7.3.1Ma


 * Grade: 7 Unit: 3 Week: 1 Dates: 11/12 – 11/16 **
 * Content: Unit Rate **


 * 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?
 * How are ratios, rates, and proportions utilized in solutions to real-world and mathematical problems?


 * Standards: **
 * ** 7.RP.1: ** Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ miles in each ¼ hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.
 * ** 7.NS.3: ** Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)


 * Objectives: **
 * The student will construct rate tables.
 * The student will use rate tables to find and compare rates.
 * The student will use fractional calculation to determine unit rates.
 * The student will use unit rates to compare different rates.
 * The student will express relationship of different quantity as ratios.
 * The student will apply ratios, rates, and proportions to solve real-world and mathematical problems.

Reminder: As you approach each lesson, keep focused on the Mathematical Practices to assure the depth of understanding is being reached and the desired teaching/learning outcome is being met according the pedagogy underlining Common Core. Stress Mathematical Practice #6, attend to precision. Ratios, rates, and proportions have no relevance without proper labeling.
 * __ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: __**

During lesson 3-1, students need to become fluent with the development of rate tables. For many struggling learner, rate tables are an alternative appropriate approach to solve many mathematical problems.

This unit builds and connects the concepts of ratios, rates, and proportional relationships. Critical considerations: Provide students with ample experiences with rate problems, graphs, tables, equations and diagrams. It is essential that students make __connections__ between each of the representations. A transfer of learning form lesson 3-1 to lesson 3-4 needs to take place in order to benefit from percentage type problems. Teachers need to assure that unit rate problems dealing with fractions per fractions (See example in 7.RP.1) are provided to students. Provide opportunities for students to see how so many of the things we do in everyday life can be related to this unit.

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/**
 * Background Information **

Building from the development of rate and unit concepts in Grade 6, applications now need to focus on solving unit-rate problems with more sophisticated numbers: fractions per fractions.
 * Taken from __Ohio Dept of Education Mathematics Model Curriculum 6-28-2022__ **

Proportional relationships are further developed through the analysis of graphs, tables, equations and diagrams. Ratio tables serve a valuable purpose in the solution of proportional problems. This is the time to push for a deep understanding of what a representation of a proportional relationship looks like and what the characteristics are:
 * A straight line through the origin on a graph,
 * A “rule” that applies for all ordered pairs,
 * An equivalent ratio or an expression that describes the situation, etc.

**This is not the time for students to learn to cross multiply to solve problems.**


 * Assessment: **
 * Product **
 * // Students will be working with a partner to develop a portfolio for this unit. // It is recommended that a modify Frayer Model be used (See example below).
 * Entry #1: (It is recommended that students be guided through Entry #1)
 * In order to obtain the data for this entry, the teacher will need a tape measure and a stop watch. The students are to walk at a casual pace for 10 seconds and record the number of inches (round to the nearest 5 inch), they traveled. Each student is to:
 * Develop a statement to match the activity.
 * Using ___ inches : 10 seconds,
 * Create a rate table for the times 0 sec., 5 sec., 10 sec., 15, sec., and 20 sec.
 * Show how the distances were determined for each ordered pair.
 * Answer the question: What assumption had to be made in developing the rate table?
 * Find the unit rate.
 * Show how each order pair in the rate table produces the same unit rate.
 * Compare your pace with your partner’s pace.
 * Use unit rate to make the comparison
 * Determine your travel in feet per minute. Compare these results.

See **__Background Information__** section above
 * Entry #2: (It is recommended that students work with partners to verify work)
 * In order to obtain data for this entry, the teacher will need a stop watch. Students are to do as many jumping jacks as possible in 30 second. Each student is to:
 * Develop a statement to match the activity.
 * Using ___ jumping jacks : 30 seconds,
 * Create a rate table for the times 0 sec., 10 sec., 20 sec., 30, sec., 40 sec. and 50sec.
 * Show how the number of jumping jacks was determined for each ordered pair.
 * Answer the question: What assumption had to be made in developing the rate table?
 * Find the unit rate.
 * Show how each order pair in the rate table produces the same unit rate.
 * Compare your jumping jack rate with your partner’s rate.
 * Use unit rate to make the comparison
 * Determine your jumping jacks per minute. Compare these results.
 * Suggestions for other entries:
 * Topic Example
 * Recipes cups of sugar : number of cup cakes
 * Food item soup ounces : price
 * Trip distance traveled : time traveled
 * Phone number of minutes : price
 * work grass cut : time to complete the work
 * fuel miles traveled : gallons of gas used


 * Key Questions **
 * How are rate tables created, expanded, and used?
 * How do you compute a unit rate? What does unit rate mean (stress labels)?
 * How do you compare rates?


 * Observable Student Behaviors (Performance) **
 * The student can create, expand, and use a rate tables given any entry into the table.
 * The student can compare rates, using unit rate or common rate.

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. ||
 * ** Mathematical Practices **


 * Vocabulary: **

proportional relationships ||
 * ** Math ** ||
 * Complex fraction unit rate ratio

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.
 * Suggested Activities ** :
 * // Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 2-1, p. 35-38
 * ABC //Mastering the Common Core in Mathematics//
 * Rates, Chapter 6.1 and Chapter 6.2, p. 60-61
 * Ratio Problems, Chapter 6.2, p. 62
 * Gizmo Correlation: None Available at this time
 * // Teaching the Common Core Math Standards with Hands-On Activities, //
 * // 7.PR.1 – Activity p.80 //
 * **Highly Recommended**
 * @http://illustrativemathematics.org/illustrations/470 ** (7.PR.1)
 * @http://illustrativemathematics.org/illustrations/82 ** (7.PR.1)
 * JBHM 7th, GP 1, p.330
 * Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 7.2, p. 292-295
 * Glencoe 7th Grade //PreAlgebra//, Chapter 6.1, p. 265-268


 * Diverse Learners **
 * Odyssey (teacher discretion)
 * Skill Tutor (teacher discretion)
 * Math’scool: Unit A Mod 7.4


 * Homework: ** (Teacher Discretion)
 * @http://www.kutasoftware.com/free.html To print assignment on a variety of topics.
 * See appropriate Glencoe On Core, JBHM and ABC Materials under Suggested Activities
 * Exit Slip (Question or problem to answer before leaving class that will help guide instruction for the following day.)


 * Terminology for Teachers: **

||  || ** 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


 * Resources: **


 * Professional Texts: **

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. Click on the following link, __ http://libguides.nl.edu/mathinchildrenslit __, and then look under __Math and Literature Bibliographies__. Many books include websites with __lesson ideas__. __ http://sci.tamucc.edu/~eyoung/middle_school_literature.html __ __ http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html __ __ http://sci.tamucc.edu/~eyoung/literature.html __
 * Literary Texts **
 * ** Ratios **
 * ** Mathematics in Children's Literature: **
 * ** Middle & High School: Literature in Mathematics **
 * ** Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine) **
 * ** Miscellaneous Math and Children's Literature **


 * Informational Texts **


 * Art, Music, and Media **


 * Manipulatives **
 * Versa Tiles
 * Chart Paper
 * Markers
 * Recipes

> https://www.teachingchannel.org/videos/junior-high-math-lesson > SMART Board Notebook file for Proportions Trail (Notebook
 * Games **
 * Proportion Trail
 * @http://www.mathchimp.com/7thGrade.php
 * @http://www.sumdog.com/ A variety of games covering many math topics
 * @http://www.mathplayground.com/SMP_index.html
 * ProportionTrail Directions (PDF)
 * Proportions Trail Wall Problems (Word Doc)
 * Transcript of Proportions Trail (Word Doc)

** Videos **
 * Discovery Learning @http://www.discoveryeducation.com/
 * 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.
 * https://www.teachingchannel.org/videos?categories=topics common-core


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

__ http://www.shodor.org/interactivate/guide/ __ __ http://www.shodor.org/interactivate/activities/ __ __ @http://illuminations.nctm.org/LessonDetail.aspx?id=L781 __
 * Other Activities, etc. **
 * @http://www.mathgoodies.com/lessons/vol5/division.html
 * __ http://www.math.com/school/subject1/lessons/S1U1L12GL.html __
 * // 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.
 * Feeding Frenzy

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