File - MATHEMATICS 6-7
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21 st Century Lessons
Introduction to Ratios
Primary Lesson Designer(s):
Stephanie Conklin
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This project is funded by the
American Federation of Teachers.
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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.
*1 st Time Users of 21 st Century Lesson:
Click HERE for a detailed description of our project.
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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.
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.
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Lesson Overview (2 of 3)
Lesson Vocabulary Ratio: a comparison of two quantities
Simplified Fraction: A numerator and denominator that have been divided by GCF and written as a fraction.
Materials
Scaffolding
Hand outs for class notes and class work
-The use of pictures and words is critical in this lesson to helping build vocabulary of ELL students.
Teachers should review words when needed.
Enrichment
- 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-formathematical-practice/
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=related
2) Introduction to Ratios: http://www.mathplayground.com/howto_ratios.html
3) www.mathtv.com
Basic Mathematics Ratios Ratios as Fractions
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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 Background
This lesson uses all real-world examples of comparing, contrasting and representing realworld 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/standardsfor-mathematical-practice/
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Warm Up
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.
Write each fraction in simplest form.
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:
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
2) Lucky Charms Launch – Whole Class
What does the word quantity mean?
Hint: How many ears do I have?
A quantity is an amount of anything that we can count.
Like my ears!
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Lucky Charms Launch
Turn and Talk:
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.
Watch the Video on the next slide to test your prediction!
Hint:
Lucky Charms Launch
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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) a colon :
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Lucky Charms Continued
Write the ratio of marshmallows to oats in 3 ways.
Let’s try together:
Remember in 1 box:
287 Marshmallows
2,583 Oats
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!
Write a ratio comparing # pizzas to # of people for each picture.
Picture #1 Picture #2
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4 pizzas: 1 person
1 pizza: 4 people
Talk to your partner
How are the ratios above alike?
Does the order matter when writing a ratio?
Yes! The situation changes if we change the order of pizza & people.
!
Explore
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Partner Work:
Use the picture above to write a ratio in 3 ways comparing the # of lions to # of birds. lions to birds
6 lions to 1 bird lions : birds
6 lions : 1 bird
Simplifying Ratios
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1) Write in simplest form the ratio of Biking to Basketball.
biking basketball
=
8 hours of biking
16 hours of basketball
=
1 hour of biking
2 hours of basketball
Let’s explain the meaning of this ratio!
This ratio means that for every 1 hour biking, Christian spent ___ hours playing basketball.
Simplifying Ratios
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.
Scaffold
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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 :
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Practice
Use the CW hand-out to complete the following problems.
Practice
Use the CW hand-out to complete the following problems.
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Practice - Answers
Practice - Answers
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Assessment
Complete the following questions on your own!
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Write a ratio comparing # of fish to # of sharks in 3 ways.
21 st Century Lessons
The goal…
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.
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21 st 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 21 st Century Lessons
Brian Connor – Technology Coordinator
