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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.

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Introduction to Character Foils

During this lesson, students will view video clips and read texts that have character foils examples. Students will complete a graphic organizer with evidence that supports their identification of foil characters. Once complete, students will use the information from the graphic organizer to discuss character foils.

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Metacognitive Approaches to Student-based Learning

In this lesson, students will learn how to make complex inferences and draw conclusions about a work of literary fiction using a combination of text evidence and background knowledge. Using a graphic organizer and a short story, students will record both text evidence and their prior knowledge, and combine these elements to make an inference about the character.

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Una Reseña de un Restaurante

Students describe a restaurant in restaurant review form using simple phrases and sentences. As they write, students focus on noun-adjective agreement and sentence structure.

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Using Linear Equations to Count Pecans

**Students will write linear equations in point-slope form given two points via a verbal description.**

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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.

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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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Quadratics: Connecting Roots, Zeros, and x-Intercepts

Given a quadratic equation, the student will make connections among the solutions (roots) of the quadratic equation, the zeros of their related functions, and the horizontal intercepts (*x*-intercepts) of the graph of the function.

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Applying the Laws of Exponents: Verbal/Symbolic

Given verbal and symbolic descriptions of problems involving exponents, the student will simplify the expressions using the laws of exponents.

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Using the Laws of Exponents to Solve Problems

Given problem situations involving exponents, the student will use the laws of exponents to solve the problems.

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Formulating Systems of Equations (Verbal → Symbolic)

Given verbal descriptions of situations involving systems of linear equations the student will analyze the situations and formulate systems of equations in two unknowns to solve problems.

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Solving Quadratic Equations Using Graphs

Given a quadratic equation, the student will use graphical methods to solve the equation.

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Determining the Meaning of Intercepts

Given algebraic, tabular, and graphical representations of linear functions, the student will determine the intercepts of the function and interpret the meaning of intercepts within the context of the situation.

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Predicting the Effects of Changing y-Intercepts in Problem Situations

Given verbal, symbolic, numerical, or graphical representations of problem situations, the student will interpret and predict the effects of changing the *y*-intercept in the context of the situations.

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Solving Linear Inequalities

The student will represent linear inequalities using equations, tables, and graphs. The student will solve linear inequalities using graphs or properties of equality, and determine whether or not a given point is a solution to a linear inequality.

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Direct Variation and Proportional Change

The student will use a variety of methods inculding tables, equations and graphs to find the constant of variation and missing values when given a relationship that varies directly.

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Analyzing Graphs of Quadratic Functions

Given the graph of a situation represented by a quadratic function, the student will analyze the graph and draw conclusions.