7.3.2Ma

** Grade: 7 Unit: 3 Week: 2 Dates: 11/19 – 11/20 (2 Days) **
 * Content: Proportional Relationships, Tables, and Equations ** 
 * Theme Essential Question: **
 * How can you analyze proportional relationships and use them to solve real-world and mathematical problems? **

** Essential Questions: **
 * What are the similarities and differences between the concepts of ratios, rates, and proportions?
 * How do rate tables expand the usage of the concepts of ratios, rates, and proportions?
 * What equation relationship is found in a proportional rate table? What is the connection between the table and equation?
 * How are ratios, rates, and proportions utilized in solutions to real-world and mathematical problems?

** Standards: **
 * ** 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.
 * ** 7.RP.2b ** Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
 * ** 7.RP.2c ** Represent proportional re lationships by equations For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn..
 * ** 7.RP.3 ** Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems.

** Objectives: **   **__ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: __** As we provided students with the opportunity to look for the constant of proportionality and develop the equation relationship, y = ax, re-introduce Mathematical Practices # 7. Students will look for and make use of structure as they use tables to draw conclusions about proportional relationships. They will also look at tables and equations to determine if the relationship of one quantity to another is constant. They will find the relational equation y = ax for table that are proportional.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will explore and discover that for every proportional relationship the ratios in the rate table are constant and this constant is known as the constant of proportionality. The student will distinguish between tables that are proportional/non-proportional.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will evaluate tables by observing the x (input) and y (output) to determine if the data is linear, nonlinear, or has no relationship. If linear the student will determine if it is an increase/decrease relationship.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will derive the equation for a proportional relationship, y = **//a//**x, where **//a//** is the constant of proportionality. The student will distinguish between equations that are proportional/non-proportional.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will identify whether a relationship presented in a table is proportional.

<span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Due to the short week, it will be important to blend lesson 3-2 and 3-3. Additional time is also found in lesson 3-6. Please reference the Teacher Matrix for needed modifications.

<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/**

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** 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;">Find the constant of proportionality for the table.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Write the equation for the table. Identify the variables x and y.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Using the equation,
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Given time find distance
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Find the distance for times 52 sec.and 128 sec.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Given distance find time
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Find the time for 204 in. and 1080 in.

<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.
 * Key Questions **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How do you know, if the values in a table produces a proportional relationship?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">If the table produces a proportional relationship, how do you find the constant of proportionality?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How does the constant of proportionality integrate into the equation?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How do you use the equations to find additional values, given input/output values?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">What conclusion can you draw about a proportional relationship by looking at an equation and/or table?

<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: **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Given a table, the student can determine if it is proportional.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Given a proportional rate table, the student can find the equation.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can use the equation to find additional values.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can explain the connections between the table and equation.
 * ** Mathematical Practices **

tables equations || <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Suggested Activities ** :
 * ** Math ** ||
 * unit rate ratio common ratio proportional relationship constant constant of proportionality directly proportionality direct variation graphs
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 2-2, p. 39-42
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">ABC //Mastering the Common Core in Mathematics//
 * Proportional Relationships, Chapter 7.1, p. 73
 * Finding Relationships in Tables, Chapter 7.2, p 74
 * Finding Relationships in Equations, Chapter 7.4, p. 76
 * <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.2c
 * 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.
 * Determining a Spring Constant
 * Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.

<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.
 * 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.
 * Geometric Probability - Activity A
 * Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it
 * Theoretical and Experimental Probability
 * Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;"> **Highly Recommended (Problems are found in Lesson 3-3)**
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">JBHM 7th, GP 3, p.75-104
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">JBHM 8th, GP 1, p.207-220
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe 7th Grade //Mathematics Application and Concepts Course 2//,
 * Chapter 7.2b, p. 296
 * Chapter 7.3, p, 297-301


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe 7th Grade //PreAlgebra//, Chapter 6.3, p. 270-275
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe Algebra I, Chapter 3.6, p. 155-159

<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;">Math’scool: Unit A Mod 7.4
 * <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;">** 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;"> <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: 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 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.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">__ Activities and tools: __

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