Math 8 Unit 8

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This chapter begins with an examination of linear and exponential growth. Students were introduced to tools for describing patterns in tables and graphs in Chapter 4 when they began working with linear functions, and further developed those tools in Chapter 7 as they studied slope and rates. At the beginning of Section 8.1, students look at various relationships and try to predict what shape their graphs will take. They then focus on comparing patterns of growth in simple interest and compound interest relationships, using the tools they have developed in previous chapters. Work with simple interest began in Chapter 7; in this chapter, students will analyze graphs and tables of values for simple interest alongside those for compound interest in order to describe the characteristics that distinguish linear growth (found in situations involving simple interest) and exponential growth (found in situations involving compound interest).

Students will then use the patterns in their tables and graphs of compound interest situations to generate expressions that can be written most simply with exponents. In Section 8.2, they will explore ways to simplify and rewrite expressions with exponents. Students will also interpret, rewrite and perform operations with numbers that are given in scientific notation.

In Section 8.3 students will be introduced to the concept of a function. Students will learn how to identify a function from a table and a graph and will learn how to completely describe graphs of functions and non-functions. Function notation, domain and range are not introduced in this course.

The main focus of Chapter 8 is for students to look for and express regularity in repeated reasoning while looking at patterns and situations that involve repeated addition or multiplication. They look for and make use of the structure of exponent notation to simplify expressions with exponents and work with numbers written in scientific notation. In the last lesson of the chapter, students make use of the structure of a function, identifying functions from tables and graphs.

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3^–5 = 3^–3 = 1/3³= 1/27.

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹, and determine that the world population is more than 20 times larger.

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

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