All about math department projects and events.

US Mathematics Students of the Trimester – Spring 2017

I am excited to announce the Upper School Mathematics Students of the Trimester – Spring 2017!

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 Spring 2017.

Please join me in congratulating these outstanding mathematics students!

Ethan Huang – Ethan is a very curious math student. He is always interested in fully understanding the concepts behind a problem rather than just knowing how to solve the problem. Ethan also is also always eager to help others understand the material as well as he does.
Kohmei Kadoya – Kohmei’s work in the Electronics, Circuitry & Programming course was exceptional. He was well prepared for each class and asked probing questions on topics that required clarity. Kohmei’s classwork in the electronic’s labs and circuit labs was outstanding and included many well thought-out answers and observations. Congratulations to Kohmei for his fine work in this class!
Caitlin Keefe – Caitlin did a wonderful job pulling together all of the material that we covered this year. Her average in the third trimester was a full five points higher than she had earned for T1 & T2 – when she already did well! The questions that Caitlin asked and her overall participation set a high level of expectation for her classmates. Very well done – especially for senior spring!
Oliver Lawrence – Beyond excelling mathematically in pre-calculus, Oliver came to be a leader in the classroom. He could always be counted on to posit an answer to a challenging question or to come up to the board to present a solution. Moreover, Oliver often went out of his way to explain topics to his peers, both in the math classroom and outside the classroom. His patience and dedication to helping his classmates was a great boon for our class.
Fin MacDonald – Fin was not only a hardworking student but he also showed a genuine interest in Geometry. He looked at the material in depth every day and always pushed himself and others to do the same.
Nat Markey – Nat works incredibly hard in and out of the classroom to master the material taught. He is helpful to those around him and is always willing to participate in class. He is an incredible student and friend to his classmates.
Anna Moran – Anna has just completed a fantastic year in Geometry. She is a diligent student who always strives to be her best. She has a natural enthusiasm for learning and she challenges herself to deeply understand each and every concept. Anna has been a class leader in terms of participation and the energy and enthusiasm she brings to the classroom is contagious. Well done, Anna!!!
Yana Pyryalina – Yana did an exceptional job this year as a student in Advanced Programming in Java. Her dedication, excitement, and enthusiasm for coding shined through in all aspects of her engagement with the course. She worked hard to understand the concepts. participated in our conversations deeply and fully, and shared her “aha” moments openly with her classmates in ways that demonstrated her generosity as well as her curiosity. She was also an excellent group member and shared her expertise both in class and out.
Erika Sasaki – Erika did a phenomenal job at stepping up this trimester! Her work remained remarkably consistent and she did an impressive job helping her classmates as we transitioned into the world of Origami. He careful explanations, patience, and folding technique were appreciated by everyone. Origami is very hard to teach and Erika made the whole process easier! Thank you Erika!
Ter Sawatyanon – T did a great job in TPS this year. He was the only 9th grader in a predominantly Junior and Senior class. This term, we did a major data analysis and T chose to study health and wealth of selected countries of the World. He worked very hard and discovered interesting insights which he was able to articulate clearly in his final presentation. Great work, T!
Molly Solan – Molly is always engaged and eager to learn every class. She patiently works with all member of the class and brilliantly explains her own solutions with ease. She has performed remarkably all year and is a model Williston student. Molly brings passion and a sense of humor into the classroom and any teacher would be lucky to have her in class.
Risa Tapanes – Risa has been so diligent all year. She always does the homework; she sits at the front of the room; she asks questions; she seeks help as soon as she doesn’t understand a concept. She had a lot of success with descriptive statistics this spring, and I so enjoyed working with her. I was particularly impressed when she emailed me two days before the play (for which she was stagemanaging) to tell me that she had worked for half an hour on the homework assignment between scenes but just had not been able to get it all done. She was so apologetic, but I was just amazed she had been able to get started on it at all, given her schedule that week.

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017

US Mathematics Students of the Trimester – Winter 2017

I am excited to announce the Upper School Mathematics Students of the Trimester – Winter 2017!

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 2017.

Please join me in congratulating these outstanding mathematics students!

Graham Allardyce – Graham has performed well in Algebra II all year and really shined in trimester two. What impresses me most about Graham is his desire to teach others around them. He is frequently helping his peers with their homework and in class during group work. He is a true role model as a student and embodies Williston’s motto of living with purpose, passion, and integrity.
Elin Blomquist – Elin is a natural mathematician, but she started out with some gaps in her background that made the trigonometry unit in the fall difficult for her. Nevertheless, she worked diligently and, by the beginning of winter term, was really starting to emerge as a leader in the class. Then, in the winter term, her facility with mathematics really came through as she showed an intuitive understanding of probability and its applications. She always works hard; she’s always prepared; and she always seeks help as soon as she has any difficulty. She’s a wonderful addition to the classroom, and I so enjoy teaching her.
Noah DeVos – Noah has been one of the most consistent and highly motivated students in AP Statistics this year. He always gets an early start on homework and ask insightful questions during class. He supports his learning with excellent study skills and works hard to understand the underlying principles of probability and statistics. His frequent contributions to class discussions show me that he is willing to take responsible risks in order to further his understanding of some very challenging concepts. He always brings insight to our conversations and serves as an excellent model for other students.
Dylan Fulcher-Melendy – Dylan has become an impressive student of geometry. She has excellent deductive reasoning skills and enjoys creating proofs. A wonderful classmate to her peers, Dylan can explain how problems tie together in clear, concrete steps. Her attention to detail is outstanding and she is relentless in her pursuit of knowledge. Despite outstanding test and quiz results, Dylan has never missed an extra help opportunity even if she has to sprint from squash practice in the freezing cold. Congratulations, Dylan, on your selection as math student of the trimester and thank you for your positive impact on our class.
Robby Hill – Robby showed great determination and work ethic this past term. We learned new intense material that challenged him. Instead of settling for an okay grade and understanding of the material, he went home, searched for practice problems and past tests on the topic, and mastered his understanding of the content. This is the definition of an honors student! His work ethic, determination, and constant class participation is why I chose him.
Sabrina Liew – Sabrina did an outstanding job this trimester, dedicating herself to fully understanding the material. Her end of term project with Destiny was well done. Her last two quizzes and last test were perfect and she had a near perfect assessment. That accomplishment came because of Sabrina’s hard work. She regularly came for extra help and asked questions in class.
Aidan McCreary – Aidan has consistently set the bar high for the quality of work submitted in this class. He is always well-prepared and asks questions that help him (and the class) to understand the finer points of robotics and programming. His Engineering Notebook is highly-detailed and carefully completed. Aidan is certainly a joy to have as a student!
Mary Kate O’Brien – Mary Kate is always attentive and engaged in every activity every day. She enjoys the challenge of every problem and her approach to class has been contagious with her peers.
Natalie Richard – Natalie has maintained a remarkable level of success throughout the entire class. Her work is impeccably organized, her focus never waivers, and she readily works with others. She also never takes her abilities for granted, always coming into all assessments more than fully prepared. She helps anchor the class and move us through particularly challenging material. All the while she is always humble about her abilities.
Alexis Ryan – Alexis was a diligent student, an engaged member of the class, and a determined and creative game designer. She executed the assignments of the class thoroughly and pushed herself to extend her understanding through each project. I was particularly impressed with her final project and how fiercely she worked toward accomplishing the very challenging design she chose for the game.
Emily Warren – Emily has been a consistently strong student throughout the year. She is very inquisitive and always willing to lend her insights into the material with the rest of the class. She is able to learn material quickly and apply what she has learned with great confidence.
Harrison Winrow – Every day, Harrison arrives in class with a cheerful attitude and an eagerness to learn more mathematics. His engagement in class is exemplary. Not only does he go out on a limb to answer challenge questions, but he frequently posits his own questions: Why does the function behave that way? What would happen if we changed that piece of the function? His questions have raised the level of discussion in class and helped create a vibrant mathematical classroom.

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016

2017 AP Calculus BC Free Response Questions & Answers!

Screen Shot 2016-05-13 at 11.36.37 AMA few days after each AP Calculus BC exam, the College Board releases the free response questions from the exam. They don’t release their very succinct answer keys for a few more weeks… so… I had my students make their own answer keys as well as screen recordings of their solutions!

All 2017 released free response questions and answer keys are online right here. Questions and answers for past years can be found right here.

Here’s the direct link to the 2017 AP Calculus BC free response questions.

Here are the answer keys and videos that my students created:

Many more Williston student screencasts can be found online right here.

AP Stats Bingo!

This just in from Mrs. Baldwin!

As we prepare for the AP statistics exam, we need to review several terms and concepts. One way we can do this is with BINGO. Students complete their grids with a list of terms, in an arbitrary (not random) order. Then they are given definitions and examples. They must match the definitions and examples with the core correct terms in order to win. It is very exciting!

Sidewalk math!

With awesome weather all around, we just had to work on math outside, in chalk, on sidewalks around campus!

From Mrs. Baldwin:

The Trig/Prob/Stats class learned about describing data with numerical summaries and graphical displays. We took our work outside to practice these skills. We studied a data set of travel times to work for 20 NYC residents. We found that the median travel time was 22.5 minutes, the minimum was 5 minutes and the maximum was 85 minutes. Students also learned to use a new measure of spread called the interquartile range. This measures the range of the middle half of observations. We found that the middle half of travel times for these New Yorkers vary from 15 minutes to 42.5 minutes. Working outside in the chalk brought a kinesthetic element to our learning that was fun and engaging.

From Mr. Seamon:

Math Classroom Success Stories (16-17, T2)

Here’s a glimpse into the world of the Williston math department from the second trimester of 16-17:

Mr. Matthias: The loved the level of engagement my Engineering & Robotics students showed during the last Trimester. Students asked many questions and demonstrated success with the last set of Challenges. I will certainly miss each one of them!

Ms. Baldwin: Three students wanted some extra help before their final assessment for the Winter term. We were not able to meet in person, but planned a time to meet using Skype for Business. We spent about an hour the night before the test going over problems and addressing their questions about all that we have been studying in probability. They were able to share their screens with me and with other members of the group and I did the same with them. Our time together was extremely productive and it was so convenient to meet in this way. We got a lot of good studying done and had a few laughs at the same time. It’s good to have one more way to connect with kids and support their learning.

Mrs. Whipple: One of my students, who works really hard, was discouraged that they were not getting the grades they would have liked on every test. We worked all trimester on their strategy and their confidence when approaching the material and by the final assessment they received a near perfect score!

Ms. Schneider: One of my favorite memories from class this past trimester was when one of my students became the teacher for part of the period. We often begin class by reviewing what we have learned in our previous lessons leading up to that day. This frequently includes discussing the homework assignment. At times the students get into small groups to review; however, on this day one student came to the front and lead the class throughout this activity. She walked the class through each problem, and kept every student engaged. Not only did her classmates gain valuable insight through her explanations and leading questions, but this student, who actually is considering a career in teaching herself, showed excellent leadership skills!

Mrs. Conroy: My Geometry assessment consisted of two parts, a group portion and an individual portion. The group portion of the assessment required students to stretch their problems solving abilities while doing geometry in a collaborative setting. As I described it to the students, “There is little you can do to prepare for this section. It will challenge you. Embrace the challenge.” The first question on the group portion was particularly challenging and involved proving triangles congruent after creating a diagram from specific instructions. Each group had the correct diagram but then the problem became interesting. Not a single group earning full credit on the problem but what I witnessed in the classroom during that question was the best math we had done this year. Students were questioning each other, everyone was participating and incredible thoughts were being debated. I was thrilled to sit back, listen and watch young minds at work. Well done my Geometry students. I am proud of your fighting spirit!

Mrs. Hill: I found a stats textbook that used a real trial from 1964 to illustrate the problems of assuming independence to calculate probabilities. A woman had been mugged in CA, and the prosecutor used the assumed probabilities of a man “driving a yellow car,” and being “over 6 feet tall,” and “having a beard,” etc to calculate that the odds of the defendant NOT committing the crime were less than one in a million. Unfortunately though, as the appeals court later determined, the prosecutor was wrongly assuming independence of events when, in fact, there was no way to be sure of that fact. It was a real life example of issues of conditional probability we had been discussing in class. Moreover, we also got the chance to discuss how, in modern times, DNA evidence is based heavily on probabilities. We were not all in agreement as to the legitimacy of that approach.

Mr. Seamon: The math team has been enjoying a very active and successful year! In additions to competing in the 6 rounds of the New England Math League, returning to the Harvard Math Competition, as well as participating in the AMC8/10/12 competitions, the team has also added in the Middle School NEML competition as well as heading to Yale for their spring HS competition. Not only is the team competing in more competitions than ever, the team is scoring as well as ever currently holding strong at 28th our of 140 teams in NEML, scoring in the top 1/3 of teams at the HMMT, and also qualifying a student for the American Invitational Mathematics Exam!

Mrs. King: I have a student who has been away at ski school during the entire second trimester and will return next Monday. Before she left her family and I had a discussion about what math class she should take, an Algebra 1 class at ski school or work with a tutor to complete our curriculum. Wanting to come back fully prepared for the third trimester she chose to work with a tutor and complete our notes, homework, quizzes and tests. I set up One Note Notebooks for both her and the tutor. After a little bit of a slow start she was off and running. The tutor and I communicated each week about what was due, what was coming up or any questions or concerns that we had. The tutor was wonderful and read all of the notes and assisted Arden after she did her assignments. Arden did a great job! It was great that she was willing to take on extra work so that she would be able to transition back into class next week. I can’t wait to have her back in class.

Ms. Smith: At the end of our unit on transformations of functions, my Pre-calculus students spent a class period designing a mathematical roller coaster. That is, using their knowledge of the parent functions and transformations, they created one continuous, piecewise-defined function that traced the vertical height of the roller coaster with respect to horizontal distance travelled. As students discovered, the trickiest part was ensuring that the functions linked up, that is, there were no unplanned gaps in the track. However, after a period of work there was a wide range of functions (or should I say roller coasters). Highlights included underground tunnels, death drops, and even a loop-the-loop made using logarithmic, exponential and even elliptic functions.

Mrs. McCullagh: We finished the winter trimester with a project in Calculus. The assignment was for each student, or student pair, to decide what they wanted to hang and from where and then find the minimum amount of wire needed to hang their object. They needed to decide how far apart their two attachments should be and how far down they wanted the object suspended. They needed to find, using calculus, the minimum amount of wire needed for their own scenario. It is a challenging calculus problem for students as they are learning how to solve maximizing/minimizing problems. Then they needed to present their findings with all calculations clearly shown and diagrams labeled with the minimum and extremes. They also needed to produce a model made to scale. The projects were outstanding! We had a target hung from a tree, donuts hung for a birthday party, a chair hung is a bedroom, a rubber ducky hung (just because), as well as a number of others. The students all reported that they learned a lot from the project. It is great to have their work on display!

US Mathematics Students of the Trimester – Fall 2016

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


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 2016.

Please join me in congratulating these outstanding mathematics students!

Cao,-AndyAndy Cao – Andy’s in depth thought, attention to detail and willingness to tackle the most difficult problems has made him an excellent Geometry student. He has shown a genuine interest in all of the material. His approach to class has helped push his classmates to excel along side of him.
Cavanaugh,-JuliaJulia Cavanaugh – I chose Julia as my student of the trimester for her work inside and outside of the classroom. Outside of the classroom she is a dedicated student who does her very best every class to prepare herself for our upcoming lesson. During class she is always focused, eager to participate, and extremely willing to help her peers out with their own work. She is a is truly a model student!
Fieldman,-ArvinArvin Fieldman – Many students work hard to find success. Arvin finds success and then some. He is not satiated with even strong understanding of material. He must dominate each topic. His work ethic and abilities have shown through in his careful yet creative group work as well as his ridiculously high and consistent quiz and test scores. Bravo Arvin.
Grabowski,-KyleKyle Grabowski – Kyle had a remarkable first trimester at Williston in geometry. His work is neat, thorough and incredibly accurate. He has a strong natural aptitude for mathematics and he thrives on the most demanding questions given both in class and on tests. On more than one occasion this fall, Kyle was the only student in two sections of geometry to get a challenge question correct. His inductive reasoning skills are impressive! 
Kim,-SimonSimon Kim – Simon has great energy in class everyday. He is always prepared and willing to help those around him. He is quick to answer questions and come up to the board. Simon is an all around great student who raises the bar everyday.
Marion,-SarahSarah Marion – Sarah is one of the most enthusiastic, most energetic students I have ever met. She is always the first student to ask a question; she stays after class to go over any concept she had difficulty with; and she is always prepared for class with her books and homework out in front of her almost as soon as she gets in the room. She has had a ton of success in Topics, mostly because of her diligent, conscientious approach to the material. It has been such a pleasure working with her this year!
Mizobuchi,-SomaSoma Mizobuchi – Soma’s work shows that he has set high standards for his academic performance. His Engineering Notebook is extremely complete and serves as a fine reference for his Engineering Labs and his code development. In writing programs, his code, and its logic, is always well thought-out and his program documentation is outstanding. Congratulations to Soma for a very impressive trimester!
Monaco,-GabbyGabby Monaco – Gabby has taken on a great challenge this year moving into AP Statistics from TPS. She is one of the most persistent students and works very hard to understand difficult concepts. She is not discouraged by setbacks, but resolves to work harder on the next challenge. I am hopeful that, with this continued level of effort, she will make great progress this year and continue to model strong study habits and the kind of determination that leads to success and innovation in the field of statistics.
Record,-GabbyGabby Record – Gabby did an outstanding job this fall in Calculus. She was always prepared and engaged in class. Her positive attitude along with interesting questions brought great energy to the class. I’m looking forward to her continued great work.
Spiegel,-AndrewAndrew Spiegel – Andrew is a talented programmer who accepted the challenge of applying is already significant background and skill to a new context, game design. Rather than executing a safe or simple final project, Andrew pushed himself to attempt a highly challenging game that relies on random room generation. The result was an amazingly polished and enjoyable project that I hope he will continue to build upon!
Thibault,-XavierXavier Thibault – Xavier has been an extremely strong AP Calculus student. He has very good insights into the material which he is always willing to share with the class. He learns material very quickly and is able to apply his knowledge well. He helps keep our class moving forward as he is always willing to participate in our discussions.
Zawacki,-MollyMolly Zawacki – Molly has been a phenomenal addition to our Discrete math course. She has shown leadership in the class, whether it is stepping up to present a hard solution or explaining her thinking to her peers. I can count on Molly to go out on a “mathematical limb” and offer new ideas, even if she is not sure they are correct. Mathematically, she has developed into a beautiful proof writing; creating clear and easy to read explanations for her work. All in all, she has really embraced the core goals of the course; to explore, conjecture and prove.

Past students of the trimester can be found right here: Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016

Steiner Point Construction

This just in from Mrs. Hill:

Topics in Discrete Mathematics students got to review some lessons from geometry when they learned how to construct the Steiner Point of a triangle. The Steiner Point in a triangle is the point from which three branches lead out to the triangle’s vertices at perfect 120° angles. (See diagram below.) This Steiner Point has important modern day applications for creating the shortest (and therefore cheapest) possible fiber optic network between any three locations. If a triangle’s angle measures are all less than 120°, then the Steiner Point can be found inside the triangle using a geometric construction first developed by Italian mathematician Evangelista Torricelli in the early 1600’s. Torricelli (most famous for his work in physics but also an accomplished mathematician) was a protégé of Galileo, and in 1641 succeeded Galileo as the court mathematician to Grand Duke Ferdinand II of Tuscany.

Figure 2
Figure 2

Torricelli’s method for finding the Steiner Point in a triangle requires only the use of the traditional geometric construction tools – straightedge and compass. Using properties of equilateral triangles and inscribed angles from elementary Euclidean Geometry, the basics of the construction are shown below in Figure 1 (a,b,c). The students in Topics further learned how the Steiner Point was used in 1989 to connect Hawaii, Japan, and Guam via the Third Trans-Pacific Cable (TPC-3). Also below, Figure 2 shows a stamp issued by the Japanese Postal Service to commemorate the completion of TCP-3. As one can see from the picture, the three undersea cables meet at 120° angles under the western Pacific Ocean.

Figures 1a, 1b, and 1c
Figures 1a, 1b, and 1c

Student constructions:

Dispatch from Calculus

CalculusThis just in from Mrs. McCullagh:

Teaching Calculus to seniors and a few juniors, I feel an obligation to help move them toward independence and self-sufficiency in their learning. I want them to learn to support themselves as learners and know how to reach out for assistance. I use two primary methods to this end.

First, I provide full solutions for all homework. Students are expected to use these solutions to check their work as they complete each problem to be sure they not only have the correct answer, but more importantly, that they have supported their work appropriately. The other way they can use these solutions is as a hint on how to start a problem if they just need a little help. No one should come to class with a blank homework saying they did not know how to do the work. With this, they know when they need help and are expected to ask for it.
CalculusMy second strategy for student increased independence is to have all students at the boards at the same time to do problems together. By being visible, at the boards, they can and should look to others around them to confirm they are headed in the right direction. Each student becomes a source of information for everyone else. Students who might not take the lead sitting at their desks are now asked for help by their peers. Again, no one is left unable to start a problem. Help is all around.

All about math department projects and events.