1. 21 st Century Lessons Solving Percent Problems with a Double Number Line Model Primary Lesson Designer: Lisa Schad 1

2. 2 This project is funded by the American Federation of Teachers.

3. 3 *1 st Time Users of 21 st Century Lesson: Click HERE for a detailed description of our project.HERE 21 st Century Lessons – Teacher Preparation Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. Please do the following as you prepare to deliver this lesson: Feel free to customize this file to match the language and routines in your classroom.

4. 4 Lesson ObjectiveStudents will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent. Lesson DescriptionThis lesson extends students’ understanding of ratios to include thinking about the relationship of part to whole in a real-life situation and the percent equivalence. Instead of merely teaching students a quick algorithm for finding the percent of a number, this approach allows students to visualize the percent as representing an equivalent ratio. This lesson is structured with a mini-lesson and guided practice intended to teach students step by step how to make and use a double number line model. This is followed by independent practice including more sophisticated multi-step non-routine challenge problems. Lesson Overview (1 of 3)

5. 5 Lesson VocabularyDouble number line, model, tool, percent MaterialsPowerpoint, class worksheets, homework worksheet ScaffoldingThis lesson is great for both special education and EL students. The heavy use of a visual model is an aid to students who can appreciate a tangible demonstration of the mathematical ideas. EnrichmentThe application problems in the class work are intended for the advanced students or for a second day of instruction. Online Resources for Absent Students http://learnzillion.com/lessons/596-find-the-part-when-the- percent-and-total-are-knownhttp://learnzillion.com/lessons/596-find-the-part-when-the- percent-and-total-are-known This LearnZillion lesson is helpful for learning what a double number line is but it is used differently than in this lesson. Lesson Overview (2 of 3)

6. 6 Lesson Overview (3 of 3) Common Core State Standard 6RP3c - Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. http://www.corestandards.org/ Before and After Other lessons in this series illustrate the use of other ratio problem solving models including the tape diagrams, ratio table and finding the unit rate. The lesson after this one (Lesson 11) has students compare all models and Lesson 12 is a review of all topics in the unit. Topic Background “Ratios and percentages are also useful in many situations in daily life, such as in cooking and in calculating tips, miles per gallon, taxes, and discounts. They also are also involved in a variety of descriptive statistics, including demographic, economic, medical, meteorological, and agricultural statistics (e.g., birth rate, per capita income, body mass index, rain fall, and crop yield) and underlie a variety of measures, for example, finances (exchange rate), medicine (dose for a given body weight), and technology (kilobits per second)…Double number line diagrams can help make visible that there are many, even infinitely many pairs in the same ratio, including those with rational number entries.” From Progressions document: http://ime.math.arizona.edu/progressions/

7. girls boys Warm Up CONTENT OBJECTIVE: Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent. LANGUAGE OBJECTIVE: Students will be able to describe verbally to another student their understanding of double number lines. They will listen to the other student share. Agenda 7 1. The ratio of the number of girls to the number of boys in a chess club is 3 to 2. There are 14 boys in the chess club. What is the number of girls in the chess club? 2. A florist sells 8 roses for a total of $10. Each rose costs the same amount. What is the cost of 12 roses? rosescost 8$10 4 $5 12 $15 21 14 77 777 Answer: 21 girls Answer: $15

8. Agenda: 1) Warm Up – Review Ratio Solving with models - Independent Double Number Line for Percent Problems 3) Guided Practice - Whole Class and Partners 5) Summary/Assessment – Think, Pair, Share - Partners 8 CONTENT OBJECTIVE: Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent. LANGUAGE OBJECTIVE: Students will be able to describe verbally to another student their understanding of double number lines. They will listen to the other student share. 4) Independent Practice – Independent 2) Launch - Whole Class

9. Launch Agenda 9 Rihanna is a very popular musical artist. Her 2012 album Unapologetic has sold close to 1 million copies worldwide. The album can be bought at most places for $15. How much money would you expect that Rihanna has made from the sales of Unapologetic? There are many costs that have to be paid from the sale of an album before the artist can receive her share of the profits. Based on most information we can assume that Rihanna only received 5% of the total sales of the album. How much money is that?

10. Launch Agenda 10 Today we are going to learn how to calculate the percent of an amount. We are going to use a tool called the Double Number Line. To find out how much money Rihanna is estimated to have made from the sale of Unapologetic we need the total sales of the album and the percent she received. $15 per album x 1 million albums sold = $15 million sales of all albums Again, Rihanna only received about 5% of the total sales of the album. New Tool: Double Number Lines Let’s use a double number line to determine: How much money is that?

11. Launch Agenda 11 $15 per album x 1 million albums sold = $15 million sales of all albums Rihanna only received about 5% of the total sales of the album. New Tool: Double Number Lines percent Sales (in millions) 0% $0 100% $15 50% 10%20%30% 40% 60% 70%80%90% $1.5 How much money is 5% of $15 million? $0.75 5% So Rihanna received about $750,000 from the sales of an album that made $15,000,000. $15 million sales worldwide 5% or $750,000

12. Launch Agenda 12 Let’s learn how to use the double number line tool. New Tool: Double Number Lines

13. Explore 13 Agenda 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? percent shots 0% 0 First, we set up the zeroes. Zero shots is zero percent. 100% 80 It says she took 80 total shots, so 80 is 100% of the shots. We are going to make a double number line to compare shots to percentage. Then we can easily find the percent. She took 20 shots, so we have to put 20 in the right position on the number line. First let’s find half. New Tool: Double Number Lines

14. Explore 14 Agenda 0% 0 Half of the 80 shots, is 40. And half of 100% is 50%. 100% 80 50% 40 So, where do I put the 20? It’s half of 40! We find halfway between 0 and 40. What percent is that? percent shots 25% 20 Let’s fill out the other side of the number line. 75% 60 You can see that every number of shots is lined up with a percent. The question asks for the percent that is equal to 20 out of 80. The answer is 25%. 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made?

15. Explore 15 Agenda 25% percent shots 0% 0 100% 80 50% 40 20 75% 60 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? Partners: Take turns asking and answering: Lefty – Ask Righty “How did we figure out where to put 20?” Righty – Ask Lefty “How do we know that 20 shots = 25%?” Lefty – Ask Righty “How did we figure out where to put 20?” Righty – Ask Lefty “How do we know that 20 shots = 25%?”

16. Explore – Let’s do the next one together! 16 Agenda 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? percent candies This time we know the part of the bag and the percent but not the total. We can still use a double number line. First we need to mark out zero and 100% 0 0%100% ? Next we need to put 30% in the right position. We can’t just put it anywhere. It has to be the right spot. Do you have any ideas? 50% 10%20%30% 40% 60%70%80%90%

17. Explore – Let’s do the next one together! 17 Agenda 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? percent candies We know that 30% is equal to 6 candies. So we can put 6 across from 30%. 0 0%100% ? Can you use this information to find out how much 100% is? Think, Pair, Share: See if you can find an answer. Then, tell your speaking partner. Listen to your partner’s idea. 50% 10%20%30% 40% 60%70%80%90% 6

18. Explore – Let’s do the next one together! 18 Agenda 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? percent candies Here is one way to solve it. There are many ways. 0 0%100%50% 10%20%30% 40% 60%70%80%90% 6421210818161420 Answer: 20 candies Answer: 20 candies

19. On Your Own – Try this one! 19 Agenda 3.) A class conducts a survey of 1,000 students. The survey reveals that 20% of the students speak Spanish. How many students is this? percent students 0% 0 100% 1,000 50% 500 100 10% 200 20% 300 30% 400 40% 600 60% 700 70% 800 80% 900 90% Answer: 200 students speak Spanish.

20. Percents in Life 20 Agenda Here are a few examples of situations in which adults calculate with percents in real life. taxes tips discounts

21. Taxes and Tips are a percent added on to a cost. 21 Agenda 4.) Cheryl had breakfast in the diner and the bill came to $12.00. She would like to leave a 20% tip. How much should she leave altogether? 5.) Martin wants to purchase a book that costs $12. The sales tax Is 5%. If Martin has $13, can he purchase the book? Both of these problems can be solved with the same double number line. percent dollars 0% 0 100% $12

22. Taxes and Tips are a percent added on to a cost. 22 Agenda 4.) Cheryl had breakfast in the diner and the bill came to $12.00. She would like to leave a 20% tip. How much should she leave altogether? Just remember to add the tip to the total amount if you are looking for the total cost! Just remember to add the tip to the total amount if you are looking for the total cost! percent dollars 0% 0 100% $12.00 50% $6.00$1.20 10% $2.40 20% $3.60 30% $4.80 40% $7.20 60% $8.40 70% $9.60 80% $10.80 90% Answer: $12.00 + $2.40 = $14.40

23. Taxes and Tips are a percent added on to a cost. 23 Agenda 5.) Martin wants to purchase a book that costs $12. The sales tax Is 5%. If Martin has $13, can he purchase the book? percent dollars 0% 0 100% $12.00 50% $6.00$1.20 10% $2.40 20% $3.60 30% $4.80 40% $7.20 60% $8.40 70% $9.60 80% $10.80 90% How do you find 5% on this number line? Do you have any ideas? 5% is halfway between 0% and 10%. What is half of $1.20?

24. Taxes and Tips are a percent added on to a cost. 24 Agenda 5.) Martin wants to purchase a book that costs $12. The sales tax Is 5%. If Martin has $13, can he purchase the book? percent dollars 0% 0 100% $12.00 50% $6.00$1.20 10% $2.40 20% $3.60 30% $4.80 40% $7.20 60% $8.40 70% $9.60 80% $10.80 90% $0.60 5% Don’t forget that a tax is also an amount added on to the total. Answer: He does have enough money because $12.00 + $0.60 = $12.60 total cost with tax.

25. Discounts are an amount taken OFF of a total cost. 25 Agenda 6.) Sam got a $12 discount off a $48 purchase. What percent discount did he get? percent dollars 0% 0 100% $48 50% $24 25% I can see that $24 is half of $48. And $12 is half of $24. $12 So, what’s half of 50%? The question could have asked: how much did Sam pay for a purchase that was 25% off of the original price of $48. What would the answer be? $48.00 - $12.00 = $36.00 is the cost of the purchase after a 25% discount. Answer : 25% Answer : 25% Remember: If the question asks for the total cost you must subtract the discount.

26. Try These! Independent Practice Agenda 26 1.) Alexis bought a CD player. She does not remember the price, but she does know that the 5% sales tax came to $4.80. What was the price of the CD player? 2.) Customers left Jill $2.50 as a tip. The tip was 20% of the total. How much was the bill?

27. Summary Agenda 27 25% percent shots 0% 0 100% 80 50% 40 20 75% 60 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? What is the answer to this problem? Partners – Take turns describing how to solve this problem, step by step. What is the answer to this problem? Partners – Take turns describing how to solve this problem, step by step.

28. Back to Lesson 28 1 st Time Users of 21 st Century Lessons Welcome to 21 st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21 st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Description of 21 st Century Lessons: Next Slide

29. 29 1 st Time Users of 21 st Century Lessons The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: Standards for This Unit Next SlideBack to Lesson

30. 30 1 st Time Users of 21 st Century Lessons In order to properly use 21 st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Requirements to teach 21 st Century Lessons: Next SlideBack to Lesson

31. 31 1 st Time Users of 21 st Century Lessons Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Strongly Suggested to teach 21 st Century Lessons: Next SlideBack to Lesson

32. 32 1 st Time Users of 21 st Century Lessons We suggest spending 30-45 minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a 45-55 minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Lesson Preparation (Slide 1 of 2) Next Slide Back to Lesson

33. 33 1 st Time Users of 21 st Century Lessons After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Lesson Preparation (Slide 2 of 2) Next SlideBack to Lesson

34. 34 1 st Time Users of 21 st Century Lessons There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Features built into each PowerPoint lesson Back to Lesson

35. The goal of 21 st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to: Support an increase in student achievement; Engage teachers and students; Align to the National Common Core Standards and the Massachusetts curriculum frameworks; Embed best teaching practices, such as differentiated instruction; Incorporate high-quality multi-media and design (e.g., PowerPoint); Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; Be available, along with videos and supporting materials, to teachers free of charge via the Internet. Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers. 21 st Century Lessons The goal… 35

36. Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21 st Century Lessons Brian Connor – Technology Coordinator 21 st Century Lessons The people… 36