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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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Conversations in Art

In this lesson, students will learn the critique process using description, analysis, interpretation, and evaluation. Students will create an evaluation of artwork using the critique process and communicate their understanding through written responses and discourse.

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Solving Equations and Inequalities

Students will be divided into four groups and work on their assigned task to become an expert. They will match vocabulary terms with definitions and examples, use the “Pass the Pen” strategy to create and solve equations or inequalities, or write a real-world problem for an equation given. The experts will then teach these concepts to their peers.

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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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Express Yourself

Students determine which expression is a truth or a lie by generating equivalent expressions.

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Keep Your Balance!

**Students are introduced to solving one-variable, one-step equations using addition and subtraction through models and hands-on activities. The students will learn the substitution method of checking answers.**

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Perfecting Percents

Students will engage in an activity that allows them to explore the different parts of percents: part, whole, and percent, and develop conceptual understanding of percents through the Concrete, Representational, Abstract (CRA) method of instruction.

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Perfectly Proportional Percents

Students will collaborate to explain verbally how to solve percent proportions and scaling while showing their thinking.

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The Key to Key Signature

Students will review previous learning about half steps, whole steps, and enharmonics and will begin to learn the construction of tetrachords using the whole and half step sequence.

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Transformations of Absolute Value Functions

Given an absolute value function, the student will analyze the effect on the graph when f(x) is replaced by af(x), f(bx), f(x – c), and f(x) + d for specific positive and negative real values.

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Up, Up, and Away

Students will determine an appropriate tabular/graphic/formulaic linear solution given 3 sets of data points.

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How Does the Cookie Crumble?

Students will self-discover how to multiply mixed numbers by using background knowledge of estimation, computations, and real world application of a recipe.

**Texas Essential Knowledge and Skills Related to the Unit **

In fifth grade, students will be able to multiply and divide whole numbers, which will lead into multiplication and division of decimals in sixth grade. That same year, they will model products and quotients of decimals to the hundredths place. This concrete model will lead them to a better understanding of the algorithm in fifth and sixth grade.

As fifth graders, students will model multiplication and division of a fraction and a whole number. The following year, students are expected to multiply and divide all types of fractions.

In addition, during sixth grade, students are introduced to integers (negative whole numbers) and will be able to model and solve all operations with integers. All of the skills previously stated will lead students to be able to perform all operations of rational numbers without models (positive and negative fractions, decimals, and whole numbers) in seventh grade.

Click below to learn more about the TEKS related to this unit. The highlighted standards have been chosen for this research lesson.

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Laws of Exponents

Students will discover the laws of exponents using problem-solving skills.

**Texas Essential Knowledge and Skills (TEKS) Vertical Alignment**

Click below to learn about the TEKS related to the unit and Research Lesson. The highlighted student expectation(s) is the chosen focus for the Research Lesson.

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Rate of Change

The students will determine the rate of change from tables and graphs by using the slope formula. The students will discover and interpret the real-world applications of rate of change.

**Texas Essential Knowledge and Skills (TEKS) Vertical Alignment**

Click below to learn about the TEKS related to the unit and Research Lesson. The highlighted student expectation(s) is the chosen focus for the Research Lesson.

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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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Finding Specific Function Values (Verbal/Symbolic)

Given a verbal and symbolic representations of a function, the student will find specific function values.

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Simplifying Polynomial Expressions

Given verbal and symbolic representations of polynomial expressions, the student will simplify the expression.