BAM Round 5
Decimals, Percentages, and Ratios
Math 37
Decimals, Percentages, and Ratios
Your Objectives for this Round:
When you complete this round successfully, you should be able to demonstrate
proficiency with the following skills:
 Operations with decimal numbers
 Comparing decimals
 Rounding decimals
 Operations on decimal numbers
 Order of operations with decimal numbers
 Converting fractions to decimals and decimals to fractions
 Ratios, Rates and Proportions
 Percent Notation
 Percent and decimal conversions
 Percent and fraction conversions
 Percent proportion and application
How will you demonstrate proficiency?
 Pass the mastery quizzes from BAM modules 10 and 11 with an 80% or better. You
have as many attempts as you need to do this.
 Pass BAM Exam 5 with an 80% or better. You have up to three attempts to do this.
 Complete all assigned Round 5 activities, homework assignments and other work your
instructor may assign.
What will you find in this packet?
 Classroom activities, including Investigate and Report Activities and activities that
focus on building your understanding of decimals, rates, proportions and
percentages.
 Homework activities, which often build or expand on the classroom activities.
Art Martinez, Abby Tatlilioglu
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BAM Round 5
Contents:
Activity Title
A
B
C
C Homework 1
C Homework 2
D
E
F
G
G Homework
H
Appendix
I
J
K
L
M
Decimals, Percentages, and Ratios
Math 37
Activity Name
Page
Home Improvement (Decimal application)
Introduction to Decimals
Linear Functions Involving Decimals (cups)
Linear Functions Involving Decimals
Linear Functions Involving Decimals
Percentages
Simple Interest
Percent Diagrams
Percents and Ratios
Percents and Ratios
Percent Increases and Decreases
3
11
17
23
29
33
41
43
49
55
59
63
65
67
73
74
78
Introduction to Decimals
Conversions from Decimals to Fractions I
Conversions from Decimals to Fractions II
Percentages
Proportions
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
Team Name:
Your Name:
Other team members:
Steve the All-in-one Handy Man
Mr. Martinez finally found his dream house, and he is ready to move in. However, Mr. Martinez
noticed that the living room and the backyard could use some floor tiling for a fresh move. The
floor plan of the house is shown below. Notice that there is a Jacuzzi in the backyard.
1. Task 1: Living room material: Mr. Martinez wants to tile the floor of his living room. He went to
home depot to buy the tile boxes. The tile that Mr. Martinez liked comes in boxes of 25 pieces.
Each piece is one square foot. The cost of each box is $55.00 including tax.
a. What are the dimensions of Mr. Martinez living room? (Do not forget units)
Length_______________
Width ________________
b. Calculate the floor area of the living room. (Do not forget units)
Area =__________ x__________
A
living room=_________x__________
A living room=____________________
c. How many boxes of tiles would Mr. Martinez need knowing that he can only buy whole boxes?
Remember each box has 25 pieces and each piece is 1 sq ft.
d. How much would the boxes cost him including tax? Remember the cost of each box is
$55.00 including tax.
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
Task 2: Living room labor: Mr. Martinez felt too lazy to do the job himself. So he tried to get an
estimate for the job. Steve, an all-in-one handy man, gave the following estimate to Mr. Martinez:
Steve can tile the floor of the living room at an $85.00 base rate and then 3.89$/sq ft. Later,
Steve would add 8.75% tax to the bill.
1. Complete the table to find subtotal cost (cost before tax) of the suggested areas. Use the
space provided below the table to show your calculations.
Number of ft2
Fixed Cost
Variable Cost
Subtotal Cost before tax
5 square feet
85.00
3.89 (5)= 19.45
10 square feet
85.00
3.89(___)=
85.00+19.45= $104.45
17 square feet
x square feet
C(x)=
2.
In number 1 part b you found that the area of the living room is 120 sq ft. Use C(x) from the table
to find the labor cost to tile the living room.
C(x) = 85 + 3.89x
3.
Complete the table to find the total cost with tax of the suggested subtotals. Remember 8.75%
is ___________in decimal form. Round your answers to two decimal places. Use the space
provided below the table to show your calculations.
Subtotal Cost before
tax
$104.45
Tax
Total with Tax
0.0875 ($104.45)= $9.14
104.45 + 9.14= 113.59
$123.90
0.0875($123.90)=______
$151.13
4. In number 2 you found that the subtotal labor cost without tax to tile the living room was
$551.80. Use table in number 3 to find out the total labor cost including tax.
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
5. Now we have all the information we need to fill out “Steve’s real Estimate Sheet”:
STEVE ALL-IN-ONE HANDY MAN
COMPANY
1145 N. Loop 337
New Braunfels, Texas 78130
Phone (830) 624-0000
Name _________________________
Purchase Date____________________
Address________________________
City___________________________
Job address______________________
City____________________________
Phone__________________________
Job approval______________________
Sold By:
Job Description
Quantity
1-
120 sq ft
Price per sq ft
Variable cost
/Price per
quantity
Fixed
Cost of
Labor
Subtotal
2345678910Invoice
Subtotal
Tax
Invoice
Total
Seller____________________________________
Purchaser(s)______________________________
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
Task 3: Backyard material: As you can see from the floor plan, Mr. Martinez’s back yard has a 6’
diameter Jacuzzi. Let’s find the area to be tiled and the number of boxes needed
1. Find the dimensions of the backyard. (Do not forget units)
Width _________________
length L____________________
2. Find the area Aall of the backyard including the Jacuzzi. (Do not forget units)
Aall =
3. Find the area Atile of the backyard to be tiled:
a. The diameter of the Jacuzzi is given by 𝑑𝐽𝑎𝑐𝑢𝑧𝑧𝑖 = __________________________ .
b. The radius of the Jacuzzi then is 𝑟𝐽𝑎𝑐𝑢𝑧𝑧𝑖 = ___________________________________ .
c. The Area of the Jacuzzi AJacuzzi is______________(below use 𝜋 = 3.14)
Since the Jacuzzi is circle-shaped, we can use the “area of a circle” formula to find the Jacuzzi’s
area.
Area of a circle = 𝜋𝑟 2
So the area of the Jacuzzi is
𝐴𝐽𝑎𝑐𝑢𝑧𝑧𝑖 = 𝜋(𝑟𝑗𝑎𝑐𝑢𝑧𝑧𝑖 )2
𝐴𝐽𝑎𝑐𝑢𝑧𝑧𝑖 =
d. So the area of the backyard to be tiled is:
The 𝐴𝑡𝑖𝑙𝑒 = 𝐴𝑎𝑙𝑙 - 𝐴𝐽𝑎𝑐𝑢𝑧𝑧𝑖
So 𝐴𝑡𝑖𝑙𝑒 =_________________-_________________
So 𝐴𝑡𝑖𝑙𝑒 =_________________________________(Do not forget units)
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
4. The tile that Mr. Matinez liked for his backyard also comes in boxes of 25 pieces where
each piece is 1 sq ft. also, the cost of each box is $55.00 including tax.
a.
How many boxes does Mr. Martinez need to buy for his backyard?
Mr. Martinez needs ____________Boxes for the backyard.
b.
What is the cost of the backyard tile boxes
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
Task 4: Backyard Labor: Steve can tile the floor of the backyard just like he would for the living
room at an $85.00 base rate and then 3.89$/sq ft. Later, Steve would add 8.75 % the tax. You can
use the estimate sheet again :
STEVE ALL-IN-ONE HANDY MAN
COMPANY
1145 N. Loop 337
New Braunfels, Texas 78130
Phone (830) 624-0000
Name _________________________
Address________________________
City___________________________
Phone__________________________
Purchase Date____________________
Job address______________________
City____________________________
Job approval______________________
Sold By:
Job Description
Quantity
1-
120 sq ft
Price per sq
ft
Variable cost
/Price per
quantity
Fixed
Cost of
Labor
Subtotal
2345678910Invoice
Subtotal
Tax
Invoice
Total
Seller___________________________________
Purchaser(s)______________________________
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Home Improvement project
Math 37
Task 5: Mr. Martinez spared $3,000.00 for the home improvement project. Is that enough, or
does he need to charge the rest on this credit card?
Cost of Home improvement project = cost of living room project + cost o backyard project
Home improvement project= Materialliving room + Laborliving room+ Materialbackyard + Laborliving room
Home improvement project =____________+___________+___________+__________
Is $3,000.00 enough?
Task 6: Steve told Mr. Martinez that when the old floor is taken out of his living room, the
baseboard has to come up as well. (Note: The baseboard goes around the edges, so it is part of the
perimeter.) Steve said that he does not charge extra to install the new ceramic cove base but that
Mr. Martinez should order it. He told Mr. Martinez to keep in mind that there is always some waste
especially as he cuts around the corners, so Mr. Martinez should be sure to buy extra. So, Mr.
Martinez went back to Home Depot and found that the cove base came 10 pieces to a carton and
each carton cost $65 including tax.
Look at the diagram to consider how many feet he must cover. To account for the waste,
order enough to go in the doorways, even though there won’t be cove base installed there.
Note: One of the 12 foot sides of the living room is open and won’t need cove base.
How many cartons of cove base should Mr. Martinez buy?
How much extra will Mr. Martinez spend so that the living room looks finished at the
edges?
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity A
Art Martinez, Abby Tatlilioglu
Home Improvement project
Page 10
Math 37
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
Your Name:
EVERY ACTION THAT I PERFROM TODAY WILL BRING ME CLOSER TO MY FINCANCIAL FREEDOM
Do you recall the place value system? It is the amount that each digit represents based on its
position in a number.
For Example: What are the place values for each digit in the number: 2,586 ?
Digit
Place Value in
words
Place Value in
numbers
Powers of ten
2
Thousands
5
Hundreds
8
Tens
6
Ones
1000’s
100’s
10’s
1’s
103
102
101
100
TASK 1
1) What are the place values for each digit in the number: 1,274 ?
Digit
Place Value in
words
Place Value in
numbers
Powers of ten
2) Looking at the Powers of ten row, what number would you say these place values are based on?
3) As we move from left to right, starting at the thousands, what number do we divide the place
value by to get to the next place value?
4) The above division, is the same as multiplying by what? {Hint: it’s a fraction}
Because of this connection with the number 10, the system of numbers that we use is
called The Decimal System (where the prefix “deci” stands for “tenths”).
1
 of the place value to the left of it.
 10 
Each place value is a tenth, 
(Thousands, hundreds, tens, ones, etc…)
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
TASK 2
Carrie and Marcos are hanging out at Marcos’ house. Marcos is trying on one of his father’s
overcoats. He hears jingling in the pockets and when he takes out all the money, he finds a whole
wad of cash and change. There are 6 hundred-dollar bills, 1 ten-dollar bill, 3 one-dollar bills, 4
dimes, and 7 pennies.
1.Fill in the chart below using the amount of money that Marcos found.
Denomination “100 Dollar
“10 Dollar
“1 Dollar
Dimes
Bills”
Bills”
Bills”
How Many?
Pennies
a) What is the value of all these coins and bills?
b) What is the symbol you included between the dollars and cents?
c) These denominations also represent “place values” Now insert the digits in their place values.
_______
Hundreds
_______
Tens
_______
Ones
_______
Ten”ths”
_______
Hundred”ths”
d) Where does the decimal go? (Insert it in its proper location above)
These place values get their name based on what portion of a single dollar they represent.
Because there are 10 dimes in one dollar, then one dime is one-tenth of a dollar. Thus, the
1
 . And 4 dimes represents four-tenths of a dollar.
 10 
place value for dimes is called “tenths” 
e) Why is the place value (column) where the pennies are, called “hundredths?”
f) How many hundredths do we have in our amount of money from the pocket?
TASK 3
1. Let’s review. Name the place value based on the coin and location in the decimal number.
Coin/Bill
Name of Place
Value
Right or Left of
Decimal
How Many Places
from the Decimal?
Dime
One-Dollar Bill
Penny
Ten-Dollar Bill
Hundred-Dollar Bill
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
2. Consider the amount of $259.62
a) What is the place value of the first 2?
b) What is the place value of the second 2?
c) Which one is smaller?
d) Explain the difference between these place values.
The place values to the right of the decimal can go beyond the hundred”ths” place value. There are
thousand”ths”, ten-thousand”ths”, etc…
e) Fill in the name of the place value under each blank
_______
_______ •
_______
_______
_______
_______
_______
f) If you’ve done this properly, you will notice a pattern in the wording of the place values to
the right of the decimal. What three-letter suffix do we attach to all the place values to
the right of the decimal?
Why?
3. Study the words for the following numbers.
Number
5.6
3.18
64.729
Place value of last
digit in the number
Tenths
0.12
The number expressed in words
Last word in “The number
expressed in words” column
Five and six tenths
Three and eighteen hundredths
Sixty four and seven hundred
twenty-nine thousandths
Twelve hundredths
0.3
49.187
0.402
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
TASK 4
1. Complete the chart below, by either writing the words for the given number with decimal or
writing the number with decimal for the given words.
Decimal
Words
17.1
Seventeen and one tenth
23.57
0.84
3.247
Three hundred ninety-five thousandths
Five hundred sixty-two thousandths
Seventy-six hundredths
2. Complete the following chart by filling in the last word.
Decimal
Words
0.72
“Seventy-two _________________________________?
0.072
“Seventy-two _________________________________?
0.00072
“Seventy-two _________________________________?
0.000072 “Seventy-two _________________________________?
0.0072
“Seventy-two _________________________________?
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
TASK 5:
For this task, we would like you to determine which decimal value is greater. Please place in each
box below an inequality symbols < or >.
TASK 6
At this point we would like you to relate the decimal wording to its equivalent visual representation.
Below are two equivalent expressions.
1.
Explain how you know this graph to be correct and true.
2.
Write the decimal equivalent of each square.
TASK 7
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity B
An Introduction to Decimals
Math 37
Translate the following into mathematical expressions.
1. Four tenths of a number
2. the sum of seven hundredths and a number
3. one and five thousandths less than two tenths of a number
4. two and three tenths times the difference of a number and four
5. the quotient of six tenths of a number and seventy-five hundredths
6. one hundred thirty three thousandths subtracted from forty nine tenths of a number
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity C
Linear Functions Involving Decimals
Math 37
Your Name:
SUCCESS IS GOING FROM FAILUR TO FAILUER WITH NO LOSS OF ENTHUSIASM
TASK 1:
The Styrofoam Cup problem
Here is the challenge. Can you estimate the number of Styrofoam
cups it will take to match the height of Professor Martinez? Here
is the problem. You only have 3 cups to work with.
1. Let’s brain storm. The only wrong answer is no answer. One by
one, ask each member of the group this question and
paraphrase their answer.
“What information will you need to know to explore this
problem?” No repeat answers allowed!
Idea 1:
Idea 2:
Idea 3:
Idea 4:
2. Use the image at right to determine the total height of the cup
It looks like the bottom of the rim four hash marks above the
9cm mark.
What is the total height of the cup?
Art Martinez, Abby Tatlilioglu
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Linear Functions Involving Decimals
Math 37
3. If you were to stack 3 cups one into the other as shown in the top page, do you think the total
height will be 3 x 11 cm = 33 cm? Explain your answer. Why or why not?
4. The answer to problem 3 is no. Use the dimensions provided in the
image at right. Now calculate the height of two cups one stacked
inside the other until the rims touch in the manner depicted in the
first image on page one.
What about three cups?
5. Notice that the height of 1 cup is broken down into two parts, the body (which is 9.4 cm) and
the rim (which is 1.6 cm).
Height 1 Cup = 9.4 [body] + 1.6 [rim] = 11.0 cm
Height 2 Cups = 9.4 [body] + 2(1.6) [two rims] = 12.6 cm
Height of 3 Cups = _______ + _____( ____ ) =
Height of 4 Cups = _______ + _____( ____ ) =
Height of 5 Cups = _______ + _____( ____ ) =
Height of 10 Cups = _______ + _____( ____ ) =
Height of 20 Cups = _______ + _____( ____ ) =
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity C
Linear Functions Involving Decimals
Math 37
6. Do you see a pattern in the above calculations? What varies from
one line of calculations to the other?
7. How is it related to the number of cups for which we are
calculating the total height?
8. If you understand the pattern well, we can calculate the height
for any number of cups, x. So for x number of cups the height
will be
Height of X Cups = H(x) = _______ + _____( ____ )
9. Fill in the table as best you can.
No of Cups
Height Calculations
Total Height
1
_______ + _____( ____ )
2
_______ + _____( ____ )
3
_______ + _____( ____ )
4
_______ + _____( ____ )
5
_______ + _____( ____ )
10
_______ + _____( ____ )
20
_______ + _____( ____ )
30
_______ + _____( ____ )
40
50
60
70
80
90
100
110
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity C
Linear Functions Involving Decimals
Math 37
10. Graph the points from the table above and draw a single straight line through them.
Art Martinez, Abby Tatlilioglu
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Linear Functions Involving Decimals
Math 37
11. Use the line from the preceding graph to place a large dot representing Professor Martinez. His
height is 175 cm. From this dot use the graph to estimate the number of cups it will take to
match his height by projecting this dot onto the x axis.
12. Now let’s use the equation you developed in problem 8. You should have this equation for the
answer to problem 8.
H(x) = 9.4 + 1.6x


x is the number of cups
H(x) is the total height
Now, if Professor Martinez is 175 cm in height, which variable does 175 represent? The x or
the H(x)?
13. Substitute 175 for the H(x) and calculate the number of cups you will need to match his height.
14. Did your calculations in problem 13 come close to your estimate from the graph in problem 11?
Explain any discrepancy.
Art Martinez, Abby Tatlilioglu
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BAM Round 5 Activity C
Art Martinez, Abby Tatlilioglu
Linear Functions Involving Decimals
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Math 37
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BAM Round 5 Activity C
Homework 1
Linear Functions Involving Decimals
Math 37
Your Name
WHO DEFINES WHAT IS POSSIBLE IN YOUR FUTURE?
TASK 1:
1. a) May Lin has driven 90 miles in a trip to visit her grandparents. So far it has taken her 2 hours to
drive this distance, and she still has a long way to go. It is through treacherous mountain roads, so
it is not possible to drive very fast. Express the ratio of the miles she drove to the number of
hours it took her as a rate in per unit form.
b) Write a sentence explaining what the rate of speed means in context to this problem.
c) At this rate, how far will she go in 4 hours? 6 hrs? 8 hrs? Fill in the table below.
Time (hours) Distance
(miles)
2
4
6
8
10
c) Plot the given points in the graph and carefully draw ONE single, long line through the points.
Abby Tatlilioglu
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Homework 1
Linear Functions Involving Decimals
Math 37
d) Use the graph above to estimate how long it will take to drive the 500 miles to visit her
grandparents.
e) Find D(5) by finding 5 on the t axis and drawing a vertical line up to the line, then draw a
horizontal line to the D(t) axis.
f) Find the equation of the function D(t)=______________
2. You’re driving from San Francisco home to Los Angeles, and you left at noon. At 2 pm you stop for
gas just outside SunnyVale and you notice a sign says you are 404 miles from Los Angeles. Three
hours later at approximately 5pm, you stop for gas again, and you notice another sign that says
you’re right outside Santa Maria, and you are now only 187 miles from Los Angeles.
a) What is your rate of speed? Explain what it means in context to the problem.
b) Fill out the distance remaining to Los Angeles for each hour listed below in the table.
Time
2pm
3pm
4pm
5pm
Abby Tatlilioglu
Distance to LA
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Homework 1
Linear Functions Involving Decimals
Math 37
c) Plot the given points in the graph and carefully draw ONE single, long line through the points.
Can you find the equation of
this model? 𝐷(𝑡) = 𝑚𝑡 + 𝑏
d) At what time will you arrive in Los Angeles?
e) What was the distance from Los Angeles when you first started your trek home (noon)?
f) Find D(3.5) = _______. (HINT: use horizontal and vertical lines on the graph).
Now find t when D(t) = 100… t=________ (HINT: go the opposite way)
What is the difference between these two questions in the context of the problem?
Explain in a sentence.
3. U-HAUL: You are going to help a friend move into a new place and you’ve decided to rent a u-haul
for the day. Since the 14’ truck and the 17’ truck are the same price, you opt for the bigger one. The
advertised price online is $29.95 per day plus $0.79/mile.
a) How would you calculate the total cost of renting the truck? What kinds of things do you need
to know or consider??
Abby Tatlilioglu
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Homework 1
Linear Functions Involving Decimals
Math 37
b) Let’s assume gas is not a factor, and you don’t get the extra insurance. Let’s create the cost
function in terms of miles driven. How much does it cost to rent the truck (even if you don’t
drive it off the lot)?
How much does it cost to rent the truck if you only have to drive 1 mile?
C(1) = __________+________(________) =
How much does it cost to rent the truck if you drive 2 miles?
C(2) = __________+________(________) =
How much does it cost if you drive 10 miles?
C(10) = __________+________(________) =
c) Write the general function for the total cost, C, in terms of the miles driven, m.
C(m) =
d) Use the values you found above and/or the
equation you’ve found to create a graph of
function.
the
e) Use the graph to predict the cost given the following number of miles driven:
C(7) = ___________
C(9.5) = ____________
C(12) = ___________
C(3.5) = ____________
f) If you have a budget of $40, how many miles can you drive max?
Abby Tatlilioglu
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Homework 1
Linear Functions Involving Decimals
Math 37
g) Your friend is a very detail-oriented person. According to google maps it’s 1.7 miles from the Uhaul to the old place, 4.6 miles from the old place to the new one, and 2.4 miles from the new place
back to the U-haul. Will you make it on your budget?
4. Using data from 1952–2004, the percent p of the eligible U.S. population voting in presidential
elections has been estimated to be p (x) = 63.20 - 0.26x, where x is the number of years past 1950.
(Source:http://www.cengagesites.com/academic/assets/sites/harshbarger_ch01.pdf page 3)
a) What is p(0)?
What does it mean in the context of the problem?
b) If we wanted to look at the percent population that voted in 1975, what would x be?
X=___________
Now plug it in to get the percent of the population which voted in 1975
p(
) = _________
c) According to this model, in what year will none of the population be voting?
TASK 2 : Function machines revisited
Moving from tabular data to verbal and symbolic descriptions of an expression:
In the following tables, fill in the steps using words in the verbal steps column
based on clues in the table of values. Then, follow the steps to find an algebraic expression (symbolic
description) in terms of x, in the expressions column. Finally, set the algebraic expression equal to the
output, y.
TABLE 1:
Input, x
0.1
0.5
1.3
-1.2
Result of Step 1
0.2
0.6
1.4
-1.1
Result of Step 2
-0.4
-1.2
-2.8
2.2
Output, y =
-0.4
-1.2
-2.8
2.2
Abby Tatlilioglu
\ Input /
X
1.
2.
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/ Output \
y=
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BAM Round 5 Activity C
Homework 1
TABLE 2:
Input, x
Result of Step 1
Linear Functions Involving Decimals
0.1
.01
0.5 1.3
.05 .13
-1.2
-.12
1.
Result of Step 2
-.04
0
.08
-.17
2.
Result of Step 3
-.12
0
2.4
-.51
3.
Result of Step 4
0.38
0.5 2.9
-.01
4.
Output, y =
0.38
0.5 2.9
-.01
Math 37
\ Input /
X
/ Output \
y=
TASK 3: Moving from the symbolic expression to the verbal description (EVALUATION
MACHINE): In the tables below, the steps of the evaluation machine are not provided. Fill in the
steps. Then follow the two given input values as they are evaluated, step-by-step. Our goal in this task
is to describe the steps needed to evaluate the expression verbally. DO NOT SIMPLIFY ANY
EXPRESSION IN THIS TASK!
Expression 1: 0.3𝑥 − 0.35
\ Input /
0.1
-1.2
0.1
-1.2
1.
2.
/ Output 𝑦 = 0.3𝑥 − 0.35\
Expression 2: −(2𝑥 + 0.2)
\ Input /
1.
2.
3.
/ Output 𝑦 = −(2𝑥 + 0.2) \
TASK 4:
Consider the evaluation machines in tasks 2 and 3. Which ones appear to be equivalent? Pick at least
two additional input values and determine if you get the same output for each evaluation machine.
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BAM Round 5 Activity C Linear Functions Involving Decimals (part2)
Homework 2
Math 37
Your Name:
THEY WHO OVERCOME THEIR FEARS WILL TRULY BE FREE.
TASK 1: Is it a solution?
1. Determine which of the following ordered pairs are solutions to -1.6x+0.8y=3.2 Justify your
answers by showing your work
a) (2, 3)
b) (0, 4)
Select 1 of the following
□ the ordered pair (2, 3) is a solution to
-1.6x+0.8y=3.2
Select 1 of the following
□ the ordered pair (0, 4) is a solution to
-1.6x+0.8y=3.2
□ the ordered pair (2, 3) is a NOT solution to 1.6x+0.8y=3.2
□ the ordered pair (0, 4) is a NOT solution to 1.6x+0.8y=3.2
2. Determine which of the following ordered pairs are solutions to y=x-7.25 Justify your answers by
showing your work
a) (1, -8.25)
b) (4.75, -3.5)
Select 1 of the following
□ the ordered pair (1, -8.25) is a solution to y=x7.25
Select 1 of the following
□ the ordered pair (1, -8.25) is a solution to y=x7.25
□ the ordered pair (1, -8.25) is a NOT solution to
y=x-7.25
□ the ordered pair (1, -8.25) is a NOT solution to
y=x-7.25
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BAM Round 5 Activity C Linear Functions Involving Decimals (part2)
Homework 2
Math 37
TASK 2 GRAPHING
1.
4𝑥 = 16.8
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BAM Round 5 Activity C Linear Functions Involving Decimals (part2)
Homework 2
2.
Abby Tatlilioglu
Math 37
3.5𝑥 + 1.2𝑦 = − 8.4
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BAM Round 5 Activity C Linear Functions Involving Decimals (part2)
Homework 2
3.
Abby Tatlilioglu
Math 37
– 𝑥 + 9.5𝑦 = 19
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BAM Round 5 Activity D
Percentages
Math 37
Your Name:
YOU ARE CONFINED ONLY BY THE WALLS YOU BUILD.
95% of a Jelly Fish is water!
Task 1:
Percent is from the Latin phrase per centum meaning “by the hundred.” Percent can be seen as Percent or Per-hundred. So to understand percentages better we look at the following diagram and notice
that there are 100 squares in total here.
1. How many squares are shaded?
2. How many squares are there in the whole piece?
3. Write a ratio (fraction) representing the parts shaded to the whole piece
4. Write a ratio (fraction) representing the parts NOT-shaded to the whole piece.
5. If the whole piece is shaded write a ratio for this.
Note: That your answer to question 5 results in 1, so we separate the fraction into the following to define the
percent.
100 100  1 
 1 


  100  
  100 %
100
1  100 
 100 
We defined percent earlier as “per the hundred” so 1  % ; now that we know this we can answer the following
100
questions:
6. What percent is shaded in the Task 1 diagram?
7. What percent is NOT shaded in the Task 1 diagram?
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BAM Round 5 Activity D
Percentages
Math 37
8. Draw a diagram that would represent the following percents:
a. 50%
b. 12.5%
Task 2: Understanding Percentages
1. Shade 50% of the rectangle given:
2. If we take half of 50% what percent would we end up with?
3. Shade 25% of the rectangle below:
4. Shade 50% of the diagram below?
5. Using the information of 50% try to find how many circles represent 25%?
6. What percentage does one circle represent to the whole?
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BAM Round 5 Activity D
Percentages
Math 37
TASK 3:
As president of the student body you are responsible for raising money for
your high school library to buy computers. The goal is to raise $60,000. To
help with matters you have created an image of a thermometer to show how
close you are to the goal.
Estimate the values for the following questions and label them onto the
drawing at right.
1. $60,000 is your entire goal. It represents 100% of your goal.
2. If you are at 50% of your goal, how much money did you raise?
3. If you are at 75% of your goal, how much money did you raise?
4. If you are at 25% of your goal, how much money did you raise?
5. If you are at 10% of your goal, estimate how much money you raised?
6. If you are at 40% of your goal, estimate how much money you raised?
7. If you are at 60% of your goal, estimate how much money you raised?
8. If you are at 90% of your goal, estimate how much money you raised?
9. If you are at 200% of your goal, estimate how much money you raised?
10. If you are over 100% of your goal, what does that mean?
11. If you raised $17,000, estimate what percent of your goal you have achieved?
12. If you raised $50,000, estimate what percent of your goal you have achieved?
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BAM Round 5 Activity D
Percentages
Math 37
TASK 4:
In the 2001 National Basketball Association finals, the Los Angeles Lakers
defeated the Philadelphia 76ers, retaining their championship status for the
second straight year. Among the outstanding players during the series were
Shaquille O’Neal and Kobe Bryant of the Lakers, and Allen Iverson and
Dikembe Mutombo of the 76ers. The data in the table represents each man’s
field goal totals for the five game championship series.
PLAYER
Bryant
Iverson
Mutombo
O’Neal
1.
FIELD GOALS MADE
44
66
33
63
FIELD GOALS ATTEMPTED
106
162
55
110
Using only the data in column 2, Field Goals Made, rank the players from the best to worst according to their
field goal performance.
2. You can also rank the player by using the data from both column 2 and column 3. For example, Kobe Bryant
made 44 field goals out of 106 he attempted. The 44 successful baskets can be compared to the 106
attempts by dividing 44 by 106. You can represent that comparison numerically as the fraction (44/106), or,
equivalently, as the decimal 0.415 (rounded to the thousandths).
Complete the following table and use your results to determine another ranking of the four players from best
to worst performance based on the ratio of goals made to goals attempted.
PLAYER
FIELD GOALS
FIELD GOALS ATTEMPTED
VERBAL
FRACTION
DECIMAL
(round to thousandths)
MADE
Bryant
44
106
Iverson
66
162
Mutombo
33
55
O’Neal
63
110
44 out of 106
44
106
0.415
The two sets of rankings are based on two different points of view. The ranking in Problem 1 is from an
absolute viewpoint in which you just count the actual number of field goals made. The ranking in problem
2 is from a relative perspective in which you are taking into account the number of success relative to
the number of attempts.
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BAM Round 5 Activity D
Percentages
Math 37
3. Which of the two measures in the table best describes field goal performance? Absolute or Relative?
Explain.
4. a.
Three friends, shooting baskets in the school yard, kept track of their performances. Ajax made 9
out of 15 shots, Paris made 28 out of 42, and Achilles made 15 out of 24. Rank their performance.
b. Which ratio form (fraction, decimal, or other) did you use to determine the ranking?
5. How would you determine if two ratios, such as “12 out of 20” and “21 out of 35”. Are equivalent?
6. a.
Match each ratio from the first column with the equivalent ratio in the second column.
Column A
15 out of 25
42 out of 60
63 out of 75
52 out of 80
Column B
84 out of 100
65 out of 100
60 out of 100
70 out of 100
b. Which set of ratios, those in column A or those in column B, is more useful in comparing and ranking the
ratios? Why?
PERCENTS
Relative measure based on 100 is familiar and natural. There are 100 cents in a dollar and 100 points on a test.
You have probably been using a ranking scale from 0 to 100 since childhood. A ratio such as 70 out of 100 can be
expressed as 70 per 100, or, more commonly, as 70 percent, 70%. Percent always indicated a ratio “out of 100”.
7. Express each ratio in column B of problem 6 as a percent, using the symbol “%”.
Abby Tatlilioglu
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BAM Round 5 Activity D
Percentages
Math 37
Suppose you need to write a ratio such as 21 out of 25 in percent format. You may recognize that the
denominator, 25, is a factor of 100 (25 • 4 = 100). Then the fraction 21/25 can be written equivalently as
21  4 84
which is precisely 84%

25  4 100
A more general method to convert the ratio 21 out of 25 into percent format is to divide the numbers.
21
 0.84 by dividing.
25
Next you convert the decimal into percent format by multiplying the decimal by
100
1
100
1
84
 100 
0.84  0.84  

 84%
  (0.84  100) 
100 100
 100 
Note that multiplying the decimal by 100 moves the decimal point in 0.84 two places to the right. This leads to a
short cut for converting a decimal to a percent!!!
8. Rewrite the following ratios in percent format.
a.
35 out of 100
b.
16 out of 50
c.
8 out of 20
d.
7 out of 8
e.
4 out of 7
f.
14 out of 10
Abby Tatlilioglu
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BAM Round 5 Activity D
Percentages
Math 37
In many applications, you will need to convert a percent into decimal format. This can be done by replacing the
“%” symbol with its equivalent meaning “out of 100”,
the process.
Example:
1
and simplifying. The following examples demonstrate
100
Convert 75% to a decimal
75% = 75/100 = 0.75
Example:
1
% to a decimal
3
83.33
83.33% 
 .8333
100
Convert 83
9. Write the following percents in decimal format.
a. 73%
b. 3.5%
c. 200%
d. 0.75%
10. Do your best and use what you have learned about fractions, decimals and percentages to fill in the table
completely.
VERBALLY
AS A FRACTION
AS A
DECIMAL
AS A PERCENT
4 out of 9
19
54
0.13
1
67 %
3
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BAM Round 5 Activity D
Abby Tatlilioglu
Percentages
Page 40
Math 37
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BAM Round 5 Activity E
Simple Interest
Math 37
Your Name:
There are two levers for moving men: interest and fear.
“The cost of borrowing money from a lender.”
If you borrow money from a bank then you expect to pay a fee for
borrowing this money. This fee for borrowing money is called interest. If you
use a credit card and you do not pay off your credit card balance right away by
end of the month, then you are expected to pay interest on the remaining credit
card balance.
One of the most common types of interest is simple interest, for which
interest is paid only the initial loan amount. The three main factors that go into
calculating how much interest you have to pay for a loan are the loan amount,
interest rate, and the amount of time you borrowed for the money. Here is the
simple interest relationship that the bank uses to calculate interest on some
loans.
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 × 𝐿𝑜𝑎𝑛 𝐴𝑚𝑜𝑢𝑛𝑡 × 𝑇𝑖𝑚𝑒
1. Using the following variables write an formula to compute simple interest
for a loan:
𝑇 = 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑡𝑖𝑚𝑒 𝑡𝑜 𝑟𝑒𝑝𝑎𝑦 𝑡ℎ𝑒 𝑙𝑜𝑎𝑛
𝑃 = 𝐿𝑜𝑎𝑛 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑟 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙
𝐼 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑅 = 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒
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BAM Round 5 Activity E
Simple Interest
Math 37
2. Use the following table to help you organize different simple interest
calculations. Use scratch paper or a calculator for your calculations.
Interest
Rate
3%
Loan Amount
$200.00
Time to repay
loan (Years)
2
3%
$300.00
2
3%
$400.00
2
4%
$500.00
3
4%
$500.00
4
4%
$500.00
5
5%
$600.00
6
6%
$600.00
6
7%
$600.00
6
Interest accumulated
$12.00
$60.00
$180.00
3. In your groups come up with three different ways to decrease the interest
you pay for a loan.
Abby Tatlilioglu
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BAM Round 5 Activity F
Percent Diagrams
Math 37
Your Name:
YOU DON’T HAVE TO BE GREAT TO START, BUT YOU HAVE TO START TO BE GREAT!
TASK 1:
1. Meredith Middle School is putting on a production of The Music Man. The eighth grade had
300 tickets to sell, and the seventh grade had 250 tickets to sell. One hour before the
show, the eighth grade had sold 225 tickets and the seventh grade had sold 200 tickets.
Which grade was closer to the goal of selling all its tickets? Explain your answer.
2. This diagram, called a percent diagram, represents the seventh and eighth grade ticket
sales. The heights of the left and right bars represent the goal for each grade. The bar in
the middle, called the percent scale, is a common scale for the two different ratios.
Notice that the three bars are the same height even though they represent different
numbers. On the percent scale, the height always represents 100%.
Percents make it possible to represent both grade’ ticket sales as some number out of 100.
For the eighth grade, 100% represents 300 tickets. For the seventh grade, 100%
represents 250 tickets.
What values do you think belong in the
boxes in the diagram?
3. The eighth grade sold 225 tickets, and the seventh grade sold 200. Why is the bar for the
seventh grade taller, when they sold fewer tickets?
Abby Tatlilioglu
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BAM Round 5 Activity F
Percent Diagrams
Math 37
TASK 2:
Jefferson Middle School has 600 students, and Memorial Middle School has 450 students.
For problems 1 – 4 only, use this percent diagram to ESTIMATE an answer.
1. A Survey of the two schools finds that 300 Jefferson
students watch more than 1 hour of television every
night, while 270 Memorial students watch more than 1
hour per night.
a. What percentage of Jefferson students watch
more than 1 hour of TV each night?
b. What percentage of Memorial students watch more
than 1 hour of TV each night?
c. Comparing percentages do more Jefferson students or more Memorial students watch
more than 1 hour of TV per night?
2. Jefferson has 275 girls and Memorial has 250 girls. Which school has a greater percent of
girls? Explain?
3. At each school 75% of the students play a musical instrument.
a. About how many students at Jefferson students play an instrument
b. About how many students at Memorial students play an instrument?
4. The math teachers at each school selected 50 students to represent the school at a math
competition.
a. About what percentage of Jefferson students attended the math competition?
b. About what percent of Memorial students attended the math competition?
Abby Tatlilioglu
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BAM Round 5 Activity F
Percent Diagrams
Math 37
TASK 3:
5. Look again at the ticket sales by the seventh and
eighth grades at Meredith Middle School. The eighth
grade had 300 tickets to sell, and the seventh grade
had 250 tickets to sell.
a. At the end of the first week, each grade had sold
40% of their goal. Draw a percent diagram to
represent this situation.
b. Explain how you can use your diagram to estimate
the number of tickets the seventh grade sold, and
give your estimate.
c. Use your diagram to estimate the number of tickets the eighth grade sold.
6. One hour before the show started, the seventh grade had sold 200 tickets and the eighth
grade had sold 225. Malik used his calculator to express the ratios of the sold tickets to
the sales goal for both grades as percentages. How could you use your calculator to find
225/300 as a percentage?
Abby Tatlilioglu
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BAM Round 5 Activity F
Percent Diagrams
Math 37
7. Suppose each grade was only 25 tickets SHORT of meeting its goal.
a. How many tickets would the eighth grade have sold?
b. How many tickets would the seventh grade have sold?
c. Calculate the percentages sold for each grade. Comparing percentages, which grade cam
closer to its goal?
8. By the time the play began, each grade had sold
exactly 270 tickets.
a. What percent of its goals did the eighth grade
sell?
b. What percent of its goal did the seventh grade
sell?
c. Draw a percent diagram to represent this situation. Since the seventh grade sold more
than its goal, you will need to extend the bar for the seventh grade.
9.
Determine which ratio in each pair is greater by finding the percentage each represents
and drawing the corresponding percent diagrams.
a.
56
76
or
69
89
Abby Tatlilioglu
b.
Page 46
50
210
or
45
205
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BAM Round 5 Activity F
Percent Diagrams
Math 37
TASK 4:
1. This type of percent diagram is used to help compare two
numbers.
a. State in words the problem represented by this
percent diagram.
b. Write a proportion that is illustrated by the diagram
and solve it. How did you think about setting up the
proportion?
2. Consider this question: What percent of 150 is 6?
a. Complete the percent diagram at right to represent
this question, by filling in the boxes.
b. Express the question as a proportion and solve it.
3. Now consider this question: What is 127% of 20?
a. Draw a percent diagram to represent this question
b. Express the question as a proportion and solve it.
Abby Tatlilioglu
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BAM Round 5 Activity F
Abby Tatlilioglu
Percent Diagrams
Page 48
Math 37
Last Modified on 8/7/2015
BAM Round 5 Activity G
Percentages and Ratios
Math 37
Your Name:
WORK UNTIL YOUR DREAMS BECOME YOUR REALITY
TASK 1: PROPORTIONAL REASONING
International public health experts are desperately
seeking to stem the spread of the AIDS epidemic in
sub-Sahara Africa, especially in the small nation of
Botswana. According to United Nations officials, over
35% of Botswana’s 800,000 adults (ages 15 – 49) are
currently infected with the AIDS virus.
The data in the paragraph above is typical of the kind
of numerical information you will find in reading
virtually any printed news article.
1. What relative data (ratio) appears in the opening
paragraph? What phrase or symbol identifies it as
a relative measure?
2. Express the ratio in Problem 1 in fraction, decimal
and verbal form.
EXAMPLE: You know the total population of Botswana and the ratio of that total population has AIDS.
Proportional reasoning allows you to estimate how many adults in Botswana are infected with AIDS.
Basic proportion equation: ratio 
part
whole
In the Botswana situation, from the given information, the adult population of 800,000 is the total and 35%=
35
=0.35 is the ratio (Don’t forget, the ratio can be written as a fraction, decimal or percent). Representing the
100
part as x, you have
Ratio = 35%
Part = x, the unknown
Whole = 800,000
part
whole
x
0.35 
800,000
0.35  800,000  x
ratio 
280,000  x
So about 280, 000 adults in Botswana are infected with AIDS.
3. In the year 2000, 1.1 million African children under the age of 15 were living with AIDS. This represents 80%
of all children worldwide who were infected in 2000. Define the ratio, the whole, and the part of the whole
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
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BAM Round 5 Activity G
Percentages and Ratios
Math 37
before using the proportion equation to estimate the total number of children worldwide who are infected
with HIV.
a. Identify the known ratio:
b. Identify the given piece of information. Does this number represent a “part” or a “Whole”?
c. Identify the unknown piece of information. Does this number represent a “part” or a “Whole”?
d. Use the formula ratio 
part
to find your estimate.
whole
4. You do further research about this disturbing problem and discover that 5 years ago in sub-Saharan Africa,
there were approximately 20,800,000 adults and children living with HIV/AIDS. This represents 7.4% of the
total population there. Define the ratio, the whole, and the part of the whole before using the proportion
equation to estimate the total population.
ratio 
Ratio = ______
part
whole
Part = _______
Whole = ______
5. Africa has buried three-fourths of the 20 million people worldwide who have died from AIDS since the
beginning of the AIDS epidemic. Define the ratio, the whole, and the part of the whole before using the
proportion equation to estimate how many people from Africa have died from AIDS.
ratio 
Ratio = ______
part
whole
Part = _______
Whole = ______
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
50
BAM Round 5 Activity G
Percentages and Ratios
Math 37
6. In 2000, 5.3 million adults and children became infected with AIDS. Seventy-two percent of these new
cases occurred in sub-Saharan Africa and 15% of the new cases occurred in South and Southeast Asia.
a. Determine how many of these new cases of AIDS
occurred in sub-Saharan Africa.
b. How many new cases of AIDS occurred in South
and Southeast Asia?
7. Of the world’s 5.6 billion people, 3 billion or less live on less than $2 per day. Calculate the percent of the
world’s population who live on less that $2 per day.
8. Your new car cost $22,500. The state sales tax rate is 8%. Define the ratio, the whole, and the part of the
whole before using the proportion equation to estimate how much sales tax will you be paying on the car
purchase?
ratio 
Ratio = ______
part
whole
Part = _______
Whole = ______
9. You happen to notice that the 8% sales tax that your uncle paid on his new luxury car came to $3800. Define
the ratio, the whole, and the part of the whole before using the proportion equation to estimate how much
the car must have cost him?
ratio 
Ratio = ______
part
whole
Part = _______
Whole = ______
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
51
BAM Round 5 Activity G
Percentages and Ratios
Math 37
TASK 2:
1. SHOPPING!!!  You have budgeted a maximum of $200.00 for shopping at the GAP, and you plan to take
advantage of the Red, White, and Blue Fourth of July sale with a 40% discount on all sales. Let’s ignore sales
tax for this exercise and just focus on the subtotal. Purchase as many items as you like given your budget.
You must pick at least one item and find the cost of your purchase. You must show all your calculations by
hand and how much money you have remaining after your purchases.
$22.95
$22.95
$39.95
$59.95
$54.95
$69.95
$59.95
$88.00
List here your purchases and the Subtotal. The Subtotal is the total amount of your purchase and the 40%
discount. Also list the amount of money you will have left over from your $200 budget.
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
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BAM Round 5 Activity G
Percentages and Ratios
Math 37
2. After the discount is calculated, you still need to pay a sales tax on your purchases. It is said that “No one
escapes death and taxes.” In Torrance, the sales tax is 9%. Can you calculate the sales tax from the subtotal
of the previous problem? What will be your Total Cost after the discount and including the sales tax? How
much money do you have remaining?
3. THE DATE!!! You are on a date with someone you
really like. They have asked you to choose a pasta
meal for them and a soft drink.
a) Please choose a meal for yourself and your date,
which includes a pasta dish for the two of you and
a soft drink. Find the total cost with sales tax.
b) Your date may not be impressed if you don’t
leave a decent tip. The tradition is to leave a 15%
tip before taxes. Can you calculate the tip amount
for your server?
c) At the end of the date you dropped off your date and while driving home you wonder what the total cost was
for the date. Calculate the total cost of the date with sales tax and tip.
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
53
BAM Round 5 Activity G
Percentages and Ratios
Math 37
This example comes from the textbook Mathematics in Action, The consortium for Foundation Mathematics, Pearson Education, Inc
2004.
54
BAM Round 5 Activity G
Homework
Percentages and Ratios
Math 37
Your Name:
I MAY NOT BE THERE YET, BUT I’M CLOSER THAN WHERE I WAS YESTERDAY
Percentages and Ratios
TASK 1: Finding Part/Whole/Rate
Identify the part, the whole and the rate for each situation, then calculate the missing information.
1. a) Multiple Sclerosis is an autoimmune disease that is thought to effect more than 2.3 million
people*. For individuals who don’t have a history of MS in their family their chance of getting MS is 1
in 750. What percent chance is that?
Part: _______
Whole: _______
Rate:________
b) If the number of students enrolled at Compton College in 2010 was 8,734 and none of those
students had immediate family with MS, how many would we expect to be diagnosed with MS at some
point?
Part: _______
Whole:_______
Rate:________
2. a) In 2012 nearly 30% of Americans looked online for Halloween costume inspiration (according to
http://bitools.org/the-data-analytics-of-halloween-2012/). If the US population is 313.9 million
people, how many were checking out the social media for advice?
Part: _______
Whole:_______
Rate:________
b) According to NRF’s Halloween Spending Survey, (National Retail Federation) 158 million Americans
will celebrate Halloween (ie…they will spend money), down slightly from last year’s high of 170 million
people. What is the percent decrease of Halloween partiers?
Part: _______
Whole:_______
Rate:________
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BAM Round 5 Activity G
Homework
Percentages and Ratios
Math 37
TASK 2: The Anniversary
So the date went well and now you’re
celebrating your 1 year anniversary. You’ve
decided to go back to the same restaurant, but
they’ve marked up their prices $1 per pasta
item and 30 cents per drink in order to
redecorate.
a) Choose the same meal for you and your
partner. Calculate the new price for each item
that you ordered (the original is at the right).
b) What is the new subtotal?
c) What tip should you leave?
d) What is the tax on the meal (recall the tax rate is 9%)?
e) What percent difference is this? (HINT: Percent change is calculated by finding the difference
between the new and original objects, then dividing by the original.)
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BAM Round 5 Activity G
Homework
Percentages and Ratios
Math 37
TASK 3: The Trip!! You’ve decided to go to London together and have set a budget of $75 for
souvenirs. You see some Prince George gear and decide to bring some back for your grandma who just
loves to follow the British Royalty.
The following items are available in the store:
A souvenir mug: £ 15
Keychain: £ 8
Rattle: £ 10
T-shirt: £ 30
Tea Set: £ 42
Baby Shoes: £ 25
Astrology Chart: £ 35
a) Choose an item or two for grandma and calculate the subtotal. Then calculate the sales tax on your
purchase if sales tax in England is 17.5%.
b) What’s your grand total?
c) Is your choice within your budget? Why or why not? Assume the conversion rate from British
Pounds to US Dollars is 1 British Pound = 1.61 US Dollar.
Bungling Bartemus
Bartemus is helping to prepare a document for the college, and he writes the following statement, “The
number of students enrolled in discipline courses rose during this period of time from 421 to 750, an
increase of 43.9%.” What’s wrong with his calculation?? (First try to figure out how he got the
43.9%)
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BAM Round 5 Activity G
Homework
Juan Ortiz
Percentages and Ratios
Math 37
58
BAM Round 5 Activity H
Percent Increase/Decrease
Math 37
Your Name:
Life is ten percent what happens to you and ninety percent how you respond to it.
Percent Increase and Percent Decrease
Task 1: Understanding the three different ways of using percentages.
News reports frequently express quantitative information with percentages.
Consider the following statements from news reports:
a. A total of 13,000 newspaper employees, 2.6% of the newspaper work force, lost their
jobs.
b. Citigroup stock fell 15% last week, to $44.25.
c. The advanced battery lasts 125% longer than the standard one, but costs 200% more.
On close examination, each statement uses a percentage in a different way.
The first uses a percentage to express a fraction of the total work force.
The second uses a percentage to describe a change in stock price.
The third uses percentages to compare the performance and costs of batteries.
Unfortunately, while percentages themselves are rather basic—they are just an alternative
form of fractions—they are often used in very subtle ways. For example, consider the
following quote that appeared in a news article:
“The rate of smoking among eighth graders was up 44 percent, to 10.4 percent.”
The percentages in this statement are used correctly, but the phrase “up 44%, to 10.4%” is
not easy to interpret correctly.
Group work: In your groups try to interpret what each percentage represents.
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BAM Round 5 Activity H
Percent Increase/Decrease
Math 37
Task 2: Understand how to use percentages to describe change for quantitative information.
Percentages are often used to describe how a quantity changes with time. As an example,
suppose the population of a town was 10,000 in the 1980 census and 15,000 in the 2010 census.
We can express the change in population in two basic ways:
a. Because the population rose by the 5000 people (from 10,000 to 15,000), we say that
the absolute change in the population was 5000.
b. Because the increase of 5000 people was 50% of the starting population of 10,000, we
say that the relative change/percent increase in the population was 50%.
In general, calculations an absolute change or relative change always involves two
quantities: a starting number, or reference value, and a new value.
Absolute and Relative Change
The absolute change describes actual increase or decrease from a reference value to a new
value:
absolute change = new value − reference value
The relative change is the size of the absolute change in comparison to the reference value
and can be expressed as a percentage:
relative change =
new value − reference value
× 100%
reference value
Note we use the phrases “percent increase” or “percent decrease” to describe the
relative change when the absolute change is positive or negative, respectively.
Group work: Answer each of the following questions.
1. The price of a four-star meal, only $100 per couple decades ago, has since increased 200%.
The current price of a four-star meal is
a. $200
b. $300
c. $400
2. You currently earn $1000 per month, but you are expecting your earnings to rise 10% per
year. This means in that in five years you expect to be earning
a. Somewhat less than $1500 per month.
b. Exactly $1500 per month
c. Somewhat more than $1500 per month
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BAM Round 5 Activity H
Percent Increase/Decrease
Math 37
3. The price of a movie ticket increased from $10 to $12. This means that the new price is
a. 20% of the old price
b. 80% of the old price
c. 120% of the old price
4. Find the absolute change and the percent increase or percent decrease in the following
cases.
Case 1. The average sale price of a house in the United States decreased from $301,000 in
February 2008 to $152,000 in February 2013.
Case 2. The congressional delegation of California increased from 30 in 1950 to 53 in 2014.
Case 3. The number of daily newspapers in the United States was 2226 in 1900 and 1382 in
2011.
Case 4. Total revenue from music sales decreased from $14.6 billion to $5.5 billion between
2000 and 2014.
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BAM Round 5 Activity H
Juan Ortiz
Percent Increase/Decrease
Math 37
62
BAM Round 5
Appendix
Math 37
Appendix for Round 5
Hello fellow BAM student. This appendix contains bonus activities to help you on your journey
to master the fundamental math concepts that you will need to succeed in this course and
future math courses.
Number
1
2
3
4
5
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Label
Topics
Activity I An Introduction to Decmals
Activity J Converting Decimals to
Fractions I
Activity K Converting Decimals to
Fractions II
Activity L Percentages
Activity M Percent Proportions
Corresponding
modules
10.1
10.9
10.9
11.1-11.5
11.4-11.5
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BAM Round 5
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Appendix
Math 37
64
BAM Round 5 Activity I
An Introduction to Decimals
Math 37
Your Name:
IT ALWAYS SEEMS IMPOSSIBLE UNTIL IT’S DONE
TASK 1:
1. Complete the chart below, by either writing the words for the given number with decimal or
writing the number with decimal for the given words.
Decimal
Words
2.9
Two and nine tenths
1.3
Thirty-one and twenty-four hundredths
Seven and two hundred fifteen thousandths
125.521
Thirteen thousandths
1.0007
Sixty nine and sixty nine millionths
2. For this task, we would like you to determine which decimal value is greater. Please place in each
box below an inequality symbol: < or >.
3. Explain how you know this graph to be correct and true.
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BAM Round 5 Activity I
4.
An Introduction to Decimals
Math 37
Write the decimal equivalent of each square.
5. For the same figures above give the fraction which describes each shaded region. Do NOT
simplify.
a.
b.
c.
d.
e.
f.
g.
h.
For the following questions, give clear and complete sentences! Not mathematical expressions,
equations, fragment sentences, run-on sentences or nonsensical jumble of words and
splintered thoughts!
6.
Explain why 0.3 = “three tenths”?
3
10
7.
Explain why 0.3 
8.
Explain why 2.64 = “two and sixty-four hundredths”
9.
Explain why 17.385  17
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385
1000
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BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
Your Name:
IMPOSSIBLE ONLE MEANS YOU HAVEN’T FOUND THE SOLUTION YET…
TASK 1: Review
1) Why does 0.7 = seven-tenths?
2) How can we represent "seven-tenths" as a fraction?
0 .7 
3) How would you draw 0.7 of the square at the right?
4) Now fill in the table as best you can.
Decimal
0.7
In English
Seven-tenths
Fraction
7
10
Decimal = Fraction
0.7 
7
10
0.8
Four-tenths
0.12
Twenty three
hundredths
64
1000
One hundred
thousandths
One and one hundred
thousandths
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BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
Consider the mixed number 1.3
5) What is the Whole number part?
6) What is the decimal part?
7) How can we represent "one and three-tenths" as a fraction?
1.3 
____
____
8) How would you draw 1.3 of the square below?
9) Now Fill in the table as best you can.
Decimal
1.38
In English
One and thirty eight hundredths
Fraction
1
38
100
Decimal = Fraction
1.38  1
38
100
Fifty seven and three hundredths
2
73
100
-14. 03
185.056  185
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1000
68
BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
TASK 2: Recall the "Expanded Notation" of a number.
483 = 4(100) + 8(10) + 3(1) = 400 + 80 + 3
1. Write 6,719 in expanded form:
2. For the digits to the right of the decimal we can use a fraction to represent their place value. Fill
in the missing fractions below.
Place Value
Tenths
Fraction
1
10
Hundredths
Thousandths
Ten-thousandths
1
10,000
In general, to convert a decimal into a fraction, identify the place value of the very last digit behind
the decimal (or to the right of the decimal). This place value will equal the denominator. The
numerator is all the digits in the number.
Example: 0.847
=
847
1,000
(because, the last digit 7, is in the thousandths (
1
) place value, the denominator = 1,000
1,000
and all the digits in the number are 847, so the numerator = 847)
Example: 0.16 =
16
4

100 25
(because, the last digit 6, is in the hundredths (
1
) place value, the denominator = 100
100
and all the digits in the number are 16, so the numerator = 16), and we simplify the fraction.
We may also write numbers with decimals in expanded form using these fractional forms of their place
values.
3. Fill in the table as best you can
Decimal
Expanded notation
Expanded notation simplified
Decimal =Fraction
37
1
1
3
7
2.37
2.37 = 2
2(1) + 3( ) + 7(
)
2 +
+
100
10
100
10
100
0.54
1 + 3 + 
6
 3 
+ 

10
 100 
 
5.06 = 5
06
100
78.063
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BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
TASK 3: Graphical Representation of Deceimals
The following examples are graphical representations of decimal numbers in relation totheir fractional
equivalent.
Complete the following table.
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BAM Round 5 Activity J
Juan Ortiz
Converting Decimals to Fractions I
Math 37
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BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
TASK 4: Graphical Representation of The Thousandths
Shown at right is the thousandths square.There are a thousand
individual cells shown in this figure. Each cell is 1/1000th (one
thousandths) of the whole square.
Example:
To graphically represent
27
, we shade 27 of
1000
these thousandths.
27
 0.027
1000
1. Shade
327
in the square at right and express as a decimal.
1000
327

1000
2. Shade
250
in the square at right and express as a decimal.
1000
250

1000
3. Shade
5
in the square at right and express as a decimal.
1000
5

1000
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BAM Round 5 Activity J
Converting Decimals to Fractions I
Math 37
4. Shade the indicated amounts and express as decimals
Shade 1/10
1

10
Shade 10/100
10

100
Shade 100/1000
100

1000
5. What do you notice about the three shaded regions above?
6. Based on what you shaded above, what can you conclude about the three fractions?
7. To summarize:
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1
10
100
. Express this equivalence in decimals and in words.


10 100 1000
73
BAM Round 5 Activity K
Converting Decimals to Fractions II
Math 37
Your Name:
YOU GET WHAT YOU FOCUS ON. SO FOCUS ON WHAT YOU WANT.
1. Use the grids below to show that 0.7 = 0.70 = 0.700. Shade the equivalence in each square.
2. Express the equality in problem 1 in terms of fractions and words!
3. Fill in the blank cells
Decimal
2.37
Expanded notation
2(1) + 3(
1
1
) + 7(
)
10
100
Expanded notation
simplified
2 +
3
7
+
10
100
Decimal =Fraction
2.37 = 2
37
100
0.264
1
 1 
 + 2

 10 
 100 
3(10) + 2(1) + 8 
14.01 = 14
01
100
123.008
0.0003 =
0.0105
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BAM Round 5 Activity K
Converting Decimals to Fractions II
Math 37
4. Show your own equivalence in terms shaded regionsin a square, fractions, decimals, and words.
5. Fill in the blank cells
Decimal
0.7
In English
Seven-tenths
Fraction
7
10
Decimal = Fraction
0.7 
7
10
2 .3 
23
10
0.19
nine-tenths
0.45
Forty three tenths
17
1000
One hundred
hundredths
Ten thousandths
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BAM Round 5 Activity L
Percentages
Math 37
Your Name
EVERYTHING YOU NEED IS ALREADY INSIDE YOU
TASK 1: Fill in the boxes below to represent 142%
TASK 2: You take your family to Cirque Du Soliel for a special treat. The tickets cost $500.
a) What would be 50% of the cost of the tickets?
b) What would be 25% of the cost of the tickets?
c) What would be 10% of the cost of the tickets?
d) What would be 20% of the cost of the tickets?
e) If your sister offers to give you $160 estimate the percent she’s paying.
CHALLENGE: Find 12.5% of the cost of the tickets. Explain 2 different ways you can get
this number without a calculator.
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BAM Round 5 Activity L
Percentages
Math 37
TASK 3: Basketball Stats revisited…
Recall the chart below from #2 in our activity…but this time we’ve added a column for the
percentages. Add the percentages and answer the questions.
PLAYER
FIELD
FIELD
GOALS
GOALS
MADE
ATTEMPTED
Bryant
44
106
Iverson
66
162
Mutombo
33
55
O’Neal
63
110
VERBAL
FRACTION
DECIMAL
PERCENTAGE
(round to
thousandths)
44 out of
106
44
106
0.415
1. Who had the lowest percentage of completed field goals?
2. Who completed the highest percentage of field goals?
3. How does it compare with what you found in the activity?
TASK 4
1. Rewrite the following as their equivalent percentages.
a) 3.57
b) 0.412
c)
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7
12
2
d) 6 15
77
BAM Round 5 Activity L
Percentages
2. Rewrite the following percentages as decimals.
a) 13%
b) 7.5%
Math 37
c) 180%
3. Rewrite the following percentages as simplified fractions.
1
a) 80%
b) 235%
c) 333%
4. Fill in the chart…
VERBALLY
AS A FRACTION
AS A
DECIMAL
AS A PERCENT
16
45
7 out of 8
1.85
1
55 %
9
What observation can you make about the numbers in the third row compared to the other
numbers?
TASK 5
Use the numbers you found in the chart above to plot the percentages on the number line.
Also label the following on the number line above…
a) 200%
b) 150%
c) 75%
Juan Ortiz
d) 25%
78
BAM Round 5 Activity M
Proportions
Math 37
Your Name:
OBSTACLES DON’T BLOCK THE PATH, THEY ARE THE PATH
1. This type of percent diagram is used to help compare two numbers.
a) State in words the problem represented by this percent
diagram.
b) Write a proportion that is illustrated by the diagram and
solve it. How did you think about setting up the proportion?
2. Consider this question: What percent of 245 is 76?
a) Complete the percent diagram at right to represent
this question, by filling in the boxes.
b) Express the question as a proportion and solve it.
3. Now consider this question: What is 245% of 35?
a) Draw a percent diagram to represent this question
b) Express the question as a proportion and solve it.
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BAM Round 5 Activity M
Proportions
Math 37
4. A gardener planted 13% of his tulips in the border of his garden and the rest in the garden
bed, in spring, every one of the bulbs grew into a tulip. He counted 45 tulips in the border.
How many bulbs had he planted altogether? Show how you found your answer.
5. Of 75 flights leaving from Hartsfield airport in Atlanta, 33 went to the West Coast. What
percentage of the 75 flights went to the West Coast? Show how you found our answer.
6. The largest land animal, the African bush elephant, may weigh as much as 8 tons. However,
that is only 3.9% of the weight of the largest animal of all, the blue whale. How heavy can a
blue whale be? Show how you found your answer.
7.
Find four ratios equivalent to 80%
8.
Find four ratios equivalent to 340%
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