7.3.3Ma

** Grade: 7 Unit: 3 Week: 3 Dates: 11/26 – 11/30 **
 * Content: Proportional Relationships and Graphs **
 * Theme Essential Question: **
 * How can you analyze proportional relationships and use them to solve real-world and mathematical problems? **

** Essential Questions: **   ** Standards: **   ** Objectives: **   **__ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: __** This week continues to build on what was learned in weeks 1 and 2 in this unit. The Mathematical Practices # 4 (Model with mathematics.) fits with this week’s objectives because students are using equations, tables and graphs. They are looking at the relationships that exist between the three. Students need to experience this learning with the activities they are given to model, practice, and discuss what they are learning.
 * What are the similarities and differences between the concepts of ratios, rates, and proportions?
 * How can you use graphs to represent and analyze proportional relationships? How does the graph correlate to the table and equation?
 * How can you identify the constant of proportionality (unit rate) in tables, graphs, and equations?
 * How are ratios, rates, and proportions utilized in solutions to real-world and mathematical problems?
 * ** 7.RP.2a ** Decide whether two quantities are in a proportional relationship, e.g.. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** 7. RP.2b ** Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** 7. RP.2d ** Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** 7. RP.3 ** Analyze proportional relationships and use them to solve real-world and mathematical problems.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will recognize and identify the constant of proportionality (unit rate) in a table, equation, and/or graph.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will use tables with a constant of proportionality (unit rate) to visually compare their equations in graphical format.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will identify and describe proportional relationships between equations, tables, and graphs and use them to solve real-world and mathematical problems.

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">**__ Background Information __** Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at **http://www.azed.gov/educator-certification/**
 * Assessment: **
 * Product **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Continuation of unit portfolio //
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Entry #1
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Each student is to
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Prepare a graph for their Walking Activity
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Show how the constant rate of change from the table and the constant of proportionality from the equation are the same graphically.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Using the same coordinate plane, graph their partner’s information. (use a difference color)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Write a statement about their observation.

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> Use the same strategies for the additional entries found in the student’s portfolio.
 * Other activities to close lesson 3-1 to 3-2 **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Have students work in small groups with sets of given tables with a constant of proportionality that match with a set of graphs. Once they are matched up display the graphs with tables and discuss what they notice about the graphs ratio if the relationship is proportional. They can then write equations that fit each table and use a graphing calculator to check their work. What do they notice about all the equations?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Plan a family trip: (Excellent portfolio entry)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Part I: Travel Expenses
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Pick a location for your vacation
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Determine the number of mile for the trip
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Prepare a table for the usage of gas and cost for interval throughout the trip
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Research the car to be used and the expected usage cost per mile and prepare a table.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Write equations and prepare graphs
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Part II: Accommodation Expenses
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Hotel Name and Location
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Prices for Economy, mid-range, and a high end
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Develop a table for 1 through 7 nights for each price range
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Develop an equation to represent the table for each price range
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Discuss unit rates and proportionality
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Graph the information for each

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Key Questions ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Observable Student Behaviors (Performance) ** 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="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Vocabulary **** : ** tables equations ||
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How can you identify the constant of proportionality (unit rate) in tables, graphs, and equations?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How can you use graphs to represent and analyze proportional relationships?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">What do you notice about a graph that identifies the constant of proportionality?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">What point must be a point on all graphs for it to have constant of proportionality?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can analyze proportional relationships and use them to solve real-world and mathematical problems
 * ** Mathematical Practices **
 * ** Math ** ||
 * unit rate ratio proportional relationships constant constant of proportionality graphs

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Suggested Activities ** :
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 2-3, p. 43-46
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">ABC //Mastering the Common Core in Mathematics//
 * Finding Relationships in Graphs, Chapter 7.3, p. 75
 * Graphing Linear Data, Chapter 7.5, p. 77-79
 * Applying Proportional Relationships, Chapter 7.6, p.80-82
 * Comparing Proportional Relationships, Chapter 7.7, p. 83-84
 * Chapter 7 Review and Test, p. 85-88
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.PR.2 – Activity p. 84 //
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Gizmo Correlation
 * 7.RP.2a
 * Direct Variation
 * Adjust the constant of variation and explore how the graph of the direct variation function changes in response.
 * Proportions and Common Multipliers
 * Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator.
 * 7.RP.2b
 * Beam to Moon (Ratios and Proportions)
 * Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights.
 * Dilations
 * Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
 * Perimeters and Areas of Similar Figures
 * Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare
 * Similar Figures - Activity B
 * Vary the scale factor and rotation of an image and compare it to the pre ‑ image. Determine how the angle measures and side lengths of the two figures are related.
 * Weight and Mass
 * Use a balance to measure mass and a spring scale to measure the weight of objects. Compare the masses and weights of objects on Earth, Mars, Jupiter, and the Moon.
 * 7.RP.2d
 * Direct Variation
 * Adjust the constant of variation and explore how the graph of the direct variation function changes in response.
 * 7.RP.3
 * Estimating Population Size
 * Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/100 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/101 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/104 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/95 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/181 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/180 (7.PR.2) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">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.
 * <span style="font-family: arial,helvetica,sans-serif;">** Highly Recommended **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe Algebra I, Chapter 5.2, p. 264-269

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Diverse Learners ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Homework: ** (Teacher Discretion)
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Algebra’scool: Unit C Mod 8.1, 9.1
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">@http://www.kutasoftware.com/free.html To print assignment on a variety of topics.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Exit Slip (Question or problem to answer before leaving class that will help guide instruction for the following day.)

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Terminology for Teachers: **
 * || ** 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="font-family: arial,helvetica,sans-serif; font-size: 11pt;">**Lesson Plan in Word Format** (Click Cancel if asked to Log In)

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Resources: **

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Professional Texts: **

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Literary Texts ** <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">http://sci.tamucc.edu/~eyoung/ratio_prop_literature.html > Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels. <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Click on the following link, __ http://libguides.nl.edu/mathinchildrenslit __, and then look under __Math and Literature Bibliographies__. <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Many books include websites with __lesson ideas__. <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">__ http://sci.tamucc.edu/~eyoung/middle_school_literature.html __ <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;"> __ http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html __ <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;"> __ http://sci.tamucc.edu/~eyoung/literature.html __ <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Informational Texts ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Art, Music, and Media ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Manipulatives ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Games ** > https://www.teachingchannel.org/videos/junior-high-math-lesson > SMART Board Notebook file for Proportions Trail (Notebook <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Videos ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** SMART Board Lessons, Promethean Lessons ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Other Activities, etc. ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">__ http://www.shodor.org/interactivate/guide/ __ <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">__ Activities and tools: __ <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;"> __ http://www.shodor.org/interactivate/activities/ __
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Ratios **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">**__ Beanstalk: The Measure of A Giant (A Math Adventure) __** Ann McCallum This fractured fairy tale tries to squeeze in a math lesson about ratios, but it isn’t successful. Jack wakes up to discover a beanstalk outside his window, climbs up, and befriends a lonely giant boy at the top. The two go off to play but quickly realize that the difference in their size is going to make most games difficult. Trying to play hoop ball, for example, proves to be impossible until Jack realizes that I need a hoop that’s as high for me as your hoop is for you. A few measurements later, the boys realize that Rays hoop is three times his height, so they figure out how tall Jacks should be, and fashion one for him. Once home, Jack decides to make a checker set for Ray and figures out what size to make it. The story ends with the two friends eating lunch outside with Jacks mother, who wishes for a word to describe the relationship between the sizes of two things, since the boys dealt with their differences so wonderfully. Jack decides that they should call it a Ray show, since Ray showed Jack that their things were the perfect size for each of them. The author sums the story up by explaining that today it is spelled //ratio//.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Mathematics in Children's Literature: **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Middle & High School: Literature in Mathematics **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Lesson Plans for Using Literature in Middle and High School Mathematics **** (developed by Leonor and edited by Elaine) **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Miscellaneous Math and Children's Literature **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Calculators
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Chart Paper
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">White board
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Markers
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Atlas & Road Maps
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Versa Tiles
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Proportion Trail
 * @http://www.mathchimp.com/7thGrade.php
 * @http://www.sumdog.com/ A variety of games covering many math topics
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">@http://www.mathplayground.com/SMP_index.html
 * ProportionTrail Directions (PDF)
 * Proportions Trail Wall Problems (Word Doc)
 * Transcript of Proportions Trail (Word Doc)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Discovery Learning @http://www.discoveryeducation.com/
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">The Teaching Channel
 * The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">https://www.teachingchannel.org/videos?categories=topics common-core
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">__ Smartboard Resource Website __ Smartboard lesson search engine.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">@http://www.mathgoodies.com/lessons/vol5/division.html
 * <span style="color: black; font-family: arial,helvetica,sans-serif; font-size: 11pt;">__ http://www.math.com/school/subject1/lessons/S1U1L12GL.html __
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Interactivate // is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.

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