Pre-Calculus+Function+Review+and+Introduction+to+Limits

**Resource File: Review of Functions and Introduction to Limits** Class Level: 12th Grade Pre-Calculus By Janelle Chong

//Disclaimer: I do not place much clout on the reading levels of these texts, both the Flesch-Kincaid and Lexile Analyzers would not process the majority of the text (primarily numerical/graphical) on any of these pages. In addition, I included two types of scores, because there are some contradictions between them. For example, the Review of Common Graphs Resource has only an 8th grade reading level according to Flesch-Kincaid, but has a lexile score of more than 3,000 which is a difficult level for even the most educated adults (This resource is really quite simple and relatively easy to understand). //
 * __Text based Resources __**

@http://www.teacherspayteachers.com/Product/CSI-Algebra-2-Pre-Calculus-STEM-Project-Complete-eBook-765901 I recommend this site teachersppayteachers.com for a variety of purposes. There are many excellent lessons, activities, and projects for use in the classroom. Many of them are free, but any paid products such as this one are paid towards the teacher who created the product. This particular project is actually a series of 9 different puzzles on the following topics: matrices, families o functions, radical functions, polynomial functions, exponential and logarithmic functions, advanced trigonometry, conic sections, series. For my unit I would utilize any of the puzzles on functions as a unique an interesting type of review. Flesch-Kincaid Grade Level: 17.6 Lexile Level: 1080L
 * CSI: Algebra 2/Pre-Calculus STEM Project **

http://mathonweb.com/help_ebook/html/functions_4.htm A quick reference page on the eight basic types of functions. Covers linear, quadratic, power, polynomial, rational, exponential, logarithmic, and sinusoidal functions. Flesch-Kincaid Grade Level: 7.3 Lexile Level: 1080L
 * Reference - Graphs of Eight Basic Types of Functions **

@http://tutorial.math.lamar.edu/Classes/CalcI/CommonGraphs.aspx <span style="font-family: Georgia,serif;">Another reference page comparing the different graphs of 15 common types of functions. Includes functions beyond those in the mathonweb.com page, such as inverse trigonometric functions. <span style="font-family: Georgia,serif;">Flesch-Kincaid Grade Level: 8.7 <span style="font-family: Georgia,serif;">Lexile Level: 3070L
 * <span style="font-family: Georgia,serif;">Review: Common Graphs **

<span style="font-family: Georgia,serif;">@http://www.wyzant.com/resources/lessons/math/calculus/limits <span style="font-family: Georgia,serif;">This is a page that goes over several examples of limit types with nice visuals and thorough explanations. I like how it explains the conceptual aspects of limits using geometric depictions (with the n-gon) and the sound wave image because I think those may be useful for other types of learners to grasp such an abstract concept. <span style="font-family: Georgia,serif;">Flesch-Kincaid Grade Level: 15.7 <span style="font-family: Georgia,serif;">Lexile Level: 1470L
 * <span style="font-family: Georgia,serif;">Limits Guide **

<span style="font-family: Georgia,serif;"> <span style="font-family: Georgia,serif;">This worksheet is a simple one-paged worksheet which covers left and right handed limits, limits that don't exist, and infinite limits. Simple and straightforward for student despite the high Flesch-Kincaid reading level. Quick check, that can be used as guided practice or as a homework assignment. <span style="font-family: Georgia,serif;">Flesch-Kincaid Grade Level: 14.9 <span style="font-family: Georgia,serif;">Lexile Level: 760L
 * <span style="font-family: Georgia,serif;">Graphing, Continuity, and Limits for Rational Functions Worksheet **

__**<span style="font-family: Georgia,serif;">Web based resources **__

<span style="font-family: Georgia,serif; line-height: 1.5;">@http://www.coolmath.com/precalculus-review-calculus-intro/ <span style="font-family: Georgia,serif;">This is probably my favorite resource of the bunch. It breaks down each topic needed for calculus in simple vocabulary, with clear eye-catching examples and even includes tips and mnemonic devices to help students to remember the processes for graphing and solving a variety of problems.
 * <span style="font-family: Georgia,serif;">Cool Math Pre-Calculus Review Page **

<span style="font-family: Georgia,serif;">@https://www.coursera.org/course/precalculus <span style="font-family: Georgia,serif;">This online pre-calculus course offered for free from UC Irvine. "This course covers mathematical topics in algebra and trigonometry and is designed to prepare students to enroll for a first semester course in single variable calculus."
 * <span style="font-family: Georgia,serif;">Coursera: Pre-Calculus **

<span style="color: #0000ee; font-family: Georgia,serif;">__http://www.brightstorm.com/math/precalculus/__ <span style="font-family: Georgia,serif;">Series of helpful video tutorials on various topics within Pre-Calculus. Useful resource for reteaching, remediation, or enrichment.
 * <span style="font-family: Georgia,serif;">Brightstorm Video Tutorials **

<span style="font-family: Georgia,serif;">@https://www.khanacademy.org/math/precalculus <span style="font-family: Georgia,serif;">Most people are familiar with Khan academy videos, These videos serve as a good supplemental teaching tool, such as for use in a flipped classroom setting, and can also be used as a reteaching resource for struggling students.
 * <span style="font-family: Georgia,serif;">Khan Academy Video Lessons **

<span style="font-family: Georgia,serif;">@http://college.cengage.com/mathematics/larson/precalculus_limits/1e2/ins_resources/ap.html <span style="font-family: Georgia,serif;">This site has a variety of lessons that are animated and interactive. It is broken down by topic and each topic includes short quizzes to check if the student grasps the concept.
 * <span style="font-family: Georgia,serif;">Textbook Companion Site for Precalculus with Limits by Larson and Hostetler **

<span style="font-family: Georgia,serif;">@http://www.youtube.com/watch?v=e9hTWs4L_-I <span style="font-family: Georgia,serif;">This video by Thinkwell video's feature Dr. Edward Burger a mathematics professor and comedian who has an entire online calculus course. However, in this video he covers all the basic concepts of differentiation and integration in 20 minutes. I would use this first part on differentiation and finding instantaneous rate of change in a pre-calculus course as part of the limits lesson so that students will get a glimpse into how limits will be applied when taking calculus.
 * <span style="font-family: Georgia,serif;">Calculus in 20 mins part 1 **

__**<span style="font-family: Georgia,serif;">Unique Resources **__

<span style="font-family: Georgia,serif;">@http://www.mathbits.com/MathBits/PPT/Algebra2Challenge.html <span style="font-family: Georgia,serif;">This Jeopardy game is designed for use to be projected on the board and is divided into two different game boards. In total the topics covered include: Algebra, Trignometry, Equations, Sequences, Quadratics (Challenge 1); Functions, Statistics and Probability, Inequalities, Complex, Exponentials and Logarithmics (Challenge 2).
 * <span style="font-family: Georgia,serif;"> Algebra 2 & Trigonometry Challenge Game **

<span style="font-family: Georgia,serif; line-height: 1.5;">@http://www.travelsinamathematicalworld.co.uk/ <span style="font-family: Georgia,serif;">Podcasts such as this one are useful for showing students the real world application of the mathematics that they are learning in the classroom. In particular, I would use clips of some of the ones on waves in regards to teaching sinusoidal functions.
 * <span style="font-family: Georgia,serif; line-height: 1.5;">Travels in a Mathematical World Podcast **

<span style="font-family: Georgia,serif;">http://www.cpm.org/technology/precalc/ <span style="font-family: Georgia,serif;">This is a good teacher resource, but you need the SMART notebook software to access the lessons. There are also links to an online graphing calculator and various other interactive resources for students.
 * <span style="font-family: Georgia,serif;">SMARTboard Lessons **

<span style="font-family: Georgia,serif;">Website @https://www.mathway.com/ or <span style="font-family: Georgia,serif;">Android App @https://play.google.com/store/apps/details?id=com.bagatrix.mathway.android&hl=en or <span style="font-family: Georgia,serif;">Apple App @https://itunes.apple.com/us/app/mathway/id467329677?mt=8 <span style="font-family: Georgia,serif;">Both a website and link to an app download for an application that can be used to solve mathematical equations. It acts as a graphing calculator, function editor, and glossary for mathematical terms as well. There are specific notations for use in pre-calculus such as limits, logs, and summations which is why I like this app best for the purposes of this unit, but there are notations for all levels of mathematics.
 * <span style="font-family: Georgia,serif;">Mathway Math Problem Solver App **

<span style="font-family: Georgia,serif;">@http://www.youtube.com/watch?v=gRgPD9CiDn4 <span style="font-family: Georgia,serif;">This video is a screencast of a gamer who built an entire city in the game Minecraft. His city is based on the OneState which is the setting for the novel which my ELA partner is teaching and I would use this video as an inspiration for a final project for this unit. The project will be to take a quote with mathematical vocabulary (there's quite a bit as the main character and narrator is a mathematician who likes to describe his world in mathematical terms) and make a visual representation of that scene in the book and explain how their visual depiction is mathematically accurate.
 * <span style="font-family: Georgia,serif;">Video of Minecraft world inspired by Yevgeny Zamyatin's novel We **

<span style="font-family: Georgia,serif;">media type="custom" key="25426104" <span style="font-family: Georgia,serif;">