Algebra 1 begins with one-variable statistics, focusing on data collection, analysis, and interpretation to understand quantities in context. Students then study linear equations and systems to model relationships, writing, evaluating, graphing, and solving them. This leads to two-variable statistics, examining relationships using tables, scatter plots, and linear models. They also solve and graph linear inequalities. 

Students deepen their understanding of functions by representing and interpreting them using function notation, domain/range, rate of change, and graph features. They explore linear, piecewise, exponential, and quadratic functions, investigating real-world contexts and analyzing their structural attributes. 

The course concludes with quadratic equations, where students use reasoning, equivalent equations, and the quadratic formula to model relationships and solve problems, encountering rational and irrational solutions.

Unit 1: One-Variable Statistics

• 19 days, Quarter 1
• Students learn how to gather, organize, and interpret numerical data. They create visual summaries, calculate key statistics, and design an experiment to answer their own questions using data.

Unit 2: Linear Equations and Systems

• 22 days, Quarter 1
• Students deepen their understanding of equations, inequalities, and systems by solving problems and explaining their reasoning. They practice representing real-world situations mathematically and finding solutions that fit given conditions.

Unit 3: Two-Variable Statistics

• 13 days, Quarter 2
• Students learn how to analyze and interpret relationships between variables, using scatter plots, correlation, and tables. They explore real-world examples and investigate the difference between correlation and causation.

Unit 4: Linear Inequalities and Systems

• 12 days, Quarter 2
• Students examine solving and graphing linear inequalities and systems of linear inequalities. The unit builds on concepts from middle school when students write and solve inequalities by reasoning about quantities.

Unit 5: Functions

• 25 days, Quarter 2 and 3
• Students explore functions by connecting graphs, equations, and real-world situations. They learn new vocabulary and tools to describe how functions behave and solve problems using different types of functions.

Unit 6: Introduction to Exponential Functions

• 28 days, Quarter 3
• Students learn about exponential relationships, comparing them to linear patterns. They explore real-world situations involving growth and decay, and use graphs and equations to understand and predict exponential change.

Unit 7: Introduction to Quadratic Functions

• 22 days, Quarter 3
• Students explore quadratic functions, which show patterns involving symmetrical curves. They compare quadratics to linear and exponential patterns, discovering how these functions model real-world scenarios differently.

Unit 8: Quadratic Equations

• 28 days, Quarter 4
• Students will be learning how to solve quadratic equations, using several methods.

Students practice conjectures, observations, and compass/straightedge constructions. They learn formal proof writing through a cycle of conjecture, drafting, peer feedback, and revision, supported by a reference chart of definitions and theorems.

Building on middle school transformations, students use transformation-based definitions of congruence and similarity to prove triangle congruence and similarity theorems. These are applied to quadrilaterals, isosceles triangles, and other figures. Similarity extends to right triangle trigonometry.

Students derive volume formulas and study dilation’s effect on area and volume. Coordinate geometry connects algebra and geometry, reviewing prior theorems and skills. Transformations and the Pythagorean Theorem are used to build equations for circles, parabolas, parallel and perpendicular lines from definitions, linking transformations to functions.

Nearing the end, students analyze circle segment and angle relationships, developing radian measure. The course concludes by extending grade 7 probability to combined and independent events.

Unit 1: Constructions and Rigid Transformations

• 25 days, Quarter 1
• Students begin by learning about geometric constructions and rigid transformations. They then apply this knowledge to understand and write basic geometric proofs.

Unit 2: Congruence

• 17 days, Quarter 1
• Students learn how to prove that different geometric figures are congruent, starting with segments and progressing to triangles and quadrilaterals. They practice writing rigorous proofs using transformations and apply these concepts to quadrilaterals.

Unit 3: Similarity

• 19 days, Quarter 2
• Students explore similar figures, understanding how they relate through rigid transformations and dilations. They also focus on writing conjectures and proving them, particularly in the context of similar triangles.

Unit 4: Right Triangle Trigonometry

• 14 days, Quarter 2
• Students build an understanding of ratios in right triangles, leading to the introduction of cosine, sine, and tangent as trigonometric ratios. They learn to calculate angle measures using arcsine, arccosine, and arctangent, and practice applying these concepts with appropriate precision.

Unit 5: Solid Geometry

• 20 days, Quarter 3
• Students practice visualizing three-dimensional shapes, including sketching cross-sections and understanding dilations of solids. They learn to derive volume formulas for various solids, such as pyramids and cones, and apply these concepts to solve problems.

Unit 6: Coordinate Geometry

• 20 days, Quarter 3
• Students connect their prior knowledge of coordinate planes with new geometric concepts to deeply study coordinate geometry. They transform figures using coordinate rules, build equations for circles and parabolas based on definitions, and write coordinate proofs about lines and quadrilaterals.

Unit 7: Circles

• 16 days, Quarter 4
• Students investigate the geometry of circles in detail, defining terms like chord, arc, and central angle, and proving theorems related to inscribed angles and tangent lines. They also learn to calculate sector areas and arc lengths, and understand radian measure.

Conditional Probability

• 13 days, Quarter 4
• Students extend their understanding of probability, sample spaces, and events, particularly for experiments with multiple parts. They learn about conditional probability and the independence of events, and test their conjectures by collecting and analyzing data.

The course starts with sequences, revisiting linear and exponential functions, and exploring mathematical modeling through various representations. This leads to analyzing polynomial-modeled situations, their graphs, equations, and arithmetic operations on polynomials and rational functions. Students learn about asymptotes, end behavior, polynomial identities, and the sum of geometric sequences.
Next, students extend exponent rules to rational exponents, solve equations with roots, and are introduced to i, which expands the number system to complex numbers, enabling the solution of quadratic equations with non-real solutions.

Building on rational exponents, students return to exponential functions, establishing that growth by equal factors over equal intervals holds for non-integer lengths. Logarithms are used to solve for unknown exponents, and students are introduced to e for continuous growth modeling. Logarithm functions and their models are also briefly covered.

Students then learn to transform functions graphically and algebraically, consolidating and generalizing previous understandings of adjusting model parameters to fit data. This is useful for studying periodic functions, where students use the unit circle to understand trigonometric functions and model periodic relationships.

The final unit focuses on statistical inference, analyzing experimental data modeled by normal distributions. Students learn to use sampling and simulations to account for data variability, estimate population mean, margin of error, and proportions, and develop skepticism about inappropriately summarized data in news stories.

Unit 1: Sequences and Functions

• 15 days, Quarter 1
• Students revisit functions and are introduced to sequences, specifically arithmetic and geometric sequences. They learn to define sequences using function notation and understand their connection to linear and exponential functions, applying these concepts to model real-world situations.

Unit 2: Polynomials

• 19 days, Quarter 1
• Students extend their understanding of polynomials beyond linear and quadratic functions, exploring their graphs, equations, and real-world applications. They investigate rational functions, learning about asymptotes and strategies for solving rational equations.

Unit 3: Rational Functions and Identities

• 14 days, Quarter 2
• Students transition to rational functions, rational equations, and identities, considering situations these functions can model and examining their asymptotic behavior. They focus on solving rational equations, identifying extraneous solutions, and studying polynomial identities.

Unit 4: Complex Numbers and Rational Exponents

• 23 days, Quarter 2
• Students extend exponent rules to include rational exponents, solve equations involving square and cube roots, and develop an understanding of complex numbers. They apply their knowledge of complex numbers to solve quadratic equations that may have complex roots.

Unit 5: Exponential Functions and Equations

• 28 days, Quarter 2 and 3
• students expand their understanding of exponential functions to include real number domains. They learn about logarithms as a way to express exponents and use them to solve exponential equations, including those involving the constant e.

Unit 6: Transformations of Functions

• 18 days, Quarter 3
• Students explore how functions can be transformed to fit different situations, focusing on vertical and horizontal translations, reflections, and scaling. They apply these transformations to various function types, including polynomial, radical, and exponential functions, to model real-world data.

Unit 7: Trigonometric Functions

• 25 days, Quarter 3 and 4
• Students are introduced to trigonometric functions, building on their knowledge of transformations to model periodic situations. They study the unit circle to understand cosine and sine as functions and apply transformations to identify key features like midline, amplitude, and period.

Unit 8: Statistical Inferences

• 20 days, Quarter 4
• students learn about important uses of randomization in statistics, including different types of studies and the significance of random selection for generalizing findings. They examine the normal distribution as a model for bell-shaped data, using it to quantify confidence in estimates and analyze experimental results.

Precalculus students build advanced math skills needed for future courses in mathematics, science, engineering, and technology. Students explore different types of functions, including exponential, logarithmic, polynomial, and trigonometric functions, and learn how to use them to solve real-world problems. They study trigonometry to understand angles, triangles, and patterns that repeat over time, while also learning about vectors, matrices, and transformations. The course introduces analytic geometry through the study of conic sections such as circles, ellipses, parabolas, and hyperbolas. Students also develop skills in probability and statistics, using data to make predictions and informed decisions. Throughout the course, students strengthen their problem-solving, critical thinking, and mathematical reasoning skills while preparing for higher-level mathematics.

Unit 1: How Functions Function

• 12 days, Quarter 1

Unit 2: Exponential and Logarithm Functions

• 12 days, Quarter 1

Unit 3: Polynomials and Rational Functions

• 14 days, Quarter 1 and 2

Unit 4: Trigonometric Fundamentals

• 15 days, Quarter 2

Unit 5: Trigonometric Functions

• 15 days, Quarter 2

Unit 6: Trigonometric Identities

• 13 days, Quarter 3

Unit 7: Matrices

• 12 days, Quarter 3

Unit 8: Vectors

• 15 days, Quarter 3

Unit 9: Conics

• 18 days, Quarter 4

Unit 10: Probability

• 15 days, Quarter 4