Category Archives: Math News

US Mathematics Students of the Trimester – Fall 2020

I am excited to announce the Upper School Mathematics Students of the Trimester – Fall 2020!

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 2020.

Please join me in congratulating these outstanding mathematics students!

Riiny Giir – Riiny excelled in both classes. He has an exceptionally clear understanding of coding and problem solving. In the Robotics class, he chose to work with MicroPython in the Mindstorms setting. This was taking a definite risk and will prompt a curricular change to that language!
Liz Gluz – Liz started off the term a bit slowly, but quickly made the changes in study habits necessary for success. She saw me frequently for extra help; she did all her homework problems and then even more for additional practice; and she was always one of the first students to raise her hand with questions during class. Her extra effort made all the difference, and her final test score of the fall term was one of the best in the whole class.
Anita Hua – Anita Hua is an exceptionally strong math student, but what makes her truly stand out is her genuine joyous passion for mathematics. She leverages her enthusiasm and academic gifts to conquer even the most complex material, and also help her peers reach the same level of understanding. She was actively engaged in class and on the math team even when she was connecting to classes remotely, and her success and large impact has continued as she transitioned to attending class in person. Bravo Anita!
Felix King – Felix has been a consistently strong AP Calculus student. He comes to class well prepared and ready to work. In class, he is always well focused and engaged in our discussions. He is always willing to lend his insights into the material with his classmates which helps the class move forward. His work ethic and devotion has been exemplary throughout the year.
Andie Kinstle – Andie has been awesome overall in Honors Geometry. Her diagrams and explanations are clear, insightful, and easy for the entire group to follow. She is always willing to share her ideas and help others. She works hard not only to understand the concepts and problems, but also to clearly show this understanding. 
Calvin Klumpp – Calvin has been a leader during discussions. Calvin articulates his thoughts well, he challenges our thinking on concepts, and he gives us alternate ways of approaching problems. Calvin has provided the class with thought provoking ideas without dominating discussion. Not only has he contributed to discussions, but he also just looks out for the class. He will let the teacher know if the screen is still frozen, he will remind us to mute or unmute on Zoom, and he will help solve technical difficulties. His community approach to learner is refreshing and necessary!
Leila Minkara – This fall, despite being virtual, Leila was able to consistently demonstrate her understanding of trigonometry scoring near the top of her class on most assessments. Additionally, Leila did all her work with great detail and always managed to turn it in even when surface issues occurred. Due to her resilience, hard work, and positive attitude I am proud to nominate Leila as my math student of the trimester. 
Sean O’Donnell – Sean has completed an exceptional trimester in Geometry. He is intellectually curious, a diligent worker and a leader with his outstanding class participation. He has strong natural instincts for geometry and his deductive reasoning skills are excellent. Always ready to explain how an answer can be found, Sean supports each of his statements with sound mathematical reasoning and enthusiasm. Congratulations, Sean, on this well earned award! 
Lorenzo Redaelli – Lorenzo has done a wonderful job this fall – adjusting to class in the gym, zoom, and a new school. He has excelled academically and has worked to help others in class. He asks great questions and contributes to the class conversation. He is a leader in class. 
Nick Sobon – Nick demonstrated a fantastic work ethic during the first trimester. In class, he was always engaged and was not shy about volunteering and asking clarifying questions. Additionally, Nick set up extra help sessions on numerous occasions and developed a plan for what was going to make him successful in Geometry. The work that he handed in was also a reflection of his commitment to trying his best. Nick sets a positive example for others and is a pleasure to have in class! 
Sydney Wegner – Sydney showed determination to not only do well, but to truly comprehend all the material. She came to every class attentive and engaged. Sydney showed her peers that giving up on a problem is not an option.

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, Spring 2017, Fall 2017, Winter 2018, Spring 2018, Fall 2018, Winter 2019, Spring 2019, Fall 2019, Winter 2020, Spring 2020

US Mathematics Students of the Trimester – Spring 2020

I am excited to announce the Upper School Mathematics Students of the Trimester – Spring 2020!

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 2020.

Please join me in congratulating these outstanding mathematics students!

Badou Ba – Badou’s commitment to developing as a programmer came to a fruition this trimester. His work in coding in a new language (his third of this year!) showed considerable growth and understanding. He showed both independence and perseverance as he worked through a wide variety of challenging problems.
Avery Brooks – Avery has just completed one amazing trimester as a student of geometry under the most unique circumstances. As we entered the unknown and sometimes unpredictable world of remote learning, Avery was a role model for her classmates by coming out of her comfort zone and volunteering multiple times each class. Avery’s determination to be her best was evident daily and her consistent effort in and out of class led to her best quiz results of the year. Always engaged, Avery set a positive tone in class and thrived on Zoom. Thank you, Avery, for your leadership and congratulations on this well deserved honor!
William Chalfant – Will struggled with math for the first two trimesters, but thrived in T3. He attended help sessions, lead his peers, and demonstrated a deep understanding of the material. He mentioned that this was his best trimester in math to date and that he is incredibly proud of himself. Will is a hard worker and is incredibly motivated, not to mention kind and fun to have in class.
Abigail Dennin – Abby stepped up on multiple fronts to help drive class during a new and challenge time! She helped create new content, manage groups of students, and go above and beyond during class discussions. She was committed, and poured genuine interest into new types of assignments, thriving independently as well as in teams. He passion for mathematics and rising to the challenge of the times was impressive and noted by everyone in class!
Sage Friedman – Sage has consistently been an excellent contributor in and out of class. Her positive spirit and determination did not fade at all, even with the transition to online learning. She continued asking insightful questions, completed her homework with the same degree of thoroughness, and demonstrated exceptional understanding of concepts. Congratulations Sage!
Sophie Gontow-Calderon – Sophie had a fabulous aspring term in Honors Discrete. Her understanding of the graph theory we studied during the spring term was truly remarkable. Moreover, she always supplements her fantastic mathematical insight with exceptional diligence and effort.
Alex Latkovski – Alex did a remarkable job this year, becoming a serious student. While we learned through zoom this spring, Alex made extra effort to ask questions and participate from a distance. It was a pleasure to work with him throughout the year as he developed and took ownership of his education.
Riley Roche – Riley showed the highest level of commitment to learn new material throughout the trimester. Her determination to challenge herself was unmatched. She never let down. She has my highest praise for not only pressing on during a trying time but succeeding at the highest level.
Abby Schulkind – Abby has been a consistently diligent and hardworking math student all year long. Abby has shown genuine curiosity and enthusiasm for AP Calculus. She always wants to learn more and to fully understand the concepts that we study.
Meryl Sesselberg – Meryl continued her excellent work in Honors Geometry during T3. She is a great, independent worker who was unfazed by online learning. She referred back to previous learning to advance her own knowledge, making great connections and showing detailed explanations.
Liam Shields – During T3 of AP CSP, Liam continued to bring his energy, interest, and enthusiasm to our virtual classes every meeting. He also poured himself into his final coding project and recreated part of one of his favorite classic games: The Legend of Zelda!
Natalie Stott – Despite the challenges faced this trimester, Natalie thrived putting together her most successful trimester this year. Natalie attended every required class, asked questions, and had strong performances on each of the assessments. For these reasons and more I am more then happy to make Natalie my math student of the trimester.

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, Spring 2017, Fall 2017, Winter 2018, Spring 2018, Fall 2018, Winter 2019, Spring 2019, Fall 2019, Winter 2020

US Mathematics Students of the Trimester – Spring 2019

I am excited to announce the Upper School Mathematics Students of the Trimester – Spring 2019!

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 2019.

Please join me in congratulating these outstanding mathematics students!

Jason Albanese – Jason pushed through some significant challenges this year and ended up not missing a beat on his progression through the class. His deeply humble and genuinely cheerful nature, as well as his deep sense of empathy, make him into a group work driver. He has fun with challenges and adores ushering his peers through complex topics. Even as we faced harder material in the land of Integrals, Jason kept on leaning in, repeatedly proving he is a creative and talented problem solver.
Katherine Borden – Katie has been a very steady and diligent math student all year long. She comes to class always ready to work and to contribute her thoughts and ideas. She learns new material quickly and is able to retain old concepts well. In class, she helps other students understand the concepts better by volunteering to lend her insights into the material.
Caroline DiFiore – Caroline worked hard right through the final project. She was determined to do her best work – getting extra help from me, friends, other teachers, and the math resource center.
Lily Harris – Lily showed initiative, enthusiasm, and drive during her work in AP CSP. Her progress in our final unit on Python was especially impressive! She brings a natural curiosity and interest in programming that will drive her success as she continues to pursue it.
Molly Kinstle – Molly sailed through this course and assembled the many pieces of Java classes and their interaction with ease. She was always engaged and participated thoughtfully at every point. Her understanding of how the topics covered in this course will serve as a solid foundation in future classes.
Jerry Landman – Jerry brought a high level of insight into each class. Whether it was asking a question or volunteering an answer, Jerry challenged his classmates to think about the material at a deeper level.
Na Kyung Lee – Na consistently distinguished herself among the top students in terms of understanding of the material of precalculus. Not only did she perform outstandingly on assessments, but her ability to work collaboratively with other students became more refined as the year has progressed. I am fully confident that Na will take the foundation she has built this year to reach new heights in any mathematical endeavor she will face in the next academic year. For the reasons stated above I am honored to nominate Na as my math student of the trimester for Spring 2019.
Keyu Lu – Keyu is obviously exceptionally talented in mathematics, but she always supplements that natural ability with incredible diligence and perseverance. I so enjoyed working with her one-on-one this year.
Tucker Motyka – Tucker completed a wonderful third trimester with a strong T3 assessment and an outstanding circles test in Geometry. Tucker thrived on the most difficult work of the year by tying previously learned concepts with challenging new material. His work was organized and he was able to articulate how to attack a multifaceted problem during class discussions. He demonstrated poise, confidence and comprehension throughout the trimester as a class leader in discussions and in his written work. Congratulations, Tucker!
Noe Perry-Greene – Noe contributes in so many ways to our geometry discussions. She shows organized work from which she insightfully explains her problem solving method. She is comfortable taking feedback about her approaches and is able to allow organic discussions to take place. She additionally is able to evaluate the methods her peers use and she works towards efficient methods. Finally, Noe is able to mix fun into the classroom that does not detract from the learning process.
Connor Touhey – Connor was an excellent student and classmate throughout the year. His performance on assessments was always strong and he was diligent in homework every night. Connor was thoroughly engaged in class, always paying full attention and processing new material carefully.
Abby Vassallo – Abby is an incredibly hard worker. She puts in so much effort in and out of the classroom, which leads to her success. She is the epitome of hard work pays off.

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, Spring 2017, Fall 2017, Winter 2018Spring 2018, Fall 2018, Winter 2019

The Math Resource Center Is Open!

The MRC is now fully operational in its new location, on the second floor of the library right next to the Writing Center! A student tutor is available during most class periods and a math department faculty member is present on Monday, Tuesday, Thursday, and Sunday evenings during study hall.

Drop on by any time!

You can learn more about the MRC right here.

Here’s the full schedule:

Click to view a larger version

 

3 new teachers!

Three new teachers have joined the Williston Math Department! They all may be new to Williston, but they are not new to teaching.

Fun facts: The Williston Math department has a combined 245 years of teaching experience. Each teach in the department has been teaching for an average of 18.8 years!

Karla Schaffer – Karla taught math and worked at the Webb School in Tennessee for the last six years. Karla earned a B.A. in Mathematics and Psychology at Mercyhurst University and earned an MEd. in Teaching and Learning from Vanderbilt University. She will coach in the girl’s soccer and tennis programs. Karla and her husband Teddy will live in Clare House.

kschaffer@williston.com

Teddy Schaffer – Teddy is an experienced math teacher who joins Williston from the Webb School in Tennessee. Teddy earned a B.S. in Mathematics and Economics from Furman University and a M.S. in Industrial and Systems Engineering from Georgia Tech. Teddy will teach math, and coach ultimate frisbee and water polo. Teddy and his wife Karla will live in Clare House.

tschaffer@williston.com

Dr. Rajendra Shrivastava – Raj comes across the country from California to join the Williston community. He has taught math, physics, and computer science at both the high school and college level. Most recently, he has been teaching math and computer science in high schools. He holds several advanced degrees including a Ph.D in Computer Science from Louisiana State University. In addition to teaching math and computer science at Williston, Raj will lead the Robotics program and coach in the spring season. Raj will live on Main St. in Easthampton.

rshrivastava@williston.com

 

 

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

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.