6.1.1Ma


 * Grade: 6 Unit: 1 Week: 1 Content: Math Dates: 8/20-8/24/12 **

**Theme Essential Question:** How do students connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems?


 * Essential Questions: **
 * How are ratios and rates related to fractions?
 * How can I use multiplication and division to solve ratio and rate problems?
 * What is the difference between a ratio and a rate?

6. RP. Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems.
 * Standards **
 * 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
 * 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1


 * Objectives **
 * The student will understand the concept of a ratio as a way of expressing relationships between quantities.
 * The student will distinguish when a ratio is describing part to part or part to whole comparison.
 * Understand that a rate is a special ratio that compares two quantities with different units of measure.
 * Understand that unit rates are the ratio of two measurements in which the second term is one (e.g., x miles per one hour).
 * Understand that when using rates 𝑎𝑏, “b” cannot be 0 (because division by 0 is undefined).


 * Reflection and/or Comments from your PCSSD 6th Grade Curriculum Team **

(Taken from Ohio Dept. of Education Mathematics Model Curriculum 5/31/2011) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. In Grade 6, students develop the foundational understanding of ratio and proportion that will be extended in Grade 7 to include scale drawings, slope and real-world percent problems.

(Taken from Ohio Dept. of Education Mathematics Model Curriculum 5/31/2011) Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 Fractions and ratios may represent different comparisons. Fractions always express a part-to-whole comparison, but ratios can express a part-to-whole comparison or a part-to-part comparison.
 * Common Misconceptions: **

Even though ratios and fractions express a part-to-whole comparison, the addition of ratios and the addition of fractions are distinctly different procedures. When adding ratios, the parts are added, the wholes are added and then the total part is compared to the total whole. For example, (2 out of 3 parts) + (4 out of 5 parts) is equal to six parts out of 8 total parts (6 out of 8) if the parts are equal. When dealing with fractions, the procedure for addition is based on a common denominator: which is equal to. Therefore, the addition process for ratios and for fractions is distinctly different. Often there is a misunderstanding that a percent is always a natural number less than or equal to 100. Provide examples of percent amounts that are greater than 100%, and percent amounts that are less 1%.

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 Taken from Ohio Dept. of Education Mathematics Model Curriculum 5/31/2011 Proportional reasoning is a process that requires instruction and practice. It does not develop over time on its own. Grade 6 is the first of several years in which students develop this multiplicative thinking. Examples with ratio and proportion must involve measurements, prices and geometric contexts, as well as rates of miles per hour or portions per person within contexts that are relevant to sixth graders. Experience with proportional and non-proportional relationships, comparing and predicting ratios, and relating unit rates to previously learned unit fractions will facilitate the development of proportional reasoning. Although algorithms provide efficient means for finding solutions, the cross-product algorithm commonly used for solving proportions will not aid in the development of proportional reasoning. Delaying the introduction of rules and algorithms will encourage thinking about multiplicative situations instead of indiscriminately applying rules. Students develop the understanding that ratio is a comparison of two numbers or quantities. Ratios that are written as part-to-whole are comparing a specific part to the whole. Fractions and percents are examples of part-to-whole ratios. Fractions are written as the part being identified compared to the whole amount. A percent is the part identified compared to the whole (100). Provide students with multiple examples of ratios, fractions and percents of this type. For example, the number of girls in the class (12) to the number of students in the class (28) is the ratio 12 to 28. Percents are often taught in relationship to learning fractions and decimals. This cluster indicates that percents are to be taught as a special type of rate. Provide students with opportunities to find percents in the same ways they would solve rates and proportions. Part-to-part ratios are used to compare two parts. For example, the number of girls in the class (12) compared to the number of boys in the class (16) is the ratio the ratio 12 to 16. This form of ratios is often used to compare the event that can happen to the event that cannot happen. Rates, a relationship between two units of measure, can be written as ratios, such as miles per hour, ounces per gallon and students per bus. For example, 3 cans of pudding cost $2.48 at Store A and 6 cans of the same pudding costs $4.50 at Store B. Which store has the better buy on these cans of pudding? Various strategies could be used to solve this problem: • A student can determine the unit cost of 1 can of pudding at each store and compare. • A student can determine the cost of 6 cans of pudding at Store A by doubling $2.48. • A student can determine the cost of 3 cans of pudding at Store B by taking ½ of $4.50. Using ratio tables develops the concept of proportion. By comparing equivalent ratios, the concept of proportional thinking is developed and many problems can be easily solved.
 * Background Information **

Store A Store B
 * 3 cans || 6 cans ||
 * $2.48 || $4.96 ||
 * 6 cans || 3 cans ||
 * $4.50 || $2.25 ||

Students should also solve real-life problems involving measurement units that need to be converted. Representing these measurement conversions with models such as ratio tables, t-charts or double number line diagrams will help students internalize the size relationships between same system measurements and relate the process of converting to the solution of a ratio.

Multiplicative reasoning is used when finding the missing element in a proportion. For example, use 2 cups of syrup to 5 cups of water to make fruit punch. If 6 cups of syrup are used to make punch, how many cups of water are needed?

Recognize that the relationship between 2 and 6 is 3 times; 2 · 3 = 6 To find x, the relationship between 5 and x must also be 3 times. 3 · 5 = x, therefore, x = 15

Other ways to illustrate ratios that will help students see the relationships follow. Begin written representation of ratios with the words “out of” or “to” before using the symbolic notation of the colon and then the fraction bar; for example, 3 out of 7, 3 to 5, 6:7 and then 4/5. Use skip counting as a technique to determine if ratios are equal. Labeling units helps students organize the quantities when writing proportions.

Using hue/color intensity is a visual way to examine ratios of part-to-part. Students can compare the intensity of the color green and relate that to the ratio of colors used. For example, have students mix green paint into white paint in the following ratios: 1 part green to 5 parts white, 2 parts green to 3 parts white, and 3 parts green to 7 parts white. Compare the green color intensity with their ratios.


 * Assessment **
 * Product **
 * Formative assessment from NYC Dept of Ed (pages 5-9)
 * What are ratios and why do we need them? Mr. Barton Maths
 * Create an array of various items from your home. Write a narrative about the item and include the ratios of the items with a hypothesis about why the ratios are what they are. Please share the items and narrative with your class. Allow students to also write about the rate that their parents drive in their vehicle, record the rate while traveling from school to home or vice-versa and the hypothesis on why they believe their parents drive at the rate that they do.
 * Key Questions **
 * How do I express ratios and rate in fraction form?
 * How do I explore ratios and the relationship between ratio and area?
 * How do I solve proportions using cross multiplication?
 * Observable Student Behaviors **
 * The student can describe ratio relationships between two quantities.
 * The student can translate relationships between two quantities using the notation of ratio language (1:3, 1 to 3, 1/3).
 * The student can communicate relationships between two quantities using ratio notation and language.

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. || ** Vocabulary ** rate proportion equivalent ratios proportional relationships unit rate scale per unit price percent || ** Suggested Activities ** @http://illustrativemathematics.org/illustrations/76 RP.1 @http://illustrativemathematics.org/illustrations/77 RP.2 @http://illustrativemathematics.org/illustrations/549 RP.2 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. Compare a ratio represented by an area with its percent, fraction, and decimal forms Go on an African safari and observe a variety of animals walking and running across the savanna. Videotape the animals, and then play back the videotape to estimate animal speeds. Which animals run fastest? Lesson 10-1 bottom pg 381 differentiated instruction intervention
 * Mathematical Practices
 * Math ||
 * ratio form
 * Houghton Mifflin OnCore Mathematics Middle School Grade 6 Lesson 1-3
 * Houghton Mifflin OnCore Mathematics/Teacher Edition-Grade 5/ Page 2-3
 * ABC Mastering the Common Core in Mathematics- Grade 6/Chapter 6, pg. 72-73
 * Teaching the Common Core Math Standards with Hands-On Activities
 * Grade 6-8/pg 2-3/Ratios All Around Us
 * Highly Recommended:
 * Gizmo Lessons **
 * ** Part-to-part and Part-to-whole ratios **
 * ** Measuring Motion **
 * Glencoe chapter 10 resource books
 * Glencoe Ch. 10 Hands-on Lab pg 384-385 Ratios and Tangrams
 * Vocabulary Builder – chapter 10 TE p. 378
 * Foldable pg. 379
 * Bell ringer pg.380
 * Open-Ended Assessment: Writing-Have students write examples of part to whole, part-to-part, and whole-to-part ratios.
 * Solving Problems: Have students work in small groups to write and solve problems. Assign roles for students, such as writer, recorder, and presenter.
 * Discovery education video clip: Defining Ratio and Proportion
 * JBHM 6th Grade, GP1, Unit 2, Page 315-346
 * Glencoe Course 1 series:

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


 * Homework **
 * See corresponding assignments from Suggested Activities
 * Glencoe Course 1 Student Study Guide and Intervention Workbook pg 60

Lesson Plan in Word Format (If asked to log in, click cancel)
 * Terminology for Teachers **
 * ||  || Multicultural Concepts 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 ||   ||   ||


 * Resources **


 * Professional Texts **
 * Houghton Mifflin OnCore Mathematics/Teacher Edition-Grade 5/ Page 2-3
 * Houghton Mifflin Oncore Mathematics Middle School/Mastering the Common Core- Grade 6/Chapter 6, pg. 72-73
 * Teaching the Common Core Math Standards with Hands-On Activities, Grade 6-8/pg 2-3/Ratios All Around Us


 * Literary Texts **


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


 * Art, Music, and Media **


 * Manipulatives **
 * 100 grids (10 x 10) for modeling percents
 * Ratio tables – to use for proportional reasoning
 * Bar Models – for example, 4 red bars to 6 blue bars as a visual representation of a ratio and then expand the number of bars to show other equivalent ratios
 * The National Library of Virtual Manipulatives: http://nlvm.usu.edu


 * Games **


 * Videos **
 * Discovery Education- @http://www.discoveryeducation.com/ Model Ratios/Mathematical Eye: Ratio and Scale


 * Websites **
 * @http://illustrativemathematics.org/standards/k8 PARCC Online (released items)
 * @http://www.khanacademy.org/math Online tutorials
 * @http://www.tli.net/ TLI Quiz Builder


 * SMART Board Lessons, Promethean Lessons **

@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/LessonDetail.aspx?ID=L775 A political map of the United States after the 2000 election is largely red, representing the Republican candidate, George W. Bush. However, the presidential race was nearly tied. Using a grid overlay, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States. @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/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=L722 By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L572 Students will measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising. @http://sciencenetlinks.com/science-news/science-updates/finger-length/ In this Science Update, from Science NetLinks, you'll hear about a study that looks to finger length for signs of a man's pre-natal exposure to testosterone. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources. @http://illuminations.nctm.org/LessonDetail.aspx?ID=U189 Every 4 years, citizens of the United States elect the person they believe should be our nation's new leader. This unit explores the mathematics of the electoral college, the system used in this country to determine the winner in a presidential election. The lessons include activities in percentages, ratios, and area, with a focus throughout on building problem-solving and reasoning skills. They are designed to be used individually to fit within your curriculum at the time of an election. However, time permitting, they can be used as a unit to give students a strong understanding of how small variations can mean one person becomes president and another does not. Additionally, the lesson extensions include many ideas for interdisciplinary activities and some possible school-wide activities. @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=U133 This two-part example illustrates how students can learn about the length, perimeter, area, and volume of similar objects using dynamic figures. In the first part, Side Length and Area of Similar Figures, the user can manipulate the side lengths of one of two similar rectangles and the scale factor to learn about how the side lengths, perimeters, and areas of the two rectangles are related. In the second part, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. Activities such as these can help students learn about geometric relationships among similar objects, as described in the Geometry Standard. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L443 In this lesson, Side Length, Volume, and Surface Area of Similar Solids, the user can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes. @http://illuminations.nctm.org/LessonDetail.aspx?ID=U98 This cluster of Internet Mathematics Excursions is based on E-example 6.3 as described in the Geometry Standard and Measurement Standards. These lessons are designed for students to understand ratio, proportion, scale factor, and similarity using perimeter, area, volume and surface area of various rectangular shapes. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L259 This Internet Mathematics Excursion is a pre-activity for E-example 6.3 from the NCTM Principles and Standards for School Mathematics. This is the first in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity. This lesson invites students to manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L260 This Internet Mathematics Excursion is based on E-example 6.3 from the NCTM Principles and Standards for School Mathematics. This is the second in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity using perimeter and area of various rectangular shapes. Students manipulate 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters of similar rectangles, and the relationship between scale factor and ratio of areas of similar rectangles. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L261 This Internet Mathematics Excursion is based on E-example 6.3.2 from the NCTM Principles and Standards for School Mathematics. This is the third in a sequence of four lessons designed for students to understand scale factor and volume of various rectangular prisms. In this lesson, the student can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships between edge lengths and volumes. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L262 This Internet Mathematics Excursion is based on E-example 6.3.2 from the NCTM Principles and Standards for School Mathematics. This is the last activity in a sequence of four lessons designed for students to understand scale factor and surface area of various rectangular prisms. Students manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships. @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. [] 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/Lessons/Scaling/Scaling-OVH-Ratios.pdf This reproducible transparency, from an Illuminations lesson, features equations for finding the ratios for surface area and volume when comparing a model to a full-size object. @http://americanhistory.si.edu/onthemove/learning/thinkfinity/AOTM_Unit5_Activity3.pdf 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. @http://illuminations.nctm.org/LessonDetail.aspx?ID=U178 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. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L281 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. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L706 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. @http://illuminations.nctm.org/LessonDetail.aspx?ID=L707 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. @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=L511 Students learn to write and solve proportions by gathering data and calculating unit rates.
 * Other Activities, etc. **
 * NYC Dept of Ed, This 4-5 week unit focuses on developing an understanding of ratio concepts and using ratio reasoning to solve problems.: @http://schools.nyc.gov/NR/rdonlyres/A9F735CB-47E4-40F8-884F-EA54D0AB5705/0/NYCDOEG6MathRatios_Final.pdf
 * Mr. Barton’s Math, ratio help and practice: @http://www.mrbartonmaths.com/number12.htm
 * Lesson resources- Listed on Glencoe Course 1, page 380 ( Math Pass CD-Rom, Parent and Student Guide on-line Worksheets, Noteables, Virtual Activities, CD-Rom)
 * ** Advanced Paper Pool **
 * ** A Swath of Red **
 * ** Bagel Algebra **
 * ** Bagel Comparison **
 * ** Bean Counting and Ratios **
 * ** Constant Dimensions **
 * ** Finger Length **
 * ** Getting into the Electoral College Unit **
 * ** How Many Squares are Crossed? **
 * ** Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figures Unit **
 * ** Side Length, Volume, and Surface Area of Similar Solids **
 * ** Linking Length, Perimeter, Area, and Volume Unit **
 * ** Blue Squares and Beyond **
 * ** Go With Green Rectangles **
 * ** Fill'r Up **
 * ** Purple Prisms **
 * ** 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 **
 * ** Ratios **
 * ** 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? **
 * ** Understanding Rational Numbers and Proportions **
 * ** What's Your Rate? **

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