Students extend their understanding of properties of exponents to include rational exponents and radicals, and investigate rates of change in linear and exponential sequences and functions.
In Unit 6, Exponents and Exponential Functions, students compare linear and exponential functions in novel ways to reveal new information about and applications of each one. They also extend their understanding of properties of exponents from eighth grade to include rational exponents and radicals.
In Topic A, students recall the properties of exponents and operations that enable complex-looking expressions to be written more simply. Students are briefly introduced to polynomials, and they add, subtract, and multiply polynomials using properties. Students learn how to write rational exponential expressions from radicals, and vice versa, and they hone their skills in simplifying and computing with both forms.
In Topic B, students are introduced to sequences, specifically arithmetic and geometric sequences. They write recursive and explicit formulas for both types of sequences, focusing on precision in their notation and language. By identifying the common difference or ratio and looking at tables and graphs of sequences, students make connections between the rate of growth of a sequence and whether it is linear or exponential.
In Topic C, students make more explicit connections between increasing or decreasing rates of change and exponential functions. They graph exponential functions and transformations of exponential functions, and they write equations for those functions using key features from the graphs. Students look at several real-world applications of exponential growth and decay, in particular the concept of compound interest.
Pacing: 24 instructional days (22 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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Properties of exponents | Polynomial, binomial, trinomial | Degree of term or polynomial | Leading coefficient |
Exponential expression | Radical | Root | Radicand |
Index | Recursive formula | Explicit formula | Sequence |
Sequence notation, $${a_n}$$ | Fibonacci sequence | Arithmetic sequence | Geometric sequence |
Common difference | Common ratio | Exponential growth/decay function | Compound interest |
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Key: Major Cluster Supporting Cluster Additional Cluster
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