1. Working with Unit Rates
Lesson (Day 2)
Working with Unit Rates
Obj. 7.RP.2b

2. Today, we will be working with rates and we will learn about a special kind of rate called a unit rate.

3. Section 1: What is a Rate?
Before we talk about Unit Rates, we must first understand what a Rate is.

4. What is a Rate? A rate compares two quantities.
Notice in the example, that the quantities being compared are of two different things. Here we are comparing sit-ups and minutes!
100 sit-ups in 2 minutes
150 sit-ups in 3 minutes
200 sit-ups in 4 minute
A rate describes how one quantity is effected when another quantity changes.

5. Here’s the thing about rates….
One of the quantities has to be the
independent quantity and the other
has to be the dependent quantity.
100 sit-ups in 2 minutes
150 sit-ups in 3 minutes
200 sit-ups in 4 minute

6. 1) Explain what the words “independent” and “dependent” mean.
2) Then, based on the meanings of the words,
try and determine which is the independent quantity and which is the dependent quantity between sit-ups and minutes.
100 sit-ups in 2 minutes
150 sit-ups in 3 minutes
200 sit-ups in 4 minute

7. Independent – In control. Can manage on it’s own.
Dependent – It relies on something else.
It changes based on circumstances.
How many sit-ups can you do?
Well, it depends on how many minutes you have.
The number of “minutes” controls how many “sit-ups” can be done.
Independent (x)
2 minutes
3 minutes
4 minutes
Dependent (y)
100 sit-ups
150 sit-ups
200 sit-ups

8. So, to sum it up:
In math there are two types of variables (quantities). Variables can be either independent or dependent. The value of the “dependent” variable is determined by the value of the “independent” variable.
When working with rates and unit rates, this is an important concept to understand.

9. Which is the independent variable and which is the dependent?
1. Measuring heartrate: heartbeats in 3 minutes.
2. Sports: Scoring 96 points in 6 games.
3. Reading your favorite book: Reading 53 pages in 2 hours.
Heartbeats (dependent) Minutes (independent)
Points (dependent) Games (independent)
Pages (dependent) Hours (independent)
Money (dependent) Pounds of Apples (independent)
4. Money: $4.94 for 3 pounds of apples.

10. Section 2: What is a Unit Rate and how do you find it?

11. 1:Uno ONE Unit Study this slide for a moment.
Can you figure out what the word UNIT means?
On this slide, follow the below script.
Ask students to study the slide for a moment and try to figure out what the word UNIT means. Ask them to not blurt out the answer. Give them a moment to look at all the different ways the number “1” is represented on the slide. Then, call on a student to answer.
The word UNIT refers to “One” of something (1 unit).
Berg Suggestion: I use to tell them that in a way, the number 1 is kind of a sad number and I would point to the little green one or the red one. It means that you are by yourself. You are isolated.
Being a unit of “1” can be sort of a lonely feeling.
I have a song to help you remember that a “unit” means “1” of something.
Warning… this is a very sad song. The name of the song is “ONE” and it was recorded by a band named “Three Dog Night”.

12. The word “unit” refers to “1” of something?

13. Now that we know what a rate is, let’s take a look at a special kind of rate called a unit rate.

14. What is a Unit Rate?
Remember, a rate describes how one quantity is effected as another quantity changes.
100 sit-ups in 2 minutes
150 sit-ups in 3 minutes
200 sit-ups in 4 minute
When rates are expressed as a quantity of one, they are called unit rates.
50 sit-ups per minute

15. How do you find the Unit Rate?
STEP 1
Take the rate that is given and write it as a ratio in fractional form.
𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕
STEP 2
Divide to find the “unit” rate.
If you drive 200 miles in 5 hours, how far did you drive in 1 hour?
𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 =
𝟐𝟎𝟎 𝒎𝒊𝒍𝒆𝒔 𝟓 𝒉𝒐𝒖𝒓𝒔 =
40 miles in one hour

16. When $ is involved it’s called Unit Price or Unit Cost.
16 slices of Velveeta Cheese costs $ What is the unit cost per slice?
STEP 1
Take the rate that is given and write it as a ratio in fractional form.
𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 is always $ 𝑸𝒕𝒚 𝒐𝒓 𝑺𝒊𝒛𝒆
STEP 2
Divide to find the “unit” price.
𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 =
$𝟑.𝟑𝟔 𝟏𝟔 𝒔𝒍𝒊𝒄𝒆𝒔 =
$ .21 per slice

17. Problem Set 1. Set up a ratio 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 and then divide to find the unit rate.
140 miles in 4 weeks
91 patients in 7 days
56 points in 14 games
64 pounds in 8 weeks
11 CDs costs $187
864 feet in 36 seconds
6 accidents in 12 months
774 liters in 9 hours
2,538 people in 27 buses
𝟏𝟒𝟎 𝒎𝒊𝒍𝒆𝒔 𝟒 𝒘𝒆𝒆𝒌𝒔
35 miles per week

18. Problem Set 1. Set up a ratio 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 and then divide to find the unit rate.
140 miles in 4 weeks
91 patients in 7 days
56 points in 14 games
64 pounds in 8 weeks
11 CDs costs $187
864 feet in 36 seconds
6 accidents in 12 months
774 liters in 9 hours
2,538 people in 27 buses
𝟏𝟒𝟎 𝒎𝒊𝒍𝒆𝒔 𝟒 𝒘𝒆𝒆𝒌𝒔
𝟗𝟏 𝒑𝒂𝒕𝒊𝒆𝒏𝒕𝒔 𝟕 𝒅𝒂𝒚𝒔
𝟓𝟔 𝒑𝒐𝒊𝒏𝒕𝒔 𝟏𝟒 𝒈𝒂𝒎𝒆𝒔
𝟔𝟒 𝒑𝒐𝒖𝒏𝒅𝒔 𝟖 𝒘𝒆𝒆𝒌𝒔
$𝟏𝟖𝟕 𝟏𝟏 𝑪𝑫𝒔
𝟖𝟔𝟒 𝒇𝒆𝒆𝒕 𝟑𝟔 𝒔𝒆𝒄𝒐𝒏𝒅𝒔
𝟔 𝒂𝒄𝒄𝒊𝒅𝒆𝒏𝒕𝒔 𝟏𝟐 𝒎𝒐𝒏𝒕𝒉𝒔
𝟕𝟕𝟒 𝒍𝒊𝒕𝒆𝒓𝒔 𝟗 𝒉𝒐𝒖𝒓𝒔
𝟐,𝟓𝟑𝟖 𝒑𝒆𝒐𝒑𝒍𝒆 𝟐𝟕 𝒃𝒖𝒔𝒆𝒔
35 miles per week
13 patients per day
4 points per game
8 pounds per week
$17 per CD
24 feet per second
0.5 accidents per hour
86 liters per hour
94 people per bus
Answer Key

19. Problem Set 2. Set up a ratio 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 and then divide to find the unit rate.
$342 for 6 rings
336 students in 8 classes
658 cars sold in 14 days
4 trips in 16 months
6 hours to complete 192 problems
3 minutes to do 54 sit-ups
39 errors on 13 tests
63 players on 9 teams
1,260 chocolate bars costs $2,520

20. Problem Set 2. Set up a ratio 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 and then divide to find the unit rate.
$342 for 6 rings
336 students in 8 classes
658 cars sold in 14 days
4 trips in 16 months
6 hours to complete 192 problems
3 minutes to do 54 sit-ups
39 errors on 13 tests
63 players on 9 teams
1,260 chocolate bars costs $2,520
$𝟑𝟒𝟐 𝟔 𝒓𝒊𝒏𝒈𝒔
𝟗𝟏 𝒑𝒂𝒕𝒊𝒆𝒏𝒕𝒔 𝟕 𝒅𝒂𝒚𝒔
𝟔𝟓𝟖 𝒔𝒐𝒍𝒅 𝟏𝟒 𝒅𝒂𝒚𝒔
𝟒 𝒕𝒓𝒊𝒑𝒔 𝟏𝟔 𝒎𝒐𝒏𝒕𝒉𝒔
𝟏𝟗𝟐 𝒑𝒓𝒐𝒃𝒍𝒆𝒎𝒔 𝟔 𝒉𝒐𝒖𝒓𝒔
𝟓𝟒 𝒔𝒊𝒕−𝒖𝒑𝒔 𝟏𝟖 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝟑𝟗 𝒆𝒓𝒓𝒐𝒓𝒔 𝟏𝟑 𝒕𝒆𝒔𝒕𝒔
𝟔𝟑 𝒑𝒍𝒂𝒚𝒆𝒓𝒔 𝟗 𝒕𝒆𝒂𝒎𝒔
$𝟐𝟓𝟐𝟎 𝟏,𝟐𝟔𝟎 𝒄𝒉𝒐𝒄𝒐𝒍𝒂𝒕𝒆 𝒃𝒂𝒓𝒔
$57 per ring
42 students per class
47 cars sold per day
0.25 trips per month
32 problems per
18 sit-up per minute
3 errors per test
7 players per team
$2.00 per chocolate bar
Answer Key

21. End of PowerPoint