1. Primary Lesson Designer(s):
21st Century Lessons
Ratios and Vocabulary
Primary Lesson Designer(s):
Stephanie Conklin

2. This project is funded by the American Federation of Teachers.

3. 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.

4. Lesson Overview (1 of 3) Lesson Objective Lesson Description
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.

5. Lesson Overview (2 of 3) Lesson Vocabulary Materials Scaffolding
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. -
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:
Directions on how to make a Golden Rectangle:
Online Resources for Absent Students
Thinking Blocks:
Review of Ratio:

6. 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
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.
OBJECTIVE: Students will use ratio language to describe a relationship between two quantities.
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.
(3-5 min) Time passed
In-Class Notes
Teachers can use the scaffold button to help students remember the 3 ways to write a ratio. Teachers should give students 1 minute or more to try to write the 3 ways without using the scaffold button. Students may want to leave the answer as 4 to 2, please encourage them to write their fractions in simplest forms. Further, the sentence strip will act as a review and introduction to the work that will be done in this lesson on ratio and vocabulary.
Preparation Notes
None
Scaffold
Agenda

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

9. Launch
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!
(4-5 mins) Time passed
In-Class Notes
Teachers should give students a chance to talk about their own language and nationality with their partner for 2-3 minutes and then share with the whole class.
This turn and talk will help students to access information in video and also help students to make connections between their own lives.
Teachers can ask students to share their information with class or take a survey of different languages spoken.
Preparation Notes
Agenda

10. Launch
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.
(7-10 mins) Time passed
In-Class Notes
Link for “If the World Were a Village Video”  (3 minutes long)
Teachers should load video before class, as there is a commerical at the start. Also, teachers should consider using a small screen view as the teachertube can become blurry when projected.
This video is a chance for students to engage in cross-curricular learning while also hearing the language of ratios introduced.
Students should watch the video and fill our sheets independently.
For classes with ELL and SPED students, we strongly recommend that teachers play this video once with students just listening and a second time with students answering questions. Teachers may want to pre-read questions. Teachers may also want to consider editing sheet to only include odds.
Preparation Notes
Each student will need a copy of the class work hand out for this lesson (scaffolded notes)
Teacher will also need a projector and speakers.
Agenda

11. Launch Continued Please check your answers! Agenda (2 min) Time passed
In-Class Notes
Teachers can review answers with students quickly to ensure that they have correct answers.
Please note that question #19 will be reviewed in the next slide as it will launch our exploration of vocab. relating to ratios.
- Teachers may want to poll students to ask them follow-up questions like, why is this video important? How can we use math to help us understand the world?
Preparation Notes
Agenda

12. Mini Lesson 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
(2 min) Time passed
In-Class Notes
This slide serves as a connection between our video and the mini lesson. Teachers should make a big deal about the term for every as this key phrase will be the focus of our lesson. This term will later help students to make connections to important terms like slope and rate of change.
Preparation Notes
Agenda

13. Explore
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
(3 min) Time passed
In-Class Notes
This will be a teacher-led example that will allow students to see that we can replace or substitute a colon or any other ratio symbol with the phrase “for every”.
Teachers can also emphasis the importance of using the letter “s” or not depending on whether words are plural or not.
Preparation Notes
Scaffolded Notes
We can also say,
An eagle has 2 wings for each beak.
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 use for each when we only have 1 thing being compared, like 1 beak!
Agenda

14. Explore 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.
(3 min) Time passed
In-Class Notes
The goal of this slide is to help reinforce writing ratio sentences and to review that we should first simplify all ratios, and also teach students that for every can start at beginning of sentence.
Preparation Notes
Scaffolded Notes
Did you simplify the ratio?
Let’s add a new step!
Yes! 20 to 8 and 5 to 2 equivalent fractions or equal fractions!
Are the ratios 20 to 8 the same as to 2?
Agenda

15. Explore – Try with a Partner
(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.
(5 min) Time passed
In-Class Notes
Teachers should read the problem and question with students and then give them 2 minutes to try to write a sentence with their ratio. After 1 minute, teachers may want to click to bring in steps to remind students. Once students have a chance to write a ratio sentence, teachers can ask for students to read their sentences and also to explain the steps.
Teachers should make sure to review both ways of writing with for every in between and for every at the beginning. Teachers should remind students that both ways are perfectly acceptable, we just want them to recognize how to use both.
Also the push pins are grouped together and teacher can move these to rest on top of each poster if it helps students.
Preparation Notes
Scaffolded Notes
Agenda

16. Challenge – Try with a Partner
(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!
(5 min) Time passed
In-Class Notes
Teachers should read the problem and question with students and then give them 2-3 minutes to try to answer questions.
It would be best to have a student come up to the board and show their answer and then the whole class can participate in discussion.
The goal of this challenge question is to get students to think about proportional reasoning.
Preparation Notes
Scaffolded Notes
Agenda

17. Challenge – Try with a Partner
(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.
(2 min) Time passed
In-Class Notes
Teachers can use this slide if students do not have a great diagram or need help with answering question.
Teachers should review how we mathematically can solve this problem using the fancy algebra way.
Preparation Notes
Scaffolded Notes
Fancy Algebra Way:
Agenda

18. Practice You have 5 minutes to work with your partners on this
class work, good luck!
(5-7 min) Time passed
In-Class Notes
Teachers should give students 5-7 minutes to work on this class work. Students who are ELL or SPED may need more time but by working in small groups, they can hopefully try each part.
Preparation Notes
Copies of class work
Agenda

19. Practice - Answers Agenda (5 min) Time passed In-Class Notes
Teachers should review answers with students and discuss any questions that they may have about the class work. Teachers should ensure that students simplify all ratios and also use labels.
Preparation Notes
Agenda

20. 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!
(3 min) Time passed
In-Class Notes
This slide helps to review the key vocab terms used in this lesson and also allows for students to see how possible mistakes can affect meaning. Teachers can also scaffold this question by drawing a cat with 2 tails and 1 ear to visually represent what Calvin said.
Preparation Notes
Agenda

21. Assessment For #1 and #2, fill in the blanks:
1) We can write ratios as sentences using the phrase,
_______ _________ .
A human being has ____ fingers for every _____ nose.
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.
(3 min) Time passed
In-Class Notes
Teachers should use calling sticks to have students fill the blanks independently and write a sentence. There is a scaffold step for students for question #3 which may help students to determine which values to use when writing a sentence.
Preparation Notes
Scaffolded Notes
Agenda

22. 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.

23. 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