Courses

Unit 1: Number Sense & Operations

Description & Expectations:
Students will compare, represent, and operate with rational and irrational numbers, using mental math and estimation strategies. They will apply these skills to solve problems involving exponents, roots, and scientific notation.

Topics Covered:

• Rational vs. irrational numbers

• Integers, fractions, decimals, and percentages

• Order of operations (BEDMAS/PEMDAS)

• Mental math and estimation strategies

• Scientific notation

• Square roots and cube roots

• Applications in real-world contexts

Unit 2: Algebraic Expressions & Equations

Description & Expectations:
Students will simplify algebraic expressions, solve linear equations/inequalities, and apply the distributive property. They will justify solutions and model real-life scenarios algebraically.

Topics Covered:

• Simplifying expressions (combining like terms, distributive property)

• Solving one-step and multi-step linear equations

• Solving inequalities and representing solutions on a number line

• Rearranging formulas (e.g., for area, speed)

• Real-world applications (e.g., word problems involving costs, distances)

Unit 3: Linear Relations

Description & Expectations:
Students will analyze linear relationships using tables, graphs, and equations. They will interpret slope as a rate of change and y-intercept as an initial value in real-world contexts.

Topics Covered:

• Graphing linear relations from equations, tables, and descriptions

• Calculating slope (rise over run, from graphs and equations)

• y-intercept and its meaning in context

• Writing equations in slope-intercept form (y = mx + b)

• Applications (e.g., distance-time graphs, earnings vs. hours worked)

Unit 4: Measurement & Geometry

Description & Expectations:
Students will solve problems involving perimeter, area, surface area, and volume. They will explore geometric properties, transformations, and the Pythagorean theorem.

Topics Covered:

• Perimeter & area of triangles, quadrilaterals, and composite shapes

• Surface area & volume of prisms, pyramids, cylinders

• Pythagorean theorem (solving for missing sides, real-world applications)

• Transformations: translations, rotations, reflections, dilations

• Angle relationships (parallel lines, triangles, polygons)

Unit 5: Data Literacy

Description & Expectations:
Students will collect, organize, and analyze data using statistical measures and visual representations. They will assess bias and draw evidence-based conclusions.

Topics Covered:

• Types of data (categorical vs. numerical, discrete vs. continuous)

• Measures of central tendency (mean, median, mode) and spread (range)

• Data visualization (histograms, scatter plots, bar graphs)

• Identifying misleading graphs and bias

• Drawing conclusions from surveys and experiments

Unit 6: Financial Literacy

Description & Expectations:
Students will apply math skills to budgeting, interest calculations, and financial decision-making. They will compare costs, analyze debt, and plan for future expenses.

Topics Covered:

• Creating and analyzing budgets (income vs. expenses)

• Simple vs. compound interest (savings, loans, credit cards)

• Financial planning (short-term vs. long-term goals)

• Comparing financial products (e.g., bank accounts, loans)

• Understanding credit scores and debt management

Unit 1: Algebraic Skills and Linear Systems

Description & Expectations:
Students will review and extend their understanding of algebraic expressions and equations. They will solve systems of linear equations using various methods and apply them to real-world problems.

Topics Covered:

• Review of linear equations

• Solving systems by graphing, substitution, and elimination

• Applications of linear systems

• Word problems involving systems

Unit 2: Analytic Geometry

Description & Expectations:
Students will explore the relationships between equations and geometric representations of lines. They will investigate properties of lines and line segments in the coordinate plane.

Topics Covered:

• Slope and equations of lines

• Midpoint and distance formulas

• Parallel and perpendicular lines

• Applications in geometry and real-life contexts

Unit 3: Quadratic Relations of the Form y = ax² + bx + c

Description & Expectations:
Students will investigate quadratic relations and their properties. They will graph and analyze parabolas and solve related problems.

Topics Covered:

• Characteristics of quadratic relations

• Vertex form and standard form

• Graphing parabolas

• Axis of symmetry and vertex

• Applications of quadratic models

Unit 4: Quadratic Equations

Description & Expectations:
Students will solve quadratic equations using a variety of methods and apply these skills to problem-solving situations.

Topics Covered:

• Factoring trinomials and special products

• Solving by factoring, completing the square, and quadratic formula

• Discriminant and nature of roots

• Word problems involving quadratic equations

Unit 5: Trigonometry

Description & Expectations:
Students will explore trigonometric ratios and solve problems involving right triangles. They will apply trigonometry to real-world and mathematical problems.

Topics Covered:

• Sine, cosine, and tangent ratios

• Solving right triangles

• Angle of elevation and depression

• Applications in measurement and design

Unit 6: Measurement and Geometry

Description & Expectations:
Students will solve problems involving surface area and volume of 3D figures. They will apply geometric reasoning to solve problems.

Topics Covered:

• Surface area and volume of prisms, pyramids, cylinders, cones, and spheres

• Composite figures

• Optimization problems

• Real-world applications

Unit 1: Introduction to Functions

Description & Expectations:
Students will explore the concept of a function and distinguish between relations and functions. They will represent functions in various forms and understand domain and range.

Topics Covered:

• Relations vs. functions

• Function notation

• Domain and range

• Evaluating functions

• Graphs of functions

Unit 2: Characteristics of Functions

Description & Expectations:
Students will investigate key features of functions and their graphs. They will analyze transformations and use function notation to describe changes.

Topics Covered:

• Intercepts, intervals of increase/decrease

• Maximum and minimum values

• Transformations (translations, reflections, stretches)

• Even and odd functions

• Piecewise functions

Unit 3: Quadratic Functions

Description & Expectations:
Students will deepen their understanding of quadratic functions, including their properties, transformations, and applications.

Topics Covered:

• Vertex form, factored form, and standard form

• Completing the square

• Solving quadratic equations

• Applications of quadratic models

• Optimization problems

Unit 4: Exponential Functions

Description & Expectations:
Students will explore exponential growth and decay. They will model real-world scenarios using exponential functions and understand their properties.

Topics Covered:

• Exponential growth and decay

• Base of exponential functions

• Graphing exponential functions

• Applications in finance and science

• Comparing linear, quadratic, and exponential models

Unit 5: Discrete Functions

Description & Expectations:
Students will study sequences and series, focusing on arithmetic and geometric patterns. They will solve problems involving these sequences.

Topics Covered:

• Arithmetic sequences and series

• Geometric sequences and series

• Recursive formulas

• Sigma notation

• Applications in real-life contexts

Unit 6: Trigonometric Functions

Description & Expectations:
Students will extend their knowledge of trigonometry to include the unit circle and sinusoidal functions. They will model periodic phenomena.

Topics Covered:

• Radian measure

• Unit circle and trigonometric ratios

• Graphs of sine and cosine functions

• Amplitude, period, phase shift

• Applications of sinusoidal models

Unit 1: Probability

Description & Expectations:
Students will explore the concepts of probability and apply them to real-world contexts. They will calculate probabilities of simple and compound events and interpret the results.

Topics Covered:

• Experimental and theoretical probability

• Probability of compound events

• Tree diagrams and organized lists

• Applications in games and real-life scenarios

Unit 2: One-Variable Statistics

Description & Expectations:
Students will collect, organize, and analyze data involving one variable. They will use statistical measures to interpret and communicate findings.

Topics Covered:

• Data collection methods

• Measures of central tendency (mean, median, mode)

• Measures of spread (range, interquartile range, standard deviation)

• Histograms and box plots

• Identifying and interpreting trends

Unit 3: Quadratic Relations

Description & Expectations:
Students will investigate quadratic relations and their applications. They will model and solve problems using quadratic equations.

Topics Covered:

• Graphing quadratic relations

• Vertex and standard forms

• Solving quadratics by factoring and using the quadratic formula

• Applications in real-world contexts

Unit 4: Trigonometry

Description & Expectations:
Students will solve problems involving right and oblique triangles using trigonometric ratios and laws.

Topics Covered:

• Sine, cosine, and tangent ratios

• Solving right triangles

• Sine Law and Cosine Law

• Applications in measurement and design

Unit 5: Exponents and Exponential Relations

Description & Expectations:
Students will explore exponential growth and decay. They will model real-world situations using exponential functions.

Topics Covered:

• Laws of exponents

• Exponential growth and decay

• Graphing exponential functions

• Applications in population growth and depreciation

Unit 6: Compound Interest and Personal Finance

Description & Expectations:
Students will apply mathematics to financial decision-making. They will explore interest, credit, and budgeting.

Topics Covered:

• Simple vs. compound interest

• Credit cards and loans

• Budgeting and saving

• Comparing financial services

Unit 1: Polynomial Functions

Description & Expectations:
Students will explore the characteristics of polynomial functions, including their graphs, equations, and applications. They will analyze polynomial expressions and solve related equations and inequalities.

Topics Covered:

• Characteristics of polynomial functions

• Factoring and solving polynomial equations

• Remainder and factor theorems

• Graphing polynomial functions

• Solving polynomial inequalities

Unit 2: Rational Functions

Description & Expectations:
Students will investigate rational expressions and functions. They will analyze their properties and solve equations involving rational expressions.

Topics Covered:

• Simplifying rational expressions

• Identifying asymptotes and discontinuities

• Graphing rational functions

• Solving rational equations

• Applications in real-world contexts

Unit 3: Trigonometric Functions

Description & Expectations:
Students will extend their understanding of trigonometric functions and apply them to model periodic phenomena.

Topics Covered:

• Radian measure and unit circle

• Graphs of sine, cosine, and tangent functions

• Amplitude, period, phase shift, and vertical shift

• Trigonometric identities and equations

• Applications of sinusoidal models

Unit 4: Exponential and Logarithmic Functions

Description & Expectations:
Students will explore exponential and logarithmic functions and their applications. They will solve equations and model real-world scenarios.

Topics Covered:

• Laws of exponents and logarithms

• Graphing exponential and logarithmic functions

• Solving exponential and logarithmic equations

• Applications in finance and science

• Comparing exponential and logarithmic models

Unit 5: Combining Functions

Description & Expectations:
Students will learn how to combine functions using operations and composition. They will analyze the resulting functions and their properties.

Topics Covered:

• Function operations (addition, subtraction, multiplication, division)

• Composition of functions

• Inverse functions

• Domain and range of combined functions

• Applications in modeling

Unit 1: Rates of Change

Description & Expectations:
Students will develop an understanding of average and instantaneous rates of change. They will explore the concept of the derivative and its connection to slopes of secants and tangents.

Topics Covered:

• Average vs. instantaneous rate of change

• Secant and tangent lines

• Introduction to limits

• Derivatives of polynomial functions

• Applications in motion and economics

Unit 2: Derivatives and Their Applications

Description & Expectations:
Students will learn rules for finding derivatives and apply them to solve problems involving optimization and motion.

Topics Covered:

• Derivative rules (power, product, quotient, chain)

• Derivatives of polynomial, rational, radical, exponential, and sinusoidal functions

• First and second derivative tests

• Optimization problems

• Related rates

Unit 3: Curve Sketching and Optimization

Description & Expectations:
Students will use derivatives to analyze and sketch functions. They will apply calculus to solve real-world problems involving maxima and minima.

Topics Covered:

• Critical points and inflection points

• Increasing/decreasing intervals

• Concavity and points of inflection

• Sketching curves using derivatives

• Real-world optimization problems

Unit 4: Trigonometric and Exponential Functions

Description & Expectations:
Students will extend their understanding of derivatives to include trigonometric and exponential functions and apply them in various contexts.

Topics Covered:

• Derivatives of sine, cosine, and exponential functions

• Applications in physics and biology

• Modelling periodic and exponential growth/decay phenomena

Unit 5: Vectors in Two and Three Dimensions

Description & Expectations:
Students will explore vector operations and apply them to geometric and algebraic problems in two and three dimensions.

Topics Covered:

• Vector notation and operations

• Scalar and vector components

• Dot product and angle between vectors

• Applications in navigation and physics

Unit 6: Lines and Planes in 3D Space

Description & Expectations:
Students will represent lines and planes in three-dimensional space and solve problems involving intersections and distances.

Topics Covered:

• Vector, parametric, and symmetric equations of lines

• Equations of planes

• Intersections of lines and planes

• Applications in geometry and engineering

Unit 1: Organization of Data for Analysis

Description & Expectations:
Students will learn how to collect, organize, and display data effectively. They will explore different types of data and methods of data collection, and assess the validity of data sources.

Topics Covered:

• Types of data (categorical, numerical, discrete, continuous)

• Data collection methods (surveys, experiments, observational studies)

• Sampling techniques and bias

• Organizing data using tables and graphs

• Evaluating data sources and reliability

Unit 2: Statistical Analysis

Description & Expectations:
Students will analyze one-variable and two-variable data using statistical measures and graphical representations. They will interpret results and draw conclusions.

Topics Covered:

• Measures of central tendency and spread (mean, median, mode, range, standard deviation)

• Histograms, box plots, scatter plots

• Correlation and causation

• Linear regression and line of best fit

• Interpreting statistical summaries

Unit 3: Introduction to Probability

Description & Expectations:
Students will explore the basic principles of probability and apply them to simple and compound events. They will use probability models to make predictions.

Topics Covered:

• Theoretical vs. experimental probability

• Sample spaces and events

• Venn diagrams and probability rules

• Independent and dependent events

• Conditional probability

Unit 4: Probability Distributions and Predictions

Description & Expectations:
Students will investigate discrete probability distributions and use them to model real-world situations. They will apply probability to make informed decisions.

TTopics Covered:

• Binomial and normal distributions

• Expected value

• Applications in games, insurance, and risk analysis

• Using technology to simulate and analyze distributions

Unit 5: Culminating Data Investigation

Description & Expectations:
Students will conduct a major investigation that integrates data collection, analysis, and interpretation. They will present their findings using appropriate mathematical and statistical tools.

Topics Covered:

• Designing a study or experiment

• Collecting and analyzing data

• Drawing conclusions and evaluating results

• Communicating findings effectively