Math 2 Course Description
The algebra and functions focus is on properties of quadratic functions and an introduction to inverse functions through the inverse relationship between quadratic and square root functions. In geometry, students use geometric reasoning to prove theorems related to lines, angles, and triangles. There is a focus on congruence, similiarity, and right triangle trigonometry. The work of middle school probability is extended to develop understanding of conditional probability, independence, and rules of probability to determine probabilities of compound events.
Unit 1 - Transformations and Symmetry
Students develop properties of rigid motion transformations and how they can be used to see symmetry in polygons.
Unit 2 - Congruence, Construction, and Proof
Students establish triangle congruence criteria based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. Students use geometric constructions as foundation of proof. They prove theorems about triangle angle sum, lines and angles, properties of triangles.
Unit 3 - Quadratic Functions
Students examine multiple representations of quadratic functions to compare and contrast rate of change, minimum and maximum values, and domain and range. They use understanding of linear and exponential functions to compare and contrast properties of quadratic functions.
Unit 4 - Structures and Expressions
Students rewrite and connect different forms of a quadratic (transformations, vertex form, visual and algebraic approaches to completing the square, understanding factored and standard forms, and intercepts) to build fluency.
Unit 5 - Solving Quadratic and Other Equations
Students develop understanding and need for rational exponents. They develop quadratic formula for finding x-intercepts and roots. Students build fluency with solving quadratic equations. They extend solutions to quadratic equations to the set of complex numbers. Students solve quadratic inequalities. They solve systems of linear and quadratic equations.
Unit 6 - Square Root and Inverse Variation Functions
Students develop properties and use of square root functions. They use knowledge of features of functions to identify features and to create functions given features. Students recognize and create inverse variation relationships. They create systems of linear, quadratic, square root and inverse variation functions.
Unit 7 - Similiarity and Right Triangle Trigonometry
Students examine, apply and compare proportionality relationships in triangles (such as the Pythagorean theorem, right triangle trigonometry) that are known to be similar to each other based on dilations. They prove theorems about triangles, lines, angles and proportional relationships when parallel lines are crossed by multiple transversals. Students solve for unknown values in right triangles using trigonometric ratios.
Unit 8 - Probability
Students estimate, examine, and interpret conditional probabilities and the addition rule for a set of data using Venn diagrams and other representations. They examine independence of events.
Student Math Practices
Practice 1: Make sense of problems and persevere in solving them.
Practice 2: Reason abstractly and quantitatively.
Practice 3: Construct viable arguments and critique the reasoning of others.
Practice 4: Model with mathematics.
Practice 5: Use appropriate tools strategically.
Practice 6: Attend to precision.
Practice 7: Look for and make use of structure.
Practice 8: Look for and express regularity in repeated reasoning.