All about math department projects and events.

US Mathematics Students of the Trimester – Winter 2015

I am excited to announce a new award, the Upper School Mathematics Students of the Trimester!

Awards Banner 14-15 T2-1024

Each math faculty member was free to choose whichever student of theirs they thought best exemplified what they are looking for in a model mathematics student. The official description of the award is as follows:

“Awarded to students who exemplify the math department’s core values of competence, confidence, and perseverance while helping their peers realize the relevance and importance of an exceptional mathematical education both for its beauty and for its practical application.”

The following students have been recognized as the Upper School Mathematics Students of the Trimester for Winter 2015.

Please join me in congratulating these outstanding mathematics students!

Here’s video of the award presentation in assembly:

Aquadro,-AnthonyAnthony Aquadro – Anthony is a consistent leader in class. He did a particularly nice job in keeping up – and improvising – while his wrist was in a cast. He asks lots of clarifying questions, helping his learning and those around him.
Bates,-BryanBryan Bates – Bryan is a diligent worker with an enthusiasm for learning algebra. Always engaged in class, Bryan asks insightful questions, volunteers answers to the most demanding questions and enjoys challenging himself as a student. After missing a week of school early in the trimester, Bryan battled back to become my top performing algebra student. Congratulations Bryan!
Cao,-YuweiYuwei Cao – Yuwei has done impressive work this year in AP statistics showing great improvement in her ability to translate sophisticated problems into symbolic form and apply the appropriate statistical techniques. Yuwei challenges herself to uphold high standards in her written interpretations and continuously works to perfect her responses. It has truly been a pleasure working with Yuwei and I look forward to seeing her continued success.
Chipouras,-MaxMax Chipouras – He is consistently top of the class. he works very hard and is always focused and on task. He is also a top notch math student.
Garofano,-NickNick Garofano – Nick achieved extraordinary high goals in Precalculus during the second trimester. He is front and center in the classroom each and every day. Nick sets an excellent example for his peers with his diligence on the nightly homework assignments. He understands the importance of the process and cares about how he reaches his goals.
Holmberg,-CalebCaleb Holmberg – He made tremendous progress in the winter term. After struggling a bit in the fall he resolved to really work hard after Thanksgiving. He started coming for extra help, and he worked diligently to focus more carefully during class time. He ended the term on a high note, with a solid score on the winter term assessment. I was particularly impressed with the improvement he showed on the proofs. He had found those problems very difficult back in the fall but now seems to have few problems with them. I’m so happy with the growth he has shown in the course.
Lawrence,-OliverOliver Lawrence – Oliver has demonstrated a consistently high level of effort and understanding on each topic in Algebra 1. He has also been able to work with a great deal of patience and thoroughness when working with other students. His level of care has not only helped him succeed but has helped the class as well.
McCreary,-HaleyHaley McCreary – Not only is Haley a strong mathematical thinker, but she is also an outstanding student in every way. She takes the time to think critically and creatively about every problem and attacks each with determination and confidence. She collaborates with enthusiasm through openly sharing her understanding while asking for others’ ideas and help as needed. Her solid A work on the Ambiguous Case essay was the perfect representation of her ability as well as her desire to always put for her best effort.
Peirent,-EmilyEmily Peirent – Emily has a singular passion and enjoyment for mathematics that’s always well-stated. She has fun with every class and is always a positive driver during class discussions. She works HARD and makes it look easy. Bravo.
Peters,-KelliKelli Peters – Kelli is an outstanding student in my algebra II class. She is a model student in the classroom. She is always found answering difficult questions in class, going to the board to explain her work to the class, and helping her peers during group work inside of class and every Tuesday night outside of class.
Warren,-MichaelMichael Warren – Michael has been a very consistent and dedicated math student. In a demanding Algebra II Honors class, he has constantly achieved high grades due to his strong work ethic and instinctive insights into the material. He is always prepared and ready to learn.
Zawacki,-MollyMolly Zawacki – She has excelled at Robotics II with nearly perfect scores!

 

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014, Fall 2014

Factoring Polynomials in Mrs. McCullagh’s Class

This just came in from Mrs. McCullagh:

In Algebra Two we’ve learned how to factor polynomials and now we’re putting those skills to work. In this unit we’re identifying expressions and equations. Once they’re identified we can use our factoring knowledge to simplify expressions and solve equations. Today we worked in groups on the board and then individually – writing on our desks. Finally, with the support of our classmates, we each made a poster showing a problem in full detail to display in the hallway.

US Math Students of the Trimester – Fall 2014

I am excited to announce a new award, the Upper School Mathematics Students of the Trimester!

Awards-Banner-14-15-T1-1024

Each math faculty member was free to choose whichever student of theirs they thought best exemplified what they are looking for in a model mathematics student. The official description of the award is as follows:

“Awarded to students who exemplify the math department’s core values of competence, confidence, and perseverance while helping their peers realize the relevance and importance of an exceptional mathematical education both for its beauty and for its practical application.”

The following students have been recognized as the Upper School Mathematics Students of the Trimester for Fall 2014.

Please join me in congratulating these outstanding mathematics students!

Natalia BaumNatalia Baum – Natalia is such a committed math student; she exemplifies the kind of diligence and perseverance I like to see! She is always the first person to ask a question or seek help when she doesn’t understand something, and she is committed to keeping up with all the material for each day’s class. Moreover, she is just such a wonderful young woman to have in the class – friendly, attentive, and always positive. She grasps concepts quickly, but more importantly, as soon as she doesn’t fully grasp something, she starts asking questions and seeking help. I so enjoy teaching her.
Saul BlainSaul Blain – Saul has had a wonderful first trimester in Algebra II. He is a diligent worker who enjoys volunteering answers and being challenged. He has performed at the highest levels on tests and quizzes. His work is thorough, thoughtful and very accurate. Never flustered, Saul enjoys inferring previously learned concepts into new problems even if he is uncertain. He is a class leader in participation and brings a positive attitude to class each day!
Caroline BordenCaroline Borden – Caroline has been a very strong and consistent math student all trimester long. Caroline learns the material quickly and well. She has been nearly flawless on all of her different assessments.
Eric ChenEric Chen – Eric was a marvelous algebra II student. He quickly mastered the material we were learning in the class. He was a role-model student who always completed his in-class work along with his homework assignments. Eric frequently answered difficult questions during class, always helped his classmates, and came to class with a positive attitude.
Stephen GoldsmithStephen Goldsmith – Stephen has done a great job in this class – full of outstanding students. He struggled a bit at the beginning of the term, worked hard in class, came for extra help and really came into his own with the material.
Umi KeezingUmi Keezing – Umi is a truly dynamic student who not only deeply understands the material, but can explain it to her peers with ease. Additionally, I have been impressed by her ability to find creative solutions. She has a strong work ethic and dominates class without ever demanding attention.
Katie MurrayKatie Murray – She is one of the very few students to ever get 100% on a calculus exam.
Loren PoLoren Po – A statistician’s job is not an easy one! To be a good statistician, one must attend to the details while keeping in mind the larger context. Additionally, one must interpret numerical results and explain them in a way that makes sense to anyone. A beautiful graphic is lost without an articulate explanation of the pattern it shows. Loren has worked hard to understand sophisticated theories and methods and has demonstrated his ability to eloquently use the language of a statistician with his thoughtful explanations. What I appreciate so much about Loren is his willingness to help others understand difficult concepts. Keep up the good work!.
Erika SasakiErika Sasaki – Erika demonstrated the most hard working and diligent work ethic in my classes during the first trimester. She always asks questions that help the rest of the class gain a deeper understanding of the material while maintaining a positive attitude. It has been a pleasure working with Erika so far this year.
Emily YaegerEmily Yeager – Emily has shown the highest level of engagement with all the material. She is inquisitive and willing to tackle any problem. Emily has done an outstanding job mastering the material in Honors Algebra 2.
Cade ZawackiCade Zawacki – Never in my teaching career can I recall having a student achieve a 100% on just about every aspect of the course. Cade earned a legitimate 100 on each of the four assessments he took in trimester 1. In terms of homework, although he did not do each problem perfectly the first time around, he showed clearly that he had taken the time to think carefully about each question and had used all of his resources to try to understand and solve the problem at hand. He made one small error on the final assessment but solved the bonus question, and did so in a unique way. What more can I say!
Molly ZawackiMolly Zawacki – Molly’s work in this class has been of the highest caliber. The programs she writes are concise, accurate and very well documented. Her program logic is well thought-out and shows the maturity of a seasoned programmer. Molly is enthusiastic, persistent, and greets each class with a smile!

 

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014

Orlee’s Solution Gets Posted by Drexel!

Every week, the Drexel University Math Forum web site poses a math question to their participants. Recently, the site asked their viewers to determine the measures of various angles formed by a pair of parallel lines and two transversals.

Orlee Marini-Rapoport, an eighth grade student in Kathryn Hill’s Geometry Honors class, used what she had learned in class to solve the problem. Her solution was one of those chosen to appear on the website as an example of a well-reasoned answer to the problem. Orlee used her knowledge of the vertical angles theorem and angles formed by a transversal intersecting two parallel lines to prove her conjecture.

Well done, Orlee!

The problem Orlee solved
The problem Orlee solved

 

Orlee’s solution:

There will be 5 different degree measures represented.

This goal is to find the angles that must be congruent to one another.

First, because I know that vertical angles are congruent, I identified which angles were congruent to which other angles using that theorem.

7 is congruent to 9
8 is congruent to 10
12 is congruent to 14
11 is congruent to 13
2 is congruent to 5
1 is congruent to 4
3 is congruent to 6

Because alternate interior angles are congruent, 8 is also congruent to 6 and therefore the measures of 8, 6, 10, and 3 are all equal. Also, 4 is congruent to 11, so the measures of 4, 11, 1, and 13 are all congruent.

So all in all:

4 = 11 = 1 = 13
8 = 6 = 3 = 10
7 = 9
12 = 14
2 = 5

The transversals aren’t parallel so there are no corresponding angles that could be congruent. (The measure of Angle 1 + the measure of Angle 2 is equals the measure of Angle 7, but no congruency there!)

After counting up the different measures, there are 5 different numbers represented.

Matt Lapolla

Mr. Lapolla’s bio is now up on the Contact page!

2014-11-17 10.53.12Mr. Lapolla joined the Williston in the fall of 2014 after teaching for five years at The Pennington School in New Jersey. He graduated from Pomona College in 2008 with a B.A. in economics. During his time in Claremont, CA, he also played on the Sagehens football team for four years. Mr. Lapolla has taught a variety of classes ranging from Algebra I to Probability and Statistics. He currently is teaching Geometry, Precalculus, and Probability and Statistics. He coaches football and baseball at Williston and lives in Ford Hall with his dog.

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