21st Century Lessons
Introduction to Rate & Unit Rate
Primary Lesson Designer(s):
Stephanie Conklin
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This project is funded by the
American Federation of Teachers.
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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.
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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.
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Lesson Overview (2 of 3)
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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.
http://pbskids.org/itsmylife/money/spendingsmarts/index.html
Online Resources
for Absent Students
http://www.virtualnerd.com/pre-algebra/ratios-proportions/rate-and-unit-ratesdefinition.php
http://www.teachertube.com/viewVideo.php?video_id=45873&title=Watch_Video_on
_Unit_Rate___Pre_Algebra_Help
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 realworld 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.
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Warm Up
OBJECTIVE: Students will understand use rates and unit rates to solve realworld 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.
1) _______
__50___ jumps to _________
____1____ minute
2) ________
___50___ jumps: __________
___1______ minute
3)
50
1
jumps
Jumps
minute
4) Write
a sentence
usingusing
ratio ratio
language.
4) Write
a sentence
language.
Alex jumps 50 times for each second.
Agenda
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Agenda:
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)
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Launch
Watch the following video about Tillman, the world-recorder
holder for fastest skateboarder in his class.
http://vimeo.com/25153812
Why is Tillman special?
How do we know he’s the fastest
skateboarding dog?
In 2009, Tillman received the Guiness Book of
Records Award for fastest skateboarding dog,
when he rode 100 meters in 20 seconds.
Agenda
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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.
Agenda
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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.
I’m fast!
Agenda
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Explore
Tillman’s rate of skateboarding:
The word
unit
means 1.
A rate with a denominator of 1 has a special name!
A unit rate is a comparison of 2 different quantities
where one measurement only has 1 unit.
Like Tillman’s speed, 5 meters to second!
Agenda
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Explore – Mini Lesson
A rate and unit rate are often found in the following real-world
situations:
(ex 1) Homer ran 60 yards in 20 seconds.
(ex 2) A brownie recipe has 4 cups of flour for every 2 cups of sugar.of
sug
ar.(ex 3) Casey spent $80 on 8 pizzas.
What
are and
the
All rates
Yes!
Yards
and
measurement
unit
rates have
seconds!
are
2 we
different
comparing in
measurements
(ex 1)?
Agenda
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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 30 seconds.
Step 1: Write as a rate in fraction form.
How
did
weis
D’oh!
For PER!
every
I get
it,
60 yards
know
thisyards
is a
The
we
getting
have
word
old!
“per”
30 seconds
rate
question?
can
and
Let’sbe
seconds,
try
used
a new
for
2
unit
word
different
rates
in our
only, is 1.
Step 2: Simplify the rate so the denominator
measurements.
sentence!
like this!
2 yards
1 seconds
This
unit rate
Homer ran 2 yards for every 1 second.
Homer
ran means
2 yardsthat,
per second.
Agenda
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Explore – Partner Work
(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
Step 2: Simplify the rate so the denominator
Wait! Is thisis
still1.a rate?
2 cups of flour
1 cup of sugar
Yes, we have 2 different
We are comparing cups
measurements cups of
of flours to cups of sugar,
flour and cups of sugar!
does that count?
This unit rate means that there are 2 cups of flour per cup of
sugar.
Agenda
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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:
80 Key Chains for $40
Ricardo completes the following calculations to find the unit price:
80 key chains
$40
=
2 key chain
$1
=
$2 per key chain
Is Ricardo right? Why or why not?
Agenda
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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:
80 Key Chains for $40
Ricardo completes the following calculations to find the unit price:
80 key chains
$40
____$40_____
80 key chains
2 key chain
$1
=
____$1___
2 key chains
=
$2 per key chain
=
$0.50 per key chain
Agenda
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Summary
1) A rate is a ratio that compares 2 different _units_.
______.
2) A unit rate represented as a fraction has a
denominator
____________ of 1.
3) How are rates and unit rates similar?
Both are ratios that have 2 different units.
4) How are rates and unit rates different?
Rates can be any #s with different units compared but unit
rates must have 1 in denominator.
5) One real world example of rates and unit rates is
________________________ .
Agenda
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Practice
Agenda
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Practice
Agenda
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Assessment
Casey spent $80 on 8 pizzas.
Write a rate as a fraction to represent this situation.
_$80_
8 pizzas
 Write a unit rate as a fraction to represent this situation.
_$10_
1 pizza
Agenda
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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.
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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
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