6.1.3Ma

** Grade: 6 Unit: 1 Week: 3 Content: Math Dates: 9/4-9/7/12 **

** Theme Essential Question: ** How do students use and understand ratio concepts and rate reasoning to solve real-world and mathematical problems? ** Essential Questions: **
 * Can students visualize different characteristics of real world problems in order to solve unit rates?

** Ratios and Proportional Relationships 6.RP ** ** Understand ratio concepts and use ratio reasoning to solve problems. **  ** Objectives **
 * Standards **
 * ** 6.RP.3: ** 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.
 * a. 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.
 * b. Solve unit rate problems including those involving unit pricing and constant speed. //For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?//
 * The student will understand that tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations support the development of ratio and rate reasoning.
 * The student will understand that rate problems compare two different units, such as miles to hours.
 * The student will recognize that a unit occurs when at least one of the units is one (1/3 or 4:1).
 * The student will understand that establishing connections between tools allow for extended reasoning and synthesis of the concept of ratios and rates (e.g., How do tape diagrams and double number lines show rate reasoning given the same context?).

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

** Assessment ** ** Product **  ** Key Questions **
 * Have students to browse several articles in the newspaper and find the ratios of various items listed in a news article and explain to the group what it means. Ex. Recipe(s), various people (2 out of 3 dentists, etc.)
 * New York City's CCSS Benchmark Assessment Questions with Rubrics-P 12

** Observable Student Behaviors **

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. || <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Vocabulary ** <span style="color: windowtext; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">equivalent ratios notation (//a/b//=//c/d)// or //a// is to //b// as //c// is to //d//; ratio; unit rate
 * ** Mathematical Practices **

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Suggested Activities ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Diverse Learners: ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Homework ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Terminology for Teachers ** <span style="color: windowtext; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">equivalent ratios notation (//a/b//=//c/d)// or //a// is to //b// as //c// is to //d//; ratio; unit rate
 * __ Houghton Mifflin OnCore Mathematics Middle School Grade 6 __ Lesson 7 and 8
 * __ Teaching the Common Core Math Standards with Hands on Activities __
 * Pg. 6-7
 * __ Mastering Common Core in Mathematics-Grade 6 (ABC) __
 * Pg. 80-81 Ch. 6.6 and 6.7
 * Glencoe Course 1 series: Chapter 10, P 381-382
 * Odyssey (teacher discretion)
 * Skills Tutor (teacher discretion)
 * Math’scool: Unit A, Module 7.4
 * See appropriate Glencoe, OnCore, JBHM, and ABC materials
 * [|**http://www.kutasoftware.com/free.html**] to print assignments on variety of topics

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * ||  || ** Multicultural Concepts ** ** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination  ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice |  ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback |  ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  ||   ||
 * ||  || ** Multicultural Concepts ** ** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination  ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice |  ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback |  ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers  ||   ||

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Resources **

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Professional Texts **

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Literary Texts **

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Informational Texts ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Art, Music, and Media **
 * @http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm This site gives detailed tasks and assessments for each standard. You can search by subject, grade, or standard.

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Manipulatives ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Games **
 * Coordinate plane handout
 * Ratio tables – to use for proportional reasoning
 * The National Library of Virtual Manipulatives: http://nlvm.usu.edu

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Videos ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Websites ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;"> <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** SMART Board Lessons, Promethean Lessons ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">SMART Board Resource Website Smartboard lesson search engine
 * Discovery Education- @http://www.discoveryeducation.com/
 * @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 __

<span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">** Other Activities, etc. ** <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Advanced.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/Bagel/Bagel-OVH-Chart.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L662 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L721 <span style="color: #162f41; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://artsedge.kennedy-center.org/educators/lessons/grade-6-8/Castles_and_Cornerstones.aspx <span style="color: #343434; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">This lesson will explore the historic importance and function of castles in King Arthur's time and introduce students to a general history of castles and architectural terms. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L422 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-SquareCross.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L743 <span style="color: #162f41; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">This lesson focuses students on the concept of 1,000,000. It allows students to see first hand the sheer size of 1 million while at the same time providing them with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=U125 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Intro.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L420 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L421 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L422 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L419 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Project.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-Rubric.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-Record.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-ScoringSamples.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/Lessons/PaperPool/PaperPool-AS-MoreTables.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L511 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Students learn to write and solve proportions by gathering data and calculating unit rates. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L284 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">In this lesson, students use real-world models to develop an understanding of fractions, decimals, unit rates, proportions, and problem solving. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L763 <span style="color: #162f41; display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">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. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://americanhistory.si.edu/onthemove/learning/thinkfinity/AOTM_Unit5_Activity3.pdf <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">In this classroom activity from the Smithsonian's National Museum of American History, students will examine primary sources from the 1970s through 2000 to learn about the impact of global migrations of workforce. The activity provides opportunities for historical analysis, interpretation, evaluation, analyzing cause/effect relationships, understanding multiple points of view, performing original research, debating and persuasive writing. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=U178 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">This unit affords students the opportunity to think about two aspects of the time required to complete space travel within the solar system. First, students consider the amount of time that space travelers must spend on the journey. Second, students think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinking about both situations improves students' concept of time and distance as well as improves their understanding of the solar system. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L281 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">This lesson affords students the opportunity to think about two aspects of the time required to complete space travel within the solar system. First, students consider the amount of time that space travelers must spend on the journey. Second, students think about what kinds of events might occur on Earth while the space travelers are on their journey. Thinking about both situations improves students' concept of time and distance as well as improves their understanding of the solar system. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L706 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance, while at the same time learn more about the solar system. <span style="display: block; font-family: arial,helvetica,sans-serif; text-align: left;">@http://illuminations.nctm.org/LessonDetail.aspx?ID=L707 <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 11pt; text-align: left;">Students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.
 * ** Advanced Paper Pool **
 * ** Bagel Comparison **
 * ** Bagel Algebra **
 * ** Capture–Recapture **
 * ** Castles & Cornerstones **
 * ** Going the Distance **
 * ** How Many Squares are Crossed? **
 * ** How Much Is a Million? **
 * ** 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 **
 * ** 1970s - 2000 The World's People and Products on the Move **
 * ** Travel in the Solar System Unit **
 * ** Travel in the Solar System **
 * ** Space Shuttle **
 * ** How Much Time Do We Need? **

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