Introduction to Ratios

Introduction to Ratios
21st Century Lessons Introduction to Ratios Need to make sure Vimmeo video “Counting Marshmallows” is ready for play. When finished with Lesson – Students should complete Workbook pg. 142 (Ratio)… 6.RP.1 Day 1

This project is funded by the American Federation of Teachers.

21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson: 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. Feel free to customize this file to match the language and routines in your classroom. *1st Time Users of 21st Century Lesson: Click HERE for a detailed description of our project.

Lesson Overview (1 of 3) Lesson Objective Lesson Description
OBJECTIVE: Students will write real-world quantities as ratios and explain their meaning. Language Objective: Students will define ratio and will be introduced to ratio language. Student- Friendly Objective: Students will define the word ratio and represent real-world situations using ratios. Students will also practice explaining what a ratio means in the real-world. Lesson Description This lesson will start with students reviewing simplifying fractions, and then ask students to represent real-world situations as fractions. Students can follow the powerpoint with the structured notes provided. We will launch this lesson with a real-world example, comparing oat pieces to marshmallows in Lucky Charms. Once students have these skills reinforced, we will then ask them to write ratios in three ways and in simplest terms. Further, we will ask students to compare part to whole (for example, hours to total hours), and then explain in everyday language what terms like 1 out of 5 mean. This is a skill that will be developed throughout this unit. A class work assignment is included in this lesson as well as homework and answers for both.

Lesson Overview (2 of 3) Lesson Vocabulary Materials Scaffolding
Ratio: a comparison of two quantities Simplified Fraction: A numerator and denominator that have been divided by GCF and written as a fraction. 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. - Enrichment Foul-Shooting Contest: Students can work in class using a trash can and crumpled up paper or go to the gym. In this lesson, students can calculate their own free-throw percent, and compare and contrast their ratios with their peers. We can also make conclusions about future success in shooting. Here is a link with more info: Online Resources for Absent Students 1) Lucky Charm Video: 2) Introduction to Ratios: 3)  Basic Mathematics  Ratios  Ratios as Fractions

Lesson Overview (3 of 3) Common Core State Standard Before and After
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 Before learning this unit, students should have a strong familiarity with fractions, and also simplifying fractions. Once this lesson is done, students will move onto topics like rate, proportions and using these in applied situations with time and units of measure. Please see 6RP2 and 6RP3 standards. Topic Background This lesson uses all real-world examples of comparing, contrasting and representing real-world shapes and situations. Students should feel comfortable at the end of this lesson with explaining situations according to numbers and ratios, and also explaining what terms like 1 out of 5 or 3 for every 6 means in a situation.

Warm Up Write each fraction in simplest form.
Write each fraction in simplest form. (5 min) Time passed In-Class Notes This warm-up will allow teachers to review key math terms like common factors, GCF, equivalent fractions, numerator and denominator. This warm-up serves as a review for simplifying fractions which is a pre-requisite skill for simplifying ratios and rates later in this lesson as well as to find unit rates in future lessons. Preparation Notes It would be helpful to utilize terms like numerator, denominator, factor and GCF when instructing this lesson. 3) Which fraction above has the greatest value? 5/9 is bigger than 3/10 because 5/9 is about 0.55 and 3/10 = 0.3 Agenda

Agenda: OBJECTIVE: Students will write real-world quantities as ratios and explain their meaning. Language Objective: Students will define ratio and will be introduced to ratio language What does the word quantity mean? Hint: How many ears do I have? (2-3 mins) Time passed In-Class Notes Teachers should take one minute to review the agenda for the day’s lesson, and also ask a student to read the objective. Teachers should also ask students to define the word quantity – this can be done as a whole class review. The hint button and final answer button can be displayed once students have a chance to brainstorm answers. Preparation Notes None A quantity is an amount of anything that we can count. Like my ears!

Lucky Charms Launch Turn and Talk:
Have you ever had Lucky Charms cereal? Are there more marshmallows or oat pieces in a box of Lucky Charms? Predict how many marshmallows pieces are 1 box. Predict how many oat pieces are in 1 box. (8-10 min) Time passed In-Class Notes This introduction will hopefully engage and “hook” students into the lesson. Teachers can have students read over each question and then work in pairs to answer each question. Teachers can ask students to write their predictions on the board or can take volunteers to give their answers. This lesson can also be done interactively with real Lucky Charms. Students can be given bowls of Lucky Charms, and can count marshmallows compared with oat pieces. If this is not possible, then students can watch the video to learn the ratio of marshmallows to oat pieces. Preparation Notes Teachers can provide students with structured class notes, please find this with the lesson as well as attached class work. Watch the Video on the next slide and then we will test your prediction! Hint: Agenda

Lucky Charms Launch Turn and Talk:
Have you ever had Lucky Charms cereal? Are there more marshmallows or oat pieces in a box of Lucky Charms? Predict how many marshmallows pieces are 1 box. Predict how many oat pieces are in 1 box. Hint: There are almost 2,500 marshmallows and oats altogether in 1 box. (8-10 min) Time passed In-Class Notes This introduction will hopefully engage and “hook” students into the lesson. Teachers can have students read over each question and then work in pairs to answer each question. Teachers can ask students to write their predictions on the board or can take volunteers to give their answers. This lesson can also be done interactively with real Lucky Charms. Students can be given bowls of Lucky Charms, and can count marshmallows compared with oat pieces. If this is not possible, then students can watch the video to learn the ratio of marshmallows to oat pieces. Preparation Notes Teachers can provide students with structured class notes, please find this with the lesson as well as attached class work. Watch the Video on the next slide to test your prediction! Agenda

Counting Lucky Charms…
Click on Black Box to start video clip

Lucky Charms Continued
 There are 287 marshmallow pieces and 2,583 Oat Pieces in 1 box of Lucky Charms. We can write this real-world situation as a ratio! A ratio is a comparison of two different quantities. We can write a ratio in 3 ways using: 1) a fraction 2) the word, “to” (3 min) Time passed In-Class Notes This part of the lesson will allow students to write down the definition of ratio and the 3 ways in which to represent ratios. Teachers should also reinforce the definition of ratio, and discuss quantity as a term that refers to real-world examples of numbers. Preparation Notes Students will need paper and pencil to write down the definition. 3) a colon : Agenda

Lucky Charms Continued
Write the ratio of marshmallows to oats in 3 ways. Remember in 1 box: 287 Marshmallows 2,583 Oats Let’s try together: 1) A Fraction 2) The Word “to 287 Marshmallows to 2,583 Oats (3 min) Time passed In-Class Notes This part of the lesson will allow students to write down the definition of ratio and the 3 ways in which to represent ratios. Teachers should also reinforce the definition of ratio, and discuss quantity as a term that refers to real-world examples of numbers. Preparation Notes Students will need paper and pencil to write down the definition. 3) A Colon 287 Marshmallows : 2,583 Oats Agenda

Practice – Work with a partner!
Write a ratio comparing # of people to # of pizzas for each picture. Picture #1 Picture #2 1 person: 4 pizzas 4 people: 1 pizza Talk to your partner How are the ratios above alike? Does the order matter when writing a ratio? (2-3 min) Time passed In-Class Notes This slide will allow students to practice writing ratios. You should encourage students to use all forms of writing with the fraction bar and the word “to” as well. We hope that in this slide, we can reinforce the importance of order in a ratio. In this example, if we switch the order then we change the situation completely. Preparation Notes Teachers can gauge student learning from last slide to determine if students can work on first part of slide (writing a ratio) by themselves or if partner work or whole group is best. Yes! The situation changes if we change the order of pizza & people.! Agenda

Explore lions to birds 6 lions to 1 bird lions : birds
(2-3 min) Time passed In-Class Notes Students will reinforce the three way to represent a ratio using the word “to,” a fraction, and a colon symbol. Students should work with a partner or in a small group to discuss. Teachers may want to ask students, particularly with an ELL population, to first point out a lion and hyena before beginning their work. This assignment can be modified to ask students to compare a lion to a bird, if teachers are concerned about the difficulty of the word hyena. Preparation Notes Teachers should consider their student population when clicking to reveal new parts of the slide. To provide scaffolding, teachers can click once to find the first hint, using the word “to”, while another click provides the set-up for a fraction and then lastly a colon. Teachers should try to just show one way at a time and give students a chance to write their own ratio. Partner Work: Use the picture above to write a ratio in 3 ways comparing the # of lions to # of birds. Agenda

Simplifying Ratios Let’s explain the meaning of this ratio!
Basketball Write in simplest form the ratio of Biking to Basketball. Let’s explain the meaning of this ratio! This ratio means that for every 1 hour biking, Christian spent ___ hours playing basketball. Basketball (2-3 min) Time passed In-Class Notes This slide helps to transition students to writing ratios by reading data from a table rather than using pictures. Students will also review how to simplify fractions by finding the GCF of numerator and denominator. Teachers should guide students through the first example, and then ask students to try the next on their own, question #2 on their own. Preparation Notes Teachers should remind students that simplifying fractions has already been reviewed in warm-up. Teachers may also want to consider that there may be many answers for the explanation of meaning. Agenda

Write in simplest form the ratio of Christian’s time spent running to total hours of activities. Let’s explain the meaning of this ratio! This ratio means that for every 25 total hours Christian spent on activities, he spent ____ hours running. (2-3 min) Time passed In-Class Notes This slide helps to transition students to writing ratios by reading data from a table rather than using pictures. Students will also review how to simplify fractions by finding the GCF of numerator and denominator. Teachers should guide students through the first example, and then ask students to try the next on their own. If students struggle with second question, teachers can click on scaffold button to provide a hint. Teachers may also want to ask at end of lesson how else we could have written our answers to #1 and #2 (i.e. using colon or word “to”) Preparation Notes Teachers should dipstick to gauge student learning, and determine if students need the hint. The hint can always be added later. Teachers may also want to consider that there may be many answers for the explanation of meaning. Scaffold Agenda

Hint: Add to find the total # of points Write in simplest form the ratio of Christian’s time spent running to total hours of activities. Let’s explain the meaning of this ratio! This ratio means that for every 25 total hours Christian spent on activities, he spent ____ hours running. (2-3 min) Time passed In-Class Notes This slide helps to transition students to writing ratios by reading data from a table rather than using pictures. Students will also review how to simplify fractions by finding the GCF of numerator and denominator. Teachers should guide students through the first example, and then ask students to try the next on their own. If students struggle with second question, teachers can click on scaffold button to provide a hint. Teachers may also want to ask at end of lesson how else we could have written our answers to #1 and #2 (i.e. using colon or word “to”) Preparation Notes Teachers should dipstick to gauge student learning, and determine if students need the hint. The hint can always be added later. Teachers may also want to consider that there may be many answers for the explanation of meaning. Agenda

Summary – Try Independently
A ratio is a comparison of two different _________. We can write a ratio in ____ different ways. Ratios can be written as  As a fraction Using the word “to” Using a colon : (3 minutes) Time passed In-Class Notes Students should use their class work sheet to fill in each blank. Teachers should make sure to give wait time for students to think about their answers, and also encourage them to look back at their notes if needed. Preparation Notes Agenda

Practice Complete the following problems. Agenda (5 - min) Time passed
In-Class Notes Teachers can have students work on this short in-class assignment individually or in pairs or small groups. Teachers can ask students to post their answers for these questions and #3-4 as they work – calling sticks would be one method to have students participate. Preparation Notes Teachers should have a photocopy of this CW for students, if possible. These can also be project and done on lined paper. Agenda

Practice - Answers Agenda (2 mins) Time passed In-Class Notes
Depending on student questions, teacher can post answers and go over any questions that students have on fractions and #1, 2. Teachers are encouraged to have students post their answers and ask them to explain how they got their answer. Preparation Notes Teachers may want to review vocabulary with students, particularly ELL students. Agenda

Practice Complete the following problems. Agenda (5 - min) Time passed
In-Class Notes Teachers can have students work on this short in-class assignment individually or in pairs or small groups. Teachers can ask students to post their answers for these questions as they work. Preparation Notes Teachers should have a photocopy of this CW for students, if possible. These can also be project and done on lined paper. Agenda

Practice - Answers Agenda (2 mins) Time passed In-Class Notes
Depending on student questions, teacher can post answers and go over any questions that students have on fractions and #1, 2. Teachers are encouraged to have students post their answers and ask them to explain how they got their answer. Preparation Notes Teachers may want to review vocabulary with students, particularly ELL students. Agenda

Assessment Complete the following questions on your own!
Write a ratio comparing # of fish to # of sharks in 3 ways. (2 min) Time passed In-Class Notes This question will help teachers to determine if students are able to apply ideas about ratios to real-world questions. Teachers can ask students to complete their work on a sticky note or sheet of paper to be collected. The goal of this last question is to determine if students know or do not know how to apply ratios – it is strongly encouraged for teachers to determine which students know and do not know how to solve this problem correctly. Preparation Notes Teachers may want flashcards, a piece of paper or sticky notes to collect students responses or go to Peardeck.com for exit ticket… Agenda

1st Time Users of 21st Century Lessons
Description of 21st Century Lessons: Welcome to 21st 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. 21st 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. Next Slide Back to Overview

Standards for This Unit The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: Next Slide Back to Overview

Requirements to teach 21st Century Lessons: In order to properly use 21st 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 Next Slide Back to Overview

Strongly Suggested to teach 21st 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. Next Slide Back to Overview

Lesson Preparation (Slide 1 of 2) We suggest spending 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 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. Next Slide Back to Overview

Lesson Preparation (Slide 2 of 2) 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. Next Slide Back to Overview

Features built into each PowerPoint lesson 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

21st Century Lessons The goal…
The goal of 21st 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.

21st Century Lessons The people…
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 21st Century Lessons Brian Connor – Technology Coordinator

Introduction to Ratios

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