Name ________________________________
Date: _________________________________
Course: Math B
Homeroom:
917-747-1693
Unit 1 Project:
Directions: Read the passage below and answer the questions that follow.
What songs motivate you or make you feel energized and why? _____________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Why might some songs be more effective at motivating people to exercise longer
and more vigorously (with more effort)?
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Guided Reading:
Directions: Your pencil should always be moving as we read together. If I call your
name, you need to pick up reading where the last person left off.
Define tempo:
________________________________________________________________
________________________________________________________________
________________________________________________________________
Define heart rate:
________________________________________________________________
________________________________________________________________
________________________________________________________________
Why is it a rate and not just a ratio?
________________________________________________________________
________________________________________________________________
________________________________________________________________
Independent Reading:
Directions: Read the questions, then read and annotate the following passage, and
answer the questions that follow.
Ms. Goldberg’s playlist includes “Don’t Phunk With My Heart” by the Black Eyed Peas (130
B.P.M.), “Mr. Brightside” by the Killers (150 B.P.M.), and “Dancing Queen” by Abba. The
musical style that often seems to contain high B.P.M. is dance music. Some D.J.’s have even
begun to remix songs on a playlist so they all have the same B.P.M. so that people can work
out to a constant tempo. A remixed track with a count of about 115 to 118 B.P.M. is great for
a slow walker going at a pace of around 3 miles an hour. For a power walker going 4.5
m.p.h., the count is 137 to 139 B.P.M., while the B.P.M. for a runner elevates to 147 to 160.
The remixed playlists are targeted mainly toward women doing cardio workouts, and there
are no pauses between songs. That constant beat allows a person to synchronize (match)
their movements to the music, which is crucial for getting the most out of your workout. It
helps you move more efficiently and improve your endurance (how long you are able to go).
Which song has a faster tempo, “Don’t Phunk With My Heart” by the Black Eyed Peas
or “Mr. Brightside” by the Killers?
 Justify your answer with evidence from the text.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
If Ms. Christy runs on the treadmill at about 6.2 miles per hour, to about how many
beats per minute should she request her remix be set?
 Justify your answer with evidence from the text.
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
Name ________________________________
Date: _________________________________
Course: Math B 917-747-1693
Homeroom:
Day 36: Independent Practice/ Review
Directions: Use your notes on rates and ratios and unit rate
Practice 1
1.
Write this ratio in two other ways: 4 to 5.
______________
_______________
2.
Write this ratio in two other ways:
______________
_______________
3.
Simplify the ratio: 33 to 44.
______________
4.
Simplify the ratio:
______________
5.
Draw a picture to represent the situation: the ratio of circles to stars is 3: 5.
.
.
Draw picture here:
Practice 2
Create a proportion to find the unit rate for each.
6.
= _____x_____
1 min
How many gallons per minute?
= __________
7.
How many feet per second?
8.
How many miles per gallon?
Practice 3
Problems: Write the ratios as fractions. Then simplify the fraction if possible.
9.
There are 65 boys and 52 girls in the drama club. What is the ratio of boys to girls, in simplest
form?
Fraction: _________________
Simplified: __________________
10. On a farm that has only two types of animals, there are 34 cows and 12 horses. What is the ratio of
horses to the total number of animals on the farm, in simplest form?
Fraction: _________________
Simplified: __________________
11. Over a period of 3 hours, 180 leaves fell from a tree. At this rate, how many leaves fell in one
hour?


Annotate
Proportion
Number of leaves that fell in one hour: ____________________________
12. Georgia drove a total of 252 miles and used 12 gallons of gasoline. What is this rate in miles per
gallon?


Annotate
Proportion
Miles per gallon: ____________________________
13. Tyler scored 21 goals in 7 soccer games. At this rate, about how many goals did he score each
game?


Annotate
Proportion
Goals scored each game: ____________________________
14. While climbing down a mountain, Anthony descended 45 feet every hour. At this rate, how many
feet will he descend in 6 hours?


Annotate
Proportion
Number of feet in 6 hours: ____________________________
Name ________________________________
Date: _________________________________
Course: Math B 917-747-1693
Day 37: Do Now
Homeroom:
4) The table shows the cost of various bags of dog food.
Which bag of dog food has the highest cost per
pound?
A. Bag A
B. Bag B
C. Bag C
D. Bag D
Set up and solve a proportion to find the cost per pound for each bag:
Bag A
Bag B
Bag C
Bag D
$11.00 = __x__
6 lbs
1 lb
$20.25 = _____
1 lb
______ = ______
Name ________________________________
Date: _________________________________
Course: Math B 917-747-1693
Homeroom:
Day 37: Independent Practice/Homework
Directions: Use your notes on rates and ratios and unit rate
Practice 1
1.
Write this ratio in two other ways: 6 to 7.
______________
2.
Simplify the ratio: 14:28.
______________
3.
Simplify the ratio:
4.
Draw a picture to represent the situation: the ratio of squares to triangles is 4 to 6.
30
72
.
_______________
______________
Draw picture here:
Challenge: draw a simplified version of the ratio here:
Draw picture here:
Practice 2
Annotate each problem, and then create a proportion to find the unit rate for each.
5. If a person runs ¾ mile in ½ hour. At what speed are they walking?
Hint: convert the fractions to decimals and then create your proportion.
3
A.
miles per hour
8
B.
1 ¼ miles per hour
C.
1 miles per hour
D.
3 miles per hour
1
2
6. Democracy Prep Harlem has 360 students and spends $72,000 each year. Find the cost per student.
A.
$200.00 per student
B.
$20.00 per student
C.
$2.00 per student
D.
$2,592.00 per student
Practice 3: Unit Rate
Size
Volume (fl oz)
Price
Regular
12
$1.20
Extra Large
28
$2.24
7. The table above shows
the cost of two different bottles of Arizona tea available at the corner store.
Which bottle size offers the cheaper price per ounce? How much cheaper is it?

Complete the proportions to determine the unit price of each bottle
Regular
$1.20
12 fl.oz.
=

Extra Large
________
1 fl.oz.
$2.24
=
__________
1 fl.oz.
Compare the price per ounce to determine which is cheaper
Answer: _______________________ is cheaper per ounce.
How much cheaper is it per ounce? _____________________________________________
8. Natasha wants to compare the price of her favorite snacks to determine which is less expensive.
The table below shows the price of each snack box and the number of bags in each Value Pack box.
SNACK BOXES
Total Bags
(in each box)
Total Price
(in each box)
Cheez-It
16
$2.72
Combos
20
$3.80
Price
(per bag)
a) Complete the table above by calculating the price per bag of each kind of snack.
Which snack is cheaper per bag? __________________________
Name ________________________________
Date: _________________________________
Course: Math B
Homeroom:
917-747-1693
Math and Music
Unit 1 Topics Reviewed:
Data Collection
Writing rates and ratios _____
Calculate unit rates _____
Use proportions to solve problems _____
Use constant of proportionality to complete tables _____
Understand proportional relationships in graphs _____
Write equations to represent proportional relationships _____
Directions: Count the number of beats you hear in 10 seconds of the song. Use that
information to determine the unit rate, or the number of beats per minute (B.P.M.)
for each audio clip.
Tempo and B.P.M
10 seconds
1 minute
Adagio
Andante
Allegro
Based on the information in the table and what you heard, how might you describe
songs that are Adagio, Andante, and Allegro?
Adagio ________________________________________________________________________________________
_________________________________________________________________________________________________

B.P.M. range: _______________
Andante: ______________________________________________________________________________________
_________________________________________________________________________________________________

B.P.M. range: _______________
Allegro: ______________________________________________________________________________________
_________________________________________________________________________________________________

B.P.M. range: _______________
Think About It: Why does it make more sense to measure the unit rate in beats per
minute rather than beats per second or beats per hour?
_________________________________________________________________________________________________
_________________________________________________________________________________________________
_________________________________________________________________________________________________
Tables and Graphs
Directions: Complete the table below with the number of beats for each amount of
time.
Number of Beats in Seconds
10 s
20 s
30 s
40 s
50 s
60 s
Andante
Adagio
Allegro
Use your knowledge of proportions to help you complete the following table.
Number of Beats in Minutes
2 min
3 min
4 min
1 min
5 min
6 min
Andante
Adagio
Allegro
Directions: Create a triple line graph to show the number of beats per minute in
each of the three audio clips. The x-axis should represent the time, and the y-axis
should represent the number of beats.
When your graph is done, mark the point(s) that represents the unit rate with a star
and label with “Unit Rate.” Record the coordinates that represent each unit rate:
Andante:
(
,
)
Adagio:
(
,
)
Allegro:
(
,
)
Write a sentence to describe what the point (0, 0) represents in terms of beats and
amount of time.
________________________________________________________________________________________________
________________________________________________________________________________________________
________________________________________________________________________________________________
Analysis
Directions: Write an equation to represent the tempo of each version of the song
using b for beats and m for minutes. Then describe how the equation is related to
the graph of each song clip.
Equation
Describe relation to graph
Andante
Adagio
Allegro

Circle the constant of proportionality in each equation above.
Songs with Tempo Changes:
“Bohemian Rhapsody” by Queen @3:00
“Wake Up” by Arcade Fire (3:50)
“Take Me Out” by Franz Ferdinand (intro)
“Proud Mary” by Tina Turner
“Come Sail Away” by Styx
“Lucy in the Sky with Diamonds” by The Beatles
Directions: Read the statement in the box below, and use your knowledge of rates to
answer the questions on the next page. Be prepared to justify your responses with
mathematical evidence and reasoning:
Some songs maintain a steady tempo throughout while others change
tempos during different parts of the song. A tempo change can give
different parts of the song a distinct feel. If a song maintains a steady
tempo, the number of beats at different time intervals will be
proportional to one another. In contrast, a song with a tempo change
may have a proportional relationship between beats and time during
one part of the song but then the relationship changes part way through.
Examine the tables and graphs below to determine whether each song maintains a
steady tempo or has a tempo change.
Song 1
Number
of Beats
0:30
70
1:00
140
1:30
210
2:00
280
2:30
330
3:00
380
Circle one: steady tempo/tempo change.
If there was a steady tempo, write the constant of proportionality here: ______________
Challenge: If there was a tempo change, put a star by the moment in the song that
the tempo changed. Next to your star, write down if the tempo became faster or
slower at the end of the song.
Song 2
Song 2
400
360
320
280
240
200
Song 2
160
120
80
40
0
0:30
1:00
1:30
2:00
2:30
3:00
Circle one: steady tempo/tempo change.
If there was a steady tempo, write the constant of proportionality here: ______________
Challenge: If there was a tempo change, put a star by the moment in the song that
the tempo changed. Next to your star, write down if the tempo became faster or
slower at the end of the song.
Song 3
Number
of Beats
0:30
65
1:00
130
1:30
195
2:00
250
2:30
325
3:00
280
Circle one: steady tempo/tempo change.
If there was a steady tempo, write the constant of proportionality here: ______________
Challenge: If there was a tempo change, put a star by the moment in the song that
the tempo changed. Next to your star, write down if the tempo became faster or
slower at the end of the song.
Song 4
Song 4
480
440
400
360
320
280
240
200
160
120
80
40
0
Song 4
0:30
1:00
1:30
2:00
2:30
3:00
Circle one: steady tempo/tempo change.
If there was a steady tempo, write the constant of proportionality here: ______________
Challenge: If there was a tempo change, put a star by the moment in the song that
the tempo changed. Next to your star, write down if the tempo became faster or
slower at the end of the song.
Extra Stuff…
Vocabulary:
Rate: Comparison between two things with different units
 Tempo: speed of the music, measured in beats per minute…
 Pace/Speed: speed of the person (or vehicle), measured in miles per hour…
 Density: mass/volume
Rhythm: pattern of sounds (not necessarily keeping the steady beat)
Metronome/metronomic: metronome keeps the temp and informs what the tempo
is, metronomic approach means that you are considering the tempo when making
the music.
Dorian mode: minor (sad)/angry sounding
Haile Gerreselassie, the Olymipian from Ethiopia who has won the gold medal at
10,000 meters, often requested that the techno song “Scatman,” which has a B.P.M.
of around 135, be played over the sound system during his race. Ask a question.
Adagio: slow and stately (literally, “at ease”)
Andante: at a walking pace
Allegro: fast, quickly and bright
SWBAT determine unit rate (use proportions)
SWBAT determine proportionality from tables
SWBAT apply constant of proportionality to complete the pattern in tables
SWBAT determine proportionality from graphs and identify the features of graphs
that indicate proportionality.
SWBAT write equations to represent proportional relationships.
7. The graph below shows a proportional relationship between velocity and
time (in seconds). Which point on the graph represents the unit rate?
A.
(4, 1)
B.
(1, 4)
C.
(0, 0)
D.
(5, 20)
8. David is making his own strawberry yogurt. In David’s mixture, the number
of strawberries is proportional to the amount of milk, in cups. David uses 4
cups of milk for every 14 strawberries.
Which equation represents the relationship between s, the number of
strawberries, and m, the number of cups of milk he uses?
2
A.
𝑠= 𝑚
B.
𝑠= 𝑚
C.
𝑠= 𝑚
D.
𝑠= 𝑚
9
7
2
2
7
9
2
9. Reynaldo started to fill in the table below showing the proportional
relationship between how far in miles he can travel for each gallon of gas
he uses.
When Reynaldo’s tank is full, it holds 20 gallons. How far can he travel on
a full tank of gas?
A.
224 miles
B.
28 miles
C.
1,120 miles
D.
560 miles
10. A scaled map of the United States has the key below showing how to
convert centimeters to miles. What is the constant of proportionality?
A.
3
4
cm per mile
1
B.
1 3 cm per mile
C.
24 cm per mile
D.
3 cm for every 4 miles
11. Use the double line diagram below to determine the unit price of potatoes.
0
Dollars
1.5
0
2
3.7
5
Potatoes
0
6
8
A.
2 dollars for 8 potatoes
B.
$4.00/potato
C.
$1.50/potato
15
D.
$0.25/potato
1) Use the data about the number of red and green blocks in different size
groups to answer the questions below.
a) Are the red blocks proportional to the green blocks? Explain in
complete sentences how you know. (2 points)
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
b) What is the constant of proportionality in the table above? (2 points)
Answer: ___________________
c) Find the missing value for X in the table above. (1 point)
Answer: ___________________
d) Write an equation to represent the proportional relationship, using the
variable g, for green, and the variable r, for red. (2 points)
Answer: ________________________________________
2) In 1985, the cell phone was first introduced to Centreville with 200 users.
The table below shows how the number of users changed every year.
Years
Users
1
350
2
600
3
800
4
925
a) Graph the points on the coordinate plane below.
Cell Phone Users Over Time
1,000
Users
75
0
50
0
250
50
1
2
3
4
5
Years
1
0
5
1,000
b) Identify features of the graph above that indicate whether the number
of users is proportional to the number of years since the phones were
introduced.
(2 points)
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
____________________________________________________________
3) Ms. Brown wants the ratio of failing to passing grades on her test to
always be 12 : 18.
a) Fill in the table below showing the number of passing and failing
grades.
Failing (x-axis)
Passing (y-axis)
1
6
15
12
18
b) Graph and connect the points on the coordinate grid below. (2
points)
c) What does the origin represent in the context of the problem? (1
point)
________________________________________________________
____
________________________________________________________
____
d) What point on the graph represents the constant of
proportionality? Use your knowledge of proportions to explain
why this makes sense.
(2 points)
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
e) Write an equation that represents the relationship between passing
grades, p, in terms of failing grades, f. (1 point)
Answer: ___________________________________
4) Jack and Jill raced cross-country on motorbikes. Jack drove 325
miles in 5 hours. Jill took 6 ½ hours to travel the same distance as
Jack. Who was travelling faster? Use your knowledge of unit rates
to explain your answer.
(2 points)
___________________________________________________________
_
___________________________________________________________
_
___________________________________________________________
_
___________________________________________________________
_
5) Amy and her family were traveling during their vacation. She looked
at her watch during the morning at Point 1 in the diagram below,
and then later that morning at Point 2 in the diagram below. Her
mom told her how far they traveled in that time, as shown below.
Amy’s watch
Amy’s watch
60 miles
Point 1
Point 2
a) What is the unit rate of the car? Explain in complete sentences
what the unit rate means in the context of this problem. (3
points)
Unit Rate = _____________________
________________________________________________________
____
________________________________________________________
____
________________________________________________________
____
b) Amy’s dad said the entire trip was 1,200 miles. How many hours
will it take to complete the trip?
Answer: __________________________
c) Write an equation for the distance, d, in terms of the hours, h. (1
point)
Answer: __________________________