1. 21 st Century Lessons Introduction to Rate & Unit Rate Primary Lesson Designer(s): Stephanie Conklin 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 OBJECTIVE: Students will understand how to a rate and unit rate relate to ratios. Language Objective: Students will define rate and unit rate using real-world examples. Lesson Description This lesson will first review the idea of ratio and then connect this idea to rate and unit rate. We will use a student-friendly video on a skateboarding bulldog to engage students in learning. Then we will calculate the dog’s rate of speed as both a rate then unit rate. We will also define these key words in the context of this example. After this example, we will then focus on other real-world examples of rates and unit rates using examples like measurement, money and distance. Students will complete examples with the whole class first and then will work with their partners. After this students will have a chance to work in partners or small groups on the classwork. Then teachers can review this work, and complete a summary question. Lesson Overview (1 of 3)

5. 5 Lesson Vocabulary Rate: a ratio that compares 2 different measurements Unit rate: comparison of 2 different quantities where one measurement only has 1 unit. Materials Specific list of necessary and optional materials with quantities - Copies of scaffolded class notes - Internet and projector - Speakers Scaffolding Teachers can use the class work as a scaffolded assignment with different expectations for students. Further, the call-outs or bubbles that characters state in the lesson can be used to help students confirm understanding and clarify definitions. Enrichment This website from PBS is kid-friendly and allosws students to access a host of topics related to money and math. http://pbskids.org/itsmylife/money/spendingsmarts/index.html Online Resources for Absent Students http://www.virtualnerd.com/pre-algebra/ratios-proportions/rate-and-unit-rates- definition.php http://www.teachertube.com/viewVideo.php?video_id=45873&title=Watch_Video_on _Unit_Rate___Pre_Algebra_Help Lesson Overview (2 of 3)

6. 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 school, students will review utilizing diagrams to represent ratios, and will also have a strong knowledge of how to write ratios and also represent them in 3 ways. After this lesson, we will focus on how to write rates as unit rates and unit prices and compare in real- world situations. Topic Background The idea of rate and unit rate applies to many real-world situations. In this lesson, we will specifically focus on time and distance, speed, measurement, and money. We will continue with these key themes in the next lessons and continue to connect to these real-world examples.

7. Warm Up Agenda 7 1) _______ jumps to _________ minute 2) ________ jumps: __________ minute 3) Jumps 4) Write a sentence using ratio language. minute Alex is trying to win a jumping jack competition. He does 100 jumping jacks in 2 minutes. 1) __50___ jumps to ____1____ minute 2) ___50___ jumps: ___1______ minute 3) 50jumps 4) Write a sentence using ratio language. 1minute Alex jumps 50 times for each second. OBJECTIVE: Students will understand use rates and unit rates to solve real- world problems. Language Objective: Students will define rate and unit rate using real-world examples.

8. Agenda: OBJECTIVE: Students will use rates and unit rates to solve real-world problems. Language Objective: Students will define rate and unit rate using real-world examples. 1) Warm Up (Individual) 2) Launch: Tillman the Skateboarder (Whole Class) 3) Explore: Mini-Lesson (Partner and Whole Class) 5) Practice: (Partner and Whole Class) 4) Summary (Whole Class) 6) Assessment: (Independent and Whole Class) 8

9. Launch Agenda 9 Watch the following video about Tillman, the world-recorder holder for fastest skateboarder in his class. http://vimeo.com/25153812 Why is Tillman special? In 2009, Tillman received the Guiness Book of Records Award for fastest skateboarding dog, when he rode 100 meters in 20 seconds. How do we know he’s the fastest skateboarding dog?

10. Launch Agenda 10 (ex 1) Write Tillman’s record time as a ratio in fraction form. *Remember to simplify and use lables!!! In 2009, Tillman received the Guinness Book of Records Award for fastest skateboarding dog, when he rode 100 meters in 20 seconds. This example is special because we have 2 different units being compared, meters and seconds. This special ratio is a rate ! Woof!

11. Explore – Mini Lesson Agenda 11 A rate is a ratio that compares 2 different measurements! (ex) Tillman’s skateboarding rate is. What happens when we simplify this rate? I’m fast! This means that Tillman travels at a rate of 5 meters for every 1 second.

12. Explore 12 Agenda A rate with a denominator of 1 has a special name! Tillman’s rate of skateboarding: The word unit means 1.

13. Explore – Mini Lesson Agenda 13 A rate and unit rate are often found in the following real-world situations: What are the measurement we are comparing in (ex 1)? Yes! Yards and seconds! All rates and unit rates have 2 different measurements

14. Explore – Mini Lesson Agenda 14 A unit rate can be found using the following steps. (ex 1) Write Homer’s speed as a unit rate. Homer ran 60 yards in 30 seconds. Step 1: Write as a rate in fraction form. 60 yards 30 seconds Step 2: Simplify the rate so the denominator is 1. 2 yards 1 seconds This unit rate means that, Homer ran 2 yards for every 1 second. How did we know this is a rate question? D’oh! I get it, we have yards and seconds, 2 different measurements. Homer ran 2 yards per second. For every is getting old! Let’s try a new word in our sentence! PER! The word “per” can be used for unit rates only, like this! PER! The word “per” can be used for unit rates only, like this!

15. Explore – Partner Work Agenda 15 (ex 2) A brownie recipe has 4 cups of flour for every 2 cups of sugar. Step 1: Write as a rate in fraction form. 4 cups of flour 2 cups of sugar Step 2: Simplify the rate so the denominator is 1. 2 cups of flour 1 cup of sugar This unit rate means that there are 2 cups of flour per cup of sugar. Wait! Is this still a rate? We are comparing cups of flours to cups of sugar, does that count? Yes, we have 2 different measurements cups of flour and cups of sugar!

16. Challenge – Partner Work Agenda 16 (ex 3) Ricardo wants to buy 40 key chains for his new business. An online merchant has the following special posted. SPECIAL: 80 Key Chains for $40 SPECIAL: 80 Key Chains for $40 Ricardo completes the following calculations to find the unit price: 80 key chains $40 2 key chain $1 $2 per key chain = = Is Ricardo right? Why or why not?

17. Challenge – Partner Work Agenda 17 (ex 3) Ricardo wants to buy 40 key chains for his new business. An online merchant has the following special posted. SPECIAL: 80 Key Chains for $40 SPECIAL: 80 Key Chains for $40 Ricardo completes the following calculations to find the unit price: 80 key chains $40 2 key chain $1 $2 per key chain = = ____$40_____ 80 key chains ____$1___ 2 key chains = $0.50 per key chain

18. Summary 18 Agenda 1)A rate is a ratio that compares 2 different ______. 2)A unit rate represented as a fraction has a ____________ of 1. 3)How are rates and unit rates similar? 4)How are rates and unit rates different? 5)One real world example of rates and unit rates is ________________________. _units_. denominator Both are ratios that have 2 different units. Rates can be any #s with different units compared but unit rates must have 1 in denominator.

19. Practice 19 Agenda

20. Practice 20 Agenda

21. Assessment 21 Agenda Casey spent $80 on 8 pizzas.  Write a rate as a fraction to represent this situation.  Write a unit rate as a fraction to represent this situation. _$80_ 8 pizzas _$10_ 1 pizza

22. Back to Overview 22 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

23. 23 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: 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 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 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 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. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Standards for This Unit Back to OverviewNext Slide

24. 24 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

25. 25 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

26. 26 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

27. 27 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

28. 28 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

29. 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… 29

30. 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… 30