21st Century Lessons

Introduction to Ratios

Primary Lesson Designer(s):

Stephanie Conklin

1

2

This project is funded by the American Federation of Teachers.

3

*1st Time Users of 21st Century Lesson:Click HERE for a detailed description of our project.

21st 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

Lesson Objective 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 (1 of 3)

5

Lesson Vocabulary Ratio: a comparison of two quantitiesSimplified 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. - http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice/

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:http://www.education.com/activity/article/Wastepaper_Basketball_fifth/

Online Resources for Absent Students

1) Lucky Charm Video:http://www.youtube.com/watch?v=XIcFf-YdSKY&feature=related2) Introduction to Ratios:http://www.mathplayground.com/howto_ratios.html3) www.mathtv.com Basic Mathematics Ratios Ratios

as Fractions

Lesson Overview (2 of 3)

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 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 BackgroundThis 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.

http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice/

Warm UpOBJECTIVE: 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. .

Agenda

7

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

Write each fraction in simplest form.

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

1) Warm Up - Individual 2) Lucky Charms Launch – Whole Class

3) Exploration - Partner

4) Summary - Individual

5) Practice – Small Group

6) Assessment - Individual

8

What does the word quantity

mean?

What does the word quantity

mean?

Hint: How many ears do I

have?

Hint: How many ears do I

have?

A quantity is an amount of

anything that we can count. Like my ears!

A quantity is an amount of

anything that we can count. Like my ears!

Lucky Charms Launch

Agenda

9

Hint:

1. Have you ever had Lucky Charms cereal?

2. Are there more marshmallows or oat pieces in a box of Lucky Charms?

3. Predict how many marshmallows pieces are 1 box.

4. Predict how many oat pieces are in 1 box.

Turn and Talk:

Watch the Video on the next slide to test your prediction!

Lucky Charms Launch

Agenda

11

http://bit.ly/M0OPng

Lucky Charms Continued

12

Agenda

1) a fraction1) a fraction

2) the word, “to” 2) the word, “to”

3) a colon :3) a colon :

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:

Lucky Charms Continued

13

Agenda

Remember in 1 box:287 Marshmallows2,583 Oats

Remember in 1 box:287 Marshmallows2,583 Oats

Write the ratio of marshmallows to oats in 3 ways.

Let’s try together:

1) A Fraction

2) The Word “to

3) A Colon

287 Marshmallows to 2,583 Oats

287 Marshmallows : 2,583 Oats

Practice – Work with a partner!

14

Agenda

Talk to your partnerHow are the ratios above alike? Does the order matter when writing a ratio?

Write a ratio comparing # pizzas to # of people for each picture.Picture #1 Picture #2

4 pizzas: 1 person 1 pizza: 4 people

Yes! The situation changes if we change the order of pizza & people.!

Explore

15

Agenda

Partner Work: Use the picture above to write a ratio in 3 ways comparing the # of lions to # of birds.

lions to birds6 lions to 1 bird

lions : birds

6 lions : 1 bird

Simplifying Ratios

16

Agenda

1) 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 ___ hoursplaying basketball.

= 8 hours of biking16 hours of basketball = 1 hour of biking2 hours of basketball

€

biking

basketball

Simplifying Ratios

17

AgendaScaffold

2) 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.

Summary – Try Independently

1) A ratio is a comparison of two different _________.

2) We can write a ratio in ____ different ways.

3) Ratios can be written as As a fraction Using the word “to”Using a colon :

19

Agenda

Use the CW hand-out to complete the following problems.

Practice

20

Agenda

Practice

21

Agenda

Use the CW hand-out to complete the following problems.

Practice - Answers

22

Agenda

Practice - Answers

23

Agenda

AssessmentComplete the following questions on your own!

Write a ratio comparing # of fish to # of sharks in 3 ways.

24

Agenda

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 LessonsThe goal…

32

Directors:Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues CommitteeTed Chambers - Co-director of 21st Century LessonsTracy Young - Staffing Director of 21st Century LessonsLeslie Ryan Miller - Director of the Boston Public Schools Office of

Teacher Development and AdvancementEmily Berman- Curriculum Director (Social Studies) of 21st Century LessonsCarla Zils – Curriculum Director (Math) of 21st Century LessonsBrian Connor – Technology Coordinator

21st Century Lessons

The people…

33