Algebra 1R Information & Expectations: 2019-2020
Course Overview: Algebra 1R is a one-year course preparing students for the Common Core Algebra Regents exam in June. Topics include quantities and reasoning with equations and their graphs, descriptive statistics, linear and exponential functions, polynomial and quadratic expressions, equations and functions, and a synthesis of modeling with equations and functions.
Materials Needed for Class: Laptop, 3-Ring Binder, Pencils, TI-Nspire, Agenda, headphones
Grading: Grades will be based on the following:
Khan academy: 30%
Algebra 1R Units
Unit 1: Statistics: This unit starts from the perspective of how we show the distribution, the central tendencies, and the variation within a data set. It then moves onto bivariate data analysis both by hand and with the calculator
Unit 2: Linear Expressions, Equations, & Inequalities: This unit is all about linear, which is a major focus of Common Core Algebra I. We develop general methods for solving linear expressions involving inverse operations. Solutions to equations and inequalities are defined in terms of making statements true.
Unit 3: Functions: In this unit we review the basic concept of a function and emphasize multiple representations of these foundational tools. Graphical features of functions, including maximums, minimums, intervals of increase and decrease along with domain and range are introduced. Classic function notation is used throughout the unit. Average rate of change is introduced as a tool for measuring the growth or decline in a function.
Unit 4: Linear Functions & Arithmetic Sequences: This unit is all about understanding linear functions and using them to model real world scenarios. Fluency in interpreting the parameters of linear functions is emphasized as well as setting up linear functions to model a variety of situations. Linear inequalities are also taught. The unit ends with a introduction to sequences with an emphasis on arithmetic.
Unit 5: Systems of Linear Equations & Inequalities: This unit begins by ensuring that students understand that solutions to equations are points that make the equation true, while solutions to systems make all equations (or inequalities) true. Graphical and substitution methods for solving systems are reviewed before the development of the Elimination Method. Modeling with systems of equations and inequalities is stressed. Finally, we develop the idea of using graphs to help solve equations.
Unit 6: Exponents: This unit begins with exponent rules and the development of negative and zero exponents. We then develop the concepts of exponential growth and decay from a fraction perspective. Finally, percent work allows us to develop growth models based on constant percent rates of change. Geometric sequences are tied to exponential growth in the last lesson.
Unit 7: Polynomials: This unit introduces polynomials as analogous to the integers and multiple parallel are drawn to the integers throughout the unit. Fluency skills are emphasized throughout the unit. These skills include adding, multiplying, and factoring polynomials. Applications problems are given in terms of primarily area models.
Unit 8: Quadratic Functions: This unit introduces quadratic polynomials from a basic perspective. We then build on the notion of shifting basic parabolas into their vertex form. Completing the square is used as a fundamental tool in finding the turning point of a parabola. Finally, the zero-product law is introduced as a way to find the zeroes of a quadratic function.
Unit 9: Roots & Irrational Numbers: This unit emphasizes basic root work and its applications in solving quadratic equations with irrational roots. We will also simplify square roots.
Unit 10: Functions & Modeling: This final unit looks back on and expands on topics that we have seen throughout the course.