Pre-Calculus: Graphs and Limits By: Bryan Price

Contents and Standards Pennsylvania Mathematics Standards: Trigonometry – Use graphing calculators to display periodic and circular functions: describe properties of graphs Calculus – Determine maximum and minimum values of a function over a specified interval

Contents and Standards – ISTE Standards Creativity and Innovation – Apply existing knowledge to generate new ideas, products, or processes – Create original works as a means of personal or group expression – Use models and simulations to explore complex systems and issues – Identify trends and forecast possibilities Communication and Collaboration – Contribute to project teams to produce original works or solve problems Research and Information Fluency – Plan strategies to guide inquiry – Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media – Evaluate and select information sources and digital tools based on the appropriateness to specific tasks – Process data and report results Critical Thinking, Problem Solving, and Decision Making – Collect and analyze data to identify solutions and/or make informed decisions – Use multiple processes and diverse perspectives to explore alternative solutions Technology Operations and Concepts – Understand and use technology systems – Select and use applications effectively and productively – Transfer current knowledge to learning of new technologies

Prerequisites Algebra 1, Geometry, and Algebra 2 Basic knowledge of limits Basic knowledge of computers

Instructional Objective: Students will achieve knowledge of domain and range of functions Students will also be able to use Wolfram Alpha or a TI-83 to compute limits and graph functions

Instructional Procedure: Before Why is graphing important? – Different ways to graph, display information Introduction to Wolfram Alpha – Differences and similarities to graphing calculator

Instructional Procedure: During Students will be handed worksheet of different functions to input in to Wolfram Alpha, working in groups – Will be asked to graph functions – Will be asked to state different ways to write the same function – Will be asked to state domain and range – Will be asked to take limits of certain functions

Instructional Procedure: After Students will discuss in a small groups why things are shifting, changing Students will be asked to graph a function of their own creation and explain the transformations from the parent graph Limits will be included within their explanation

Materials and Equipment – Graphing calculator To reassure students that wolfram is graphing correctly To see how wolfram is more powerful the graphing calculator – Pens, pencils To draw graphs – Graphing paper To have paper to draw on – Computer (Mac of PC) To access the internet and use Wolfram Alpha

Assessment and Evaluation – Students will be given homework requiring them to graph different functions – A similar worksheet will be given out from one in class but with more complex problems – Students will be encouraged to use Wolfram Alpha to help complete homework – Students may also use graphing calculator to complete the homework

Accommodations – Students with Learning Disabilities will be asked to do the same lesson but there will be less complex graphs – Homework will be given a few extra days to complete – Another lab day may be necessary

Technology – Wolfram Alpha Mathematics Wolfram Alpha Mathematics – Wolfram Alpha will be demonstrated using a projector This technology will assist in learning because it will allow students to visualize functions and see if limits exist

Self-Assessment – Near the end of class students will be polled to see how they enjoyed using Wolfram Students will be asked if they would have liked more knowledge of the site than was given – During lesson teacher will see how attentive students are to using the computer and internet to demonstrate pre-calculus concepts – Homework grades will demonstrate the collective understanding of the day’s lesson