1. 21 st Century Lessons Unit Rates with Fractions Primary Lesson Designer(s): Kristie Conners Sean Moran 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 Objective Content Objective: Students will be able to find unit rate involving fractions. Language Objective: Students will be able to explain how to find the unit rate verbally and in writing. Lesson Description This lesson is designed to build on students’ understanding of unit rates. This lesson uses complex fraction, a concept students have not typically seen at this level. The warm up is designed for students to review division with fractions and find the missing value of two equal ratios. A concept that is used throughout the entire lesson. More practice is provided, if needed, as well as if time prevails. The launch activates student’s prior knowledge on unit rates. The explore is designed as a challenge problem is for students to work in groups as it may be difficult, but is manageable. There is an enrichment piece provided at this time for students who need an extra challenge. Discussion of this part of the lesson is crucial as students will be seeing complex fractions for the first time. An explanation of all possible outcomes is provided. The class work is given for students to continue their practice on unit rates with complex fractions. To wrap up the lesson, an exit slip is given to see what students can individually produce after the lesson. Note: Using the extra problems in the warm up, discussing the enrichment problem, and providing an explanation for all the class work assignments, is geared towards a sixty minute class. Lesson Overview (1 of 4)

5. 5 Lesson VocabularyRatio: Comparison of two quantities. Rate: A ratio that is used to compare two different quantities. Unit Rate: A rate in which the rate is expressed as a quantity of 1. Complex Fraction: a fraction where the numerator, denominator, or both contain a fraction. MaterialsCopies of the explore worksheet, class work assignment, homework and exit slip. Common Core State Standard 7.RP.1 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 mile in each ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour. Lesson Overview (2 of 4)

6. 6 Scaffolding Scaffolding is throughout the entire lesson. Each problem is explained in great detail providing a visual for solving the equation. Then a step by step process is provided in each of the division problems. The warm up is designed to activate prior knowledge, which is crucial for this lesson. There is an opportunity for more practice on this skill with the step by step process shown. Enrichment In the Explore part of this lesson, there is an opportunity for students to interpret the question another way. The question asks who runs faster. Typically the kids will focus on laps per hour, however, the enrichment asks students who is faster by determining how long it will take to run one lap. This changes students’ thinking on how to interpret the question. In the first method you are looking for the larger number; whereas in the second method you are looking for the smaller number, but will still result in the same outcome. Online Resources for Absent Students https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th- ratio-proportion/cc-7th-rates/v/rate-problem-with-fractions-1 http://www.ixl.com/math/grade-7/divide-fractions-and-mixed- numbers-word-problems Lesson Overview (3 of 4)

7. 7 Lesson Overview (4 of 4) Before and AfterStudents’ prior knowledge should consist of a basic understanding of ratios, rates and unit rates. 21 st Century Lesson 6 th grade Ratio and Proportion unit is recommended for students who need review on this topic. This lesson adds some complexity to students finding unit rates. This, in turn, will help students in future lessons based around proportional quantities. Students’ prior knowledge may consist of using the word proportion. In the lesson the word proportion is not used, however, the focus is two equal ratios, an equation. Using the vocabulary word, proportion, is the teacher’s discretion. Later lessons in this unit will be connecting unit rate to constant of proportionality. Topic Backgroundhttp://www.shmoop.com/video/unit-rate This video gives a quick overview of how rates are used in the real world. Although, most of the examples used deal with integer numbers, there is one example using fractions. This video is still very valuable as a teaching tool with rates containing fractions, as the situations are very applicable to middle school students. (There is an optional slide prompting this video in the lesson.)

8. Warm Up Objective: Students will be able to find the unit rate involving complex fractions. Agenda 8 Language Objective: Students will be able to explain how to find the unit rate verbally and in writing. 1) Explain why the model represents and how to find the solution. 2) Evaluate. 3) Find the value of x.

9. Warm Up Objective: Students will be able to find the unit rate involving fractions. Agenda 9 Language Objective: Students will be able to explain how to find the unit rate verbally and in writing. 1) Explain why the model represents and how to find the solution. 2) Evaluate. There are 4 whole circles divided into thirds. To find the solution one must count up how many thirds are in the 4 wholes which are 12. More Practice 3) Find the value of x.

10. Warm Up Objective: Students will be able to find the unit rate involving fractions. Agenda 10 Language Objective: Students will be able to explain how to find the unit rate verbally and in writing. 5) Find the value of x. a) b) 4) Evaluate each expression. b)

11. Agenda: 1) Warm Up 2) Launch 3) Explore Shopping With Marvin – Whole Class/Partner 5) Practice 6) Assessment 11 Objective: Students will be able to find the unit rate involving fractions. Language Objective: Students will be able to explain how to find the unit rate verbally and in writing. 4) Summary Who Is Faster? - Groups Fraction Review – Whole Class Who Is Faster? – Whole Class Class work – Individual/Partner Exit Ticket – Individual

12. Launch: Shopping With Marvin Agenda 12 On my trips to many magic shops, I see signs advertising magic equipment at different rates for example, b) How many wands can I buy for a $1? a) How much does 1 wand cost? 20 wands for $10.

13. Agenda 13 On my trips to many magic shops, I see signs advertising magic equipment at different rates for example, 20 wands for $10 a) How much does 1 wand cost? $0.50 per wand wands Launch: Shopping With Marvin $0.50 for 1 wand Explain your process. split $10 between 20 wands wands Ratio and Equation

14. Agenda 14 On my trips to many magic shops, I see signs advertising magic equipment at different rates for example, 20 wands for $10 b) How many wands can I buy for a $1? 2 wands for $1 wands Video Launch: Shopping With Marvin Explain your process. Split 20 wands between $10 wands Ratio and Equation

15. Agenda 15 Play Launch: Shopping With Marvin

16. Agenda 16 Quick Review A Rate: is a ratio that is used to compare two different quantities. 20 wands for $10 A Unit Rate: is a rate in which the rate is expressed as a quantity of 1. 20 wands $10 2 wands for $1$0.50 per wand Launch: Shopping With Marvin 2 wands $1 1 wand $0.50 20 wands : $1020 wands to $10 Any rate has two unit rates

17. Explore: Who Is Faster? 17 Agenda Challenge Who is the faster runner? Provide evidence to support your answer. Raj can run laps in of an hour. Yvonne can run laps in of an hour. Hint

18. Explore: Who Is Faster? 18 Agenda Challenge Who is the faster runner? Provide evidence to support your answer. Raj can run laps in of an hour. Yvonne can run laps in of an hour. Hint: How many laps can each person run in 1 hour? Make a ratio.

19. 19 Agenda Who is the faster runner? Raj can run laps in of an hour. Yvonne can run laps in of an hour. Explore Summary: Who Is Faster? Click to reveal Raj’s Multiplication Evidence Raj’s Unit Rate Evidence Yvonne’s Unit Rate Evidence Final Answer Enrichment question

20. Explore Summary: Who Is Faster? 20 Agenda Challenge - Raj’s Multiplication Evidence Who is the faster runner? Provide evidence to support your answer. Raj can run laps in of an hour. Since there are 4 fourths in a whole hour and Raj can run laps in 1 fourth of an hour, I can multiply by 4. Laps per hour Press to Return

21. Explore Summary: Who Is Faster? 21 Agenda Challenge - Raj’s Unit Rate Evidence Who is the faster runner? Provide evidence to support your answer. Raj can run laps in of an hour. This rate can be written as a ratio. laps hour = laps Then write an equation to find the unit rate. laps Laps per hour Press to Return

22. Explore Summary: Who Is Faster? 22 Agenda Challenge - Yvonne’s Unit Rate Evidence Who is the faster runner? Provide evidence to support your answer. Yvonne can run laps in of an hour. This rate can written as a ratio. laps hour = laps Then write an equation to find the unit rate. laps Laps per hour Press to Return

23. Explore Enrichment: Who Is Faster? 23 Agenda Extra Challenge - Enrichment question Who is the faster runner? Find out how long it will take Raj and Yvonne to each run 1 lap. Press to Return Raj can run laps in of an hour.Yvonne can run laps in of an hour. Raj is faster because he completes one lap in less time. hours per lap

24. Explore Summary: Who Is Faster? 24 Agenda Challenge – Final Answer Who is the faster runner? Provide evidence to support your answer. Laps per hour Raj Yvonne He runs more laps per hour than Yvonne. Press to Return

25. Check in: Painting 25 Agenda At this rate, how many square feet can she paint each hour? Tia is painting her house. She paints square feet in of an hour.

26. Check in: Painting 26 Agenda At this rate, how many square feet can she paint each hour? Write the rate as a ratio. Tia is painting her house. She paints square feet in of an hour. per hour Write an equation.

27. Practice: Class work 27 Agenda Name ________________________________________________________________ Date __________________ I. Find the value of x that makes the equation true. Show all work. II. Solve the following word problems. Show all work.

28. Practice: Class work Answers 28 Agenda I. Find the value of x that makes the equation true. Show all work.

29. Practice: Class work Answers 29 Agenda II. Solve the following word problems. Show all work. A machine made pencils in of a minute. At this rate, how many pencils can be made per minute? a.Write the rate as a ratio. b. Use the rate to write an equation. c. Solve the equation to find the unit rate. Pencils per minute

30. a.Write the rate as a ratio. b. Use the rate to write an equation. c. Solve the equation to find the unit rate. Practice: Class work Answers 30 Agenda II. Solve the following word problems. Show all work. It takes spoons of chocolate syrup to make of a gallon of chocolate milk. How many spoons of chocolate syrup are needed to make one gallon of chocolate milk? Spoons of chocolate per gallon

31. Exit Slip- What is the mistake? 31 Agenda A student’s work for solving the problem is below. What is the student’s mistake? teaspoons of sugar per ounce A 14 ounce energy drink contains teaspoons of sugar. How much sugar is in 1 ounce?

32. Exit Slip- What is the mistake? 32 Agenda A student’s work for solving the problem is below. What is the student’s mistake? ounces for 1 teaspoon The student found the number of ounces of energy drink for 1 teaspoon of sugar. A 14 ounce energy drink contains teaspoons of sugar. How much sugar is in 1 ounce?

33. Back to Overview 33 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

34. 34 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 Back to OverviewNext Slide

35. 35 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: Back to OverviewNext Slide

36. 36 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: Back to OverviewNext Slide

37. 37 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) Back to OverviewNext Slide

38. 38 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) Back to OverviewNext Slide

39. 39 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 OverviewNext Slide

40. 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… 40

41. 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 Wendy Welch - Curriculum Director (Social Studies and English) Carla Zils – Curriculum Director (Math) Shane Ulrich– Technology Director Marcy Ostberg – Technology Evaluator 21 st Century Lessons The people… 41