RATIOS & RATES
UNIT
DAY 1
Ratio Introduction
Today’s Lesson;
I can write a ratio in multiple forms.
I can identify the parts and whole of a ratio.
Explain
What is a ratio?
How do you write a ratio?

RATIO: expresses the relationship between two quantities.
Ratios compare two measures of the same types of things.
The order of the numbers in a ratio is important.

Ways to write ratios….
 1 to 1 - use the word “to”
 1 : 1 – use a colon “:”
 1/1 – write as a fraction (top number is 1st number in ratio)
Explain
Ratio Relationships
A class has 30 total students.
20 of the students are boys and 10 of the students are girls.
Part to Part: boys to girls
Part to Whole: girls to class
Whole to part: class to boys
Explain
Ratios in Real Life
Builders and Contractors
■ As a contractor or builder, it would be imperative to
know how many pounds of weight each beam could
support and to make sure that buildings are made to
code.
■ Codes or regulations include ratios like: thickness to
height ratios; occupancy to area; and height to length
(the slope) of ramps.
■ Contractors also need to understand ratios so that
they can order the correct number of parts or
estimate additional costs. If every additional wall
requires 3 sheets of plywood and 84 nails (3 sheets:
84 nails reduces to 1 sheet: 28 nails), you could find
the quantities and costs of the project.
Explain
Ratios in Real Life
Power Outages 9/11/17
What is the ratio of
customers affected to
customers served in the
Duluth Area?
Screen clipping from www.gapower.com – Georgia Power outage map on day of school closure 9-11-17.
Evaluate
■ On an index card…
1.) Write the Ratio of
to
3 DIFFERENT WAYS ?
2.) What is the Ratio of
to
?
3.) What is the ratio of
to All of the shapes?
DAY 2
Equivalent Ratios
Today’s Lesson;
I can write equivalent ratios.
ENGAGE:
Video:
Equal Ratios | All Those Different Size Screens
PBSMathClub
https://www.youtube.com/watch?v=VyhRv_MuxvA
Explain: Equivalent Ratios
=
■ Equivalent ratios are two ratios that express the same relationship between numbers
■ Equivalent ratios are similar to equivalent fractions.
■ You can use a ratio table to help you find equivalent ratios.
■ Continue the pattern below using multiples.
Red candy
2
4
Blue candy
3
6
Explain:
MULTIPLY to find Equivalent Ratios
To make 1 box of pasta salad, you add 3 tablespoons of
vegetable oil and 1 tablespoon of water to the cooked pasta.
If you want to make 6 boxes of pasta, how many tablespoons
of vegetable oil will you need?
X6
Vegetable Oil
3
18
Boxes of Pasta
1
6
X6
Explain:
DIVIDE to find Equivalent Ratios
12 cans of green beans can be purchased for $6. How many
cans can you purchase for $2?
÷3
Cans of beans
Cost ($)
12
4
6
2
÷3
Explain:
PRACTICE finding Equivalent Ratios - multiply
It takes 6 eggs to bake 5 chocolate cakes. Jim wants to bake
10 chocolate cakes. How many eggs will he need?
eggs
6
cakes
5
10
Explain:
PRACTICE finding Equivalent Ratios - multiply
It takes 6 eggs to bake 5 chocolate cakes. Jim wants to bake
10 chocolate cakes. How many eggs will he need?
ANSWER
eggs
6
12
cakes
5
10
Explain:
PRACTICE finding Equivalent Ratios - divide
To make sweet tea, you need 4 cups of sugar for every 8 cups
of tea. How many cups of sugar will you need for 24 cups of
tea?
sugar
4
tea
8
24
Explain:
PRACTICE finding Equivalent Ratios - divide
To make sweet tea, you need 4 cups of sugar for every 8 cups
of tea. How many cups of sugar will you need for 24 cups of
tea?
ANSWER
sugar
4
12
tea
8
24
Explain:
SCALING to find Equivalent Ratios
Sometimes you have to do a combination of multiplication and
division to find equivalent ratios.
Packages of gum are on sale at 10 for $4. Find the cost of 15
x3
÷2
packages of gum.
Packages
Of Gum
10
5
15
Price ($)
4
2
6
÷2
x3
Scale back by dividing by 2, then scale forward by multiplying by 3.
Explain:
SCALING to find Equivalent Ratios
Sometimes you have to do a combination of multiplication and division to find equivalent ratios.
Thomas edits videos to earn extra money. He edited 8 videos in 14
hours last weekend. How many videos could he edit in 49 hours if
he works at this same pace?
x7
÷2
Videos
8
4
28
Hours
14
7
49
÷2
x7
Scale back by dividing by 2, then scale forward by multiplying by 7.
Explain:
PRACTICE SCALING to find Equivalent Ratios
Sometimes you have to do a combination of multiplication and division to find equivalent ratios.
Kimora works at a manufacturing plant. For every 25 products she
uses 10 gallons of paint. How many gallons of paint will she need
to produce 55 products?
Gallons of
Paint
10
Products
25
55
Explain:
PRACTICE SCALING to find Equivalent Ratios
Sometimes you have to do a combination of multiplication and division to find equivalent ratios.
Kimora works at a manufacturing plant. For every 25 products she
uses 10 gallons of paint. How many gallons of paint will she need
to produce 55 products?
ANSWER
Gallons of
Paint
10
2
22
Products
25
5
55
EXTEND: Real World Problem
Copy and solve this problem in your math journal.
The ratio of Karen’s CDs to the number of
Sarah’s CDs is 4:5. If the total number of CDs is
45, how many CDs does Karen and Sarah have?
DAY 3
Rates and Unit Rate
Today’s Lesson;
I can describe the difference between
a rate and a unit rate.
Engage:
■ I went to Kroger this weekend to purchase Cinnamon Toast Crunch
cereal. The Cinnamon Toast Crunch is packaged and sold in 3
different box sizes. Which box do you think I bought, knowing that I
like to shop for the best value?
Explain: Rate
A rate is a special ratio in which the
two terms are in different units.
You can buy 5 hamburgers for $15.
The rate is $15 for 5.
You pay $15 for every 5 hamburgers.
Explain:
■ Rate: $3.79 for 20.25 ounces
■ Rate: $3.25 for 16.2 ounces
■ Rate: $2.98 for 12.2 ounces
Explain: Unit Rate (a special ratio)
unit rate
A rate that is simplified so that it has a
denominator of 1.
unit ratio
A unit rate where the denominator is one unit.
Examples:
What is the price per pound?
How far will you travel in 1 hour?
How many can you complete in 1 minute?
80 copies in 4 minutes = 20 copies per minute.
1
Two options to find unit rate…
1.) Use methods used to find
equivalent ratios.
OR
2.) Identify the item that is in the
denominator that you need to be
a 1. Then divide the numerator by
the denominator.
Explain:
■ Rate: $3.79 for 20.25 ounces
■ Unit Rate: How much for 1 ounce?
$
3.79
0.19
ounce
20.25
1
■ Rate: $3.25 for 16.2 ounces
■ Unit Rate: How much for 1 ounce?
$
3.25
0.20
ounce
16.2
1
■ Rate: $2.98 for 12.2 ounces
■ Unit Rate: How much for 1 ounce?
$
2.98
ounce
12.2
0.24
1
Explain:
■ Rate: $3.79 for 20.25 ounces
■ Unit Rate: How much for 1 ounce?
$
3.79
0.19
ounce
20.25
1
■ Rate: $3.25 for 16.2 ounces
■ Unit Rate: How much for 1 ounce?
$
3.25
0.20
ounce
16.2
1
■ Rate: $2.98 for 12.2 ounces
■ Unit Rate: How much for 1 ounce?
$
2.98
ounce
12.2
0.24
1
Solve on Index Card
■ Karen is building a tiny house. She can buy
an 8 pound box of nails for $7.40 or a 4
pound box of the same nails for $5.38.
Which is the better buy?
Extend - Golden ratio / golden rectangle
Extend: Golden Ratio/Rectangle in Nature
See Notes for Image Credits
Extend: Golden Ratio/Rectangle in Architecture
See Notes for Image Credits
Extend: Golden Ratio/Rectangle in Art
See Notes for Image Credits
Extend: – Golden Ratio/Rectangle – other uses
Your Turn….
On the 8 ½ x 11 paper provided, use the golden rectangle template to create your own work of art.
Your masterpieces will be displayed in our classroom, so do your best to make it visually appealing and neat.
DAY 4
Other Ways You May Encounter Ratios
Mini Engineering Design Process (EDP) Project
Today’s Lesson;
I can find equivalent ratios and graph them.
Engage:
Answer the following questions.
1.) What should you do first?
a.) cross the street
b.) look both ways
2.) What should you do first?
a.) jump up and down on the diving board
b.) run to the end of the diving board
3.) What should you do first?
a.) count up on the y-axis
b.) count over on the x-axis
Explain: Other Ways You May See
Ratio Problems
Vertical Ratio Tables
Horizontal Ratio Tables
(what we have used most in class)
Footballs
Baseballs
2
3
4
6
$
3.79
0.19
8
12
ounce
20.25
1
16
24
Explain: Other Ways You May See
Ratio Problems
Bar Diagrams
45 miles
1 hour
15 miles
1 hour
Double Number Lines
1 hour
0
7
3.50
7
0
1
2
10.50 14 17.50 21 24.50
Cost
Packages
3
4
5
6
7
Explain: Other Ways You May See
Ratio Problems
Graphs
Sam saved the same amount of money each week.
She recorded her savings on the graph below.
How much money did Sam have in her savings account in week 3?
After how many weeks will Sam have saved $90?
Explain: Creating a Ratio Graph
Every hour Stefano walks 2 miles.
Create a ratio table showing the miles traveled over the course of 5 hours.
Then, plot the values on the coordinate plane.
Explain: Creating a Ratio Graph – Your Turn
Every hour the city bus travels 20 miles.
Create a ratio table showing the miles traveled over the course of 5 hours.
Then, plot the values on the coordinate plane.
EXPLORE:
Ratio Structures
Mini-EDP Project
Use the Engineering Design
Process to build a structure
that will support my apple
stress ball. The only materials
you may use are the 20
miniature marshmallows and
15 pieces of spaghetti in your
bag.
1. Discuss ideas using protocol (see below)
2. Sketch a drawing of the idea you want to build and have it
approved by the Construction Supervisor (your teacher) Your
idea should include the ratio of marshmallows to spaghetti you
plan on using in your build.
3. Build your idea. During this step, record the ratio of the number
of pastel colored marshmallows to the number of white ones
used in your build.
4. Test your idea.
5. Revise and Improve your idea.
This activity should take about 25-30 minutes from start to finish.
PROTOCOL:
Silent 1 minute to think.
You will work with a group of
3-4 students at your table.
Then each person has 1 minute to share their idea while the other people
listen. (see the unit rate there…. 1 person per minute)
After all have shared, as a group decide which ideas sound like the best
to use for the design.
DAY 5
Measurement Conversions Using Ratios
Today’s Lesson;
I can use ratios to convert measurements.
Engage:
Mr. Barnes lives in Georgia. He has recently purchased
a new car. When he purchased it, he did not realize that
it had been manufactured for use in Europe. In Europe,
they use the metric system. His new car’s speedometer
is marked in kilometers per hour. What are some ideas
for what Mr. Barnes can use or do when driving his car
in Georgia where the speed limit signs are in the
customary units of miles per hour?
Explain: Measurement Conversions – using ratios
Example 1 (customary to customary):
How many gallons is equivalent to 20 quarts?
1st: Find the measurement fact(s) that you need and create a
ratio.
2nd Use the information in the problem to set up equivalent
ratio. Make sure your units match up.
3rd Multiply or divide to find the missing information.
See Notes for Image Credits
Explain: Measurement Conversions – using ratios
Example 2 (metric to metric):
A container holds 2,500 mililiters of water. How many
liters does it hold?
1st: Find the measurement fact(s) that you need and create a
ratio.
2nd Use the information in the problem to set up equivalent
ratio. Make sure your units match up.
3rd Multiply or divide to find the missing information.
See Notes for Image Credits
Explain: Measurement Conversions – using ratios
Example 3 (customary to metric) (Note: conversion factors given in all problems):
A door for your tiny house is 7 feet tall. How many centimeters tall is your door?
1st: Find the measurement fact(s) that you need and create a ratio. (1 foot = 30.48 centimeters)
2nd Use the information in the problem to set up equivalent ratio. Make sure your units match up.
3rd Multiply or divide to find the missing information.
Explore:
Teacher Group:
Continue practicing converting ratios by going to one fo the following
websites:
• MathGames.com (skills section)
• Quizizz.com (pre-made quizzes)
• Quizlet.com (pre-made quizzes)
Extend: Independent Group
■ Step One: Examine the home square footages below
– Square footages in a house:
■
Living Room: 400 square feet
■
Bedroom: 250 square feet
■
Kitchen: 200 square feet
■
Bathroom: 100 square feet
■ Step Two: On a piece of copy paper, draw a blueprint of the house – be creative! It is
completely up to you to decide the layout of the house. When you draw the blueprint,
please follow the following guidelines:
– 1 square foot = ½ inch on your paper
■ Step Three: Convert the measurements of the room into centimeters, where
– 1 inch = 2.54 centimeters
Evaluate:
Ticket out the Door – on an index card
Ryan purchased a 2-liter bottle of sports
drink. How many quarts of sports drink did
he purchase? (1 liter = 1.05669 quarts)
DAY 6 – 7
Real Life Applications of Ratios
Today’s Lesson;
I can use ratios in real life situations.
ENGAGE (part 1):
Copy this problem in your notebook and solve.
Gabby is creating a product display at the local hardware
store. The display contains a combination of gallon paint
cans and quart paint cans. The ratio of gallon cans to
quart cans is 2:3. If she has 24 quart cans, how many
gallon cans will she need to complete the display?
Endcap Design & Display Project: Research
Article on End Cap Design
https://www.staples.com/sbd/cre/retail/store-displays/floor-displays/end-caps/retail-end-cap-display-anddesign/
Article on Writing a Business Proposal
https://www.paperlessproposal.com/how-to-write-a-compelling-and-effective-business-proposal/
Explore: End Cap Design Proposal
■ Select a partner you would like to work with for this project.
■ Read the letter from Pierre’s again.
■ Review the Spec Sheet and the Conversion Page
■ Read the Articles on end cap design and business proposal writing.
■ Discuss which items you could potentially include in your design.
Lesson continued on Day 7
Explore:
End Cap Design Proposal
Work Day 7 - Goals
■ Select at Least 3 Products for End Cap
■ Complete Measurement Conversion Chart for
Each Product
■ Complete Price Conversions for Each Product
Lesson continued on Day 8
DAY 8
Real Life Applications of Ratios
Today’s Lesson;
I can use ratios in real life situations.
Explore:
End Cap Design Proposal
Work Day - Goals
■ Work with Partner on Initial End Cap Design
■ Gallery Walk – Peer Review of Initial Designs
■ Begin Revisions of End Cap Design
Lesson continued on Day 9
Gallery Walk – Peer Review of Initial Designs
(supplies: tape or tacks/staples, sticky notes, pen/pencil, timer)
■ Step 1: Hang your designs on the classroom wall or bulletin board using tape, tacks, or
staples.
■ Step 2: You will have nine minutes give feedback to three individuals/pairs groups using
post-it notes. Take three minutes at each design to provide feedback. I will use a timer to
manage rotations.
– Feedback should be constructive in nature.
– Give at least one “I wonder….” feedback statement. (Ex: I wonder if you have
considered turning the product package a different direction.)
– Give at least one “I like…” feedback statement. (Ex: I like how you put your larger
products on the bottom shelf.)
■ Step 3: Retrieve your designs and feedback to review and revise if needed.
DAYS 9-10
Real Life Applications of Ratios
Today’s Lesson;
I can use ratios in real life situations.
Explore:
End Cap Design Proposal
Work Day - Goals
■ Complete End Cap Design.
■ Write Proposal Letter to Accompany Design.
■ Submit Completed Design Proposal.