7.3.4Ma

** Grade: 7 Unit: 3 Week: 4 Dates: 12/3 – 12/7 **
 * Content: Apply Percents **
 * Theme Essential Question: **
 * How can you analyze proportional relationships and use them to solve real-world and mathematical problems? **

** Essential Questions: **
 * How do you apply the concept of percent to solve real-world and mathematical problems?

** Standards: **   ** Objectives: ** Review Concepts   **__ Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: __** Using the rate table concept or solving equation techniques, help students make the connection to the simplified strategy of cross-multiply and divide in solving ratio equal to ratio problems. **__ 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/**
 * ** 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. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
 * The student will change decimals and fractions to percents and percents to decimal and fractions.
 * The student will change ratios to percents and percents to ratios.
 * The student will apply the concept of percent to real world situations such as finding simple interest, tax, commissions, fees, and percent of error to solve problems.
 * The student will determine the percent of increase and decrease of given problems.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student will use mental math to calculate reasonableness of their answers to percent problems.

<span style="color: black; font-family: arial,helvetica,sans-serif; font-size: 11pt;">Because percents have been introduced as rates in Grade 6, the work with percents should continue to follow the thinking involved with rates and proportions. Solutions to problems can be found by using the same strategies for solving rates, such as looking for equivalent ratios or based upon understandings of decimals. Previously, percents have focused on “out of 100”; now percents above 100 are encountered.

<span style="color: black; font-family: arial,helvetica,sans-serif; font-size: 11pt;">Providing opportunities to solve problems based within contexts that are relevant to 7th graders will connect meaning to rates, ratios and proportions. Examples include: researching newspaper ads and constructing their own question(s), keeping a log of prices (particularly sales) and determining savings by purchasing items on sale, timing students as they walk a lap on the track and figuring their rates, creating open-ended problem scenarios with and without numbers to give students the opportunity to demonstrate conceptual understanding, inviting students to create a similar problem to a given problem and explain their reasoning. <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;">// Continue with the portfolio concept //
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Using the Frayer Model concept//,// adjust by changing the center from”Proportional Relationships” to “Percentage”
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Simple Interest Activity:
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student has $__ to put into a saving account.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Create a table to determine simple interest give the rates of 0%, 2%, 4%, and 6% for one year, rate vs. interest
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Develop of graph (rate, Interest)
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Write an equation
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">AND/OR
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Continue with the Family Trip from lesson 3-3; find the price for hotel accommodations for the three price ranges.
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Given: A 15% discount for a three nights stay and
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">Sales tax on the rooms 8.25%

<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;">What does percent mean?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How do you write a percent as a decimal?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How do you find a percent of a number?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How can you use percents to solve problems?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">How do you estimate a 15% tip without a calculator?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">To find simple interest on an original amount, what two pieces of the information do you need?
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">What is meant by percent of increase/decrease?

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Observable Student Behaviors **
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">The student can apply the concept of percent to solve real-world and mathematical problems.

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 **** : **
 * ** Mathematical Practices **

percent increase/decrease simple interest tax commission fees || <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** Suggested Activities ** :
 * ** Math ** ||
 * Ratio proportional relationships percent
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Review Concepts
 * ABC //Mastering the Common Core in Mathematics//
 * Decimals/Percents, Chapter 5.1, p.43
 * Fractions/Percents, Chapter 5.2, p. 44-45
 * Ratios/Percents, Chapter 6.4, p. 63-65
 * Basic Percent Word Problem, Chapter 5.3, p. 45
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">// Houghton Mifflin On Core Mathematics Middle School // Grade 7 Unit 2-4, p. 47-50
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">ABC //Mastering the Common Core in Mathematics//
 * Finding the percent of a total, Chapter 5.4, p. 46
 * Percent of Increase or Decreased, Chapter 5.5, p. 47-48
 * Tips and Commissions, Chapter 5.6, p. 49
 * Finding the Amount of Discount, Chapter 5.7, p.50
 * Finding the Discounted Sale Price, Chapter 5.8, p. 51
 * Markups, Chapter 5.9, p. 52
 * Sales Tax, Chapter 5.10, p. 53
 * Understanding Simple Interest, Chapter 5.11, p. 54
 * Percent Error, Chapter 5.12, p. 55
 * Review and Test, p. 56-59


 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Gizmo Correlation
 * 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.
 * Percent of Change
 * Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations.


 * Percents and Proportions
 * Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.

<span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/148 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/130 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/121 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/117 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/102 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/105 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/106 (7.PR.3) ** <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;">** @http://illustrativemathematics.org/illustrations/266 (7.PR.3) ** <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; font-size: 11pt;"> **Highly Recommended**
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">JBHM 7th, GP 1, p. 301-358
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">JBHM 8th, GP 1, p. 175-238
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe 7th Grade //Mathematics Application and Concepts Course 2//, Chapter 8.2 -8.6, p. 340 - 363
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe 7th Grade //PreAlgebra//, Chapter 6.4–6.8, p.281-308
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Glencoe Algebra I, Chapter 3.7, 160-164

<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;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 14.6667px;"> <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 4.1-4.2 and 4.4, Mod 7
 * <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 ** @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="color: blue; 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 ** <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">@http://www.mathplayground.com/mathatthemall1.html > 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: 11pt;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">** 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: 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;">Ruler
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Graph Paper
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Versa Tiles
 * <span style="font-family: arial,helvetica,sans-serif; font-size: 11pt;">Per Cent Problems:
 * <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="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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