BSI Workshop:
Reading/English/Math
PERCENTAGES IN OTHER DISCIPLINES
"Come, Watson, come! The game is afoot. Not a word! Into your clothes and come!"
BSI Workshop:
Mathematics
PROBLEM SOLVING INVOLVING PERCENTAGES
BSI Workshop:
Mathematics
WHO ARE THE 99%, 37%, 12%, 0.2%?
http://www.youtube.com/watch?feature=player_profilepage&v=k8AkjWQ3P-M
BSI Workshop:
Mathematics
THE STUDY OF PERCENT STARTS WITH FRACTIONS.
BSI Workshop:
Mathematics
Divide region A into
two identical sections.
BSI Workshop:
Mathematics
Did you make the
following division?
BSI Workshop:
Mathematics
Divide region B into
three identical sections.
BSI Workshop:
Mathematics
Did you make the
following division?
BSI Workshop:
Mathematics
Divide region C into
four identical sections.
BSI Workshop:
Mathematics
That wasn’t so bad.
BSI Workshop:
Mathematics
Divide region D into
seven identical sections.
BSI Workshop:
Mathematics
Was your brain on
overdrive?
BSI Workshop:
Mathematics
PEOPLE ARE DIFFERENT, BUT
SHARE COMMON FEARS.
BSI Workshop:
Mathematics
FOR ME, IT IS SCARY NURSES.
BSI Workshop:
Mathematics
FOR MANY STUDENTS, IT IS MATH
and more often
than not, we
just see the
RESULTS.
BSI Workshop:
Mathematics
LET’S ADDRESS BOTH FEARS.
SYRINGES COME IN DIFFERENT SIZES.
BSI Workshop:
Mathematics
Find ¾ of 80.
THE BASIC IDEA BEHIND
FINDING A FRACTIONAL
PART OF A QUANTITY IS :
1)
FIRST FIND ¼ OF
THE QUANTITY.
2) THEN MULTIPLY
BY 3.
BSI Workshop:
Mathematics
Find 5/4 of 80.
THE CONCEPT REMAINS
UNCHANGED EVEN IF THE
FRACTION IS IMPROPER :
BSI Workshop:
Mathematics
WHAT IS 92% OF 50?
A SYRINGE CONTAINS 50 ML OF
MEDICATION OF WHICH 92% IS SALINE.
HOW MUCH SALINE SOLUTION IS IN THE SYRINGE?
AS DETERMINED BY THE
TECHNO-SAVY STUDENT.
Percent x Whole = Portion; so
0.92 x 50 = Portion (saline solution)
and
0.92 x 50 = 46 ml of saline solution.
BSI Workshop:
Mathematics
MATHEMATICAL
SYRINGES
IN MATH, ALL
SYRINGES ARE
PROPORTIONAL.
BSI Workshop:
Mathematics
WHAT IS 92% OF 50?
A SYRINGE CONTAINS 50 ML OF
MEDICATION OF WHICH 92% IS SALINE.
HOW MUCH SALINE SOLUTION IS IN THE SYRINGE?
AS DETERMINED BY
MATHEMATICAL UNIFORMITY.
The two are proportional.
If the unknown, N,
represents the amount of
saline solution, then
46 ml of saline solution
BSI Workshop:
SADLY,
Mathematics
CHARLIE BROWN
U N D E R S T A ND S P R O P O R T I O N S .
BSI Workshop:
Mathematics
WHAT IS 92% OF 50?
ALL THINGS ARE NOT CREATED EQUAL.
BSI Workshop:
Mathematics
WHAT IS 92% OF 50?
A SYRINGE CONTAINS 50 ML OF
MEDICATION OF WHICH 92% IS SALINE.
HOW MUCH SALINE SOLUTION IS IN THE SYRINGE?
AS DETERMINED BY THE LOGICAL
VISUALISTS.
The left side is divided in
100 sections; so divide the
right side into 100 sections
or 0.50 each, consider 92
sections, totaling 0.50 x 92
equals 46 ml of saline
solution.
BSI Workshop:
Mathematics
48 IS WHAT % OF 60?
A SYRINGE CONTAINS 60 ML OF
MEDICATION OF WHICH 48 ML IS SALINE.
WHAT PERCENT OF THE SYRINGE IS THE SALINE
SOLUTION?
AS DETERMINED BY THE
TECHNO-SAVY STUDENT.
Percent x Whole = Portion; so
Percent = Portion ÷ Whole
Percent = 48 ÷ 60 = 0.80 = 80%.
BSI Workshop:
Mathematics
48 IS WHAT % OF 60?
A SYRINGE CONTAINS 60 ML OF
MEDICATION OF WHICH 48 ML IS SALINE.
WHAT % OF THE SYRINGE IS SALINE SOLUTION?
AS DETERMINED BY
MATHEMATICAL UNIFORMITY.
If N represents the
percentage of saline
solution, then
80% saline solution
BSI Workshop:
Mathematics
48 IS WHAT % OF 60?
A SYRINGE CONTAINS 60 ML OF
MEDICATION OF WHICH 48 ML IS SALINE.
WHAT % OF THE SYRINGE IS
SALINE SOLUTION?
AS DETERMINED
BY THE LOGICAL
VISUALISTS.
The right side is divided in
60 sections; so divide the
left side into 60 sections of
5/3 each, consider 48
sections, totaling 48 x 5/3
or 80% saline solution.
BSI Workshop:
Mathematics
96% OF WHAT QUANTITY IS 60?
A SYRINGE CONTAINS 60 ML OF SALINE
SOLUTION WHICH REPRESENTS 96%
OF THE MEDICATION.
HOW MUCH TOTAL MEDICATION WAS CONTAINED
IN THE SYRINGE?
AS DETERMINED BY THE
TECHNO-SAVY STUDENT.
Percent x Whole = Portion; so
0.96 x Whole = 60, and
Whole Amount = 60 ÷ 0.96
= 62.5 ml of medication.
BSI Workshop:
Mathematics
96% OF WHAT QUANTITY IS 60?
A SYRINGE CONTAINS 60 ML OF SALINE
SOLUTION WHICH REPRESENTS 96%
OF THE MEDICATION.
HOW MUCH TOTAL MEDICATION WAS CONTAINED
IN THE SYRINGE?
AS DETERMINED BY
MATHEMATICAL UNIFORMITY.
If N represents the amount
of total medication in the
syringe, then
62.5 ml of solution.
BSI Workshop:
Mathematics
96% OF WHAT QUANTITY IS 60?
A SYRINGE CONTAINS 60 ML OF SALINE
SOLUTION WHICH REPRESENTS 96% OF
THE MEDICATION.
AS DETERMINED BY THE LOGICAL
VISUALISTS.
The left side is divided in
96 sections; so divide the
right side into 96 sections
of 60/96 = 5/8 each. Now
consider 100 such sections
100 x 5/8 or 62.5 ml of
medication
BSI Workshop:
Mathematics
TECHNO-SAVY STUDENTS ARE SUCCESSFUL
IF THEY HAVE NUMBER SENSE.
BSI Workshop:
Mathematics
NUMBER SENSE IS ALSO A COMMON TRAIT
OF SUCCESSFUL STUDENTS WHO VALUE
MATHEMATICAL UNIFORMITY.
BSI Workshop:
Mathematics
LOGICAL VISUALISTS HAVE NUMBER
SENSE BUT LIVE IN A WORLD FOCUSED
ON AUDITORY SEQUENTIAL LEARNERS.
BSI Workshop:
Mathematics
PERCENTAGES ARE A MATTER OF
SCALING AND NOT COMPARING.
A QUANTITY IS 100% OF ITSELF.
STILL, WE HAVE TO RECOGNIZE DIFFERENT LEARNING STYLES.
BSI Workshop:
Mathematics
ADDRESSING BASIC SKILLS AND DEMANDING
ANALYSIS AND CRITICAL THINKING WHILE
PROVIDING SUPPORT IS NEEDED.
Entrepreneurs are resourceful, but …
there is no shortcut for “hard work.”
BSI Workshop:
Mathematics
MATHEMATICAL TIME CHECK
ANY REQUESTS?
BSI Workshop:
Mathematics
PROBLEM SOLVING W/MATHEMATICAL REASONING
A BASIC PERCENT PROBLEM
#1
There are 20 workers in the library. 55% of them were males. How many fewer
females than males worked in the library?
BSI Workshop:
Mathematics
MATHEMATICAL REASONING
APPLIED TO
READING/ENGLISH
AS STATED, THE CHOICE OF
SHERLOCK HOLMES WAS NOT
A COINCIDENCE.
WHAT WAS HIS 7% SOLUTION?
IT IS NOT MY PLACE TO SPOIL
A GOOD READ.
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN RETAIL FLORISTRY
#2
Fifteen floral displays were to be created of which 12% of the flowers were red roses.
Additional displays were requested. The designer wants to reduce the percentage of roses
to only 7% by adding other types of flowers and redistribute the roses. How many
additional flowers much be added to reduce the percentage of roses?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN CHEMISTRY
#3
How much of a 6% solution of an alcohol and water mixture must be added to
20 ml of a 10% alcohol mixture to reduce the percentage of alcohol to 7%?
BSI Workshop:
Mathematics
PROBLEM SOLVING W/MATHEMATICAL REASONING IN ART
IT’S BEEN CALLED “THE
GOLDEN RATIO” OR
“DIVINE PROPORTION”
BSI Workshop:
Mathematics
PROBLEM SOLVING W/MATHEMATICAL REASONING IN ART
IT IS “APPROXIMATED” BY RECTANGLES
WHOSE SIDES ARE FIBONACCI NUMBERS.
#4
WHAT WOULD BE AN APPROXIMATE
OF THE DIVINE PROPORTION OR
GOLDEN RATIO AS A PERCENTAGE?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN BIOLOGY
#5
Mary determined that the population of monarch butterflies
at a particular site was 12,000. She estimated that next year
there would be a 6% increase. What would be the estimated
population of monarch butterflies next year?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN PHYSICS
#6
With a 12% increase in velocity, it is now 68
miles per hour. What was the initial velocity?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN SCIENCE, ENGINEERING, AND MATH
#7
A rectangular container, 15 cm long and 10
cm wide, contains water to a depth of 4 cm.
When a stone of volume 300 cm3 is put in,
the water level rises. What was the percent
increase in height?
(First find the height of the new water level
by assuming that the stone is completely
under water.)
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN BUSINESS
#8
A shopkeeper had 4
handbags which were of
the same cost price. He
sold 3 of them at 40%
more than the cost
price. He sold the
fourth handbag at cost
price. He received a
total of $260 altogether.
Find the cost price of
each handbag.
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN ECONOMICS
#9
Sally is given $5 more
allowance than Megan each
week. They each spend $12
per week and save the rest.
When Sally has saved $60,
Megan saved $20. What
percent of Sally’s allowance
did she spend each week?
First find out Sally’s
allowance.
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN POLITICAL SCIENCE
#10
Ali had $130 and his brother had $45. When their mother gave each of them
an equal amount of money, Ali had twice as much as his brother. What
percent of Ali’s total was her mom’s contribution? (First find out the amount
of contribution made by her mother.)
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN ENGLISH AS A SECOND LANGUAGE
#11
Read and underline each key word. Draw the illustration of the relationship
of the given information, then set out a plan to solve the problem.
Fred could not divide the amount of money in his pocket
equally among his 4 kids. His wife gave him an additional
$3 after which each of his 4 kids received $8. What percent
was his wife contribution?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN HOSPITALITY MANAGAGEMENT
#12
To plan for next month’s
expenses, a restaurateur
estimated that he would need
a 5% increase from this month
cost. Foods cost this month
was $12,800 while the
beverage costs was 30% of the
food costs. What is the
estimated cost for both food
and beverage next month?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN CHILD DEVELOPMENT
#13
According to NIMI, what was the percentage of children affected
by autism in 2006?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN ACCOUNTING
#14
The Excel spreadsheet did not balance!!! Well, it did, but I am not balanced;
that is, it did not match my total of $306.74. What was my percent error?
Expense A
Expense B
Expense C
Expense D
Expense E
$
$
$
$
$
43.20
25.72
142.13
215.50
11.65
Total
$
438.20
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN NUTRITIONAL SCIENCE
#15
Add up the
percentages on the
right side of the
can. If the total is
NOT 100%, explain
why ?
BSI Workshop:
Mathematics
BASIC PROBLEM SOLVING W/MATHEMATICAL REASONING
PERCENT PROBLEMS IN PHILOSOPHY
#16
I walked up a mountain to ask my guru, “What’s the meaning of life?” I had
to trek 4 days in snow and rain, dealing with shivering nights and poor
terrain. When I got to the top, he was there with the answer. To get the
answer, please solve this problem.
I started up the mountain at an
elevation of 65 feet and reach
my teacher sitting at 10, 432
feet above sea level. If on my
last day before reaching the
top, I climbed 1244 feet,
approximately what percent of
the elevation was done on the
last day?
MATHEMATICAL REASONING CONTINUES
BUT, BYE FOR NOW,
Presented by Karl Ting, Department of Mathematics
March 15, 2013
Basil Rathbone and Nigel Bruce
Peter Cushing and Nigel Stock
Jeremy Brett and Edward Hardwicke
Christopher Lee and Patrick MacNee
Christopher Plummer and James Mason
Nicol Williamson and Robert Duvall
Michael Caine and Ben Kingsley
Benedict Cumberbatch and Martin Freeman
Robert Downey Jr. and Jude Law
Jonny Lee Miller and Lucy Liu
"Come, Watson, come! The game is afoot. Not a word! Into your clothes and come!“ Who are we?
We first see the famous phrase in the Canon in
"The Adventure of the Abbey Grange" when
Holmes tells Watson: "Come, Watson, come! The
game is afoot. Not a word! Into your clothes and
come!" The word "game" has two meanings. One is
"quarry" or "spoils," and it would be the main
meaning in Shakespeare's and Holmes' words.
However, the other meaning of "game" is, "a
diversion, pastime, or amusement; or a form of
mental or physical competitive play, governed by
specific rules and testing the skill, endurance, or
luck of the participants."