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 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.
Kid2Kid: Determining the Meaning of Slope and Intercepts
Kid2Kid videos on determining the meaning of slope and intercepts in English and Spanish
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.
Developing the Concept of Slope
Given multiple representations of linear functions, the student will develop the concept of slope as a rate of change.
Using Multiplication by a Constant Factor
Given problems involving proportional relationships, the student will use multiplication by a constant factor to solve the problems.
Generating Different Representations of Relationships
Given problems that include data, the student will generate different representations, such as a table, graph, equation, or verbal description.
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.
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.
Predicting, Finding, and Justifying Data from Verbal Descriptions
Given data in a verbal description, the student will use equations and tables to solve and interpret solutions to problems.
Solving Quadratic Equations Using Concrete Models
Given a quadratic equation, the student will use tiles to factor and solve the equation.
Solving Quadratic Equations Using Algebraic Methods
Given a quadratic equation, the student will solve the equation by factoring, completing the square, or by using the quadratic formula.
Approximating the Value of Irrational Numbers
Given problem situations that include pictorial representations of irrational numbers, the student will find the approximate value of the irrational numbers.
Expressing Numbers in Scientific Notation
Given problem situations, the student will express numbers in scientific notation.
Predicting, Finding, and Justifying Data from a Graph
Given data in the form of a graph, the student will use the graph to interpret solutions to problems.
Solving Systems of Equations with Graphs
Given verbal and/or algebraic descriptions of situations involving systems of linear equations, the student will solve the system of equations using graphs.
Determining if a Relationship is a Functional Relationship
The student is expected to gather and record data & use data sets to determine functional relationships between quantities.
Graphing Dilations, Reflections, and Translations
Given a coordinate plane, the student will graph dilations, reflections, and translations, and use those graphs to solve problems.