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Course Description
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Integrated Math 1 Support
Core Connections Integrated I is the first course in a five-year sequence of college preparatory mathematics courses. This course focuses on developing fluency with solving linear equations, inequalities, and systems. These skills are extended to solving simple exponential equations, exploring linear 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 are required to 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.
By the end of this course students will be able to:
- 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.
- Use of rigid transformations (reflection, rotation, translation) and symmetry to demonstrate congruence and develop triangle congruence theorems.
- Using coordinates to prove geometric theorems.
- Geometric constructions (with compass and straightedge).
- Simple geometric proofs (investigate patterns to make conjectures, and formally prove them).
- Representations of arithmetic and geometric sequences, including using tables, graphs, and explicit or recursive formulas.
- Use of exponential models to solve problems, and to compare to linear models.
- Use of function notation.
- Statistical analysis of two-variable data, including determining regression lines, correlation coecients, and creating residual plots.
- The dierences between association and causation, and interpretation of correlation in context.
- Comparison of distributions of one-variable data.
Course Syllabus
- Michael Dow mdow@njuhsd.com 530.273.4431