Geometry A

[Roderick Faulkner]

Cara-Jean Kitchi
Gavriila Shahar
Natalie Popović
Sebastian Michael West
Thomas Oliver
Tinsley Elena Rutherford

Board

Textbook

Rod was more than a little happy to be back teaching. The classes were small, which was nice. It was easier for him to adjust his lesson plans or give students one-on-one attention if they needed it. Plus, a small class had a more intimate feel where he wasn't some abstract professor figure that just stood up for an hour and droned on about math. In college, he loved his classes where there were only maybe ten other students. He got to know his professor and felt more comfortable approaching him or her with questions.

He sat down in his chair to wait for the students to arrive, the board all ready for the day's lesson. Geometric Mean was a bit of a bore, but necessary to really understand the Pythagorean Theorem. A calendar for the month was posted near the door with all the homework assignments and test dates. He also had it written up on the board as an extra reminder. A manila folder sat on an extra desk titled HOMEWORK 8.1. As he said in the previous class session, homework was always due at the beginning of class. He was grading more for completion, though one point was given for correctness. He would randomly check four problems, and a quarter of a point was awarded for a correct answer with work shown.

He wrote today's homework on the far right side in purple, HW: 8.2 1-3, 9-19 odd, 30-33, 41-44, 49. The heading was the Pythagorean Theorem, a² + b² = c²[/sup][/b], and underneath, he had a big triangle with the angles and sides listed in green. To the left of that were the Pythaogrean Triples.

3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

They were worth memorizing in his opinion especially given how often they would come up in homework. Underneath the homework and to the right of the main triangle, he had six sample problems for students to work through. The first three were to establish that any side could be found, not just c, and the bottom three all used a Pythagorean Triple, though it wasn't readily apparent. He started class as soon as the bell rang.

"Good morning, class. If you haven't turned in your homework to the folder, please do so now. I'll hand back the homework next time, and we can go over any questions then. Your first quiz is next Wednesday, and that will cover sections eight-point-one through eight-point-four."

He proceeded to take roll call as a way to refresh his memory of names and faces. He felt bad for his wife who had four sections to teach and a lot more students. Then again, student teaching in the New York area was interesting as those classes could have around twenty students in each section.

"Today we'll be covering the Pythagorean Theorem. Pythagoras was a Greek philosopher and mathematician in the sixth century B-C-E. He proved that the square of the hypotenuse is equal to the square of each leg added together. We write this out as a squared plus b squared equals c squared. There is a proof in your textbook on page 541. For example, if we set side a to three and side b to four, we can solve for c. Three squared is nine plus four squared--sixteen. Nine plus sixteen is twenty-five, and the square root of twenty-five is five."

He erased the lowercase letters and replaced them with numbers as he demonstrated. It took him a little longer as he couldn't erase with one hand and write with the other, but speed was not important in math.

"The three-four-five triangle is particular is special. We call it a Pythagorean Triple. The rest are listed here on the board--five-twelve-thirteen, eight-fifteen-seventeen, and seven-twenty-four-twenty-five. I highly suggest you memorize these as they will appear on your homework and throughout the term."

Like any good math teacher, he could recite them from memory and didn't need to look at the board. He gave the students to copy it down in their notes before continuing.

"Now, you can also solve for sides a and b as well using elimination. For example, if you knew that side c is thirteen and side b is twelve, you can solve for a. A squared plus twelve squared equals thirteen squared, or a squared plus one hundred forty-four equals one hundred sixty-nine. Subtract one hundred forty-four from each side to get a squared equals twenty five, square root of both sides, and a equals five. Any questions?"

He scanned the room for any raised hands. It started off fairly simply, but he wanted to make sure everyone understood the basics before covering more complex ideas such as what the converse of the Pythagorean Theorem proved.

"For practice, here are six problems. I want you to work through them all for about five minutes, then write an answer up on the board."

He erased the numbers from the big triangle and rewrote a, b, and c for the sides. In his opinion, the best way to understand and get good at solving math problems was to just do them. He assigned homework to solidify the material, not to give his students busy work.

[Cara-Jean Kitchi]

Cara adjusted how her messenger bag was sitting on her shoulder as she wove her way around the other students in the hallway, doing her best to be as unnoticed as possible. Yes, a lot of changes had happened since the summer vacation, but she wasn't quite ready to embrace a new life just yet. Right now she was happily just trying to fit into the mould that others wanted her to be.

Walking into the geometry classroom, she walked over to the desk and placed the sheets of paper she was holding into the homework folder and then hurried over to her desk. Sitting down she went through the process of setting up her work place and as soon as the glasses were on, she turned her attention to the board.

She opened her geometry folder and wrote down everything that was on the board, adding the homework bit into the homework section of the folder and into her homework book, and used her rule and pencil to draw in the six triangles that were on the board and added the numbers that Mr Faulkner had given, each number was a different colour a; blue, b; black and c; red. The title gave away what they would be doing with the triangles, but for now she put her writing instruments down in their place at the top of her desk.

She turned her attention to the teacher as he began the lesson, she watched the board as he spoke about the Pythagorean Theorem. Her eyebrows shot up as he finished his talk and instructions. She pressed her lips together as she realised that he expected her to go up and write in the number for one of those triangles. Giving herself a mental shake, she started working through the triangles, working the easier ones first and then tackling the others.

When she had finished she wished that she had a defiant bone in her body and was able to remain in her seat, however, what she was was another thing. Rising to her feet, she walked forward, picked up the pen and on the bottom right triangle on the opposite leg, she wrote; 60, capped the pen and double-timed it back to her seat, her shoulders reaching up for her ears as she sat down.

[Thomas Oliver]

Tommy strolled into the geometry room, he was probably surrounded by enough confidence for a dozen people, but his confidence was for himself, not that he was better than others, as it was egotistical confidence, just him knowing he could do what needed to be asked.

He sat down in his seat and pulled his stuff from his bag and copied the things off the board, though he had to rummage through his bag to find his homework planner and wrote down the assigned homework in there. When Mr Faulkner started the class, he gave a chuckle and took the homework from the back of his folder and quickly got up to place it on the folder at the front of the room before sliding back into his seat.

He worked his way through the triangles and prepared to stand up when he was finished, his eyebrows rose when he saw that it was Cara who was the first to get up and write on the board and he gave her an encouraging smile as she turned to return to her table. Taking her place at the board, he uncapped the pen and wrote 39 on the bottom middle triangle and then returned to his seat.

[Natalie Popović]

Natalie didn't consider herself to be a math person. She was okay at the subject, but it wasn't natural or easy. She hated how small the class was and that there was no way to hide in the back. She sat down and pulled out her math notebook and textbook. The homework wasn't too hard, though she hated how much it cut into the amount of time she could spend trail riding with Dixie. This was practically summer weather compared to Minnesota. She ripped the homework out of her notebook and turned it into the folder only to return to her desk and try to act like she wasn't really paying attention. The lecture was dull, and quite frankly, she thought that she could have learned it all from the textbook.

When prompted, the girl scribbled out the work into his notebook drawing little triangles and labeling them. The problems were pretty easy, and she half-heartedly hoped that the homework would be slightly more difficult. Math wasn't her strong suit, but this was stupidly simple. She stepped up to the board and picked up one of the dry erase markers. Underneath the top middle triangle, she wrote a 6 and returned to her desk.

To kill time, she flipped through her textbook to the homework just to see what sort of problems they would be doing. Maybe she could get it done really quick over the lunch period. It was bad enough that the rest of her teachers liked to give homework as though she didn't have a horse of her own to take care of and ride.