Tuesday, August 7, 2007

Who figured this out?

1) Fold a NEW PINK $20 bill in half...







2) Fold again, taking care to fold it exactly as below














3) Fold the other end, exactly as before










4) Now, simply turn it over...












What a coincidence! A simple geometric fold creates a catastrophic premonition printed on all $20 bills!!!
COINCIDENCE?

YOU DECIDE

As if that wasn't enough .. here is what you've seen...
First, The Pentagon on fire...
Then The Twin Towers.


















... And now ... look at this!




TRIPLE COINCIDENCE ON A SIMPLE $20 BILL

This is too interesting to pass up!

Twist your brain

These are definitely not "no-brainers"

Below are four (4) questions. You have to answer them instantly. You can't take your time, answer all of them, immediately.











First Question:

You are participating in a race.

You overtake the second person.

What position are you in?

























Answer:

If you answered that you are first, then you are absolutely wrong!

If you overtake the second person and you take his place, you are second!






Try not to screw up in the next question.







Second Question:

If you overtake the last person, then you are...?











Answer:

If you answered that you are second to last, then you are wrong.

Tell me, how can you overtake the LAST person? YOU are the last person.






You're not very good at this are you?











Third Question:

Very tricky math! Note: This must be done in your head only. Do NOT use paper and pencil or a calculator. Try it.



Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?









Answer:

Did you get 5000? The correct answer is actually 4100. Don't believe it? Check with your calculator!





Today is definitely not your day. Maybe you will get the last question right?











Fourth Question:

Mary's father has five daughters:

1. Nana, 2. Nene, 3. Nini, 4. Nono.

What is the name of the fifth daughter?

(a, e, i, o, u)?









Answer:

Nunu? NO! Of course, not. Her name is Mary. Read the question again.

Mathematics Tricks 3

Click here

Mathematics Tricks 2

Click here

Mathematics Tricks 1

Click here

Monday, July 30, 2007

Other trigonometric Identities (for BSEE: I - 1)

Sum and difference formulas

sin ( + β) = sin cos β + cos sin β

sin ( − β) = sin cos β − cos sin β

cos ( + β) = cos cos β − sin sin β

cos ( − β) = cos cos β + sin sin β


Double-angle formulas

sin 2A = 2 sinA cosA
cos 2A = cos^2(A)- sin^2(A)
= 2 cos^2(A)- 1
= 1 - 2 sin^2(A)

Products as sums

a) sin cos β = ½[sin ( + β) + sin ( − β)]

b) cos sin β = ½[sin ( + β) − sin ( − β)]

c) cos cos β = ½[cos ( + β) + cos ( − β)]

d) sin sin β = −½[cos ( + β) − cos ( − β)]


Sums as products

e) sin A + sin B = 2 sin ½ (A + B) cos ½ (A − B)

f) sin A − sin B = 2 sin ½ (A − B) cos ½ (A + B)

g) cos A + cos B = 2 cos ½ (A + B) cos ½ (A − B)

h) cos A − cos B = −2 sin ½ (A + B) sin ½ (A − B)

Saturday, July 28, 2007

Assignment: for BSE IV-1

In each of the following, eliminate the arbitrary constants.

1. y = c1x + c2 e^x
2. y = c1x^2 +c2e^-x
3. y = x^2 + c1x + c2e^-x
4. y = c1x^2 + c2e^2x

PS: Bring your own 1x1 ID picture on monday.

Thursday, July 26, 2007

Action Research: ROTATED AND FIXED GROUPINGS: THEIR EFFECTS ON THE PERFORMANCE OF FOURTH YEAR STUDENTS IN MATHEMATICS AT MALINTA NATIONAL HIGH SCHOOL

ROTATED AND FIXED GROUPINGS: THEIR EFFECTS ON THE PERFORMANCE OF FOURTH YEAR STUDENTS IN MATHEMATICS AT MALINTA NATIONAL HIGH SCHOOL

Fourth year students of Malinta National High School presently taking up Mathematics IV were selected for the study. This was a subject taught in a self-contained classroom. At the beginning of the school year, the students were randomly placed in the class by the committee of enrolment. This committee is made up of two teachers who were in charge of scheduling and sectioning of students. Before the third year students move to fourth year level, they were fully screened by the said committee. The committee ranked the students according to their performance in all subject areas, then they cut-off the number of students for the selection of pilot section. The pilot section contained students who had high performance in all subject areas as compared to other students. Beyond the pilot section, the rest of the students were randomly placed in the remaining seven sections. They were equally and fairly distributed to their respective sections.
From the seven randomly distributed sections, three of them were subject of the study, Amethyst, Pearl, and Emerald.
The researcher wanted to find out the answers to the following questions: (1) What is the mathematical performance of the students before and after the use of fixed and rotated groupings; and the learning unit? (2) Is there a significant difference between and among the students who belong to fixed group, rotated group and traditional setting in their Performance toward Mathematics?
To determine the effects of the fixed and rotated groupings on the performance of the students toward Mathematics, the researcher administered a pretest and posttest (2nd Periodic test) before and after the learning.
Initially the three sections (groups) were pre-tested and they all fall on below average performance. For No grouping set-up, after the learning unit they recorded an average performance in Math. Likewise, students belong to fixed grouping recorded also an average performance after the learning unit. On the other hand, the students belong to rotated grouping recorded above average performance in Mathematics after the learning unit and the application of the intervention itself.
The increased in mathematical performance level of the students belong to rotated group was perhaps due to the fact that they enjoyed to be re-tracked to their classmates weekly. As one of the students said, “I like the rotated grouping because it gives me a chance to be a leader, sometimes a member or a contributor of the group”. Others said that they could share their ideas with their peers and learned from them, as well.
The researcher used the t-test for Independent means to determine the significant difference between and among the three groups.
There is no significant difference between the no-grouping set-up and fixed grouping on mathematical performance of fourth year students of Malinta National High School as revealed by the computed t value. On the contrary, there exists a significant difference between the no grouping set-up and rotated grouping. The conclusion was that rotated grouping is better than no grouping set-up on the mathematical performance of fourth year students in Malinta National High School. This also showed that students in rotated grouping gained more knowledge than no-grouping set-up. The significant difference between the rotated and no groupings implies that the students in rotated group perform well than no grouping set-up. Probably, they triggered their interest to learn mathematics or to help one another and share their own ideas for a certain topic. Unlike the students in rotated group, students in no grouping set-up work individually thus they only relied on their own understanding about the concept in math and from the ideas of their teacher and from their reference books. Likewise, it was found out that there is a significant difference between the fixed grouping and rotated grouping. This further suggested that there was a significant difference in the effect between Rotated grouping and Fixed Grouping on the mathematical performance of fourth year students of Malinta National High School, implying that rotated grouping was more effective intervention in facilitating students’ mathematical performance than fixed grouping. Probably, because the students worked cooperatively and collaboratively in Rotated Grouping than in fixed grouping and they showed much enthusiasm in learning mathematics. The Rotated Grouping enhanced students’ interests and drives to brainstorm topics with their classmates. Thus mathematical performance had been increased.




CONCLUSIONS

Based on the thorough investigations and findings, the researcher arrived at following conclusions:
· Using rotated grouping in fourth year high school increased learning.
· Fixed grouping and rotated grouping engendered more learning in Mathematics than no grouping.
· Fourth year students believed that they learned more by working in rotated groups than in fixed grouping and individual work.
· In using rotated grouping, all students were given a chance to be a leader and a follower.
· Cooperative learning using rotated grouping and fixed grouping was more effective than traditional instruction.

RECOMMENDATIONS

· Based upon the findings of the study, it was recommended that Rotated grouping should be used in cooperative learning.
· Teachers should learn the proper techniques of rotated grouping. He/she should attend seminars related to cooperative learning.
A similar study involving larger groups of respondents be undertaken to further affirm the findings of this study.





Prepared by

MR. RODERICK M. DE LEON
(Teacher III)Malinta National High School