Solids of Revolution Project

This just in from Mrs. McCullagh:

For the last few days in Calculus, with help from Mr. Roe in the Art Department, my classes built models as part of a project exploring solids of revolution. Partners were assigned an equation, asked to sketch and graph that equation and then find the volume of the solid that would be created by revolving that graph around the x-axis. They needed to sketch and estimate the volume if filled with only four cylinders, then find the estimated volume if filled with eight cylinders using a computer generated model. Using Calculus they were able to find the actual volume and compare it with their estimates. Next they needed to create a three dimensional model of their solid using wire and foam core. On the last day of classes they presented their project to their classmates. The projects were on display in the Reed Center in time for graduation for their families to see.

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US Mathematics Students of the Trimester – Spring 2016

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


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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 2016.

Please join me in congratulating these outstanding mathematics students!

Cuevas,-ElizabethElizabeth Cuevas Lizzie is an outstanding student who not only does well on all of her assignments, from daily homework to trimester assessments, but also encourages her classmates to succeed.  She is constantly helping her peers both inside and outside of the classroom.  She is gifted at explaining her work and ideas to others and often volunteers to do so in class.
DeVos,-NoahNoah Devos – Noah is one of the leaders in our Precalculus class.  He is always actively engaged with the material and asks questions that benefit the entire class.  I can always rely on him to come to class ready to work.  It has been a pleasure working with Noah this year.
Frometa,-JustinJustin Frometa – Justin has been one of the most active participants in AP statistics this year.  He arrives in class with detailed assignments and always has questions prepared.  He models the curiosity and relentless pursuit of knowledge that we all hope to see in our math students.
Ikuku,-EniEni Ikuku – Eni has easily leveraged his previous experience in electronics to expand his knowledge of topics taught in this class. He dedicates himself to understanding the course material and asks intelligent and well though-out questions. He is well prepared for every assignment, every day.
Janocha,-KarenKaren Janocha – Karen has been an able geometry student all year, but this spring her work has just been fantastic.  She has been excelling on proofs involving similarity and right triangles, and she is always the first person to reach out to help other students.  It’s been wonderful seeing her emerge as such a leader in the classroom.
O'Sullivan,-KevinKevin O’Sullivan – Kevin has been a strong student in Precalculus all year long. He learns concepts quickly, and is able to apply his knowledge to new material. In class, he is always willing to lend his insights into the material to help the class keep moving forward.
Okaisabor,-ZoeZoe Okaisabor – Zoe has worked hard all year in Algebra 1. She has gained a confidence in her work that has enabled her to make valuable contributions to the class. She has become an excellent math student through hard work and perseverance.
Ryan,-AlexisAlexis Ryan – Alexis’ work reflects this award.  She “exemplifies the math department’s core values of competence, confidence, and perseverance while helping her classmates realize the relevance and importance of an exceptional mathematical education both for its beauty and for its practical application.” She gets gets excited when she works hard and masters a new concept.  She works tirelessly to help her classmates.  Her skills are very good and she believes in her ability.

Setwipatanachai,-ChaiwatChaitwat Setwipatanachai
– Team exemplifies the dedication, drive, and curiosity necessary to master a programming language. His reasoning is excellent, his attention to detail in his work is of the highest quality, and his contribution to our class discussion is steady, focused, and, at times, appropriately humorous.
Small,-GabbyGabby Small – Every class needs a leader. Gaby Small has led her algebra class from day one this year. She is relentless in her pursuit of learning algebra, always willing to volunteer or to ask the key question that helps everyone understand a concept. With two complete notebooks, Gaby has never settled for anything less than her best. As a senior, her passion for learning has never waivered and she has demonstrated that learning math can be fun.  I am so proud to award Gaby Small my student of the trimester award.

Servin,-MiloMilo Servin
– Milo has shown himself to be a strong critical thinker and problem solver all year.  This trimester all of the pieces to the puzzle have come together for him.  As always, he is the group leader, sharing his quick understanding with his peers, but his depth of clarity has strengthened because he is taking more time to process and problem-solve.  With more effort, focus and detail with his daily work, Milo has supported his ability beautifully which has translated into outstanding work on his assessments of all types.  He has become a more complete mathematician by learning the value of paying attention to precision, the perfect complement to a student who is such a bright mathematical thinker!
Ticknor-Swanson,-CalvinCalvin Ticknor-Swanson – Even though class has become demonstrably harder over the past trimester, Calvin has not stepped off his domination of Calculus. He continues to demolish tests with carefully crafted work that shows, clearly, his complete command of the material. Additionally, he is humble about his abilities and is excited to work with others. I very much hope Calvin continues to take more math courses in college!

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

The Star Project Continues

Star folding!
Star folding!

After my BC Calculus students rocked the 2016 AP exam (check out their custom answer keys!), we started working on the Star Project.

The learned how to fold a 60-piece star, and then I asked them two straight-forward questions:

What’s the surface area of the star in terms of the side length of one of the pieces of paper?

What’s the volume of the star in terms of the side length of one of the piece of paper?

Here are some of their video solutions. The complete playlist of videos is online here.

Surface Area


2016 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 released free response questions and answer keys are online right here.

Here’s the direct link to the 2016 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.

9/6/16 Update: The official CollegeBoard scoring guidelines are now online.