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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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Proving an Ecosystem’s Health Through Succession

**Students engage in viewing day three of ecosystem changes in lab groups to determine if the ecosystem is healthy or unhealthy based on scientific data and factors. **

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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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Mendelian Genetics Using Monohybrids

Students will work collaboratively through a fictitious, real-world scenario to determine the probability of each breeding pair of dogs producing offspring with the desired trait for a fictitious client.

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Producing Plump Produce

In collaborative groups, the students investigate the transport of water within potato cells placed in various tonicity solutions.

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Plant, Parts, and Function

Students use prior knowledge of body systems as they make connections to systems in plants. Students learn that some plant systems have similar functions as the respective animal systems. The lesson highlights the following systems in plants: root system, shoot system, vascular system, and reproductive system.

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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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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*.

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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.

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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.

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Investigating Methods for Solving Linear Equations and Inequalities

Given linear equations and inequalities, the student will investigate methods for solving the equations or inequalities.

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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.