Woohoo!

# 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!**

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!**

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!

A 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:

**2017 #1:**Answer key 1, Answer key 2, Video 1, Video 2, Video 3, Video 4**2017 #2:**Answer key, Video 1, Video 2**2017 #3:**Answer key 1, Answer key 2, Answer key 3, Video 1, Video 2, Video 3, Video 4, Video 5, Video 6**2017 #4:**Answer key 1, Answer key 2, Video 1, Video 2, Video 3**2017 #5:**Answer key, Video 1**2017 #6:**Answer key 1, Answer key 2, Video 1, Video 2, Video 3, Video 4

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:**

My @WillistonNS #APCalc class creating some ultra amazing #calculus graffiti! pic.twitter.com/YVd21Stpvd

— Josh Seamon (@MrJoshSeamon) April 10, 2017

The @WillistonNS #APCalc math graffiti continues! @maanow pic.twitter.com/gF01h8dOWI

— Josh Seamon (@MrJoshSeamon) April 11, 2017

# 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!**

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.

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.

**Student constructions:**

# Dispatch from Calculus

This 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.

My 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.