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RP2 Num Line Oct12 MatrixMath Instructional Guide Alan Amundsen Contributors: Sara Munshin, Lida Lim, Amy Murphy MetaFour Productions, a 501 (c)(3) 2189 Fern Dell Place Los Angeles, CA 90068 [email protected] • (323) 465-7347 • MetaFourProductions.org MatrixMath Instructional Guide Numericon Table of Contents I. Ratio and Proportion II. Linear Equations III. Data, Statistics, and Probability IV. Geometry Numericon is a game-like math video series addressing Ratio & Proportion; Linear Equations; Data, Statistics, & Probability; and Geometry. Numericon motivates students to learn and apply math concepts while answering the age-old question, “How does this math apply to real life?” While each episode offers a satisfying beginning and conclusion that can be used as a stand-alone teaching tool, the complete narrative includes character development that underscores values such as teamwork, loyalty, trust, and responsibility to oneself and others. Numericon is a cinematic 26-episode science fiction adventure, filled with action-packed cliffhanger sequences. A highly diverse team of space mercenaries follows the instructions of their captain, the student, to solve increasingly complex standards-based math problems that will ultimately determine the fate of the universe. Each Numericon episode consists of three segments: Challenge – The story begins and the team finds itself in a predicament that must be solved using math. Counselor – Students can check with the counselor. She will offer hints and strategies to help complete the mission. Resolution – Once the student has helped the crew to solve the math problem, the mission is completed and the episode concludes. The crew is one step closer to saving the universe. Supporting the Numericon Video Series – MatrixMath Instructional Guide The purpose of the MatrixMath Instructional Guide is to help teachers assist students in understanding the mathematics behind the problems posed in Numericon video episodes. The MatrixMath Instructional Guide defines the mathematical concepts needed in each episode. Guides include “Lesson Concepts” as well as classroom activities to further the students’ understanding. The guide discusses the key mathematics topics accompanied by examples and practice problems. It is suggested that the teacher plan each lesson using the information and activities presented in this guide to sequence the material for each topic. Before beginning work on a concept, students can view the Numericon video. The video will highlight a student’s understanding or lack of understanding of the concept, yet provide an impetus for learning and mastery. Following the “challenge,” students work in pairs, small groups, or as a class to cooperatively reach a solution. 2 ©Alliance for Distance Education in California and Ohio Board of Regents MatrixMath Instructional Guide Numericon Episodes and Mathematics Content Matrix Star Schools Project - This guide and other products produced by the Alliance for Distance Education in California under the title, MatrixMath, were developed as part of the national project, Matrix Learning, which was funded by the federal Matrix Star Schools grant. 4 ©Alliance for Distance Education in California and Ohio Board of Regents MatrixMath Instructional Guide Ratio and Proportion I. Introduction Why study ratio and proportion? II. Number Lines and Rational Numbers Numericon Videos: Episode: #1 “Into the Warp” Episode: #2 “Ghost Ship” Lesson Concepts: Locating fractions on a number line Common Core Standards: Number Lines and Rational Numbers Grade Six - The Number System Apply and extend previous understandings of numbers to the system of rational Numbers. #6 Rewriting Common Fractions Grade Six -Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #3 Grade Six – The Number System Apply and extend previous understandings of numbers to the system of rational Numbers, #6 III. Ratio Numericon Videos: Episode: #3 “The Eye of Power” Episode: #4 “The Deadly Chase” Episode: #5 “The Gift of Destiny” Episode: #6 “The Deal of Doom” Lesson Concepts: Comparing two quantities o Writing ratios in simplest form o Ratios and rates Part to Whole Equivalent ratios Graphing equivalent ratios o Writing fractions in lowest terms o Writing ratios in lowest terms o Ratios as decimals Common Core Standards: Comparing Two Quantities; Part to Whole; Equivalent Ratios 5 ©Alliance for Distance Education in California and Ohio Board of Regents Grade Six -Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #3. Graphing Equivalent Ratios Grade Six -Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #1 and #3. Grade Seven -Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems, #2. IV. Proportion Numericon Videos: Episode: #7 “Horrible Surprise” Episode: #8 “Crash Landing” Episode: #9 “Marooned!” Lesson Concepts: Finding Missing Parts of Proportions: Cross Product Rule Map Reading Scale drawings (unit conversion) o Dilation Common Core Standards: Introduction to Proportion Grade Seven -Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems, #2. Scale Drawings (Unit Conversions) Grade Six -Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #3. Grade Seven -Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems, #2.Common Core Standards V. Percents Numericon Videos: Episode: #10 “The Underground” Lesson Concepts: Percents, Fractions, Ratios Solving Percent Problems with Vertical Number Lines Common Core Standards: Grade Six -Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #3. Grade Seven -Ratios and Proportional Relationships 6 ©Alliance for Distance Education in California and Ohio Board of Regents Analyze proportional relationships and use them to solve real-world and mathematical problems, #2. VI. Rate Numericon Videos: No episodes - Practice Problems Lesson Concepts: Unit Rate and Unit Price Common Core Standards: Grade Six – Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #2 and #3. Grade Seven - Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems, #1. VII. Direct Variation Numericon Episodes: No episodes - Practice Problems Lesson Concepts: Using Proportion to Solve Direct Variation Problems Common Core Standards: Grade Eight – Functions Use functions to model relationships between quantities, # 4 and #5. VIII. Glossary English and Spanish mathematical terms with English explanations IX. Numericon Episode Titles/Problems/Answers 7 ©Alliance for Distance Education in California and Ohio Board of Regents MatrixMath Instructional Guide Numericon Episodes 1-10 Why Study Ratio and Proportion? Ratio and proportion provides the underpinnings to understanding the rational numbers and their representations. Proportional reasoning is the foundation of a deeper understanding of equivalent ratios and their applications. Student understanding of ratio and proportion is essential for success in algebra and beyond. The connection among equivalent ratios, similar figures and the concept of slope is key to knowledge of linear functions. Additional applications of ratio and proportion occur in probability, trigonometry, and statistics and in other situations where linearity is involved. This unit on ratio and proportion will assist teachers in: • developing the concepts of ratios and equivalent ratios • showing how ratios are used in a proportion to represent equivalent quantities • exploring rates in different applications of proportions. 8 ©Alliance for Distance Education in California and Ohio Board of Regents MatrixMath Instructional Guide Number Line Number Lines and Ra tional Numbers COMMON CORE STATE STANDARDS: MATHEMATICS Number Lines and Rational Numbers Grade Six - The Number System Apply and extend previous understandings of numbers to the system of rational numbers, #6. Rewriting Common Fractions Grade Six - Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems, #3. Grade Six – The Number System Apply and extend previous understandings of numbers to the system of rational numbers, #6c. Relevant Numericon episodes: #1 “Into the Warp” #2 “Ghost Ship” PRESENTING EXPLANATIONS Help students through this lesson by using the information in this section. The definition that follows might prove helpful to you. The examples presented in the form of problems are invaluable to the students. Be sure the students understand the concepts before they proceed to independent practice. You might want to ask students to restate the explanation once you have gone over it with them. Understanding Rational Numbers The study of ratio and proportion assumes an understanding of rational numbers. Rational numbers are a natural extension of the whole numbers and their additive inverses, i.e., integers. Let’s look at numbers and how we represent them. Numbers are first introduced to students by asking them to count things. Kindergartners count the days of the week by forming a correspondence
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