![]() This lesson is built for use on classroom computers and tablets. Graphing Lines and Generating Tables in the Graphing Calculator Opens a new window Using This Site Simulation 1: Exponential Growth, Sampling without Replacement Opens a new windowįor additional resources, visit the following site: The following website is linked to from this module: In addition, multimedia on these externally linked sites may not be accessible to all users, such as those individuals requiring a screen reader or using a tablet. Teachers should preview all websites before introducing the activities to students and adhere to their school system's policy for Internet use. Efforts are made to minimize linking to websites that contain advertisements or comments, but some websites may contain these features. The site has been chosen for its content and grade-level appropriateness. In this module, students are provided with links to external websites. Use tables and patterns to find the quantity at which point a given geometric sequence exceeds the quantities in an arithmetic sequence.Extend arithmetic sequences and geometric sequences to find values in order to solve problems.Determine the common ratio, or constant factor, in a geometric sequence.Determine the common difference in an arithmetic sequence.Quadratic functions and polynomial functions are not addressed in this module. *Note that this module focuses on arithmetic sequences and geometric sequences, building the background knowledge students need to study linear functions and exponential functions. .LE.A.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function..LE.A.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)..LE.A.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.Visit the Glossary page for definitions of key vocabulary in this module. ![]() Explicit and recursive formulas are found.Arithmetic Sequences and Geometric Sequences This activity builds the fundamentals of geometric sequences by finding missing terms and then slowly abstracting the process. Explicit formulas are found and the connection between the explicit formula and the slope-intercept form of a line is emphasized.Īrithmetic Sequences Activity 2c – Geometric Sequences ![]() This activity builds the fundamentals of arithmetic sequences by finding missing terms and then slowly abstracting the process. ![]() Recursion and Abstraction Activity 2b – Arithmetic Sequences If so, students should be encouraged to learn how to express formulas recursively, and writing recursive formulas is a good outcome even for students that are unable to write the explicit formula. Depending on the students’ familiarity with equations of lines, they may be adapt at writing explicit formulas. Students are asked to put results in a table, and may also be able to express formulas. This description should be done in words, and can also be used as an introduction to the mathematically notation for sequences. This activity encourages students to look for patterns and to describe a step-by-step procedure. Activities – Chapter 2 Activity 2a – Recursion and Abstraction ![]()
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