1. Real –World Practice with Rates and Unit Rates
21st Century Lessons
Real –World Practice with Rates and Unit Rates
Primary Lesson Designer(s):
Stephanie Conklin

2. Hint: Convert the time from hours to minutes.
Warm Up
OBJECTIVE: Students will use unit rates to compare quantities in real-life situations.
Language Objective: Students will use vocabulary relating to rates like per and for every.
Kyle can mow 3 lawns in 2 hours. If Kyle takes the same time to mow each lawn, how long does it take him to mow 1 lawn? Write a sentence!
We’ll use a unit rate to solve this question:
2 hours  2 (60 minutes) = 120 minutes
Hint: Convert the time from hours to minutes.
120 minutes
3 lawns
40 minutes
1 lawn =
(4 min) Time passed
In-Class Notes
Teachers can use this as a review of unit rates.
Students may need to be reminded to simplify their rate and also to write a rate and then unit rate in order to solve this problem.
Preparation Notes
This means that Kyle can mow 1 lawn in 40 mins.
Agenda

3. What are some real-world examples of rate?
Agenda:
OBJECTIVE: Students will use unit rates to compare quantities in real-life situations.
Language OBJECTIVE: Students will use vocabulary relating to rates like per and for every.
1) Warm Up (Individual)
2) Launch – Fastest Man in World (Whole Class and Partner)
3) Explore – Mini Lesson and Practice (Whole Class and Partner)
4) Summary (Whole Class)
What are some real-world examples of rate?
5) Practice (Partner and Whole Class)
6) Assessment (Individual)
(2-3 min) Time passed
In-Class Notes
As a whole class, make sure to read through the objective for the day.
Teachers can lead students through a quick brainstorm of real-world examples of rate (see the question from lawn mower guy)
Possible real-world examples could be Kyle’s lawn mowing, how fast or slow someone walks, creating recipes (i.e. 2 cups of sugar for every cup of flour), hourly pay at a job
Preparation Notes

4. Launch 9.69 9.69 seconds After 70 meters Jamaica
Please watch the following video on Usain Bolt, the Olympic Gold Medalist in the Men’s 100-meter spring. Answer the questions below!
1) How fast does Usain run the 100 meter sprint?
9.69
2) Does he run this race in seconds, minutes or hours?
9.69 seconds
3) After how many meters can Usain tell if he will win a race?
After 70 meters
4) What country is Usain from?
(8 min) Time passed
In-Class Notes
Teachers should read the slide and review questions with students before watching the video.
Teachers can show the video and then give students a chance to answer questions.
After students have written answers in their notes, teachers can ask for volunteers to answer questions.
Preparation Notes
Class set of scaffolded notes
Jamaica
Agenda

5. Hold up! How can we simplify this rate?
Launch
Let’s find the Usain’s speed using rates and unit rates! We will compare distance (meter) to time (seconds).
100 meters
9.69 seconds
Step 1: Write a rate in fraction form
Step 2: Simplify to write as a unit rate
Let’s learn a trick to convert a rate to a unit rate!
Yahhh! Tricks make math easier!
(3 min) Time passed
In-Class Notes
Teachers should read through the problem and ask students to help in creating the answer for Step 1.
Teachers can read Step 2 with students and should pause to ask students how they can simplify the weird rate in Step 1.
From here we will teach students that they do not need to simplify rates but rather can divide numerator and denominator to find the unit.
Preparation Notes
Agenda

6. Launch
Divide is right!! Let’s divide 100 meters by 9.69 to find a unit rate!
What operation does the fraction bar represent in the ratio?
Let’s learn a trick to convert a rate to a unit rate!
REVIEW:
A unit rate is a rate with a denominator of ____ .
A unit rate is a rate with a denominator of _1__ .
100 meters
9.69 seconds
We can write this as division problem:
This unit rate means Usain runs seconds per second.
Step 2: Simplify to write as a unit rate
(3 min) Time passed
In-Class Notes
This slide will reinforce students’ knowledge of unit rate, and also teach them how to find unit rates using division.
Students should listen and follow in notes with this slide, they do NOT need to fill in any aspects of this slide on their notes.
Preparation Notes
Scaffolded class notes
This unit rate also means that in 1 second Usain Bolt runs meters.
Agenda

7. What does this unit rate mean?
Explore: Mini-Lesson
Let’s find the unit rate of each real-world situation!
(ex 1) Kenny goes to the grocery store and buys 5 pounds of
Apples for $8.40.
$8.40_
5 pounds
Step 1: Write a rate in fraction form.
Step 2: Divide to find the unit rate. .
$8.40 ÷ 5 pounds = $1.68 per pound
(4 min) Time passed
In-Class Notes
Teacher should pause to have students try to write step 1 on their own, and then review this answer with students
Teachers can also pause to see if any students are able to calculate the unit rate.
Students should write in their notes to follow lesson.
Preparation Notes
Scaffolded notes
What does this unit rate mean?
Kenny paid $____ per
______ of apples. .
Kenny paid $1.68 per
pound of apples. .
Agenda

8. Explore: Try with a Partner
Let’s find the unit rate of each real-world situation!
(ex 2) Michelle is computer programmer who designs video games.
She works 30 hours each week and makes $2,535.
$2,535_
30 hours
Step 1: Write a rate in fraction form.
Step 2: Divide to find the unit rate. .
$2,535 ÷ 30 hours = $84.50 per hour
(5 min) Time passed
In-Class Notes
Students should be give 2-3 mins to try this problem on their own, and should use the model from the last example to write a sentence
Teachers can review answers with students.
Preparation Notes
Scaffolded notes
Write a sentence to explain this situation.
Michelle makes $84.50 per hour
Agenda

9. Explore: A New Challenge
(ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for working 8 hours. At the school’s day camp, he will be paid $78 for working 6.5 hours.
Brainstorm with your partner:
Which job should Cameron take?
(5 min) Time passed
In-Class Notes
Teachers should ask students to read the problem and also the brainstorm question. Teachers should also make sure students know vocab in question before sending students to work in their groups.
Teachers may also want to make a big deal about “job choice” – why is this important? Why does pay matter in their decision? What other factors enter into someone’s decision?
Students should be give 3 mins to brainstorm with a partner.
After this time is up, teachers can ask students to review how they would solve this problem.
The next slide will review how to solve and organize work.
Preparation Notes
Scaffolded notes
Use your note’s from today to help you!
Agenda

10. Explore: A New Challenge
(ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for every 8 hours of work. At a school day camp, he will be paid $78 for every 6.5 hours of work.
Brainstorm with your partner:
How can we decide which job pays Cameron the most per hour?
Create a table to organize your work!
YMCA Job
School Job
$90 ÷ 8 hours = $11.25 per hour
$78 ÷ 6.5 hours = $12 per hour
(5 min) Time passed
In-Class Notes
Teachers should ask students to read the problem and also the brainstorm question. Teachers should also make sure students know vocab in question before sending students to work in their groups.
Students should be give 3 mins to brainstorm with a partner.
After this time is up, teachers can ask students to review how they would solve this problem.
The next slide will review how to solve and organize work.
Preparation Notes
Scaffolded notes
Write a sentence to answer question.
Cameron should choose the school job because he will
make $12 per hour which is $0.75 more than at the YMCA.
Agenda

11. Explore: Practice with a Partner
(ex 4) Maria is a clothing designer and needs to buy a lot of buttons to make her clothes! The following shows button advertisements from 2 different stores:
Button R’ Us Button-Up!
55 Buttons for $5.50
120 Buttons for $10.80
Answer the following questions:
What is the unit rate for buttons at Button R’ Us?
What is the unit rate for buttons at Button-Up?
Which store do you think Maria should buys buttons from?
(5 min) Time passed
In-Class Notes
Teachers should ask students to read the problem and also the brainstorm question. Teachers should also make sure students know vocab in question before sending students to work in their groups.
Students should be give 3 mins to brainstorm with a partner.
After this time is up, teachers can ask students to review how they would solve this problem.
The next slide will review how to solve and organize work.
Preparation Notes
Scaffolded notes
Agenda

12. Explore: Practice with a Partner
Button R’ Us Button-Up!
55 Buttons for $5.50
140 Buttons for $12.60
Answer the following questions:
What is the unit rate for buttons at Button R’ Us?
What is the unit rate for buttons at Button-Up?
Which store do you think Maria should buys buttons from?
Explain your answer!
$5.50 ÷ 55 buttons = $0.10 per button
$12.60 ÷ 140 buttons = $0.09 per button
(3 min) Time passed
In-Class Notes
Teachers can use calling sticks to review students’ answers. Teachers should make sure that students are labeling their answers with correct vocab and labels.
Preparation Notes
Scaffolded notes
Button-Up is cheaper than Button R’Us
by 2 cents.
Agenda

13. Challenge: Practice with a Partner
Button-Up!
140 Buttons for $12.60
Maria has decided to use the Button-Up! Company! Remember,
she found a unit price of $0.09 per button. How much would it
cost her to buy 500 buttons?
500 buttons x $0.09 per button = $45.00
(3 min) Time passed
In-Class Notes
This slide is to help students prepare for the next lesson that focuses on how to develop proportional reasoning.
Students should brainstorm how to solve this and teachers can review the steps to solving.
Preparation Notes
Scaffolded notes
Agenda

14. Practice Agenda (10 – 12 min) Time passed In-Class Notes
Students can work on the class work in partners or small groups.
Preparation Notes
Agenda

15. Practice Agenda (3 min) Time passed In-Class Notes
Teachers can post answers for students as they work or can review them with the class after students are done with their work.
Preparation Notes
Agenda

16. Summary – Partner Work
1) Today, we learned that to compare rates, we can first find the ______ ______ .
A unit rate is a comparison of 2 different quantities where one measurement has only _____ unit.
We can use unit rates to find things like how much a job pays per hour. What other real-world examples are there for using unit rates?
unit rate 1
(3 -4min) Time passed
In-Class Notes
Teachers should call on students using calling sticks to ellict answers from students.
Please note that teachers should fill in answer for #3 based on student suggestions.
Preparation Notes
Agenda

17. Assessment Try on your own:
Martina drives 360 miles in 6 hours and Carlos drives 248 miles in 4 hours. Who drives the fastest?
Martina: miles ÷ 6 hours = 60 miles per hour
Carlos: miles ÷ 4 hours = 62 miles per hour
Carlos has a faster rate at 62 miles per hour!
(3 – 5 min) Time passed
In-Class Notes
The goal of this assessment is to see if students can calculate rates relating to speed on their own and also compare these.
Preparation Notes
Teachers may want to have this as a hand-out or ask students to write answers on post-it notes or index card to evaluate student learning.
Agenda

18. 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.

19. 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