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Learning about functions and coding with pro-bots
​CORE CONNECTIONS ALGEBRA
Core Connections Algebra is the first course in a five-year sequence of college preparatory mathematics courses that starts with Algebra I and continues through Calculus. It aims to deepen and extend student understanding built in previous courses by focusing on developing fluency with solving linear equations, inequalities, and systems. These skills are extended to solving quadratic equations, exploring linear, quadratic, and exponential functions graphically, numerically, symbolically, and as sequences, and by using regression techniques to analyze the fit of models to distributions of data.  
On a daily basis, students in Core Connections Algebra use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas.
The course is well balanced among procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and application). The lessons in the course meet all of the content standards, of Appendix A of the Common Core State Standards for Mathematics. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.
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Key concepts addressed in this course are:
  • Representations of linear, quadratic, and exponential relationships using graphs, tables, equations, and contexts.
  • Symbolic manipulation of expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc.
  • Analysis of the slope of a line multiple ways, including graphically, numerically, contextually (as a rate of change), and algebraically.
  • Solving 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).
  • Solving systems of two equations and inequalities with two variables using a variety of strategies, both graphically and algebraically.
  • Representations of arithmetic and geometric sequences, including tables, graphs, and explicit or recursive formulas.
  • Use of exponential models to solve problems, and to compare to linear models.
  • Investigation of a variety of functions including square root, cube root, absolute value, piecewise-defined, step, and simple inverse functions.
  • Use of function notation.
  • Statistical analysis of two-variable data, including determining regression lines, correlation coefficients, and creating residual plots.
  • The differences between association and causation, and interpretation of correlation in context.
  • Comparison of distributions of one-variable data.

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