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 Theoretical and Experimental Probability to Make Predictions
Given an event to simulate, the student will use theoretical probabilities and experimental results to make predictions and decisions.
Using Logical Reasoning to Prove Conjectures about Circles
Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Creating Nets for Three-Dimensional Figures
Given nets for three-dimensional figures, the student will apply the formulas for the total and lateral surface area of three-dimensional figures to solve problems using appropriate units of measure.
Drawing Conclusions about Three-Dimensional Figures from Nets
Given a net for a three-dimensional figure, the student will make conjectures and draw conclusions about the three-dimensional figure formed by the given net.
Generalizing Geometric Properties of Ratios in Similar Figures
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
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.
Converting Between Measurement Systems
Given a real-world situation with measurements in either metric/SI or customary units, the student will solve a problem requiring them to convert from one system to the other.
Making Conjectures About Circles and Segments
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
The student will apply the formula for the area of regular polygons to solve problems.
Making Conjectures About Circles and Angles
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.
Using Multiplication by a Constant Factor
Given problems involving proportional relationships, the student will use multiplication by a constant factor to solve the problems.
Predicting, Finding, and Justifying Data from a Table
Given data in table form, the student will use the data table to interpret solutions to problems.
Interpreting Scatterplots
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)
Given verbal descriptions and tables that represent problem situations, the student will make predictions for real-world problems.
Collecting Data and Making Predictions
Given an experimental situation, the student will write linear functions that provide a reasonable fit to data to estimate the solutions and make predictions.
Determining the Domain and Range for Quadratic Functions
Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine the domain and range of the function.
Determining the Domain and Range for Quadratic Functions: Restricted Domain/Range
Given a situation that can be modeled by a quadratic function or the graph of a quadratic function, the student will determine restrictions as necessary on the domain and range of the function.
Analyzing the Effects of the Changes in "a" on the Graph y = ax^2 + c
Given verbal, graphical, or symbolic descriptions of the graph of y = ax^2 + c, the student will investigate, describe, and predict the effects on the graph when a is changed.