Course Overview
FIRST SEMESTER
Unit 1: Polynomial Expressions
Expected Dates: Beginning of School Year to Mid-August In this unit, students will be able to use geometric shapes to justify operations with polynomial expressions. Contextual situations, which utilize expressions, will be used to add, subtract and multiply polynomials. Students will be able to make connections between integers and polynomials by using a concrete-representational-abstract (C-R-A) approach to problem solving Unit 2: Geometric Foundations, Construction and Proofs Expected Dates: Mid-August to End of September In this unit, students will be introduced to the basic building blocks of geometry. Students will further develop their understanding of basic elements by learning constructions using a straightedge and a compass. Students will begin the fundamental geometric practice of writing proofs. Unit 3: Congruence Expected Dates: October to Mid-November Students apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. Unit 4: Similarity Expected Dates: Mid-November to December In this unit, students will explore nonrigid transformations and proportional reasoning to develop an understanding of similarity. Students will use the definition of dilation to describe similarity and the criterion for triangles to be similar. They will use this to prove similarity involving triangles |
SECOND SEMESTERUnit 5: Right Triangle Trigonometry
Expected Dates: January In this unit, students will use similarity in right triangles to understand right triangle trigonometry. They will use the relationship between the sine and cosine of complementary angles to solve problems involving right triangles. Unit 6: Circles Expected Dates: Late January to End of February In this unit, students will examine and apply theorems involving angle relationships, find arc lengths, and find the area of sectors of circles. Students will graph and write equations of circles. Students will extend their understanding of arc length in circles and begin exploring angles within the unit circle as a fraction of the circumference all the way around the unit circle. They will fluently convert between degrees and radians. Students will use special right triangles concepts to define the value of the sine, cosine, and tangent and understand the x (cosine), y (sine), and r (1) values of each angle measure found at all terminal angles that are multiples of π/6, π/3 and π/4 around the unit circle, and will be able to find the sine, cosine, and tangent at all of these radian measures, as well. Unit 7: Equations and Measurement Expected Dates: March In this unit, students will develop informal arguments for geometric formulas and solve contextual problems involving volume. Unit 8: Probability and Statistics Expected Dates: April to End of the School Year In this unit, students will organize real-life data in two-way frequency tables. They will use the two-way frequency tables to find probabilities. Students calculate, model, and interpret probabilities of compound events. Students will calculate permutations and combinations within real-world contexts and develop probability distributions based on the entire sample space. Students will calculate expected value of a probability distribution and understand it to be the mean of that probability distribution. Using expected value, students will make decisions about risk vs. reward in real-world situations such as games of chance and insurance. |