2. 21 st Century Lessons Real –World Practice with Rates and Unit Rates 1 6.RP.2 Day 3

3. 2 This project is funded by the American Federation of Teachers.

4. 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.

5. 4 Lesson Objective OBJECTIVE: Students will use unit rates to compare quantities in real-life situations. Language Objective: Students will use vocabulary relating to rates like per and for every. Lesson DescriptionThis lesson will begin with a review of finding unit rate in a real-world situation. Then, students will be introduced to finding unit rates using decimals, like Usain Bolt’s time. We will then ask students to use unit rates to compare costs and also to make choices based on unit rates. For example, students will decide when we want to have a higher unit rate (i.e. earnings per hour) or a low unit rate (i.e. cost per package of buttons). We will finish the lesson with scaffolded class work and a summary and assessment. Lesson Overview (1 of 3)

6. 5 Lesson Vocabulary A unit rate is a comparison of 2 different quantities where one measurement only has 1 unit. MaterialsTeachers will need -Set of class notes for students to follow -Calculators or students have strong knowledge of dividing decimals -Set of class work and homework hand-outs ScaffoldingThis lesson provides steps to solve, guided practice and also review of key definitions for this lesson. EnrichmentStudents will use unit rates to solve questions that ask students to show further understanding of unit rates. They will use unit rates to calculate costs and rates of larger quantities. Online Resources for Absent Students http://www.math.com/school/subject1/lessons/S1U2L3GL.html http://www.khanacademy.org/math/arithmetic/basic-ratios- proportions/v/finding-unit-rates Lesson Overview (2 of 3)

7. 6 Lesson Overview (3 of 3) Common Core State Standard 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” 1 Before and After Before this lesson, students will learn how to calculate a rate and a unit rate. Calculators can be used for this lesson or if not, students should have strong knowledge of dividing decimals. In this lesson, we will extend this to calculate rates that are not whole #s. Further, students will compare rates. We will then use this in our next lesson to calculate desired quantities. For example, if we pay $75 for 15 hamburgers, how much is 25 hamburgers? Topic BackgroundThis lesson asks students to use unit rates to solve problems with distance and time as well as price per hour and salary. We will teach students how to answer real-world situations like “what’s the better value?” or “which job should he take?”

8. Warm Up OBJECTIVE: Students will use unit rates to compare quantities in real- life situations. Language Objective: Students will use vocabulary relating to rates like per and for every. Agenda 7 Kyle can mow 3 lawns in 2 hours. If Kyle takes the same time to mow each lawn, how long does it take him to mow 1 lawn? Write a sentence! Hint: Convert the time from hours to minutes. We’ll use a unit rate to solve this question: 2 hours  2 (60 minutes) = 120 minutes 120 minutes 3 lawns 40 minutes 1 lawn = This means that Kyle can mow 1 lawn in 40 mins.

9. Agenda: 1) Warm Up (Individual) 2) Launch – Fastest Man in World (Whole Class and Partner) 3) Explore – Mini Lesson and Practice (Whole Class and Partner) 4) Summary (Whole Class) 5) Practice (Partner and Whole Class) 6) Assessment (Individual) 8 OBJECTIVE: Students will use unit rates to compare quantities in real-life situations. Language OBJECTIVE: Students will use vocabulary relating to rates like per and for every. What are some real- world examples of rate?

10. Launch Agenda 9 http://vimeo.com/46634479 Please watch the following video on Usain Bolt, the Olympic Gold Medalist in the Men’s 100-meter sprint. Answer the questions below! 1) How fast does Usain run the 100 meter sprint? 2) Does he run this race in seconds, minutes or hours? 3) After how many meters can Usain tell if he will win a race? 4) What country is Usain from? 9.58 9.58 seconds After 70 meters Jamaica

11. Launch Agenda 10 Let’s find the Usain’s speed using rates and unit rates! We will compare distance (meter) to time (seconds). Step 1: Write a rate in fraction form Step 2: Simplify to write as a unit rate Let’s learn a trick to convert a rate to a unit rate! 100 meters 9.58 seconds Hold up! How can we simplify this rate? Yahhh! Tricks make math easier!

12. Notes To find a Unit Rate  Set up your ratio in fraction form with labels. The item or quantity you are looking to find the unit rate for should be the denominator; then substitute numbers into the ratio/fraction.  Divide the numerator by the denominator.

13. Launch Agenda 12 Step 2: Simplify to write as a unit rate Let’s learn a trick to convert a rate to a unit rate! 100 meters 9. 58 seconds What operation does the fraction bar represent in the ratio? Divide is right!! Let’s divide 100 meters by 9.58 to find a unit rate! REVIEW: We can write this as division problem: This unit rate means Usain runs 10.44 meters per second. This unit rate also means that in 1 second Usain Bolt runs 10.44 meters. 9.5810.44

14. Explore: Mini-Lesson 13 Agenda Let’s find the unit rate of each real-world situation! (ex 1) Kenny goes to the grocery store and buys 5 pounds of Apples for $8.40. Step 1: Write a rate in fraction form. Step 2: Divide to find the unit rate.. $8.40_ 5 pounds $8.40 ÷ 5 pounds = $1.68 per pound Kenny paid $____ per ______ of apples.. What does this unit rate mean? Kenny paid $1.68 per pound of apples..

15. Explore: Try with a Partner 14 Agenda Let’s find the unit rate of each real-world situation! (ex 2) Michelle is computer programmer who designs video games. She works 30 hours each week and makes $2,535. Step 1: Write a rate in fraction form. Step 2: Divide to find the unit rate.. $2,535_ 30 hours $2,535 ÷ 30 hours = $84.50 per hour Michelle makes $84.50 per hour Write a sentence to explain this situation.

16. Explore: A New Challenge 15 Agenda (ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for working 8 hours. At the school’s day camp, he will be paid $78 for working 6.5 hours. Brainstorm with your partner: Which job should Cameron take? Use your note’s from today to help you!

17. Explore: A New Challenge 16 Agenda (ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for every 8 hours of work. At a school day camp, he will be paid $78 for every 6.5 hours of work. Brainstorm with your partner: How can we decide which job pays Cameron the most per hour? YMCA JobSchool Job $90 ÷ 8 hours = $11.25 per hour $78 ÷ 6.5 hours = $12 per hour Create a table to organize your work! Write a sentence to answer question. Cameron should choose the school job because he will make $12 per hour which is $0.75 more than at the YMCA.

18. Explore: Practice with a Partner 17 Agenda (ex 4) Maria is a clothing designer and needs to buy a lot of buttons to make her clothes! The following shows button advertisements from 2 different stores: Button R’ UsButton-Up! Answer the following questions: a)What is the unit rate for buttons at Button R’ Us? b)What is the unit rate for buttons at Button-Up? c)Which store do you think Maria should buys buttons from? 55 Buttons for $5.50 140 Buttons for $12.60

19. Explore: Practice with a Partner 18 Agenda Button R’ UsButton-Up! Answer the following questions: a)What is the unit rate for buttons at Button R’ Us? b)What is the unit rate for buttons at Button-Up? c)Which store do you think Maria should buys buttons from? Explain your answer! 55 Buttons for $5.50 140 Buttons for $12.60 $5.50 ÷ 55 buttons = $0.10 per button $12.60 ÷ 140 buttons = $0.09 per button Button-Up is cheaper than Button R’Us by 1 cents.

20. Challenge: Practice with a Partner 19 Agenda Button-Up! Maria has decided to use the Button-Up! Company! Remember, she found a unit price of $0.09 per button. How much would it cost her to buy 500 buttons? 140 Buttons for $12.60 500 buttons x $0.09 per button = $45.00

21. Practice 20 Agenda

24. Practice 23 Agenda

25. Summary – Partner Work 24 Agenda 1) Today, we learned that to compare rates, we can first find the ______ ______. 2)A unit rate is a comparison of 2 different quantities where one measurement has only _____ unit. 3)We can use unit rates to find things like how much a job pays per hour. What other real-world examples are there for using unit rates? unit rate 1

26. Assessment 25 Agenda Try on your own: Martina drives 360 miles in 6 hours and Carlos drives 248 miles in 4 hours. Who drives the fastest? Martina: 360 miles ÷ 6 hours = 60 miles per hour Carlos: 248 miles ÷ 4 hours = 62 miles per hour Carlos has a faster rate at 62 miles per hour!

27. Back to Lesson 26 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

28. 27 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

29. 28 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

30. 29 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

31. 30 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

32. 31 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

33. 32 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

34. 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… 33

35. 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… 34