysis standards that extend the studies of the composition and inverses of functions and the function families including the absolute value function and a specific piecewise function, the step function. Absolute value functions are useful for scenarios that focus on magnitude and not direction such as temperature fluctuations, distance, and error analysis. Students will return to the data cycle and the data collected earlier in the year to pose and investigate questions that may be answered by modeling with absolute value functions and piecewise-defined functions. Students will apply previous learned skills of all the function families to determine which function best models specific contextual situations.
Standards Covered: A2.F.1, A2.F.2, A2.ST.2
Assessment Window: March 10-14, 2025
Unit 11: Exploring Univariate Data Distributions through The Data Cycle
In this unit, students will study how univariate data can be examined in a variety of ways, including analyzing the shape of the distribution and using measures of center and spread. They will explore how the normal distribution can be used to compare data sets and identify various data points relationship to the mean. In previous mathematics courses, students have collected, plotted, and analyzed a set of data collected from a sample. Algebra 2 provides the first opportunity for students to use the sample to hypothesize what the distribution of the full population would look like. Students fit a histogram with a smooth curve, which is a normal curve for unimodal symmetric distributions. Students use this idealized curve to analyze and make predictions about the population. Additionally, students will use data to determine appropriate linear, quadratic, and exponential best-fit curves that model the data.
Standards Covered: A2.ST.1
Assessment Window: March 24-28, 2025
Quarter 4
Unit 12: Permutations, Combinations, Sequences, and Series
In this unit, students consider the number of ways that events can occur to discover the Fundamental Counting Principle, the foundational concept of permutations and combinations. Students distinguish between permutations and combinations and apply appropriate formulas in these situations. Students use technology to verify their answers.
Standards Covered: A2.ST.3, MA.FR.3
Data Science
Data Science Pacing and Units of Study
Through the use of open-source technology tools, students will identify and explore problems that involve the use of relational database concepts and data-intensive computing to find solutions and make generalizations. Students will engage in a data science problem-solving structure to interact with large data sets as a means to formulate problems, collect and clean data, visualize data, model using data, and communicate effectively about data formulated solutions.
Quarter 1
Unit 1: Data for All
In this unit, students will be introduced to the foundational concepts of data science through a framework of storytelling. By exploring stories told by data visualizations and how it relates to their own lives, students will learn how to critically examine questions in different parts of society and make informed decisions through the lens of a data scientist. They will learn the characteristics of which questions lend themselves to data science. Additionally, students will explore bias, implication, and issues of producing and consuming data.
Standards Covered: DS.1, DS.2, DS.3, DS.4, DS.5, DS.7
Unit 2: Univariate Data
In this unit, students build on prior knowledge with opportunities to interpret graphical representations of data and to generate visualizations of their own with a focus on univariate data. These may include conventional statistical charts to unconventional/emerging data visualizations to more complex visualizations to learn to understand, inquire about, compare, interpret, and communicate both visualizations they are familiar with and those that may be novel. By working with visualizations, students will discover relationships between observations of different data sets and visualizations of the same data set, recognize patterns and trends exposed by visualizations, and assess the level of uncertainty.
Standards Covered: DS.2, DS.6, DS.8, DS.10, DS.11, DS.12
Quarter 2
Unit 3: Bivariate Data with Modeling
In this unit, students will explore the concept of bivariate data and how it can be used to model relationships between two variables. They will learn how to collect, represent, and analyze bivariate data using scatter plots, correlation coefficients, and lines and curves of best fit. The unit will also cover different types of relationships and how to interpret these relationships in context. Students will engage in hands-on activities, using technology and real-world data sets to enhance their understanding and apply their skills in modeling and interpreting bivariate relationships.
Standards Covered: DS.1, DS.2, DS.4, DS.6, DS.9, DS.10, DS.11
In this unit, students will explore big data and look at scenarios with multiple data sets. They will understand how data scientists use big data to build data trust across an organization. They will also analyze the reliability of a data source and assess processing source data for reliability based on various factors. Students will study ways to gather data and use matrices, along with technology, to organize the data. Once the data is organized, students will be able to manipulate it for presentation, make calculations to summarize it, and present the results in a clear and concise manner.
Standards Covered: DS.1, DS.2, DS.6, DS.7, DS.8, DS.9, DS.12
Quarter 3
Unit 5: Python
In this unit, students will explore the fundamentals of data analysis using Python, starting from loading and exploring datasets to perform complete data analyses. They will learn how to clean and prepare data by handling missing values, correcting data types, and ensuring data consistency. Students will analyze the reliability of data sources, perform exploratory data analysis, and use visualization techniques to uncover patterns and trends. By the end of the unit, students will be able to apply these skills to create customized visualizations, build basic models to interpret relationships, and communicate findings clearly for specific audiences.
Standards Covered: DS.6, DS.7, DS.8, DS.10, DS.12
Unit: 6 Multivariate Data
In this unit, students will explore the concept of multivariate data and how it is used to model relationships between three or more variables. They will learn how to represent and analyze multivariate data using visualizations such as 3-D scatter plots, bubble charts, heat maps, and other emerging data visualizations. Students will also examine how these relationships can be interpreted and communicated effectively, focusing on the importance of selecting the right type of visualization for different data sets. Throughout the unit, students will engage in hands-on activities, working with contextual situation datasets to construct, interpret, and critique a variety of multivariate visualizations, enhancing their ability to tell data-driven stories and gain deeper insights from complex datasets.
Standards Covered: DS.10
Quarter 4
Unit 7: Final Project
In this unit, students will use the skills and concepts learned throughout the course to complete a comprehensive data science project. They will tackle real-world problems with potential future impacts, starting with refining problem statements and formulating measurable questions or hypotheses. Students will design ethical data collection plans that address potential biases, analyze datasets to uncover patterns and trends, and use modeling techniques to test hypotheses and draw actionable conclusions. Students will focus on creating effective visualizations and crafting compelling data narratives to communicate their findings. By the end of the unit, students will deliver polished presentations showcasing their projects, reflecting on the impact of their work and the broader role of data science in addressing real-world challenges.
Standards Covered: DS.1, DS.2, DS.3, DS.5
Unit 8: Additional Distributions and Goodness of Fit
In this unit, students will explore statistical models and their applications, focusing on identifying and testing appropriate distributions for data sets. Students will learn to use statistical distributions such as normal, binomial, and Poisson, and apply the concept of goodness-of-fit testing to evaluate how well these models describe observed data. Through hands-on activities, students will use conceptual datasets to make predictions, test hypotheses, and identify patterns. Emphasis will be placed on developing data literacy, critical thinking, and computational skills to support data-driven decision-making.
Standards Covered: DS.11