6.1.2Ma


 * Grade: 6 Unit: 1 Week: 2 Content: Math Dates: 8/27-8/31/12 **

**Theme Essential Question:** How do you use ratio and rate reasoning to solve real-world and mathematical problems?
 * Essential Questions: **
 * How can I use tables and equivalent ratios, tape diagrams, double number line diagrams, or equations to compare rates of change?
 * What important elements do I need to know about proportional reasoning and when should I apply it?


 * Standards **
 * 6. RP. Ratios and Proportional Relationships
 * Understand ratio concepts and use ratio reasoning to solve problems.
 * 6.RP.3a: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 * Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.


 * Objectives **
 * The student will understand how to make, complete, and read a table of equivalent ratios.
 * The student will understand that tools such as tables of equivalent ratios support the development of ratio and rate reasoning.
 * The student will understand that pairs of values from a table can be plotted on the coordinate plane.
 * The student will understand that establishing connections between tables and plotted points on the coordinate plane allow for extended reasoning and synthesis of the concept of ratios and rates.

@http://www.azed.gov/standards-practices/files/2011/06/2010mathgr6.pdf Ohio Dept of Education Mathematics Model Curriculum 6-28-2011
 * Background Information **
 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.


 * Assessment **
 * Product **
 * Students must create a proposal for pizza(s) that will feed the entire class. Each student has to decide on the type of pizza, the size of pizza, and how many slices of pizza each student will receive. They have to decide the ratio for each piece of pizza that they give to each student and also write a ratio to compare prices of at least 2 different pizza establishments.


 * Key Questions **
 * How do you create tables of equivalent ratios relating quantities with whole number measurements?
 * How do you find the missing value in a table?
 * How do you plot the pairs of values on the coordinate plane?
 * How do you use tables to compare ratios?


 * Observable Student Behaviors **
 * The student can use a table to compare ratios.
 * The student can determine missing values using ratio reasoning.
 * The student can identify relationships in ratio tables.
 * The student can plot pairs of values from a table to a coordinate plane.

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Constant speed Rate of change Multiplicative relationship Coordinate plane x-axis y-axis origin ordered pairs
 * Vocabulary **

**Suggested Activities** [see Legend to highlight MCO and HYS]
 * Houghton Mifflin OnCore Mathematics Middle School Grade 6 Lesson 4-6
 * ABC Mastering the Common Core in Mathematics- Grade 6/Chapter 6, pg. 74-79
 * Teaching the Common Core Math Standards with Hands-On Activities, Grade 6-8/ p.6-7
 * Highly Recommended:
 * @http://illustrativemathematics.org/illustrations/498
 * @http://illustrativemathematics.org/illustrations/66
 * The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
 * JBHM 6th Grade, GP3, Unit 2, P. 161
 * Glencoe Course 1 series: Chapter 10

Diverse Learners:
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: Unit A, Module 7.4


 * Homework **
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials
 * @http://www.kutasoftware.com/free.htmlto print assignments on variety of topics

> Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination > High Yield Strategies > Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice | > Non-Linguistic representation | Cooperative Learning | Objectives/Feedback | > Generating-Testing Hypothesis | Cues, Questions, Organizers Lesson Plan in Word Format (If asked to Log In, Click Cancel)
 * Terminology for Teachers **
 * Multicultural Concepts


 * Resources **
 * Professional Texts **


 * Literary Texts **
 * If You Hopped Like a Frog
 * This book introduces the concepts of ratio and proportion by comparing what humans would be able to do if they had the capabilities of different animals.


 * Informational Texts **
 * See New York Common Core Aligned Task (other resources)


 * Art, Music, and Media **


 * Manipulatives **
 * Multiplication tables
 * Ratio tables – to use for proportional reasoning
 * The National Library of Virtual Manipulatives: http://nlvm.usu.edu


 * Games **


 * Videos **
 * Discovery Education- @http://www.discoveryeducation.com/


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * Discovery Education
 * @http://www.khanacademy.org/math Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder
 * http://www.youtube.com/watch?v=d625kdtsUIw
 * UEN: Price-Earnings ratio @http://www.uen.org/Lessonplan/preview.cgi?LPid=25290


 * SMART Board Lessons, Promethean Lessons **
 * SMART Board Resource Website Smartboard lesson search engine

@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Advanced.pdf This reproducible worksheet, from an Illuminations lesson, presents a table on which students record their predictions about the behavior of pool balls on pool tables of different dimensions. Three related questions accompany the table. @http://illuminations.nctm.org/Lessons/Bagel/Bagel-OVH-Chart.pdf This reproducible transparency, from an Illuminations lesson, presents information from a sign displayed by a real bagel retailer, comparing the price of their bagels to that of their competitor. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L662 A real-life example—taken from a bagel shop, of all places—is used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop’s owner is trying to make. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L422 The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-SquareCross.pdf This reproducible activity sheet, from an Illuminations lesson, presents a table on which students record data about the number of squares that are crossed during a ball's path across paper pool tables of different dimensions. @http://illuminations.nctm.org/LessonDetail.aspx?ID=U125 The interactive paper pool game provides an opportunity for students to develop their understanding of ratio, proportion, greatest common denominator and least common multiple. This investigation includes student resources for the Paper Pool project, preparation notes, answers, and a holistic-by-category scoring rubric with guidelines for how it can be used to assess the project. Samples of two students' work and a teacher's comments accompany the suggested rubric. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Intro.pdf This reproducible activity, from an Illuminations lesson, introduces students to the game of Paper Pool, in which students explore how the dimensions of a pool table affect the pocket into which a ball will fall when hit at a 45 degree angle from a given corner. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L420 The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L421 The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L422 The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L419 In this lesson, one of a multi-part unit from Illuminations, students further develop their understanding of ratio, proportion, and least common multiple by playing an interactive paper pool game. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Project.pdf This reproducible worksheet, from an Illuminations lesson, outlines the instructions for a project in which students use the interactive Paper Pool tool to investigate how the dimensions of a pool table affect a pool ball's behavior. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-Rubric.pdf This reproducible rubric, from an Illuminations lesson, provides a framework for teachers to use when evaluating students' projects researching the effect of a pool table's dimensions on a pool ball's behavior. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Record.pdf This reproducible activity sheet, from an Illuminations lesson, provides a table on which students organize data they collect regarding the number of times a pool ball hits a bumper and in which pocket it lands for pool tables of various dimensions. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-ScoringSamples.pdf This reproducible teacher sheet, from an Illuminations lesson, features samples of students' reports on their investigations of the effect of a pool table's dimensions on the behavior of a pool ball. @http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-MoreTables.pdf This reproducible worksheet, from an Illuminations lesson, depicts several pool tables with different dimensions. Students are asked to determine, if a ball is hit from corner A in each case, the corner in which the ball will eventually land, the number of hits it will make, and the dimensions of the table. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L511 Students learn to write and solve proportions by gathering data and calculating unit rates. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L284 In this lesson, students use real-world models to develop an understanding of fractions, decimals, unit rates, proportions, and problem solving. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L763 In this lesson, students will design a playground using manipulatives and multiple representations. Maximum area with a given perimeter will be explored using tickets. The playground will include equipment with given dimensions, which decreases the maximum area that can be created. This is an interesting demonstration of how a real-world context can change a purely mathematical result. Finally, scale models will be created on graph paper and a presentation will be made to a playground planning committee for approval.
 * Other Activities, etc. **
 * Ohio Resource Center Something Fishy
 * ORC #257: Students will estimate the size of a large population by applying the concepts of ratio and proportion through the capture-recapture statistical procedure.
 * How Many Noses Are in Your Arm?
 * ORC # 130: Students will apply the concept of ratio and proportion to determine the length of the Statue of Liberty’s torch-bearing arm.
 * If You Hopped Like a Frog
 * This book introduces the concepts of ratio and proportion by comparing what humans would be able to do if they had the capabilities of different animals.
 * Glencoe Course 1 textbook: The Game Zone –Fishin’ for Ratios pg 399
 * ** Advanced Paper Pool **
 * ** Bagel Comparison **
 * ** Bagel Algebra **
 * ** Going the Distance **
 * ** How Many Squares are Crossed? **
 * ** Paper Pool: Analyzing Numeric and Geometric Patterns Unit **
 * ** Paper Pool Game **
 * ** Explore More Tables **
 * ** Look for Patterns **
 * ** Going the Distance **
 * ** Paper Pool Game Lesson **
 * ** Paper Pool Project **
 * ** Paper Pool Project Rubric **
 * ** Paper Pool Record Sheet **
 * ** Paper Pool Sample Scoring **
 * ** Paper Pool Tables **
 * ** What's Your Rate? **
 * ** Understanding Rational Numbers and Proportions **
 * ** Planning a Playground **

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