1. Introduction to Rate & Unit Rate
21st Century Lessons
Introduction to Rate & Unit Rate
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
OBJECTIVE: Students will understand how to a rate and unit rate relate to ratios.
Language Objective: Students will define rate and unit rate using real-world examples.
Lesson Description
This lesson will first review the idea of ratio and then connect this idea to rate and unit rate. We will use a student-friendly video on a skateboarding bulldog to engage students in learning. Then we will calculate the dog’s rate of speed as both a rate then unit rate. We will also define these key words in the context of this example. After this example, we will then focus on other real-world examples of rates and unit rates using examples like measurement, money and distance. Students will complete examples with the whole class first and then will work with their partners. After this students will have a chance to work in partners or small groups on the classwork. Then teachers can review this work, and complete a summary question.

5. Lesson Overview (2 of 3) Lesson Vocabulary
Rate: a ratio that compares 2 different measurements
Unit rate: comparison of 2 different quantities where one measurement only has 1 unit.
Materials
Specific list of necessary and optional materials with quantities
Copies of scaffolded class notes
Internet and projector
Speakers
Scaffolding
Teachers can use the class work as a scaffolded assignment with different expectations for students. Further, the call-outs or bubbles that characters state in the lesson can be used to help students confirm understanding and clarify definitions.
Enrichment
This website from PBS is kid-friendly and allosws students to access a host of topics related to money and math.
Online Resources for Absent Students

6. Lesson Overview (3 of 3) Common Core State Standard
6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1
Before and After
Before this school, students will review utilizing diagrams to represent ratios, and will also have a strong knowledge of how to write ratios and also represent them in 3 ways. After this lesson, we will focus on how to write rates as unit rates and unit prices and compare in real-world situations.
Topic Background
The idea of rate and unit rate applies to many real-world situations. In this lesson, we will specifically focus on time and distance, speed, measurement, and money. We will continue with these key themes in the next lessons and continue to connect to these real-world examples.

7. Warm Up Alex is trying to win a jumping jack competition. He does
OBJECTIVE: Students will understand use rates and unit rates to solve real-world problems.
Language Objective: Students will define rate and unit rate using real-world examples.
Alex is trying to win a jumping jack competition. He does
100 jumping jacks in 2 minutes.
Write a ratio in three ways comparing jumping jacks to minutes.
Remember to simplify!
1) _______ jumps to _________ minute
2) ________ jumps: __________ minute
3) Jumps 4) Write a sentence using ratio language.
minute
1) __50___ jumps to ____1____ minute
2) ___50___ jumps: ___1______ minute
3) 50 jumps ) Write a sentence using ratio language.
1 minute Alex jumps 50 times for each second.
(3-5 min) Time passed
In-Class Notes
Students will review how to write ratios in 3 ways. Teachers should project the second slide only as a hint if students need help remembering how to write ratios in 3 ways.
The purpose of this warm-up is to remind students how to write ratios, remind students to label each part of a ratio, and also to simplify each ratio.
Preparation Notes
Agenda

8. Agenda: 1) Warm Up (Individual)
OBJECTIVE: Students will use rates and unit rates to solve real-world problems. Language Objective: Students will define rate and unit rate using real-world examples.
1) Warm Up (Individual)
2) Launch: Tillman the Skateboarder (Whole Class)
3) Explore: Mini-Lesson (Partner and Whole Class)
4) Summary (Whole Class)
5) Practice: (Partner and Whole Class)
6) Assessment: (Independent and Whole Class)
(Time on this slide - min) Time passed
In-Class Notes
Preparation Notes

9. Launch Watch the following video about Tillman, the world-recorder
holder for fastest skateboarder in his class.
Why is Tillman special?
How do we know he’s the fastest
skateboarding dog?
(5 min) Time passed
In-Class Notes
Teachers should plan on starting the video clip at the 2 minutes mark and finish. The entire video is too much for the motivation and launch, and the music gets a little annoying.
Teachers should use then use calling sticks to ask students the follow-up questions. For the second question, how do we know he’s the fastest, we hope to encourage students to say their must have been a race or contest that involved a distance and timed event.
Then we can show his time.
Preparation Notes
In 2009, Tillman received the Guiness Book of
Records Award for fastest skateboarding dog,
when he rode 100 meters in 20 seconds.
Agenda

10. Launch In 2009, Tillman received the Guinness Book of
Records Award for fastest skateboarding dog,
when he rode 100 meters in 20 seconds.
(ex 1) Write Tillman’s record time as a ratio in fraction form.
*Remember to simplify and use lables!!!
This special ratio is a rate! Woof!
This example is special because we have 2 different units being compared, meters and seconds.
(3 min) Time passed
In-Class Note:
Teachers will use this ratio as a way to introduce the idea of rate. We will focus on the definition of rate in the next slide but it is important for teachers to make a big deal about a rate being a special kind of ratio because we are looking at 2 different units of measure.
Before moving to next slide, teachers should pause to ask students if they can write these ratios in a different way, i.e. using the colon or word to
Preparation Notes
Scaffolded Class notes
Agenda

11. Explore – Mini Lesson
A rate is a ratio that compares 2 different measurements!
(ex) Tillman’s skateboarding rate is
What happens when we simplify this rate?
This means that Tillman travels at a rate
of 5 meters for every 1 second.
(2-3 min) Time passed
In-Class Notes
Teachers should ask students to fill in definition of rate on their class notes.
We will focus on the language and wording of rates in the next lesson but this slide will help introduce students to this concept.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
I’m fast!
Agenda

12. UNIT RATE Explore Tillman’s rate of skateboarding:
The word unit means 1.
Tillman’s rate of skateboarding:
A rate with a denominator of 1 has a special name!
UNIT RATE
A unit rate is a comparison of 2 different quantities where one measurement only has 1 unit.
Like Tillman’s speed, 5 meters to 1 second!
(3 min) Time passed
In-Class Notes
This slide will introduce students to the idea of unit rate. Students should copy down the definition in their class notes.
Preparation Notes
Class notes
Agenda

13. Explore – Mini Lesson
A rate and unit rate are often found in the following real-world situations:
Distance and Time
(ex 1) Homer ran 60 yards in 20 seconds.
Cooking and Mixtures
(ex 2) A brownie recipe has 4 cups of flour for every 2 cups of sugar.of sug
ar.
What are the measurement we are comparing in (ex 1)?
All rates and unit rates have 2 different measurements
Yes! Yards and seconds!
Prices
(ex 3) Casey spent $80 on 8 pizzas.
(2-3 min) Time passed
In-Class Notes
Teachers may want to ask students to answer questions like, why are these real-world examples? How do we use distance and time everyday?
The call-out bubbles are to help reinforce students understanding of the definition of rate and unit rate.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
Agenda

14. Explore – Mini Lesson
A unit rate can be found using the following steps.
(ex 1) Write Homer’s speed as a unit rate.
Homer ran 60 yards in 20 seconds.
Step 1: Write as a rate in fraction form.
How did we know this is a rate question?
For every is getting old! Let’s try a new word in our sentence!
PER!
The word “per” can be used for unit rates only, like this!
D’oh! I get it, we have yards and seconds, 2 different measurements.
60 yards
20 seconds
Step 2: Simplify the rate so the denominator is 1.
3 yards
1 seconds
(2-3 min) Time passed
In-Class Notes
Teachers can ask students what Homer is doing in his photo – how does this connect with the real world?
The real goal of this slide is to help students reinforce simplifying rates down to unit rates using simple numbers. In the next PP, we will tackle simplifying with more complex #s.
Teachers can introduce per in this slide, and remind students that it is just like “for each” when we use per, it replaces the 1.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
This unit rate means that, Homer ran 2 yards for every 1 second.
Homer ran 3 yards per second.
Agenda

15. Explore – Partner Work Step 1: Write as a rate in fraction form.
(ex 2) A brownie recipe has 4 cups of flour for every 2 cups of sugar.
Step 1: Write as a rate in fraction form.
4 cups of flour
2 cups of sugar
Wait! Is this still a rate? We are comparing cups of flours to cups of sugar, does that count?
Step 2: Simplify the rate so the denominator is 1.
Yes, we have 2 different measurements cups of flour and cups of sugar!
2 cups of flour
1 cup of sugar
(6 min) Time passed
In-Class Notes
Teachers can begin this slide by asking students why this is a real world example.
Students can then try this with a partner on their scaffolded notes and then the teacher can review the question or go over any questions with students.
Teachers should emphasis that a unit rate again tells us that we have a 1 for the denominator in our ratio fraction.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
This unit rate means that there are 2 cups of flour per cup of sugar.
Agenda

16. Challenge – Partner Work
(ex 3) Ricardo wants to buy 40 key chains for his new business. An online merchant has the following special posted.
SPECIAL:
40 Key Chains for $80
Ricardo completes the following calculations to find the unit price:
40 key chains
$80
0.5 key chain $1 = =
$1 per half key chain
(4 min) Time passed
In-Class Notes
Teachers should ask students to try to work through this problem first in their partners and then work as a whole class.
The goal of this slide is to help students understand that units must go with their correct labels and also that we must find the UNIT for the object or key chain not the dollar amount.
This topic will be explored more in-depth in this lesson but hopefully we will introduce idea in this last higher-order question.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
Is Ricardo right? Why or why not?
Agenda

17. Challenge – Partner Work
(ex 3) Ricardo wants to buy 40 key chains for his new business. An online merchant has the following special posted.
SPECIAL:
40 Key Chains for $ 80
Ricardo completes the following calculations to find the unit price:
40 key chains
$80
0.5 key chain $1 =
$1 per half key chain
(2 min) Time passed
In-Class Notes
Teachers can ask students how they found the answer, and then go through this slide to show students the correct work.
Preparation Notes
Students will use their scaffolded class notes to fill in and follow along with lesson
____$80_____
40 key chains
____$2___
1 key chain = =
$ 2 per key chain
Agenda

18. Summary _measurements_.
A rate is a ratio that compares 2 different ______.
A unit rate represented as a fraction has a ____________ of 1.
How are rates and unit rates similar?
How are rates and unit rates different?
One real world example of rates and unit rates is ________________________ .
denominator
Both are ratios that have 2 different measurements.
Rates can be any #s with different measurement compared but unit rates must have 1 in denominator.
(5-7 min) Time passed
In-Class Notes
Teachers should call on students using calling sticks to illict answers from students.
Please note that teachers should fill in answer for #3 based on student suggestions.
Preparation Notes
Agenda

19. Practice Agenda (10 min) Time passed In-Class Notes
Students should work on the following class work assignment for 10 minutes or less (depending on how much time you have left in class.
Preparation Notes
Copies of class notes for teachers.
Agenda

20. Practice Agenda (5 min) Time passed In-Class Notes
Teachers can review answers with students.
It is suggested that teachers let students check their answers, and then review 1-2 questions as a whole class to ensure that students have reviewed.
Preparation Notes
Agenda

21. Assessment _$80_ 8 pizzas _$10_ 1 pizza Casey spent $80 on 8 pizzas.
Write a rate as a fraction to represent this situation.
Write a unit rate as a fraction to represent this situation.
_$80_
8 pizzas
_$10_
1 pizza
(3-5 min) Time passed
In-Class Notes
Students can complete this assignment on a post-it note or independently.
Students should write their names and answers on the post-it or index card, and teachers can collect.
Before students leave class, teachers can quickly review answers.
Preparation Notes
Index cards, post-it notes or half-sheet of paper
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