Fibonacci Haiku: The Cosmic Order

Fate

is

not one

for pity.

Our souls are like stars,

binary stars, woefully caught

in the most beautifully tragic cosmic collapse.

But nobody in the world had ever said that this love was going to be easy.

http://img.dictionary.com/binary_star-308870-400-234.jpg

(Syllables)

SP 5: Unit J Concept 6: Decomposing Fractions with Repeated Factors

The trickiest part of this problem is remembering to count up the powers when you write a new expression using new variables in place of the numerator. In addition, solving the system of equations is also a difficult aspect of the problem. Instead of using matrices, you have to solve it by eliminating one variable at a time, then finding an answer.

SP 4: Unit J Concept 4: Partial Fraction Decomposition with Distinct Factors

The trickiest part of this problem is decomposing the fraction back again. The student needs to pay attention to how to set up the problem using new variables, such as A, B, and C. The factoring and the distribution must all be correct, because one simply mistake in multiplication could cause the whole problem to be wrong. Finally, the student needs to set up the system of equations correctly using terms that correspond with one another, and then plug that system into the calculator to solve.

SV 5: Unit J Concept 3: Solving 3-Variable Systems with Matrices

The part of this problem that a student needs to pay attention to is how to find the equations to get certain numbers in their spots. The student needs to make sure that when solving for the row, he or she is careful with their math and doesn't make a mistake, because one error or miscalculation could make the whole matrix wrong, and then he or she would have to start over. In addition, the student needs to pay attention to the equations in the system before putting them in the matrix, seeing which ones would be more convenient to place in the rows. For example, if an equation has "0x", it is smart to put it in the third row, because the first step is to find a 0 in the bottom left hand corner. Since there is already a 0, the student will have less work to do.