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.
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.
Writing Expressions to Model Patterns (Table/Pictorial → Symbolic)
Given a pictorial or tabular representation of a pattern and the value of several of their terms, the student will write a formula for the nth term of a sequences.
Kid2Kid: Determining the Meaning of Slope and Intercepts
Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish
Writing Equations to Describe Functional Relationships (Table → Equation)
Given a problem situation represented in verbal or symbolic form, the student will identify functions.
Writing Verbal Descriptions of Functional Relationships
Given a problem situation containing a functional relationship, the student will verbally describe the functional relationship that exists.
Writing Inequalities to Describe Relationships (Graph → Symbolic)
Given the graph of an inequality, students will write the symbolic representation of the inequality.
Writing Inequalities to Describe Relationships (Symbolic → Graph)
Describe functional relationships for given problem situations, and write equations or inequalities to answer questions arising from the situations.
Connecting Multiple Representations of Functions
The student will consider multiple representations of linear functions, including tables, mapping diagrams, graphs, and verbal descriptions.
Writing the Symbolic Representation of a Function (Graph → Symbolic)
Given the graph of a linear or quadratic function, the student will write the symbolic representation of the function.
Determining Parent Functions (Verbal/Graph)
Given a graph or verbal description of a function, the student will determine the parent function.
Determining Reasonable Domains and Ranges (Verbal/Graph)
Given a graph and/or verbal description of a situation (both continuous and discrete), the student will identify mathematical domains and ranges and determine reasonable domain and range values for the given situations.
Interpreting Graphs
Given a graph, the student will analyze, interpret, and communcate the mathematical relationship represented and its characteristics.
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.