Rebecca Binkley -- Mathematics -- DeTour High School
Algebra 1 thoroughly covers linear functions, linear inequalities, concepts of functions, real numbers, manipulating algebraic symbols, and solving real world word problems using algebraic expressions and equations. Topics include factoring, quadratic equations, the coordinate plane, and graphing linear, quadratic, and exponential functions. Technology is integrated as appropriate during the course.
High School Geometry affords students opportunities to build facility with reasoning and proof and use geometric methods to model the world around them. The course begins with explorations that acquaint students with definitions, constructions, and features of geometric language (e.g., if/then statements) that they use throughout the course. They engage with familiar coordinate contexts (e.g., slope, perimeter) to prove geometric theorems algebraically. Next, students study transformations that, along with the first unit, lay a foundation for proof and reasoning that is developed and applied contextually in subsequent units on triangles, quadrilaterals and circles. Students also use ideas of transformations to define trigonometric ratios which, with the Pythagorean theorem, are used to solve for unknown angles and side lengths. The culminating unit provides students an opportunity to apply geometric concepts in modeling three dimensional figures.
The study of functions that began in eighth grade and Algebra I continues in Algebra II, as students connect familiar linear and exponential functions to make sense of sequences and series. In addition, students are introduced to functions that have new features like limiting end behaviors, asymptotes, amplitude, and periodicity (i.e., rational, logarithmic, and trigonometric functions). Quadratic functions and conic sections provide a context for students to work with complex numbers, examine new features like the focus and directrix, and make connections between algebraic and geometric representations.
Students also engage in a more mathematically sophisticated study of statistics and probability that began in middle school. Students continue to summarize, represent, and interpret one variable statistics. In addition, they make inferences and justify conclusions from surveys, experiments, and observational studies. They work with independent and conditional probability, use rules to compute probabilities, and use probability to evaluate outcomes of decisions.
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.