Category Archives: Math News

Make a Mathy Valentine!

Screen Shot 2016-02-10 at 2.42.40 PMThis just in from Mrs. McCullagh via Science Friday!

What better way to impress your valentine than with beautiful mathematical patterns?

The human eye is naturally drawn to patterns, which is why repetitive designs adorn our homes and churches, printed fabrics and wallpapers are design staples, and dishes feature motifs of rotational symmetry.

With a little math, you can use hearts to create captivating and ornate graphic patterns perfect for making valentines!

Read the full article right here!

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.

October Updates

The school year is absolutely flying by in the Williston Math Department! Here’s a snapshot of what’s been going on via my @MrJoshSeamon Twitter feed:

US Math Students of the Trimester – Spring 2014

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 Spring 2014.

Please join me in congratulating these outstanding mathematics students!

Cody CavanaghCody Cavanagh – Cody is my student of the trimester because of the way in which he delves into the intricacies of mathematical concepts. Cody completes all of the more straight-forward problems accurately and then spends his time and effort on the most challenging ones. He has consistently shown skill with proofs, with logical thinking, and with making connections. He has had a great year in Geometry in every way!
Marquis FrancoisMarquis Francois – Marquis is one of my most dedicated students. He is always prepared, and his quiet nature belies a strong intellect. I love teaching him, and I can always count on him to fully master the material
Lauren HelmLauren Helm – During T3 Lauren has stepped up her already strong math game. She has been even more laser focused in class, has totally dominated recent topics, and she’s a fantastic driver during small group projects. Her mature yet fun-loving attitude has helped stabilize an energetic class. Her work product has been extraordinarily consistent.
Lanxi KangLanxi Kang – Nancy has excelled in Algebra 2 honors all year. She has thought deeply about each topic that we have covered this year. Each day she has brought the highest level of preparation to class. She has shown a genuine interest in each topic that we have covered and even more importantly a genuine interest in the topic of mathematics in general.
Jasmine Movassaghi

Jasmin Movassaghi – Jasmin has been a B+/ A student all year. More importantly than that is her work ethic and commitment to understanding the concepts. She can always be counted on to take risks to answer questions. As important is that she will not allow the teacher to continue if she is the least bit confused. Putting all that together makes her a pleasure to teach and a great role model for her fellow students.

Gleb PashchenkoGleb Pashchenko – Gleb is our first ever double award winner! From one teacher: Gleb has done impressive work in AP statistics this year. He has come to understand the underlying principles of statistical analysis. In this course, students learn the language of a statistician and practice interpreting results with quantified measures of uncertainty. Gleb has been a model for this practice and consistently demonstrates his desire to improve his knowledge and skills. From another teacher: Gleb has excelled in all aspects of this course. He has had perfect test scores and regularly submits outstanding quality coding projects. Gleb’s attention to detail is superb and he is a joy to have in class.
Ryan PatenaudeRyan Patenaude – Ryan is an outstanding math student and has done well all year in pre-calculus. Ryan always answers difficult questions during class, completes his work with thoughtfulness and effort, and helps his classmates frequently.
Taylor PotaskyTaylor Potasky – She has been consistently at the top of the class. She works very hard and is always focused and on task. she is one of the most likeable people in the school.
Alexis RyanAlexis Ryan – Alexis is always engaged and works hard. She has been particularly responsible about staying on top of her work when she has been away from school for outside commitments. She is helpful to the others in the class and helps to keep a fun and positive atmosphere in class.
Evan StarkEvan Stark – Evan has been a very consistent student all year long. This trimester, he has been nearly flawless on all of his assessments. In class, he is always well focused and engaged in our discussions. He has been a leader, and has helped the class move forward on a daily basis.
Lindsay WhippleLindsay Whipple – Lindsay has been a diligent worker in every aspect of Geometry. Always focused and on task in class, Lindsay enjoys a challenge. She has battled through the demanding questions of the third trimester by drawing on previously learned concepts while looking for new ways to solve a problem. Her work is accurate and she has learned from the few mistakes she has made this semester. I commend her determination to be her best!


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

PSAT Math Review

Screen Shot 2014-02-05 at 10.37.34 AM

Last night I ran a review session for math section of the upcoming PSAT examination. My screen recording of the session is below along with a few resource documents. A few helpful things to remember:

1) Always guess if you can eliminate at least one answer.
2) Make sure you guess randomly.
3) Make sure you are answering what the question is asking.
4) Just because the answer you came up with is listed as a choice doesn’t necessarily mean it’s the correct answer.

PSAT2014 – Math review session – my notes (PDF)
PSAT2014 – Blank practice test w/answer key (PDF)
PSAT2014 – Practice test w/my work for the math problems and the answer key (PDF)