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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.

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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.

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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.

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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.

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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.

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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.

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Kid2Kid: Determining the Meaning of Slope and Intercepts

Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish

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Conservation of Momentum

This resource was created to support TEKS IPC(4)(E).

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Writing Equations to Describe Functional Relationships (Table → Equation)

Given a problem situation represented in verbal or symbolic form, the student will identify functions.

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Writing Verbal Descriptions of Functional Relationships

Given a problem situation containing a functional relationship, the student will verbally describe the functional relationship that exists.

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Writing Inequalities to Describe Relationships (Graph → Symbolic)

Given the graph of an inequality, students will write the symbolic representation of the inequality.

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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.

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Connecting Multiple Representations of Functions

The student will consider multiple representations of linear functions, including tables, mapping diagrams, graphs, and verbal descriptions.

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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.