Algebra Connections is the first course in a five-year sequence of college preparatory mathematics courses that delivers traditionally rigorous algebraic content using a problem-based approach. It has strong threads woven throughout the course on multiple representations and the meaning of a solution. A major focus of the course is to develop multiple strategies to solve problems and to recognize multiple ways of understanding concepts.
Upon completing this course, students should be able to:
- Represent a function with a graph, table, rule, and context and should be able to find any representation when provided one of the others (for linear and quadratic relationships).
- Collect and analyze data and make predictions based on the trend of the data.
- Symbolically manipulate expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, reducing rational expressions, expanding exponential expressions, etc.
- Solve simple and complex equations and inequalities using a variety of strategies, including rewriting (such as factoring, distributing, or completing the square), undoing (such as extracting the square root or subtracting a term from both sides of an equation), and looking inside (such as determining the possible values of the argument of an absolute value expression).
- Solve contextual word problems using multiple strategies, including making tables, looking for patterns, drawing diagrams, and creating “Guess and Check” tables to assist with writing and solving a variable equation.
- Analyze the slope of a line multiple ways, including graphically, numerically, contextually (as a rate of change), and algebraically.
- Solve a system of two linear or non-linear equations and inequalities with two variables using a variety of strategies, both graphically and algebraically. Read More...
Chapters are divided into sections that are organized around core topics. Within each section, lessons include activities, challenging problems, investigations, and practice problems. Teacher notes for each lesson include a “suggested lesson activity” section with ideas for lesson introduction, specific tips and strategies for lesson implementation to clearly convey core ideas, and a means for bringing the lesson to closure. Read More...