Treasury Yields Not LInear!

http://blogs.wsj.com/marketbeat/2011/06/30/treasury-yields-go-parabolic/#

Maybe parabolic or even exponential!!

SAT II Scores

An 800 is only 88th percentile for Level 2 as so many students who take it are very good Math students and are planning on pre-engineering, pre-med, etc types of majors.
780 is 98th percentile.

TEST DATE	TEST	SCORE
06/2011	SAT Subject Test
	Mathematics Level 1	780
	Mathematics Level 2	800

Check back on June 28 for your full score report, with detailed analysis! If you took the SAT Reasoning Test you'll also be able to view a copy of the actual essay you wrote.

June 2011 Brain Teaser Solution

When I divide it by 2, the remainder is 1. When I divide it by 3, the remainder is 2. When I divide it by 4, the remainder is 3. When I divide it by 5, the remainder is 4. When I divide it by 6, the remainder is 5. When I divide it by 7, the remainder is 6. When I divide it by 8, the remainder is 7. When I divide it by 9, the remainder is 8. When I divide it by 10, the remainder is 9. Find the smallest number that satisfies these conditions.

Since the remainder is always so close to the next multiple, the main idea is lowest common multiple so as George Polya, suggested solve a simpler problem.
Polya's Main Ideas in How to Solve It

Let's use just the first three criteria

When I divide it by 2, the remainder is 1.When I divide it by 3, the remainder is 2.When I divide it by 4, the remainder is 3. The number will be one less than the lowest common multiple of 2, 3 and 4 Counting by 2s 3s and 4s will yield 2 4 6 8 10 12 3 6 9 12 4 8 12  So 12 is the LCM -- notice that if we were to multiply 2 x 3 x 4, we would get 24 which is not the lowest common multiple.  The number is one less than this so 11 would be the number that satisfies all three criteria. With a longer list of numbers we might not want to write out all of the multiples.  In fact, for 2, 3 and 4, if we break them down to prime factors 2 is 2 and 3 is 3 but 4 is 2 x 2.  If we already have 2 and 3 we only need one more 2 to make a 4. So 2 x 3 x 2 will cover 2, 3, and 4 (2 x 2). So for all the way up to 10, we need the LCM of 2, 3, 4, 5, 6, 7, 8, 9, 10 For 2, 3, 4, 5 we need to add a 5 so 2 x 3 x 2 x 5 = 60 For 2, 3, 4, 5, 6, we already have a 6 because 2 x 3 = 6 so the LCM of 2, 3, 4, 5 ,6 is 60. For 2, 3, 4, 5, 6, 7 we need to add a 7 so 2 x 3 x 2 x 5 x 7 = 420 For 2, 3, 4, 5, 6, 7, 8, we need to add a 2 (8 is 2 x 2 x 2 and so far we only have two 2s) = 840 For 2, 3, 4, 5, 6, 7, 8, 9 we need to add a 3 (9 is 3 x 3 and so far we only have one 3) = 2520 For 2, 3, 4, 5, 6, 7, 8, 9 , 10 we already have a 10 because 2 x 5 = 10 so the LCM = 2520.

So the answer is 1 less than 2520: 2519

May 2011 Brain Teaser Solution

Q: Six men have 6 bags each. In every bag there are 6 cats, each cat has 6 kittens. How many legs in all? A: 6060 Each man has 6 bags with 6 cats each -- that's 36 cats. 36 cats x 6 kittens = 216 kittens Each bag has 252 cats (36 cats and 216 kittens): 252 x 4 legs = 1008 cat legs per bag 6 men each have 1008 cat legs = 6048 Plus the 6 men have 12 legs so the total is 6060.

Three Steps to Shoo Away Math Anxiety

http://www.good.is/post/could-math-anxiety-become-a-thing-of-the-past/

MATHCONFIDENCE 
Three Steps to Shoo Away Math Anxiety as a Thing of the Past:

First, call it “Increasing Math Confidence”

Second, solve Math problems (Math opportunities) including multiple choice as compare/contrast with “good wrong answers” can increase knowledge, skills, attitude and scores!

Third, embrace Math mistakes! Learning from errors can be challenging emotionally but will improve critical thinking, build confidence and expand educational and career options.

Robin Schwartz aka Robin the Math Lady
www.mathconfidence.com
Author, Build Math Confidence e-newsletter

Response to Darren Hardy's SUCCESS Blog

Jim Rohn’s Challenge to Succeed along with Darren’s Living Your Best Year Ever are cutting edge tools for all ages. Their messages of accountability and discipline are essential inputs for planning and achieving one’s goals. As an educator and a parent, I champion these ideas and principles and am delighted to see SUCCESS magazine in the mainstream!

Many college students do not have financial independence as a goal and a college education may not pay back for quite a long time (especially with student loans). As Jim Rohn says “If they’d offered Wealth 1 and Wealth 2, I would have taken both classes”. Math provides the foundation for processing and understanding personal finance and economic terms to increase savviness and savings while reducing debt.

Math teachers often hear “When I am ever going to use this Math?” which is not really a question but a complaint posed as a question. I have prepared my response with an acronym — MATH teaches Mental Fitness, Accountability, Teamwork and Horizon. And these principles learned in Math class (or on the baseball field or at church or on a job) are life skills that can be applied to the entire Wheel of Life.

http://darrenhardy.success.com/2011/05/helping-grads/

Response to Change the Equation's on Learning to Love Math

 Thank you for featuring this book -- "Learning to Love Math" by Dr. Judy Willis has an awesome subtitle "Teaching Strategies That Change Student Attitudes and Get Results".  How can Math teachers share their enthusiasm so that students will embrace the challenges and enjoyment of Math?  While this book emphasizes the utility of Math, Dr. Willis also points out ways and reasons for students to learn including convincing people that they can change their intelligence, supporting students in setting short-term and long-term goals and reducing mistake anxiety.  She also recommends teachers/parents sharing their own stories of learning including tales of endurance and fortitude.  

These ideas are especially important for girls as it is still not very cool to be good at Math.  Having a stronger Math background creates more career choices and boosts  confidence. – for example, engineering is a great career and solid foundation and is still only about 20% women (about the same as the 1980's when I was in engineering school!).  Best wishes to your daughter, Barbara!

This book was reviewed in Math Confidence's e-newsletter in December 2010:

 http://archive.constantcontact.com/fs086/1102574170134/archive/1103856670244.html

April 2011 Brain Teaser Solution

Joe buys a 5 foot long fishing pole but cannot take the bus home because the bus driver will not let him board the bus with anything over 4 feet long.  Joe goes to a hardware store and buys one thing then returns and boards the bus.  The pole can not be cut, bent, broken, or taken apart. What did Joe buy to allow him to board the bus with the fishing pole?


Joe bought a BOX!!  Since the maximum dimension can be 4 feet maximum, use the Pythagorean Theorem!!

a^2 + b^2 = c^2

Joe bought a box that was at least 3 feet by 3 feet by 4 feet -- the diagonal of the box will be 5 feet (the sides of the box and the fishing pole will form a 3,4,5 right triangle).

March 2011 Brain Teaser Solution

Julie travels from A to B at 2 minutes per mile and returns over the same route at 2 miles per minute.  Find her average speed, in miles per hour, for the entire trip.


She travels from A to B at 30 miles per hour (60 minutes for 30 miles = 2 minutes per mile).
She travels from B to A at 120 miles per hour (2 miles per minute for 60 minutes).


We can pick a distance that works well with both 30 and 120 such as 120 miles.


From A to B at 30 mph, it will take her 4 hours to go 120 miles.
From B to A at 120 mph, it will take her 1 hour to go 120 miles.


Total distance = 120 + 120 = 240 miles
Total time = 4 + 1 = 5 hours


Average speed = (Total distance)/ Total time = 240 miles / 5 hours = 48 mph

Get Smart! Take the SAT! Power Point

Get Smart! Take the SAT! Power Point

February 2011 Brain Teaser Solution

There are 8 similar balls. Seven of them weigh the same and the eighth is a bit heavier. How would you identify the heavier ball if you could use a two-pan balance scale only twice?

1. Put three balls on each side of the balance scale.  If they balance with one another, then all of these six are the same weight.
2. Take the last two balls and put them on the balance scale to find the heavier one.

OR


1. Put three balls on each side of the balance scale.  If they do not balance, take the three balls from the heavier side for the next step.

2. Pick two out of these three balls and put one on each side of the balance scale.  If they are different weights, you will find the heavier ball.  If they balance, then the heavier ball is the third ball.

What is the right order for high school Math classes? Washington Post

This is a response to Valerie Strauss' blog:
http://voices.washingtonpost.com/answer-sheet/math/high-school-math-whats-the-rig.html

Thanks for this article on order of Math courses. I am not sure what order they should be in -- it may depend on how the topics are divided up. A2 is usually more rigorous than the others but it can depend on the school/class/state.


It would benefit students to learn and know the Math on the ACT/SAT/GED/ACCUPLACER (placement tests used by colleges). Many students have not seen the topics enough times, or have had the topics slivered (and are unused to multiple topics on the same exam), or have not developed the speed that will help them problem solve 20 questions in 25 minutes.

While the Common Core are under development, we already have these standards at the high school and college level.

Studying multiple choice items can improve metacognition due to compare/contrast and by studying "good wrong answers" (for example, exponent rules questions always have "good wrong answers"!!).

Students, teachers and parents can use the free SAT Question of the Day (and other free or reasonably priced resources) to better scores and knowledge and skills!
http://sat.collegeboard.com/practice/sat-question-of-the-day

Perhaps, we can bring academic and cognitive abilities up to the level of respect that athletics commands.

Robin Schwartz
Author, Build Math Confidence e-newsletter
http://www.mathconfidence.com/

Posted by: mathconfidence
January 14, 2011 12:37 PM

January 2011 Brain Teaser Solution

Q: What is the largest number of consecutive integers that will add up to 2011?

A:  A good way to think about this problem is to do what Polya said "Solve a simpler problem"
So first think about  -- What is the largest number of consecutive integers that will add up to 11?

The least number of numbers would be one -- 11
You could use two consecutive numbers -- 5 and 6.
If you think about negative integers, -4, 3, -2, -1 would cancel out 1, 2, 3, and 4
so - 4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 would give a total of 11 numbers

But we can do even better

-10 would cancel out with 10
-9 would cancel out with 9 and so on

-10, -9, -8 , -7, -6, -5, - 4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 , 9, 10 would make zero if you sum them.
so just now add an 11
-10 thru -1 is 10 integers
0 is 1 integer
1 thru 10 is 10 integers and
11 is 1 integer for a total of 22.
(22 = 2 x 11)

so the number of integers is always 2 times the number itself.

For 2011,
The lowest number would be -2010 (it would cancel out with +2010)
The next number would be -2009 (it would cancel out with +2009)
The next number would be -2008 (it would cancel out with +2008)
and so on...
until -2 cancels out with +2
and -1 cancels out with +1

and then there is 0

so there would be 2010 negative numbers -2010 through -1
2010 postiive numbers 1 through 2010
plus 0
and also 2011
2010 negative integerss + 2010 positive integers + 2 more (for 0 and 2011)
for a total of 4022
4022 is the answer.

December 2010 Brain Teaser and Solution

Q: At a hardware store, I can buy 1 for $0.75 and I can buy 2761 for $3.00. What am I buying?

A: House numbers

November 2010 Brain Teaser Solution

Which is larger -- 8^98 or (8^99 - 8^98)?  (8^98 means "8 to the 98th power")

You can put this into a calculator and it will give you back scientific notation because both these numbers are REALLY BIG.

so 8^98 is about 3.12 x 10^88 (10 to the 88th power) but 8^99 - 8^98 is about 2.22 x 10^89 (10 to the 89th power) therefore 8^99 - 8^98 is larger.  But by how much?
Here is where the cool factoring comes in:
8^99 - 8^98 can be rewritten as: 8^98(8 - 1) making it 7 times bigger than 8^98.

Math is a Gatekeeper

October 2010 Brain Teaser Solution

Q: What is the greatest possible product of two positive whole numbers whose sum is 100?
A: 2500 (50 x 50)

Let x = one number then 100 - x = other number
So we want to maximize the product of this algebra, x(100 - x) = 100x - x^2
see the graph below:

This result can also be achieved through Calculus.  If we take the derivative of the algebra and set that equal to 0, then solve for x.
The derivative of 100x - x^2 is 100 - 2x, when 100 - 2x = 0 is solved x = 50.
When we substitute 50 into 100x - x^2, we get
100(50) - (50)^2

5000 - 2500 = 2500
So the maximum point is at x = 50 -- at the (x,y) point (50, 2500).
The list below shows:
Column 1 first number
Column 2 100 - first number
Column 3 product of Column 1 and Column 2

1 99 99

2 98 196

3 97 291

4 96 384

5 95 475

6 94 564

7 93 651

8 92 736

9 91 819

10 90 900

11 89 979

12 88 1056

13 87 1131

14 86 1204

15 85 1275

16 84 1344

17 83 1411

18 82 1476

19 81 1539

20 80 1600

21 79 1659

22 78 1716

23 77 1771

24 76 1824

25 75 1875

26 74 1924

27 73 1971

28 72 2016

29 71 2059

30 70 2100

31 69 2139

32 68 2176

33 67 2211

34 66 2244

35 65 2275

36 64 2304

37 63 2331

38 62 2356

39 61 2379

40 60 2400

41 59 2419

42 58 2436

43 57 2451

44 56 2464

45 55 2475

46 54 2484

47 53 2491

48 52 2496

49 51 2499

50 50 2500

51 49 2499

52 48 2496

53 47 2491

54 46 2484

55 45 2475

56 44 2464

57 43 2451

58 42 2436

59 41 2419

60 40 2400

61 39 2379

62 38 2356

63 37 2331

64 36 2304

65 35 2275

66 34 2244

67 33 2211

68 32 2176

69 31 2139

70 30 2100

71 29 2059

72 28 2016

73 27 1971

74 26 1924

75 25 1875

76 24 1824

77 23 1771

78 22 1716

79 21 1659

80 20 1600

81 19 1539

82 18 1476

83 17 1411

84 16 1344

85 15 1275

86 14 1204

87 13 1131

88 12 1056

89 11 979

90 10 900

91 9 819

92 8 736

93 7 651

94 6 564

95 5 475

96 4 384

97 3 291

98 2 196

99 1 99

100 0 0

24 x 12

The huge Excel handbook had been my intense focus as a potential deskside banker support person.
 
On a third round at a big investment bank, a banker asked "What's 24 x 12?"
I said "288" He asked me how -- "12 x 12 doubled is 24 12s" = 288
He responded 24 x 10 + 24 x 2 = 240 + 48 = 288

I then said 24 x 24 = 576 -- take half of this (12 24s)which is 288

Both of us were at least 30, so I then said:
 "If you remember your high school algebra -- 24 and 12 are both 6 from 18 so you can write 24 x 12 as (18 + 6)(18-6) and when you FOIL that  it becomes 18^2 + 6(18) - 6(18) - 6^2. which is 324 - 36 = 288!"

I got the job!

September 2010 Brain Teaser Solution

When writing the whole numbers from 1 to 20, there are 12 1s (one in 1, 10, 12, 13, 14, 15, 16, 17, 18 and 19 and two in 11).  When writing the whole numbers from 1 to 1000, how many 1s will you write?

1- 99           20
100 - 199  120
200 - 299    20
300 - 399    20
400 - 499    20
500 - 599    20
600 - 699    20
700 - 799    20
800 - 899    20
900 - 999    20
1000              1

Total          301    

There are 12 1's from 1- 20

then 21, 31, 41, 51, 61, 71, 81, and 91

From 1 - 99, you will write a total of 20 ones

The same is true for 200 - 299, 300 - 399, 400 - 499, 500-599, 600 - 699, 700 - 799, 800 - 899, and 900-999. So from 200 - 999, there are a total of 160 ones (8 x 20)

From 100 - 199,

there are 20 ones in the second and/or third digit:

101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 131, 141, 151, 161, 171, 181, 191

plus all the ones that begin every number from 100 - 199 inclusive: 100

"H" is for Horizon