Module 2: Developing Function Foundations
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Module 3: Investigating Growth and Decay
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Algebra I - Module 1, Topic 2: Sequences
In this topic, students explore sequences represented as lists of numbers, in tables of values, by equations, and as graphs on the coordinate plane. Students move from an intuitive understanding of patterns to a more formal approach of representing sequences as functions. In the final lesson of the topic, students are introduced to the modeling process. Defined in four steps—Notice and Wonder, Organize and Mathematize, Predict and Analyze, and Test and Interpret—the modeling process gives students a structure for approaching real-world mathematical problems.
Algebra I - Module 1, Topic 3: Linear Regressions
In this topic, students focus on the patterns that are evident in certain data sets and use linear functions to model those patterns. Using the informal knowledge of lines of best fit that was built in previous grades, students advance their statistical methods to make predictions about real-world phenomena. They differentiate between correlation and causation, recognizing that a correlation between two quantities does not necessarily mean that there is also a causal relationship. At the end of this topic, students will synthesize what they have learned to decide whether a linear model is appropriate.
Using Logical Reasoning to Prove Conjectures about Circles
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Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Generalizing Geometric Properties of Ratios in Similar Figures
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Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.
Determining Area: Sectors of Circles
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Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.
Making Conjectures About Circles and Segments
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Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.
Determining Area: Regular Polygons and Circles
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The student will apply the formula for the area of regular polygons to solve problems.
Making Conjectures About Circles and Angles
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Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.
Domain and Range: Numerical Representations
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Given a function in the form of a table, mapping diagram, and/or set of ordered pairs, the student will identify the domain and range using set notation, interval notation, or a verbal description as appropriate.
Interpreting Scatterplots
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Given scatterplots that represent problem situations, the student will determine if the data has strong vs weak correlation as well as positive, negative, or no correlation.
Making Predictions and Critical Judgments (Table/Verbal)
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Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.