1. 21 st Century Lessons Ratios and Vocabulary 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 Students will use ratio language to describe a relationship between two quantities. Language Objective: Students will determine when to use singular and plural nouns. Student-Friendly Objective: Students will write sentences that describe real-world comparisons. Lesson Description This lesson will begin with a review of how to write ratios and then focus on how students can write ratios in sentence form. Students will start the lesson with a launch of watching a video that uses ratio language. Students will fill in numerical values using a scaffolded worksheet and will write these as basic ratios. Then, a mini-lesson will help students to use the phrase “for every” as a way to replace our ratio symbols. Students will learn to write these statements with for every in between the two comparing topics, and also in the beginning of a sentence. The class work will continue with more practice like this, along with the summary and assessment. At the end of the lesson, student should be able to write and explain ratios in real-world examples. Lesson Overview (1 of 3)

5. 5 Lesson Vocabulary Ratio: a comparison of two quantities For every: a term that can be used to write ratios Materials Hand outs for class notes and class work Scaffolding - The use of pictures and words is critical in this lesson to helping build vocabulary of ELL students. Teachers should review words when needed. - Based on common core standards, all of the examples provided in this lesson can be modeled using real-world shapes and also real-world examples. - http://www.corestandards.org/the-standards/mathematics/introduction/standards-for- mathematical-practice/ Enrichment Students who are artistic and advanced in this area of ratios should consider studying the Golden Ratio. Many textbooks offer activities on these but one website with detailed instructions and handouts are included in these websites: Background info: http://www.ldlewis.com/Teaching-Mathematics-with-Art/golden-ratio- instructions.html Directions on how to make a Golden Rectangle: http://www.learner.org/workshops/math/golden.html Online Resources for Absent Students Thinking Blocks: http://www.thinkingblocks.com/tb_ratios/ratios.html Review of Ratio: http://www.mathplayground.com/howto_ratios.html Lesson Overview (2 of 3)

6. 6 Lesson Overview (3 of 3) Common Core State Standard 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.” Before and After This lesson reinforces students’ ability to speak about real-world examples of ratios. Previous to this lesson, students will review how to write ratios in 3 ways, as a fraction, using the word “to” and using a colon. These topics relate directly to mathematical modeling and also to topics like fractions and simplifying fractions. Future lessons on this topic will focus on using unit rates and explaining these as real-world examples. Further, this unit will focus on solving real-world problems using equivalent rations, tape diagrams, double number lines or equations to solve questions about percent of quantity as a rate per 100 and converting measurements. Topic Background The goal of this lesson is to help students understand that ratios are in their everyday lives, and often spoken in words. For example, students will learn that “for every” is comparison word that relates 2 quantities to each other, just like a ratio! At the end of the lesson, students should be able to determine if ratio sentences make sense. Further, students will be able to write ratio sentences using the words for every in the middle and at the beginning of a sentence.

7. Warm Up Write a ratio in three ways comparing # of ducks to # of pigs. Remember to simplify your answer! 2 ducks to 1 pig 2 ducks : 1 pig Fill in the blank. For every 2 ducks, there is____ pig. OBJECTIVE: Students will use ratio language to describe a relationship between two quantities. Agenda 7 Scaffold

8. Warm Up Write a ratio in three ways comparing # of ducks to # of pigs. Remember to simplify your answer! 2 ducks to 1 pig 2 ducks : 1 pig Fill in the blank. For every 2 ducks, there is____ pig. OBJECTIVE: Students will use ratio language to describe a relationship between two quantities. Agenda 8 1) a fraction 2) the word, “to” 2) the word, “to” 3) a colon : Scaffold

9. Agenda: OBJECTIVE: Students will use ratio language to describe a relationship between two quantities. 1) Warm Up (Independent) 2) Launch -Challenge (Partner Work) 5) Summary – (Whole Class) 4) Practice – (Partner Work, Whole Class) 6) Assessment – (Independent) 9 -If the World Was a Village Video (Independent)If the World Was a Village Video (Independent) -Follow-up Questions (Partner Work)Follow-up Questions (Partner Work) 3) Explore -Mini Lesson (Whole Class and Partner Work)Mini Lesson (Whole Class and Partner Work)

10. Launch Agenda 10 We will practice writing ratios by watching a video on the world. Turn and Talk:  What country were you born in?  What languages do you speak? Be ready to share with class!

11. Launch Agenda 11 We will practice writing ratios by watching a video on the world. This video pretends that there is a village of 100 people who equally represent every country and language in the world. Watch the “If the World Were a Village Video” and answer questions #1-14.“If the World Were a Village Video”

12. Launch Continued Please check your answers! 12 Agenda

13. Mini Lesson 13 Agenda Let’s answer this question together: How can we write a ratio using words? (ex ) For every 100 people in the village, there are 61 people from China.  SUPER important term for writing ratios  “For every” can be used to replace the fraction bar, colon : or word “to” in a ratio  “For each” can also be used to replace the fraction bar, colon : or word “to” in a ratio

14. Explore 14 Agenda  For every and for each can be used to replace the fraction bar, colon : or word “to” in a ratio (ex 1) Write a ratio in words comparing beaks to wings for an eagle. Step 1: Write a ratio of beaks to wings 1 beak: 2 wings Step 2: Write this ratio in words An eagle has Why does beak not have a letter s at the end? There is only 1 beak so we do not need to make the word plural. We can also say, An eagle has 2 wings for each beak. We use for each when we only have 1 thing being compared, like 1 beak!

15. Explore 15 Agenda We can also start sentences with for every, let’s try! (ex 2) In a class election, Juan received 20 votes and Kevin received 8 votes. Write a ratio in words comparing Juan and Kevin’s votes. Step 1: Write a ratio of Juan’s votes to Kevin’s votes 20 Juan’s votes to 8 Kevin’s votes Step 2: Simplify the ratio 5 Juan’s votes to 2 Kevin’s votes Step 3: Write this ratio in words For every, 5 votes that Juan received Kevin received 2 votes. Did you simplify the ratio? Let’s add a new step! Did you simplify the ratio? Let’s add a new step! Are the ratios 20 to 8 the same as 5 to 2? Yes! 20 to 8 and 5 to 2 equivalent fractions or equal fractions!

16. Explore – Try with a Partner 16 Agenda (ex 3) Kaylee buys 2 posters that are the same size. She wants to hang up each poster using the following push pins. Write a sentence using for each to answer the question. How many push pins should she use for each poster? Step 1: Write a ratio of push pins to posters 8 push pins : 2 posters Step 2: Simplify the ratio 4 push pins : 1 poster Step 3: Write this ratio in words Kaylee needs 4 push pins for each poster. For each, poster, Kaylee needs 4 push pins.

17. Challenge – Try with a Partner 17 Agenda (ex 4) Brian also wants to decorate his room. He has 4 posters that need the same ratio of push pins as Kaylee’s Posters. How many push pins does Brian need to hang up his posters? - Draw a picture and explain your steps!

18. Challenge – Try with a Partner 18 Agenda (ex 4) Brian also wants to decorate his room. He has 6 posters that need the same ratio of push pins as Kaylee’s Posters. How many push pins does Brian need to hang up his posters? - Draw a picture and explain your steps! Explanation: Since we have 4 posters and each poster needs 4 push pins, we know that Brian needs at total of 16 push pins. Fancy Algebra Way:

19. Practice You have 5 minutes to work with your partners on this class work, good luck! 19 Agenda

20. Practice - Answers 20 Agenda

21. Summary We can use the phrase, for every, to help us write ratios as sentences! Turn and Talk: (ex) Calvin told his friend that his cat has 2 tails for every 1 ear. Is he right? Why or why not? Calvin is wrong. He should have said that his cat has 2 ears for every 1 tail. If Calvin was right then he has a cat with 1 ear and 2 tails, ek! 21 Agenda

22. Assessment For #1 and #2, fill in the blanks: 1) We can write ratios as sentences using the phrase, _______ _________. 2)A human being has ____ fingers for every _____ nose. 3)A brownie recipe calls for 3 cups of white sugar, 2 cups of brown sugar and 1 cup of flour. Write a sentence comparing cups of flour to cups of brown sugar. 1 cup of flour: 2 cups of brown sugar A brownie recipe has 1 cup of flour for every 2 cups of brown sugar. 22 Agenda

23. Back to Overview 23 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

24. 24 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

25. 25 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

26. 26 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

27. 27 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

28. 28 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

29. 29 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

30. 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… 30

31. 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… 31