# ANSWERS FOR POP QUIZ! OK, All You Parents & Mature Types – If The Kids Can’t Do These Math Problems, Show Them How Good You Are! If You Can Do 1, All 10 Or Any Number In Between, Comment Below Showing Your Computations. I Will Publish Your Work Unless You Indicate ‘Do Not Publish’ – Let The Neighbors Know How Smart You Are! Ready, Set, GO! – Answers Will Be Published In Due Course! Published 11/06/13 – Back Dated 09/06/13 To Follow Pop Quiz, Published 09/07/13

For These Problems

GO TO:

http://wyandanch.t-a-b-a-c-c-o.org/?p=789

These are the Answers to the Pop Quiz:

1 – Series: 1, 4, 9, 16, 25, Next Number is ?

What kind of Series is this?

Answer: You should recognize that those numbers above in Series are perfect squares:

12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25

Therefore the Next Number is: 62 = 36

Another technique is with differences:

1

> (4-1 =       3)

4

> (9-4 =       5)

9

> (16-9 = 7)

16

> (25-16 = 9)

25

11 must be the difference between 25 and Next Number since the differences between each number in the series increases by 2, which therefore must be 36

2 – Is 111,111,111 evenly divisible by 9? If so, why?

Answer: Any number divisible by 9 reduces to 9 or a multiple of 9 when digits are added together. Thus 9 ones (as above) = 9. Therefore the number is divisible by 9 and the quotient is       12,345,679

3 – Series: 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, Next Number is ?

What is the name of this Series?

Answer: The Series above is composed of Prime Numbers, which are only divisible by themselves and 1 evenly. Note 2 is the only Even Prime since all other Even numbers are divisible by 2 and cannot be Primes.

The Next Prime Number is 29

25 = 52 and 27 = 33, so neither 25 nor 27 is a Prime Number

4 – The Applicable Term is 2n-1 where n is ALL INTEGERS between 1 and (Infinity)! That is stated as

Write the 1st 6 Numbers in this Set beginning with n = 1 and ending with n = 6.

What is the Name of this Set?

Answer: 2×1 – 1 = 1

2×2  – 1 = 3

2×3  – 1 = 5

2×4  – 1 = 7

2×5  – 1 = 9

2×6  – 1 = 11

Therefore the six numbers in this set are

1, 3, 5, 7, 9, 11

The Set is Odd Numbers or Odd Integers

5 – Series: 1, 8, 27, 64, 125, Next Number is ?

What kind of Series is this?

216!

The Series is n3 or 1x1x1, 2x2x2, 3x3x3, 4x4x4, 5x5x5 and 6x6x6.

6 – Question: If I give you a choice between

(A)      Receiving during the next 31 day month 1-cent on day 1, 2-cents on day 2, 4-cents on day 3, and continuing to double the previous amount each day until Day 31 –

AND

(B)      Receiving \$100.00 today,

Which Option would you take, (A) or (B)?

Answer: Take (A) unless you hate fortunes and are daft!

1 – \$.01

2 – \$.02

3 – \$.04

4 – \$.08

5 – \$.16

6 – \$.32

7 – \$.64

8 – \$1.28

9 – \$2.56

10 – \$5.12

11 – \$10.24

12 – \$20.48

13 – \$40.96

14 – \$81.92

15 – \$163.84 (On Day 15 you already passed \$100.00 for a Single Day! Those, who picked \$100.00 or Option (A) – and you know who you are – are ashamed of yourselves, aren’t you!)

16 – \$327.68

17 – \$655.36

18 – \$1,310.72

19 – \$2,621.44

20 – \$5,242.88

21 – \$10,485.76

22 – \$20,971.52

23 – \$41,943.04

24 – \$83,886.08

25 – \$167,772.16

26 – \$335,544.32

27 – \$671,088.64

28 – \$1,342,177.28

29 – \$2,684,354.56

30 – \$5,368,709.12

31 – \$10,737,418.24

This is known as another ‘Geometric Progression’.

To get the sum of your newfound wealth, add all 31 totals up, and you, who selected Option (B), have joined the MILLIONAIRES’ CLUB!

That’s the process that created you too. Remember we all began from a single cell, which divided into 2, into 4, into 8 and so on and so on! A Regular Progression such as 1, 2, 3, 4, 5, 6 etc. would have taken you centuries of decades to be born, not just a paltry 9 months!

To all you mothers out there – I guess you’re glad now for Geometric Progressions!

http://en.wikipedia.org/wiki/Geometric_progression

———————————————————————–

The following is NOT a Problem for you, but I thought you ought to see it. This is how the value of pi can be determined mathematically:

———————————————————————-

From here on, the Problems get more difficult!

(The following Problem “ain’t” what it looks like; so be very careful!)

7 – Series: 1, 10, 11, 100, 101, 110, 111, 1000, Next Number is ?

What type of Series is this? Write this Number in words as well as numbers!

(Side Note: A young lady, working at Radio Shack in Sunset Plaza, got it right on her first try.)

Whenever you see Numbers containing only 1s and 0s, you should automatically consider Binary, NOT Decimals!

In Decimals, this sequence makes no sense! It is Binary.

In Decimals, the 1st number, starting from the one’s column, represents 100 x the digit. 100 = 1

Any Number n0 = 1. Therefore in Binary, 20 = 1

In Decimals, the 2nd number from the right represents 101 x the digit. 101 = 10

In Binary 21 = 2

Therefore in Decimals 25 = 2×10 + 5×1

In Binary 11 = 1×2 + 1×1 = 3 (In Decimals)

1             – 1

2             – 10

3             – 11

4             – 100

5             – 101

6             – 110

7             – 111

8             – 1000

9             – 1001

Written in Decimals, the number is “nine”,

But the Answer in BINARY is 1001!

8 – Series: 1 + 3 + 5 + 7 + 9 + 11 = n2

What is n? Which other Problem does this relate to?

Answer: n = 6 because there are 6 terms in Series

1 + 3 + 5 + 7 + 9 + 11 = n2 = 36 = 62

See Problem 4 above and Problem 1 (the differences, not the Series)

The Generalization of this Series is

It can be solved for any finite range beginning with 1. The number of terms in that finite Series = n.

This is a Summation Series.

http://en.wikipedia.org/wiki/Series_%28mathematics%29

9 – Quadratic Roots Proof: If aX2 + bX + c = 0

Where a, b & c are all Constants, then Prove that the Equation –

Is Valid in determining the Values for X in any 2nd Degree Polynomial Equation.

Solution:

10 – A Novelty Store purchases 100 toy animals and sells them for \$100.00. It sells toy cows \$5.00 each, toy horses \$1.00 each and toy sheep \$.05 each. How many of each toy animal did the Novelty Store have initially?

(Note: There is an Extraneous Solution, which does not apply: ‘100 \$1.00 Toy Horses’, which does yield 100 toy animals at \$100.00. But that Extraneous Solution excludes toy cows and toy sheep, so it is NOT our Solution)

Despite being a very tricky Problem, there are several ways to solve it.

Method I: This Problem has 3 Unknowns, but only 2 Equations. That is the PROBLEM! However, we can reduce it to a Series of 4 Problems and thereby find which of the 4 solves our Problem.

Let X = number of sheep

Y = number of horses

Z = number of cows

Therefore, using plain numbers instead of dollar signs, we have the 2 Principal Equations:

X + Y + Z = 100 and

5X + 100Y + 500Z = 10000 (\$ suppressed for convenience)

Because sheep are 5-cents each, the total must be a multiple of 20 or you will not achieve \$100.00. Therefore X must be 20, 40, 60 or 80. It cannot be 0 or 100.

(A)      X = 20 and substituting into our 2 Principal Equations

20 + Y + Z = 100 and

100 + 100Y + 500 Z = 10000

From 1st Principal Equation we have Y = 80 – Z, and substituting, we get

100 + 100x(80-Z) + 500Z = 10000

8000 – 100Z + 500Z = 9900

400Z = 1900 or

Z = 19/4, which is not an Integer and Incorrect

(B)      X = 40 and substituting into our 2 Principal Equations

40 + Y + Z = 100 and

200 + 100Y + 500Z = 10000

From 1st Principal Equation we have Y = 60 – Z, and substituting, we get

200 + 100x(60-Z) + 500Z = 10000

6000 – 100Z + 500Z = 9800

400Z = 3800 or

Z = 19/2, which is not an Integer and Incorrect

(C)      X = 60 and substituting into our 2 Principal Equations

60 + Y + Z = 100 and

300 +100Y + 500Z = 10000

From 1st Principal Equation we have Y = 40 – Z, and substituting, we get

300 + 100x(40-Z) + 500Z = 10000

4000 – 100Z + 500Z = 9700

400Z = 5700 or

Z = 57/4, which is not an Integer and Incorrect

(A)      (D) X = 80 and substituting into our 2 Principal Equations

80 + Y + Z = 100 and

400 + 100Y + 500Z = 10000

From 1st Principal Equation we have Y = 20 – Z, and substituting, we get

400 + 100x(20-Z) + 500Z = 10000

2000 -100Z + 500Z = 9600

400Z = 7600 or

Z = 19, which IS an Integer and CORRECT!

Since Y = 20 –Z, Y= 1

And X = 80

Answer is 80 sheep, 1 horse and 19 cows!

Method 2: THE DEDUCTIVE METHOD

I have found an alternative method, which involves a more cerebral technique requiring you to think it out.

For the sake of argument, let’s just say that Y = 3 (number of toy horses).

If that is so, then X + Z must equal 97. From the original parameters, we know that if this is true,

X * \$5 + Z * \$.05 must also equal \$97.00 since

Y(3) * \$1 = \$3.

Therefore,

X + Y + Z = 100 and

X * \$5 + Y * \$1 + Z * \$.05 = \$100

And here is where it gets cerebral:

Equation A: (X + Z) * \$1 = X * \$5 + Z * \$.05

Because Y * \$1 = \$Y since (X + Y + Z) * \$1 = \$100

Multiplying both sides of Equation A by 20 to get rid of the \$.05 consideration:

20 (X + Z) * \$1 = 20X * \$5 + 20Z * \$.05, or

X * \$20 + Z * \$20 = X * \$100 + Z * \$1, simplifying

Z * \$19 = X * \$80

The only way this could be true is if

Z = 80 and X = 19

Therefore Y = 1

Q.E.D.

TABACCO: Now, Readers, ask yourselves if our Wyandanch B.O.E. is preparing our Students to SOLVE PROBLEMS SUCH AS THOSE ABOVE!

Then ask yourselves if merely Hiring their Friends and Family & Firing their Enemies will achieve that goal and how!

If we want our Students to LEARN, which is measured by the State Tests, then we MUST CHALLENGE our Students in the CLASSROOM and with HOMEWORK.

MEMO TO OUR B.O.E.:

No Amount of

PATRONAGE & NEPOTISM will EVER EDUCATE A SINGLE STUDENT!

PS Board Members like Charlie Reed are so fond of promoting DANCING, MUSIC, BASKETBALL & CHEERLEADING! These “studies” lead to Entertainment for folks like Charlie Reed. We all know how Charlie Reed loves to be entertained!

All these are fine endeavors, but Educating our Students MUST come FIRST!

Sorry, Charlie, but Math, Science, History, Social Studies & Languages don’t lend themselves very well for your Entertainment!

Despite what our B.O.E. does with its Time, B.O.E. does NOT mean

“Board Of Employment”,

nor “Board Of Entertainment’.

B.O.E. stands for

BOARD OF EDUCATION!

Did you get that, Charlie!

‘COMMON CORE’

WORSHIPERS!

(More Bush-like Testing Emphasis!)

# A ridiculous Common Core test for first graders

###### ·       October 31 at 4:00 pm

·

·       Why are some kids crying when they do homework these days? Here’s why, from award-winning Principal Carol Burris of South Side High School in New York. Burris has for more than a year chronicled on this blog the many problems with the test-driven reform in New York (here, and here and here and here, for example). She was named New York’s 2013 High School Principal of the Year by the School Administrators Association of New York and the National Association of Secondary School Principals, and in 2010, tapped as the 2010 New York State Outstanding Educator by the School Administrators Association of New York State. She is the co-author of the New York Principals letter of concern regarding the evaluation of teachers by student test scores. It has been signed by more than 1,535 New York principals and more than 6,500 teachers, parents, professors, administrators and citizens. You can read the letter by clicking here.

·       By Carol Burris

·       My speech teacher came to see me.  She was both angry and distraught.  In her hand was her 6-year-old’s math test.  On the top of it was written, “Topic 2, 45%”. On the bottom, were the words, “Copyright @ Pearson Education.”   After I got over my horror that a first-grader would take a multiple-choice test with a percent-based grade, I started to look at the questions.

·       The test provides insight into why New York State parents are up in arms about testing and the Common Core. With mom’s permission, I posted the test here.  Take a look at question No. 1, which shows students five pennies, under which it says “part I know,” and then a full coffee cup labeled with a “6″ and, under it, the word, “Whole.” Students are asked to find “the missing part” from a list of four numbers. My assistant principal for mathematics was not sure what the question was asking.  How could pennies be a part of a cup?

·       Then there is Question No. 12.  Would (or should) a 6 year old understand the question, “Which is a related subtraction sentence?”  My nephew’s wife, who teaches Calculus, was stumped by that one.  Finally, think about the level of sophistication required to answer the multiple-choice question in No. 8 which asks students to “Circle the number sentence that is true” from a list of four.

·       Keep in mind that many New York State first graders are still 5 years old at the beginning of October, when this test was given.

·       It is easy to point fingers at the teacher or school for giving the test, or to point fingers at Pearson for creating it.  The problem, however, goes much deeper. The problem (no pun intended) is at the core.

·       Question 1 on the first-grade test is based on the New York Common Core Standard, 1.OA4 Understand subtraction as an unknown-addend problem. Question 12 tests standard  1.OA6, which requires students to use the relationship between addition and subtraction to solve problems. Question 8 assesses Standard 1.OA 7 which requires students to determine whether addition or subtraction sentences are true or false. You can find the New York Common Core standards here.

·       This Pearson first-grade unit test is the realization of the New York Common Core math standards.  Pearson knows how the questions will be asked on the New York State tests, because they, of course, create them.  Certainly, districts buy Pearson materials in the hope of preparing their students for the tests that will evaluate teachers, principals, students and the school itself.

·       Part of the problem with the rushed implementation of this reform is that there was never sufficient opportunity for schools to carefully examine and critique the standards themselves.  In the field, it has been “whack a mole” as districts implement evaluation systems, testing and data driven networks while wading through thousands of pages of modules.

·       Are the standards reasonable, appropriate and developmentally sound—especially for our youngest learners?  In order to answer that question, it is important to understand how the early primary standards were determined.  If you read Commissioner John King’s PowerPoint slide 18, which can be found here, you see that the Common Core standards were “backmapped” from a description of 12th grade college-ready skills.  There is no evidence that early childhood experts were consulted to ensure that the standards were appropriate for young learners.  Every parent knows that their kids do not develop according to a “back map”—young children develop through a complex interaction of biology and experience that is unique to the child and which cannot be rushed.

·       We also know that the standards were internationally benchmarked. We are told continually that we are “falling behind.”  Yet the age at which students begin school varies from nation to nation.

·       In the United States, students begin Grade 1 at the age of 5 or 6.

·       In Finland, students begin Grade 1 at age 7.

·       In Singapore, students begin Grade 1 at age 7 after two years of kindergarten.

·       This is not an argument for starting school at a later age.  Canadian students also begin first-grade at age 6.  But we must recognize, especially given that Singapore’s standards were used to develop the Common Core, that we are asking our young children to engage in intellectual tasks for which they may not be developmentally ready.

·       Finally, let’s do a quick comparison of the standards of the Common Core and those of high-performing Finland.  You can find the math curriculum of Finland here (beginning on page 158). You can find the New York Common Core standards for math here.

·       Notice that the first Finnish math objective incorporates the importance of students deriving satisfaction and pleasure from problem solving.  In contrast, the Common Core does not speak of enjoyment but rather “a habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.”

·       The Finnish “description of good performance at the end of second grade” (there are no kindergarten or first-grade standards) can best be described as topical, open-ended and descriptive, thus allowing teachers to differentiate while working with tasks such as geometry or measurement.  In contrast, the Common Core standards are behavioral and prescriptive such as, second-grade standard: 2MD9.

·       “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurement by making a line plot, where the horizontal scale is marked off in whole-number unit”. P 19.

·       Finns do not have an equivalent standard 2MD 19: Work with time and money. I will let readers draw their own conclusions.

·       I am amused by all of the politicians and bureaucrats who love the Common Core and see it as the salvation of our nation.  I suspect they are supporting standards that they have never studied. I wonder if they have ever read the details that ask first-graders to “compose and decompose plane and solid figures” and “to determine if equations of addition or subtraction are true or false.”  It is likely that much of the support for the Common Core is based on the ideal that we should have national standards that are challenging, yet the devil in the detail is ignored.

·       When one actually examines the standards and the tests like the sample I provided, it quickly becomes apparent why young students are crying when they do their homework and telling their parents they do not want to go to school.  Many New York children are simply not developmentally ready to do the work. Much of the work is confusing. When you add the pressure under which teachers find themselves to quickly implement the standards and prepare students for standardized testing, it becomes clear why New York parents are expressing outrage at forums across the state.

·       It is time for New York State to heed, at the very least, the New York State United Teachers’ call for a three-year moratorium on high-stakes testing, thus providing time for New York to re-examine its reforms, and change course.  New York, sadly, has been a canary in the Common Core coalmine, and if we do not heed the danger, a generation of students will be lost.

TABACCO: Several Generations of Wyandanch Students have already been “lost” with NO END IN SIGHT!

Did you get that, Pless!

Tabacco: I consider myself both a funnel and a filter. I funnel information, not readily available on the Mass Media, which is ignored and/or suppressed. I filter out the irrelevancies and trivialities to save both the time and effort of my Readers and bring consternation to the enemies of Truth & Fairness! When you read Tabacco, if you don’t learn something NEW, I’ve wasted your time.

Tabacco is not a blogger, who thinks; I am a Thinker, who blogs. Speaking Truth to Power!

In 1981’s ‘Body Heat’, Kathleen Turner said, “Knowledge is power”.

T.A.B.A.C.C.O.  (Truth About Business And Congressional Crimes Organization) – Think Tank For Other 95% Of World: WTP = We The People

WYANDANCH/WHEATLEY HEIGHTS CITIZENS’ COALITION

NEXT WYANDANCH B.O.E. MEETING(S)

Friday, November 8, 2013 @11:00am

SPECIAL SESSION

+

Wednesday, November 13, 2013 @7:00pm

WORK SESSION

Administration Bldg, 1445 Straight Path, Wyandanch

Main: 631-870-0400  District Clerk: 631-870-0405

Meetings List:

http://wyandanch.t-a-b-a-c-c-o.org/?p=922

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COMMENTER’S BIBLE

Anyone may Comment here, but if you want your Comment published, you must obey the TABACCO RULES as stipulated in:

TABACCO’S RULES OF ENGAGEMENT! Most Comments Here Don’t Get Published. This Post Is Not Aimed At Those Charlatans; It is Intended To Edify My Veto Stance To The Intellectually Honest Readers Among You.

http://tabacco.t-a-b-a-c-c-o.org/?p=180

W042\058

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