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Product and Quotient Properties of Exponents
This lesson helps students understand two foundational exponential properties: The Product and Quotient Properties of Exponents. Students will collaborate to formulate a rule for these properties. Ultimately, students should conclude that when the same bases are being multiplied, exponents will be added; and when the same bases are being divided, exponents will be subtracted. As the lesson progresses, students will apply these rules to simplify expressions of various difficulties.
Using Linear Equations to Count Pecans
Students will write linear equations in point-slope form given two points via a verbal description.
Working with Literal Equations
The lesson will provide a conceptual basis for illustrating the parallelism between solving multi-step equations and translating literal equations into solutions for specified variables.
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 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.
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.
Finding Specific Function Values (Verbal/Symbolic)
Given a verbal and symbolic representations of a function, the student will find specific function values.
Simplifying Polynomial Expressions
Given verbal and symbolic representations of polynomial expressions, the student will simplify the expression.
Solving Equations and Inequalities
Given verbal and symbolic representations in the form of equations or inequalities, the student will transform and solve the equations or inequalities.
Analyzing the Effects of the Changes in m and b on the Graph of y = mx + b
Given algebraic, graphical, or verbal representations of linear functions, the student will determine the effects on the graph of the parent function f(x) = x.
Writing Equations of Lines
Given two points, the slope and a point, or the slope and the y-intercept, the student will write linear equations in two variables.
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.
Predicting, Finding, and Justifying Data from an Equation
Given data in the form of an equation, the student will use the equation to interpret solutions to problems.
Determining the Domain and Range for Linear Functions
Given a real-world situation that can be modeled by a linear function or a graph of a linear function, the student will determine and represent the reasonable domain and range of the linear function using inequalities.
Investigating Methods for Solving Linear Equations and Inequalities
Given linear equations and inequalities, the student will investigate methods for solving the equations or inequalities.