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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*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.

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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 DescriptionThis 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.

Lesson Overview (1 of 3)

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Lesson Vocabulary Rate: a ratio that compares 2 different measurementsUnit 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-rates-definition.phphttp://www.teachertube.com/viewVideo.php?video_id=45873&title=Watch_Video_on_Unit_Rate___Pre_Algebra_Help

Lesson Overview (2 of 3)

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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.

Warm Up

Agenda7

1) _______ jumps to _________ minute 2) ________ jumps: __________ minute 3) Jumps 4) Write a sentence using ratio language.

minute

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) __50___ jumps to ____1____ minute 2) ___50___ jumps: ___1______ minute 3) 50 jumps 4) Write a sentence using ratio language.

1 minute Alex jumps 50 times for each second.

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.

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)

5) Practice: (Partner and Whole Class)

4) Summary (Whole Class)

6) Assessment: (Independent and Whole Class)

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Launch

Agenda9

Watch the following video about Tillman, the world-recorder holder for fastest skateboarder in his class.

http://vimeo.com/25153812

Why is Tillman special?

In 2009, Tillman received the Guiness Book of Records Award for fastest skateboarding dog, when he rode 100 meters in 20 seconds.

How do we know he’s the fastest skateboarding dog?

Launch

Agenda10

(ex 1) Write Tillman’s record time as a ratio in fraction form. *Remember to simplify and use lables!!!

In 2009, Tillman received the Guinness Book of Records Award for fastest skateboarding dog, when he rode 100 meters in 20 seconds.

This example is special because we have 2 different units being compared, meters and seconds.

This special ratio is a rate! Woof!

Explore – Mini Lesson

Agenda11

A rate is a ratio that compares 2 different measurements!

(ex) Tillman’s skateboarding rate is .

What happens when we simplify this rate?

I’m fast!

This means that Tillman travels at a rate of 5 meters for every 1 second.

Explore

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Agenda

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!

A rate with a denominator of 1 has a special name!

Tillman’s rate of skateboarding:

UNIT RATE

The word unit

means 1.

Explore – Mini Lesson

Agenda13

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.Prices (ex 3) Casey spent $80 on 8 pizzas.

What are the measurement

we are comparing in

(ex 1)?

Yes! Yards and seconds!

All rates and unit rates have

2 different measurements

Explore – Mini Lesson

Agenda14

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.60 yards30 seconds Step 2: Simplify the rate so the denominator is 1.

2 yards1 seconds

This unit rate means that, Homer ran 2 yards for every 1 second.

How did we know this is a

rate question?

D’oh! I get it, we have yards and seconds, 2

different measurements.

Homer ran 2 yards per second.

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!

Explore – Partner Work

Agenda15

(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 flour2 cups of sugar

Step 2: Simplify the rate so the denominator is 1.

2 cups of flour1 cup of sugar

This unit rate means that there are 2 cups of flour per cup of sugar.

Wait! Is this still a rate? We are comparing cups of flours to cups of sugar, does that count?

Yes, we have 2 different measurements cups of flour and cups of sugar!

Challenge – Partner Work

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(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?

Challenge – Partner Work

Agenda17

(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

=

=

____$40_____ 80 key chains

____$1___2 key chains = $0.50 per key chain

Summary

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Agenda

1) A rate is a ratio that compares 2 different ______.2) A unit rate represented as a fraction has a

____________ of 1. 3) How are rates and unit rates similar?

4) How are rates and unit rates different?

5) One real world example of rates and unit rates is ________________________ .

_units_.

denominator

Both are ratios that have 2 different units.

Rates can be any #s with different units compared but unit rates must have 1 in denominator.

Practice

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Agenda

Practice

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Agenda

Assessment

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Agenda

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

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

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between experienced and novice teachers.

21st Century LessonsThe goal…

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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

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