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### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

### BSI Workshop: Mathematics

Reading/English/Math

Percentages in other disciplines

"Come, Watson, come! The game is afoot. Not a word! Into your clothes and come!"

Problem solving involving percentages

Who are the 99%, 37%, 12%, 0.2%?

http://www.youtube.com/watch?feature=player_profilepage&v=k8AkjWQ3P-M

The study of percent starts with fractions.

Divide region A into two identical sections.

Did you make the following division?

Divide region B into three identical sections.

Did you make the following division?

Divide region C into four identical sections.

That wasn’t so bad.

Divide region D into seven identical sections.

Was your brain on overdrive?

People are different, but share common fears.

For me, it is scary nurses.

For many students, it is math

and more often than not, we just see the RESULTS.

Find ¾ of 80.

The basic idea behind finding a fractional part of a quantity is :

First find ¼ of the quantity.

Then multiply by 3.

Find 5/4 of 80.

The concept remains unchanged even if the fraction is improper :

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 = 46mlof saline solution.

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

46mlof saline solution

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.

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%.

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

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.

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

= 62.5mlof medication.

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.

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

Techno-savy students are successful if they have number sense.

number sense is also a common trait of successful students who value mathematical uniformity.

Logical visualists have number sense but live in a world focused on auditory sequential learners.

A quantity is 100% of itself.

Percentages are a matter of scaling and not comparing.

Still, We have to recognize different learning styles.

Entrepreneurs are resourceful, but …

Addressing basic skills and demanding analysis and critical thinking while providing support is needed.

there is no shortcut for “hard work.”

#1

There are 20 workers in the library. 55% of them were males. How many fewer females than males worked in the library?

problem solving w/mathematical reasoning

A basic Percent problem

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.

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?

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%?

It’s been called “the golden ratio” or “divine proportion”

problem solving w/mathematical reasoning in art

It is “approximated” by rectangles whose sides are fibonacci numbers.

#4

problem solving w/mathematical reasoning in art

What would be an approximate of the divine proportion or golden ratio as a percentage?

#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?

Basic problem solving w/mathematical reasoning

Percent problems in biology

#6

With a 12% increase in velocity, it is now 68 miles per hour. What was the initial velocity?

Basic problem solving w/mathematical reasoning

Percent problems in physics

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.)

#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.

Basic problem solving w/mathematical reasoning

Percent problems in business

#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.

Basic problem solving w/mathematical reasoning

Percent problems in economics

#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.)

Basic problem solving w/mathematical reasoning

Percent problems in political science

#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.

Basic problem solving w/mathematical reasoning

Percent problems in english as a second language

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?

#12

Basic problem solving w/mathematical reasoning

Percent problems in Hospitality managagement

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?

#13

Basic problem solving w/mathematical reasoning

Percent problems in child development

According to NIMI, what was the percentage of children affected by autism in 2006?

#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?

Basic problem solving w/mathematical reasoning

Percent problems in accounting

#15

Add up the percentages on the right side of the can. If the total is NOT 100%, explain why ?

Basic problem solving w/mathematical reasoning

Percent problems in Nutritional science

#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.

Basic problem solving w/mathematical reasoning

Percent problems in philosophy

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."

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