# ORMC Meetings Archive • Fall 2007–Summer 2021

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### For the current schedule, visit the Circle Calendar

2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 2012–2013 2013–2014 2014–2015 2015–2016 2016–2017 2017–2018 2018–2019 2019–2020 2020–2021
 Fall 2020 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2ABeginners 2BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 10/11/2020 Advanced 1A [gr.9-10 (Nikita)]: Warm up We warm-up for the new academic year by solving problems from some mathematical competitions.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Warm-up We warm-up for the new academic year by solving problems from some older mathematical competitions.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Competition problems warm-up! We kick off the academic year with some competition-style problems gathered from AMC, AIME, and Olympiads.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Competition Problems We will start the year with a wide variety of competition style problems.Handouts: Competition ProblemsAdvanced 3 [gr. 12 (Aaron/Harris)]: Euler's Number Prove the existence of e, and see it arise in various natural situations.Handouts: eulers_number_handoutAMC10/12 Training: Logic and Puzzles For our first meeting, we're going to cover logic problems and do some fun puzzles.Beginners 1A [gr.2-3 (Vivian)]: Split the Difference The main goal of the first lesson is to engage students and show them several mathematical surprises. We will also look at an optical illusionBeginners 1B [gr.2-3 (Vivian)]: Split the Difference The main goal of the first lesson is to engage students and show them several mathematical surprises. We will also look at an optical illusionBeginners 1C [gr.2-3 (only if attended BNP bridge)]: Split the difference We will talk about some sharing problems, and start to think about how we can make careful arguments to justify our answers.Beginners 2A [gr.3-4 (Ashin/Cassandra)]: First Meeting We will go over a simple version of "I cut, you choose" and some brain teasers!Handouts: Handout: I_Cut_You_ChooseBeginners 2B [gr.3-4 (Ashin/Cassandra)]: First Meeting We will go over a simple version of "I cut, you choose" and some brain teasers!Handouts: Handout: I_Cut_You_ChooseIntermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Pooled Testing For our first lesson, we will introduce pooled testing in the context of coronavirus.Handouts: Key | HandoutIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Pooled Testing For our first lesson, we will introduce pooled testing in the context of coronavirus.Handouts: Key | HandoutIntermediate 2A [gr.7-8 (Preston/Richard)]: Problem Solving 1 First meeting of the year for intermediate 2A. We will be doing some fun problem solving!Handouts: Intermediate 2A Problem SolvingIntermediate 2B [gr.7-8 (Kyle)]: Start of the year game! This year we will be starting off with a great worksheet filled with a variety of problems, and we will go through it in teams in competition. cant wait!Handouts: Solutions | WorksheetOlympiads 1: Induction in Olympiad Problems We quickly review mathematical induction and then solve a few related problems of various levels of difficulty, from easy to very hard.Handouts: HandoutOlympiads 2: Angle Chasing 1 Many nontrivial Olympiad problems can be solved by angle chasing. This class we covered inscribed angles, cyclic quadrilaterals, and properties of the orthocenter.Handouts: Homework | Lecture Notes 10/18/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic Equations I (Vieta's Theorem) We start our exploration of quadratic equations with Vieta's Theorem. As usual, we also do some geometry.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Quadratic equations Some low degree polynomial analysis starting with quadratics including Vieta's formulas.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Gaussian Integers I We will introduce Gaussian integers in order to decide which prime numbers can be written as a sum of two squares.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Gaussian Integers I We will introduce Gaussian integers in order to decide which integers can be written as a sum of two squares.Handouts: Gaussian Integers IAdvanced 3 [gr. 12 (Aaron/Harris)]: The Least Upper Bound Does e really exist? Let's try to fill in missing details of our previous claims.AMC10/12 Training: AMC 10/12 Training: Algebraic Manipulation Handouts: Week 2 slidesBeginners 1A [gr.2-3 (Vivian)]: Sharing Problems and Birthday Cakes Beginners 1B [gr.2-3 (Vivian)]: Sharing Problems and Birthday Cakes Lesson 2 - Sharing Problems and Birthday CakesBeginners 1C [gr.2-3 (only if attended BNP bridge)]: Sharing Problems and Birthday Cakes We will return to the fair share problems that we introduced in week 1, by considering what happens when we have to divide among three people. We will also think about the geometry of plane figures and how many places lines will intersect with different figures.Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Logic Puzzles: Wizards and Hats We will be developing logic skills by looking at problems with different colored hats. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Logic Puzzles: Wizards and Hats We will be developing logic skills by looking at problems with different colored hats. The goal of this handout is to learn how to make an assumption, test the assumption, and readjust the original assumption if necessary.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Modular Arithmetic part 1 We will be introduced to modular math. We completed pages 1-6 of the handout.Handouts: HandoutIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Modular Arithmetic part 1 We will be introduced to modular math. We completed pages 1-6 of the handout.Handouts: HandoutIntermediate 2A [gr.7-8 (Preston/Richard)]: Permutations 1 - Introducing Permutations We introduce permutations and the 15 puzzle problem!Handouts: HandoutIntermediate 2B [gr.7-8 (Kyle)]: Algebra Start (1/3) This week we will be learning about a very important topic to the theory of Abstract Algebra: Permutations.Handouts: Worksheet | SolutionsOlympiads 1: Computing Areas Today we will approach problems involving area computations, that should hopefully cover all necessary techniques for Olympiad problems.Handouts: HandoutOlympiads 2: Angle Chasing 2 Directed angles, incenter/excenter lemma, problems.Handouts: Homework | Lecture Notes 10/25/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic Equations II (Long division) We start the long handout with a long division.Handouts: Handout | HWAdvanced 1B [gr.9-10 (Hunter)]: Convex Property and Cubics We finish last weeks handout with the convex property and start cubic equations.Handouts: Cubics | ConvexAdvanced 2A [gr.11-12 (Eilon/Yan)]: Gaussian Integers II We will wrap up the discussion of Gaussian integers and prove which prime numbers are the sum of two squares.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Gaussian Integers II We will wrap up the discussion of Gaussian integers and prove which integers are the sum of two squares.Handouts: Gaussian Integers IIAdvanced 3 [gr. 12 (Aaron/Harris)]: Axiom of Choice and more... Handouts: Hats AMC10/12 Training: Quadratics and Factoring Slides for this week: https://docs.google.com/presentation/d/1nhl_yW5xpqtiZZOn1Dv4G5eVvvJ1qe6tlebHdXeK6x8/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Recap and Quiz #1 More optical illusions and crossing problems.Beginners 1B [gr.2-3 (Vivian)]: Recap and Quiz #1 More optical illusions and crossing problems.Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Logic Puzzles: Wizards and Hats (Continued) We will continue with our exploration of logic puzzles involving hats and if we have additional time, work through some math kangaroo problems.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Logic Puzzles: Wizards and Hats (Continued) We will continue with our exploration of logic puzzles involving hats and if we have additional time, work through some math kangaroo problems.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Modular Arithmetic part 2 We will be continuing the second half of the handout on modular math. We will also learn modular math applications, such as checksums.Handouts: Handout | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Modular Arithmetic part 2 We will be continuing the second half of the handout on modular math. We will also learn modular math applications, such as checksums.Handouts: Handout | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Permutations 2 - Continuing Permutations This week we continue developing some more language and notation to be able to prove whether or not the 15 puzzle has a solution...Handouts: Permutations Part 2 - handoutIntermediate 2B [gr.7-8 (Kyle)]: 2nd round of permutations Hello! This week we are continuing on the topic of permutations.Handouts: Worksheet | SolutionsOlympiads 1: Diophantine Equations Today we will discuss various standard techniques in solving diophantine equations (i.e. equations with integers). The material is for 2 weeks.Handouts: HandoutOlympiads 2: Angle Chasing 3 More advanced angle chasing problemsHandouts: Homework | Lecture Notes 11/1/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic Equations III (Quadratic equations in different contexts) Handouts: Handout | HomeworkAdvanced 1B [gr.9-10 (Hunter)]: More on Cubics We continue the cubic handout from last week.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Prime Generating Functions I We will study the limitations of polynomials as prime generating functions.Handouts: Prime Generating Functions IAdvanced 2B [gr.11-12 (Matt/Glenn)]: Prime Generating Functions I We will study the limitations of polynomials as prime generating functions.Handouts: Prime Generating Functions IAdvanced 3 [gr. 12 (Aaron/Harris)]: Exploring Manifolds Handouts: WorksheetAMC10/12 Training: Polynomials https://docs.google.com/presentation/d/1EemxMNiCYWj3wna_inEKic_Z_X2BXtopN7d2y1A7Vw0/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Review Quiz #1 and Lesson 3 Recap Beginners 1B [gr.2-3 (Vivian)]: Review Quiz #1 and Lesson 3 Recap Beginners 1C [gr.2-3 (only if attended BNP bridge)]: Intro to Roman Numerals We will review the homeworks from lesson 3, and introduce Roman numerals as a new topic. Remember to bring your craft sticks to class!Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Challenge Problem and Halloween Math This week, we will finish up the wizards and hats packet by completing the challenge problem. We will then work through some Halloween math problems.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Challenge Problem and Halloween Math This week, we will finish up the wizards and hats packet by completing the challenge problem. We will then work through some Halloween math problems.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Modular Arithmetic part 3 We will finish up our review on modular math, learning how to subtract and divide in modular math as well as learning how to prove divisibility rules with modular math.Handouts: Handout | Divisibility Rules | Answer KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Modular Arithmetic part 3 We will finish up our review on modular math, learning how to subtract and divide in modular math as well as learning how to prove divisibility rules with modular math.Handouts: Answer Key | Handout | Divisibility RulesIntermediate 2A [gr.7-8 (Preston/Richard)]: Permutations 3 - Cracking the Puzzle Handouts: HandoutIntermediate 2B [gr.7-8 (Kyle)]: Final day of permutations. Solving the 15 puzzle! Today is the last day of this topic and we finally be able to combine taxicab distance and permutations to solve the 15 puzzle.Handouts: WorksheetOlympiads 1: Diophantine Equations, Part II The handout is the same as last time (see Part I)We will move on to problems 4, 5, 6... and so on today.Olympiads 2: Circles 1 Power of a Point and Radical Axis 11/8/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic Equations IV (Vieta's formulas again) Advanced 1B [gr.9-10 (Hunter)]: Complex numbers and cubic solutions We have a more in depth coverage of complex numbers.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Prime Generating Functions II We will study recursive formulas for generating primes.Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Prime Generating Functions II We will study recursive formulas for generating primes.Handouts: Prime Generating Functions IIAdvanced 3 [gr. 12 (Aaron/Harris)]: Exploring Manifolds 2 Handouts: WorksheetAMC10/12 Training: Number Theory Part 1 https://docs.google.com/presentation/d/1PGTLoVpI4mN1a6ucCoe-fMBd2I32JwJKkpjp5LrVYts/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 4 Roman Numerals We will look at the rules for making Roman numerals and we will learn how to add and subtract with Roman numerals.Beginners 1B [gr.2-3 (Vivian)]: Lesson 4 Roman Numerals We will look at the rules for making Roman numerals and we will learn how to add and subtract with Roman numerals.Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Venn Diagrams This week, we finish up the Halloween Math packet and begin our exploration of Venn Diagrams.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Venn Diagrams This week, we finish up the Halloween Math packet and begin our exploration of Venn Diagrams.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Egyptian Fractions part 1 We will be exploring an ancient Egyptian technique of splitting fractions into their unit parts. We completed pages 1-16.Handouts: Handout | KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Egyptian Fractions part 1 We will be exploring an ancient Egyptian technique of splitting fractions into their unit parts. We completed pages 1-16.Handouts: Handout | KeyIntermediate 2A [gr.7-8 (Preston/Richard)]: Constructing Triangles Handouts: HandoutIntermediate 2B [gr.7-8 (Kyle)]: Geometry I Today we are going to test the limits of zoom by going through an awesome geometry worksheet that focuses on the use of compass and straight edge.Handouts: WorksheetOlympiads 1: Game Theory Today we are doing problems involving mathematical games, and talk about the method of retrograde analysis.Handouts: HandoutOlympiads 2: Circles 2 Harder problems with Power of a PointHandouts: Homework 11/15/2020 Advanced 1A [gr.9-10 (Nikita)]: Functions We get back to small handouts for one lesson. This one is about functions.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: e and Trigonometric functions We discuss e and one of its definitions coming off Euler's equation.Handouts: handoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Algorithms I We will take our first peak into algorithms, with the goal of discussing the P vs NP problem the following week. Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Algorithms I We introduce some classic algorithms and the notion of runtime.Handouts: Intro to AlgorithmsAdvanced 3 [gr. 12 (Aaron/Harris)]: Cryptography and Finite Fields Handouts: CryptographyHandoutAMC10/12 Training: Number Theory Part 2 https://docs.google.com/presentation/d/1csp0eYKJrFWvBkwCMrCf_zZYoP9U85WB3K1AErb-lBE/edit?usp=sharingBeginners 2A [gr.3-4 (Ashin/Cassandra)]: Venn Diagrams (Continued) This week, we will be continuing our exploration of Venn Diagrams and we if have additional time, work through some Math Kangaroo problems.Handouts: Venn Diagrams SolutionsBeginners 2B [gr.3-4 (Ashin/Cassandra)]: Venn Diagrams (Continued) This week, we will be continuing our exploration of Venn Diagrams and we if have additional time, work through some Math Kangaroo problems.Handouts: Venn Diagram SolutionsIntermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Egyptian Fractions part 2 We will continue our exploration of Egyptian fractions (pages 17-24). Homework is pages 25-26.Handouts: Handout: part 1Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Egyptian Fractions part 2 We will continue our exploration of Egyptian fractions (pages 17-24). Homework is pages 25-26.Handouts: Handout: part 1Intermediate 2A [gr.7-8 (Preston/Richard)]: Geometry 2 Continuing from last week but with even more detailed constructions and Euclidian proofs!Handouts: WorksheetIntermediate 2B [gr.7-8 (Kyle)]: Geometry 2 Continuing from last week but with even more detailed constructions and Euclidian proofs!Handouts: WorksheetOlympiads 1: Game Theory, part II This lecture we continue with the same topic. We added a few extra problemsHandouts: HandoutOlympiads 2: Circles 3 Today we did three challenging problems whose solutions involved Power of a Point in a fundamental way.Handouts: Handout | Homework 11/22/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic inequalities We will solve the rest of the problems from the previous lesson and Handouts: Handout | HWAdvanced 2A [gr.11-12 (Eilon/Yan)]: Algorithms II We continue our unit on algorithms by discussing the most famous open problem in the field, P vs NP.Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Algorithms II Following the introduction to algorithms, we are able to discuss the nuances of the P vs. NP problem.Handouts: P vs NPAdvanced 3 [gr. 12 (Aaron/Harris)]: Finite Geometry Handouts: finite_geometryAMC10/12 Training: Sequences and Series https://docs.google.com/presentation/d/1jZfw6Ng6CNeKB_VKY-KmY9pGI6NsZRV8mVnUZ_htH1s/edit?usp=sharingBeginners 1B [gr.2-3 (Vivian)]: Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Egyptian Multiplication and Binary Numbers This week, we'll finish up Venn Diagrams by going over any of the challenge problems the students may have had difficulty with. Afterward, we'll begin our exploration of a new topic: Egyptian Multiplication. We'll also explore its relationship with binary numbers.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Egyptian Multiplication and Binary Numbers This week, we'll finish up Venn Diagrams by going over any of the challenge problems the students may have had difficulty with. Afterward, we'll begin our exploration of a new topic: Egyptian Multiplication. We'll also explore its relationship with binary numbers.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Egyptian Fractions part 3 To conclude our exploration of Egyptian Fraction Representation, we will complete the Egyptian Fractions part 1 handout and begin Egyptian Fractions part 2. Pages 6-8 EFR part 2 are assigned as homework.Handouts: EFR part 1 | EFR part 2 | EFR part 1 Key | EFR part 2 KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Egyptian Fractions part 3 To conclude our exploration of Egyptian Fraction Representation, we will complete the Egyptian Fractions part 1 handout and begin Egyptian Fractions part 2. Pages 6-8 EFR part 2 are assigned as homework.Handouts: EFR part 1 | EFR part 2 | EFR part 1 Key | EFR part 2 KeyIntermediate 2A [gr.7-8 (Preston/Richard)]: Combinatorics Part 1! We introduce combinatorics, the mathematics of counting. Handouts: Combinatorics 1Intermediate 2B [gr.7-8 (Kyle)]: Combinatorics I Today we go into a new and really awesome topic: Combinatorics!Handouts: Combinatorics Worksheet | SolutionsOlympiads 1: Practice Session Today we will do practice problems, with no particular theme.Handouts: HandoutOlympiads 2: Lengths and Ratios 1 We will introduce Ceva's Theorem, Menelaus' Theorem, the Extended Law of Sines, and some basic length formulas in a triangle.Handouts: Lecture Notes | Homework 11/29/2020 Advanced 1B [gr.9-10 (Hunter)]: Functions We talk about functions and some relations between them.Handouts: Handout | ExtraAdvanced 3 [gr. 12 (Aaron/Harris)]: No Meeting! AMC10/12 Training: No meeting this week. Happy Thanksgiving! Beginners 2A [gr.3-4 (Ashin/Cassandra)]: No Meeting Happy Thanksgiving! There is no class today, but we do have Math Kangaroo problems to work on!Handouts: Math KangarooBeginners 2B [gr.3-4 (Ashin/Cassandra)]: No Meeting! Happy Thanksgiving! There is no class today, but we do have Math Kangaroo problems to work on!Handouts: Math KangarooIntermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: No class. Have a great Thanksgiving! Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: No class. Have a great Thanksgiving! 12/6/2020 Advanced 1A [gr.9-10 (Nikita)]: Quadratic Equations V (Problem solving) Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: More on Quadratic Equations We do a little more analysis of quadratic equationsHandouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Fundamental Theorem of Algebra The Fundamental Theorem of Algebra... Everyone's heard of it. If it's so fundamental then why haven't we seen a proof?! Look no further, we consider complex polynomials and graphing techniques to prove that every complex polynomial has a root.Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Fundamental Theorem of Algebra We prove the Fundamental Theorem of Algebra with a focus on graphing.Handouts: Fundamental Theorem of AlgebraAdvanced 3 [gr. 12 (Aaron/Harris)]: Finite Geometry - Continued We continue with the previous worksheet on Finite Geometry.Handouts: finite_geometryAMC10/12 Training: Counting https://docs.google.com/presentation/d/1yIBsli9ojgR6OKqJ9g21Nwqaewk8cWMPhc4Vt4yRaIs/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 7 Converting to Roman Numerals Beginners 1B [gr.2-3 (Vivian)]: Lesson 7 Converting to Roman Numerals Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Egyptian Multiplication and Binary Numbers (Continued) This week, we'll continue with our exploration of Egyptian Multiplication and Binary Numbers. If we have additional time, we'll go through the Math Kangaroo problems.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Egyptian Multiplication and Binary Numbers (Continued) This week, we'll continue with our exploration of Egyptian Multiplication and Binary Numbers. If we have additional time, we'll go through the Math Kangaroo problems.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Proof by Induction We will look a method to prove mathematical hypotheses: proof by induction. Handouts: Induction | Completed ProofsIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Proof by Induction We will look a method to prove mathematical hypotheses: proof by induction. Handouts: Induction | Completed ProofsIntermediate 2A [gr.7-8 (Preston/Richard)]: Combinatorics Part 2! This week we continue and finish off our introduction to combinatorics.Handouts: Combinatorics HandoutIntermediate 2B [gr.7-8 (Kyle)]: Combinatorics II This week we will be continuing what we stared last week and talk more about combinatorics. We will be starting with a brief review of what we spoke about last week, before moving onto completely new problems.Handouts: HandoutOlympiads 1: Geometry: Angle chasing and Constructions Today we discuss angle chasing, properties of angles inscribed in circles, and a few constructions.Handouts: HandoutOlympiads 2: Lengths and Ratios 2 Two proofs of Heron's Formula; Nine-Point Circle, Euler Line, Monge's TheoremHandouts: Lecture Notes 12/13/2020 Advanced 1A [gr.9-10 (Nikita)]: Game No handout, just game!Handouts: GameAdvanced 1B [gr.9-10 (Hunter)]: Game We ran a math dominoes competition.Advanced 2B [gr.11-12 (Matt/Glenn)]: Class Competition The students battle it out in a full class Kahoot competition.Advanced 3 [gr. 12 (Aaron/Harris)]: Competition Day Handouts: ProblemsAMC10/12 Training: Probability https://docs.google.com/presentation/d/1qjqnqtXTYAdYSixph04VEq5T54YDbws0VmPuZgB5raA/edit?usp=sharingBeginners 1B [gr.2-3 (Vivian)]: Review Lesson 7 Homework and Quiz #2 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Review Game This week, we'll be playing a review game consisting of the topics we've explored this far. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Review Game This week, we'll be playing a review game consisting of the topics we've explored this far. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Proof by Induction and Contradiction We will continue to explore proof by induction and introduce proof by contradiction. *Last class of fall quarter, Happy Holidays!Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Proof by Induction and Contradiction We will continue to explore proof by induction and introduce proof by contradiction. *Last class of fall quarter, Happy Holidays!Intermediate 2A [gr.7-8 (Preston/Richard)]: Kahoot Math Competition! There is no handout for this class (Instructors can access the private attachments).Intermediate 2B [gr.7-8 (Kyle)]: Math Dominos We are going to be playing a zoom adapted math circle favorite! I hope everyone has a great time.Olympiads 1: Angle Chasing II We continue with the topic from last time.Handouts: Handout | Lecture NotesOlympiads 2: Olympiad Configurations Simson line configuration (including proof that Simson(P) bisects PH) and incenter touch-point configuration.Handouts: Homework Winter 2021 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2ABeginners 2BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 1/10/2021 Advanced 1A [gr.9-10 (Nikita)]: Weighings, Logic and Geometric Constructions We go from quadratic equations to something more elementary but not easier!Handouts: HandoutAdvanced 1A [gr.9-10 (Nikita)]: Complex numbers I Today we will be starting on one of the most interesting and important topics in mathematics, at least in my opinion. I hope everyone learns something!Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Weighings, Logic, and Geometric Constructions We start the year with problems using weight, logic, and geometry.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Group Competition! To start off the new year we are going to split the class into two competing groups. There will be a variety of problems to work on and it will be up to the teams to organize how they feel is best.Handouts: Competition Problems | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Competition Problems Handouts: Competition ProblemsAdvanced 3 [gr. 12 (Aaron/Harris)]: Prime Generating Functions We study various functions that output lots of prime numbers.Handouts: Prime_Generating_FunctionsAMC10/12 Training: Speed & Strategy Beginners 1A [gr.2-3 (Vivian)]: Lesson 8 Recap on Roman Numerals Beginners 1B [gr.2-3 (Vivian)]: Lesson 8 Recap on Roman Numerals Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1 Welcome Back! This week, we'll begin our exploration of a new topic: Exponential Functions.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1 Welcome Back! This week, we'll begin our exploration of a new topic: Exponential Functions.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Breaking Sticks Suppose we break a stick into three pieces randomly. What are the chances the resulting pieces will form a triangle?Handouts: HandoutIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Breaking Sticks Suppose we break a stick into three pieces randomly. What are the chances the resulting pieces will form a triangle?Handouts: HandoutIntermediate 2A [gr.7-8 (Preston/Richard)]: Complex Numbers 1! We have an introduction to the complex numbers in this meeting.Intermediate 2B [gr.7-8 (Kyle)]: Complex numbers 1 An introduction to something awesome: Complex Numbers.Handouts: Handout | SolutionsOlympiads 1: Board Problems Today we will discuss board problems, involving colorings, tilings and more.Handouts: HandoutOlympiads 2: Geometry Review We will go over the winter break geometry homework and review last quarter's material, and do some Olympiad problems from other subjects if time allows. 1/17/2021 Advanced 1A [gr.9-10 (Nikita)]: Weighings, Logic and Geometric Constructions We continue our studies in elementary math.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Weighings, Logic, and Geometric Constructions part 2 We continue with questions using scales, logic and of course more geometry.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Graphs Part 1: Planar Graphs We start our unit on graphs with a dive into planar graphs and the Euler characteristic.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Graph Theory I We will attempt to determine when a given graph is planar, culminating in Kuratowski's Theorem.Handouts: Planar GraphsAdvanced 3 [gr. 12 (Aaron/Harris)]: Borsuk-Ulam Theorem Handouts: Borsuk Ulam ProblemsAMC10/12 Training: Similar Triangles https://docs.google.com/presentation/d/1UAbiQFgUwJIPL8r-7HQq0-6s_z3o87LRb5cIMGCpZS8/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 9 Cutting Logs Beginners 1B [gr.2-3 (Vivian)]: Lesson 9 Cutting Logs Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1: Multiplying Negative Numbers This week, we'll take a deeper look into what happens when we multiply negative numbers and use what we learn to further our exploration of exponential functions. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1: Multiplying Negative Numbers This week, we'll take a deeper look into what happens when we multiply negative numbers and use what we learn to further our exploration of exponential functions. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Breaking Sticks part 2 We will continue and complete our packet on breaking sticks. In which scenario are we most likely able to form a triangle from our broken sticks?Handouts: Breaking Sticks | Answer Key | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Breaking Sticks part 2 We will continue and complete our packet on breaking sticks. In which scenario are we most likely able to form a triangle from our broken sticks?Handouts: Breaking Sticks | Answer Key | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Algebra Along our exploration of the complex numbers and our journey to trigonometry, we take a brief stop at some algebra.Handouts: AlgebraIntermediate 2B [gr.7-8 (Kyle)]: Complex numbers 2 This week we will continue the worksheet from last week and then move onto a worksheet going into the details of the number systems we went over last week.Handouts: HandoutOlympiads 1: Inequalities Today we cover various methods of solving inequality problems.Handouts: HandoutOlympiads 2: Complex Numbers Complex numbers and AIME problems 1/24/2021 Advanced 1A [gr.9-10 (Nikita)]: Weighings, Invariants and Geometric Constructions This week we continue solving problems concerning some of the most interesting areas of school mathematicsHandouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Weighings, Invariants, and Geometric Constructions We cover more weighings and geometric constructions, as well as look at some problems using invariant solutions.Handouts: handoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Graphs Part 2: Colorings We continue our unit on graph theory with a handout on graph colorings. We will define what it means to color a graph, connect this to coloring maps (geographically speaking), and prove some bounds on how many colors are needed. Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Graph Theory II We will explore many interesting results about graph coloring.Handouts: Graph ColoringAdvanced 3 [gr. 12 (Aaron/Harris)]: Dynamical Systems We explore some famous dynamical systems, and study the logistic map and the Mandelbrot set.Handouts: Dynamics_problemsAMC10/12 Training: Circles https://docs.google.com/presentation/d/186hkAvj76yIzn0eznHHnii5rZNhLuLcRMzid1rvrQ0A/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Continue Lesson 9 Cutting Logs Continue Lesson 9 Cutting LogsBeginners 1B [gr.2-3 (Vivian)]: Continue Lesson 9 Cutting Logs Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1 (Continued) This week, we'll continue with our exploration of exponential functions by picking up where we left off in the packet. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1 (Continued) This week, we'll continue with our exploration of exponential functions by picking up where we left off in the packet. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Fractions and Decimals Part 1 This week we will learn how to convert between fractions and decimals, while also exploring the properties of terminating and non-terminating decimals.Handouts: Review and HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Fractions and Decimals Part 1 This week we will learn how to convert between fractions and decimals, while also exploring the properties of terminating and non-terminating decimals.Handouts: Review and HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Introduction to Trigonometry 1 This will be our first time dealing with some trignometry! This will give us the necessary information to talk about Euler's formula next week.Handouts: Intro to trigIntermediate 2B [gr.7-8 (Kyle)]: Trigonometry I This week we start in the topic of trigonometryHandouts: HandoutOlympiads 1: Ceva and Menelaus Today we will review similarity of triangles, and we will do problems involving the Menelaus and Ceva theorems.Handouts: HandoutOlympiads 2: Counting with Recurrences 1/31/2021 Advanced 1A [gr.9-10 (Nikita)]: Invariants and Geometric Constructions We discuss the plots from the previous week in more detailHandouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Invariants and Geometric Constructions Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Graphs Part 3: Colorings Continued We continue with a proof of the 5-color theorem and some Ramsey theory.Handouts: Solutions | HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Graph Theory III We will finish the study of graph coloring and introduce basic ideas in Ramsey Theory.Handouts: Graph ColoringAdvanced 3 [gr. 12 (Aaron/Harris)]: Dynamical Systems 2 We continue exploring dynamical systems.AMC10/12 Training: Angle Bisectors, Medians, and More https://docs.google.com/presentation/d/1ptDmIXjt-pVIM37OgiRHuLuw10l1KD4RoY23BqfGGAc/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 10 Cutting Bagels Beginners 1B [gr.2-3 (Vivian)]: Lesson 10 Cutting Bagels Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1: (Continued) + Math Kangaroo This week, we'll continue with our exploration of exponential functions by using its properties to solve a myriad of problems. If we have extra time, we'll work through some Math Kangaroo problems. Handouts: Handout: Math Kangaroo P2Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Exponential Functions P1: (Continued) + Math Kangaroo This week, we'll continue with our exploration of exponential functions by using its properties to solve a myriad of problems. If we have extra time, we'll work through some Math Kangaroo problems. Handouts: Handout: Math Kangaroo P2Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Fractions and Decimals Part 2 We will continue to explore terminating and non-terminating decimals. WHY do decimals have these properties? How can we write non-terminating decimals as fractions?Handouts: Class notes | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Fractions and Decimals Part 2 We will continue to explore terminating and non-terminating decimals. WHY do decimals have these properties? How can we write non-terminating decimals as fractions?Handouts: Class notes | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Trigonometry and Complex Numbers (Euler's Formula) We finally arrive at Euler's Formula!Handouts: Euler's Formula Applications HandoutIntermediate 2B [gr.7-8 (Kyle)]: Trigonometry II Today we connect what we learned last week with the complex numbers!Handouts: HandoutOlympiads 1: Modular Arithmetic -- Part I Handouts: HandoutOlympiads 2: Olympiad Problem Session 1 Handouts: Handout 2/7/2021 Advanced 1A [gr.9-10 (Nikita)]: Law of Sines & Cosines https://docs.google.com/presentation/d/1ehJAFzTun5NkE9QzED1908bas7wy7FpjVaIboCjGyW8/edit?usp=sharingAdvanced 1A [gr.9-10 (Nikita)]: Weighings, Invariants, and Geometric Constructions part 4 We continue with mostly invariants and geometric constructions.Handouts: New handout | Last week's handoutAdvanced 1B [gr.9-10 (Hunter)]: Invariants and geometric constructions Handouts: Handout from last meeting | New problemsAdvanced 1B [gr.9-10 (Hunter)]: Invariants and Geometric Constructions We cover more explicitly Invariant problems and a couple geometric constructions.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Continued Fractions We look at continued fractions and their relation to rational and irrational numbers.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Continued Fractions Continued fractions are an interesting way to represent real numbers. We will develop an algorithm for computing continued fractions and attempt to classify periodic continued fractions.Handouts: Continued FractionsAdvanced 3 [gr. 12 (Aaron/Harris)]: 3D Sections We study how to project 3-dimensional figures onto planes, and find out the intersection of 3d figures with planes.Handouts: 3D_Sections_problems | AMC10/12 Training: AMC 10/12 Training AMC Review AMC10/12 Training: AMC 10/12 Training AMC Review Beginners 1A [gr.2-3 (Vivian)]: Lesson 11 Recap and Quiz #3 Beginners 1B [gr.2-3 (Vivian)]: Lesson 11 Recap and Quiz #3 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Math Kangaroo This week, we'll finish up our exploration of exponential functions by finish the remaining challenge problems. Afterward, we'll solve some Math Kangaroo problems. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Math Kangaroo This week, we'll finish up our exploration of exponential functions by finish the remaining challenge problems. Afterward, we'll solve some Math Kangaroo problems. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Sequences We will write and define sequences and numbers through explicit and recursive definitions. We will also explore arithmetic sequences and how we can generalize the sum of n-terms in the sequence.Handouts: Class NotesIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Sequences We will write and define sequences and numbers through explicit and recursive definitions. We will also explore arithmetic sequences and how we can generalize the sum of n-terms in the sequence.Handouts: Class NotesIntermediate 2A [gr.7-8 (Preston/Richard)]: Probability and Geometry We investigate and explore some ideas in probability for this class!Handouts: Probability applied to GeometryIntermediate 2B [gr.7-8 (Kyle)]: Probability with Geometry Hello Intermediate 2A students!Today we will be investigating some ideas in probability in combination with some familiar ideas in geometry. We think today's handout will be great for those that found our previous topics less than exciting compared to usual. We hope that these probability problems will be a good change of pace!Handouts: Handout | SolutionsOlympiads 1: Modular Arithmetic -- Part II Today we are continuing with the topic from last time. Some of the problems in this handout are left-overs from the previous handout.Handouts: HandoutOlympiads 2: AIME Algebra 2/14/2021 Advanced 3 [gr. 12 (Aaron/Harris)]: No Meeting We will not meet on 2/14/2021. Happy Valentine's Day/President's Day/long-weekend-in-the-middle-of-the-quarter.AMC10/12 Training: No Class Today! President's Day Beginners 2A [gr.3-4 (Ashin/Cassandra)]: No Class (President's Day) Beginners 2B [gr.3-4 (Ashin/Cassandra)]: No Class (President's Day) Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: No class: Presidents' Day Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: No class: Presidents' Day Intermediate 2B [gr.7-8 (Kyle)]: No Class (Holiday) President's Day Weekend. Class on the 21st. 2/21/2021 Advanced 1A [gr.9-10 (Nikita)]: Game Problems will appear here with the start of the gameHandouts: GameAdvanced 1B [gr.9-10 (Hunter)]: Midquarter Game We will be playing a game today.Advanced 2A [gr.11-12 (Eilon/Yan)]: Metrics Part 1: The taxicab metric We introduce the concept of metrics using a motivating example: the taxicab metric. This worksheet is especially useful for all those of you who are part time students and part time taxi drivers in New York City.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Taxicab Geometry We introduce the taxicab metric, a new way of measuring distance in Euclidean space. We will study its properties and figure out how it relates to the Euclidean metric.Handouts: Taxicab GeometryAdvanced 3 [gr. 12 (Aaron/Harris)]: P vs. NP We discuss algorithmic complexity, and learn the difference (if indeed there is one) between P and NP problems.Handouts: PNP_problemsAMC10/12 Training: AMC 10/12 B Review Beginners 1A [gr.2-3 (Vivian)]: Lesson 12 Squares on a Chessboard Beginners 1B [gr.2-3 (Vivian)]: Lesson 12 Squares on a Chessboard Beginners 2A [gr.3-4 (Ashin/Cassandra)]: An Introduction to Polyhedra This week, we will begin by working through the remaining math kangaroo problems in the packet. Afterward, we'll begin our exploration of the world of polyhedra.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: An Introduction to Polyhedra This week, we will begin by working through the remaining math kangaroo problems in the packet. Afterward, we'll begin our exploration of the world of polyhedra.Handouts: Handout: Polyhedra_P1Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Arithmetic Sequences and Series We will continue our work on arithmetic sequences, then transition to learning about arithmetic series.Handouts: Class Notes | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Arithmetic Sequences and Series We will continue our work on arithmetic sequences, then transition to learning about arithmetic series.Handouts: Class Notes | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Chinese Remainder Theorem - Divisibility! We investigate the Chinese Remainder Theorem in this week's handout. Handouts: Chinese Remainder TheoremIntermediate 2B [gr.7-8 (Kyle)]: Some topics in Number Theory Hello everyone! This week we will be working on some problems that have to do with number theory! Number theory is a very important subject in math and is considered one of the most difficult!Handouts: Solutions | HandoutOlympiads 1: Mixed Problem Session Handouts: HandoutOlympiads 2: AIME Number Theory AIME Number Theory problems, which tend to be computational 2/28/2021 Advanced 1A [gr.9-10 (Nikita)]: Invariants and Geometric Constructions III We continue with invariants, semi-invariants and geometric constructions.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Invariants and Geometric Constructions II We are continuing with Invariant question and geometric constructions.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Metrics Part 2: General Metrics We use the first part as motivation to define metrics in general. We talk about a few different examples and introduce the notion of convergence of a series.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Metrics We generalize different notions of distances, as motivated by the taxicab distance, into something called a metric space. We then discuss convergence of sequences in metric spaces.Handouts: Advanced 3 [gr. 12 (Aaron/Harris)]: Ordinals Handouts: ordinals_problemsAMC10/12 Training: Law of Sines & Cosines https://docs.google.com/presentation/d/1ehJAFzTun5NkE9QzED1908bas7wy7FpjVaIboCjGyW8/edit?usp=sharingBeginners 1B [gr.2-3 (Vivian)]: Beginners 2A [gr.3-4 (Ashin/Cassandra)]: An Introduction to Polyhedra (Continued) This week, we'll continue with our exploration of Polyhedra.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: An Introduction to Polyhedra (Continued) This week, we'll continue with our exploration of Polyhedra.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Geometric Sequences and Series We will introduce geometric sequences and explore how using geometric series can help us convert non-terminating decimals to fractions.Handouts: Class Notes | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Geometric Sequences and Series We will introduce geometric sequences and explore how using geometric series can help us convert non-terminating decimals to fractions.Handouts: Class Notes | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Chinese Remainder Theorem Continued This week we are continuing our problems on the Chinese Remainder Theorem (CRT) along with a small introduction to ‘if and only if' proofs within the context of remainders and divisibility.Handouts: divisibility_crt_2Intermediate 2B [gr.7-8 (Kyle)]: Chinese Remainder Theorem Continued This week we are continuing our problems on the Chinese Remainder Theorem (CRT) along with a small introduction to ‘if and only if' proofs within the context of remainders and divisibilityHandouts: HandoutOlympiads 1: Counting Problems Handouts: HandoutOlympiads 2: Olympiad Problem Session 2 3/7/2021 Advanced 1A [gr.9-10 (Nikita)]: Invariants and geometric construction IV This week we finish our introduction to geometric constructions and invariants.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Drawing Contest and Invariants More on Invariants and a geometry drawing exercise.Handouts: Extra | HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Gini Index We take a look at a measure of income inequality in a given population.Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Gini Index In economics, the Gini index is a measure intended to represent income inequality. We will take a mathematical approach to the study of the Gini index.Handouts: Gini IndexAdvanced 3 [gr. 12 (Aaron/Harris)]: Lattices, Orchards, and the Four-Square theorem Handouts: HandoutAMC10/12 Training: Analytical Geometry: Circles & Lines Beginners 1B [gr.2-3 (Vivian)]: Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Introduction to Polyhedra Continued + Math Kangaroo This week will finish up our packet on polyhedra and practice some Math Kangaroo Problems!Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Introduction to Polyhedra Continued + Math Kangaroo This week will finish up our packet on polyhedra and practice some Math Kangaroo Problems!Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Combinatorics I Today, we introduce combinatorics: the mathematics of counting.Handouts: Handout | Key | HomeworkIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Combinatorics I Today, we introduce combinatorics: the mathematics of counting.Handouts: Handout | Key | HomeworkIntermediate 2A [gr.7-8 (Preston/Richard)]: Greatest Common Divisor and the Division Algorithm We study the GCD and the Euclidean algorithmHandouts: GCD and Euclid HandoutIntermediate 2B [gr.7-8 (Kyle)]: Continuation of number theory This week we are continuing some more on divisibility with problems around the greatest common divisor as well as Euclid's division algorithm. The handout is attached below.Handouts: HandoutOlympiads 1: Counting Problems - Part II We are continuing with the same topic as last time. Problems have been added to the previous handout.Handouts: HandoutOlympiads 2: Trees 3/14/2021 Advanced 1A [gr.9-10 (Nikita)]: Game 2 This week we have a game! Prepare your pen, pencil, paper and spirit!Handouts: Advanced 2A [gr.11-12 (Eilon/Yan)]: Competition! Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Competition Problems Handouts: Competition ProblemsAdvanced 3 [gr. 12 (Aaron/Harris)]: Competition We have a competition in which we review this term's topics.Handouts: ProblemsAMC10/12 Training: Analytical Geometry: Ellipses https://docs.google.com/presentation/d/1q3ZuUtGr3FlPf8SYaCmkhABypIr9QKtT1c53lRpwCzQ/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 13 Chessboard Games Beginners 1A [gr.2-3 (Vivian)]: Lesson 14 Recap and quiz 4. Digits and Numbers Beginners 1B [gr.2-3 (Vivian)]: Lesson 13 Chessboard Games Beginners 1B [gr.2-3 (Vivian)]: Lesson 14 Recap and Quiz 4. Digits and Numbers Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Introduction to Polyhedra (Continued) We'll continue with our exploration of Polyhedra, solve some math kangaroo problems, and do a short review of exponential functions.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Introduction to Polyhedra (Continued) We'll continue with our exploration of Polyhedra, solve some math kangaroo problems, and do a short review of exponential functions. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Combinatorics II We will complete the combinatorics worksheet from last week. Furthermore, we will explore what happens if the order of the items in our list matters.Handouts: Handout | KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Combinatorics II We will complete the combinatorics worksheet from last week. Furthermore, we will explore what happens if the order of the items in our list matters.Handouts: Handout | KeyIntermediate 2A [gr.7-8 (Preston/Richard)]: Math Dominoes Today we have a math dominoes game for the last meeting of the quarter.Intermediate 2B [gr.7-8 (Kyle)]: MATH GEOPARTY! 3/21/2021 Beginners 1A [gr.2-3 (Vivian)]: Quiz #4 and Review Lesson 14 Beginners 1B [gr.2-3 (Vivian)]: Quiz #4 and Review Lesson 14 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: No Class (Spring Break) Beginners 2B [gr.3-4 (Ashin/Cassandra)]: No Class (Spring Break) 3/28/2021 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: No Class (Spring Break) Beginners 2B [gr.3-4 (Ashin/Cassandra)]: No Class (Spring Break) Spring 2021 quarter // Filter groups by: Advanced 1AAdvanced 1BAdvanced 2AAdvanced 2BAdvanced 3AMC10/12 TrainingBeginners 1ABeginners 1BBeginners 1CBeginners 2ABeginners 2BIntermediate 1AIntermediate 1BIntermediate 2AIntermediate 2BOlympiads 1Olympiads 2 4/4/2021 Advanced 1A [gr.9-10 (Nikita)]: Random Events? We are very excited to start a new quarter with all of you starting with this Sunday's topic on random events (random variables).Handouts: WorksheetAdvanced 1A [gr.9-10 (Nikita)]: Combination We start a new topic of combinations and Pascal's triangle. Also a problem with triangle similarity.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Combinatorics We start learning basic counting methods in combinatorics.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: A Study of Measurement Errors as an Introduction to Differential Calculus. (Oleg Gleizer) Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.Handouts: handoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: A Study of Measurement Errors as an Introduction to Differential Calculus I (Oleg Gleizer) Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.Handouts: handoutAdvanced 3 [gr. 12 (Aaron/Harris)]: Graph Theory 1 We cover several graph theory topics, including planarity, colorability, and Ramsey Theory.Handouts: ProblemsAMC10/12 Training: Curved Surfaces https://docs.google.com/presentation/d/11-UtV4dS7yELTHYrED40r73QbCTKN01WMVQcuneLx6Y/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 15 The Abacus, Addition Beginners 1B [gr.2-3 (Vivian)]: Lesson 15 The Abacus, Addition Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 We finished up the first part of our exploration of Polyhedra and went through the Math Kangaroo problems. This week, we'll explore a new topic: Sets and Venn Diagrams.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 We finished up the first part of our exploration of Polyhedra and went through the Math Kangaroo problems. This week, we'll explore a new topic: Sets and Venn Diagrams.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Lever Playing Field Can you move the earth with a lever? Today's math circle lesson will require creativity, physics, and a little intuition to balance levers.Handouts: Key | HandoutIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Lever Playing Field Can you move the earth with a lever? Today's math circle lesson will require creativity, physics, and a little intuition to balance levers.Handouts: Key | HandoutIntermediate 2A [gr.7-8 (Preston/Richard)]: Random Events and Applications This Sunday we explore random variable and events beyond just geometric probabiltiy (as we've done before).Handouts: randomEvents_handoutIntermediate 2B [gr.7-8 (Kyle)]: Randomness Handouts: HandoutOlympiads 1: Linear Recurrences We will cover linear recurrences and how to solve themHandouts: Handout 4/5/2021 Intermediate 2B [gr.7-8 (Kyle)]: Mid Quarter Game This week we took a break from our regular scheduled programming for a fun math game! 4/11/2021 Advanced 1A [gr.9-10 (Nikita)]: Combinations II (Pascal's Triangle) We continue studying combinations, introducing Pascal's triangle.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Combinations and Pascal's Triangle He continue with combinations and how they relate to Pascal's triangleHandouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: A Study of Measurement Errors as an Introduction to Differential Calculus Part 2 (Oleg Gleizer) We use the error formulas derived in the first part, throw in the concept of limits, and see some applications for measurement error. Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: A Study of Measurement Errors as an Introduction to Differential Calculus II (Oleg Gleizer) Students will learn what an error of measurement is and how the said error propagates through computations that use the result of the measurement. In the process, the students will derive the sum, product, and quotient rules for the derivative using an engineering approach instead of taking limits.Advanced 3 [gr. 12 (Aaron/Harris)]: Graph Theory 2 We cover several graph theory topics, including planarity, colorability, and Ramsey Theory.AMC10/12 Training: AM-GM Inequality https://docs.google.com/presentation/d/10fP6mjiBJ-PTNw5sPwFDYQQbiw-ixFBs9hxcxZieMgY/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 16 The Abacus, Subtraction Beginners 1B [gr.2-3 (Vivian)]: Lesson 16 The Abacus, Subtraction Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 (Continued) This week will start off by learning about the difference between a set and a list as well as some new notation to learn about some special sets such as the empty set and the set of natural numbers.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 (Continued) This week will start off by learning about the difference between a set and a list as well as some new notation to learn about some special sets such as the empty set and the set of natural numbers.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Combinatorics III We will refresh our minds on combinations and permutations from before spring break, and we will also begin to explore probability. Handouts: questions | class notesIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Combinatorics III We will refresh our minds on combinations and permutations from before spring break, and we will also begin to explore probability. Handouts: questions | class notesIntermediate 2A [gr.7-8 (Preston/Richard)]: Random Events II and Binomial Distribution We continue some probability theory ideas and introduce the binomial distribution!Handouts: randomEventsII_handoutIntermediate 2B [gr.7-8 (Kyle)]: Randomness II Hello Intermediate 2B students!We are continuing a bit of work from last week and introducing some additional and useful ideas in probability. Handouts: HandoutOlympiads 1: Ordinary Differential Equations Handouts: HandoutOlympiads 2: Algebraic Topology Handouts: Handout (3 Weeks) 4/18/2021 Advanced 1A [gr.9-10 (Nikita)]: Spring Game I Handouts: GameAdvanced 2A [gr.11-12 (Eilon/Yan)]: Lattices and Orchards We'll define the most common lattice and get some results relating regions to lattice points. We'll also see an application to Polya's Orchard problem. Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Lattice Points We will show that certain regions of Euclidean space must contain integer lattice points.Handouts: LatticesAdvanced 3 [gr. 12 (Aaron/Harris)]: Incidence Combinatorics 1 We explore the field of Incidence Combinatorics, learning about the Szemeredi-Trotter Theorem, sum-product estimates, and Erdos's unit and distinct distances problems.Handouts: ProblemsAMC10/12 Training: Trig Identities https://docs.google.com/presentation/d/1P9r9DyJ7LfomvKD1eP5vSxTR8tTKup82SM_UBtwCpg8/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 17 Recap and Quiz #5 Beginners 1B [gr.2-3 (Vivian)]: Lesson 17 Recap and Quiz #5 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 (Continued) This Sunday, we will continue with our exploration of sets by practicing with the concepts we have learned so far, learning about cardinality, and potentially attempting some challenging problems.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P1 (Continued) This Sunday, we will continue with our exploration of sets by practicing with the concepts we have learned so far, learning about cardinality, and potentially attempting some challenging problems.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Combinatorics Conclusion To test our knowledge of combinatorics that we learned over the past few weeks, we will go over 4 tough problems.Handouts: KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Combinatorics Conclusion To test our knowledge of combinatorics that we learned over the past few weeks, we will go over 4 tough problems.Handouts: class notesIntermediate 2A [gr.7-8 (Preston/Richard)]: Introduction to functions and formal proofs! We introduce some important ideas of functions and proofs, the bread and butter of maths. Handouts: functions and proofsIntermediate 2B [gr.7-8 (Kyle)]: Introduction to functions and proofs This week we introduce some general ideas about functions and proofs.As a friendly reminder, please change your zoom profile name to your actual ORMC registered name (this will help us identify you at the beginning of class)!Handouts: WorksheetOlympiads 1: Ordinary Differential Equations, Part II Handouts: Handout 4/25/2021 Advanced 1A [gr.9-10 (Nikita)]: Combinations III This week we continue our studies in combinatorics. We will finally see and apply the binomial theorem.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Pascal Advanced 1B [gr.9-10 (Hunter)]: Combinations and Pascal's Triangle 1.5 We review our last worksheet and continue with Combination questions.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Smart Codes I We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.Handouts: Handout | SolutionsAdvanced 2B [gr.11-12 (Matt/Glenn)]: Smart Codes I We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.Handouts: Smart CodesAdvanced 3 [gr. 12 (Aaron/Harris)]: Incidence Combinatorics 2 We explore the field of Incidence Combinatorics, learning about the Szemeredi-Trotter Theorem, sum-product estimates, and Erdos's unit and distinct distances problems.AMC10/12 Training: Piecewise Functions https://docs.google.com/presentation/d/1nQ6NQyNWm9-Tk3rhUhX-c-wQUcmYuSQDZfFfvDQI22k/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Continue with Lesson 17 Beginners 1B [gr.2-3 (Vivian)]: Continue with Lesson 17 Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 This week, we'll finish up with the first part of our exploration of sets and connect it to Venn Diagrams.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 This week, we'll finish up with the first part of our exploration of sets and connect it to Venn Diagrams.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Probability How can we estimate our dartboard score by using probabilities? Today we explore the first 7 problems (pages 1-4) of our probability packet.Handouts: Handout | class notesIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Probability I How can we estimate our dartboard score by using probabilities? Today we explore the first 7 problems (pages 1-4) of our probability packet.Handouts: Handout | class notesIntermediate 2A [gr.7-8 (Preston/Richard)]: Area Approximation of Shapes and Graphs! We learn to approximate areas of shapes and graphs; this is basically a small teaser to ideas of integration in calculus.Handouts: Area Approximation handoutOlympiads 1: Ordinary Differential Equations, Part III Handouts: HandoutOlympiads 2: Week 4 USAJMO Review reviewing the 2021 USAJMOHandouts: Notes p1 | Notes p2 | Notes p3 | main 5/2/2021 Advanced 1A [gr.9-10 (Nikita)]: Combinatorics IV (Stars and Bars) This week we will learn the technique called "Stars and Bars" and also solve some funny problems.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Combinatorics stars and bars We cover the technique of stars and barsHandouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Smart Codes II Advanced 2B [gr.11-12 (Matt/Glenn)]: Smart Codes II We will develop and study different types of binary codes that detect when a user has made an error. These will include ISBN, repeating codes, Hamming's square code, and Hamming's [7,4]-code. We will also be able to compare the efficiency of these codes.Handouts: Smart CodesAdvanced 3 [gr. 12 (Aaron/Harris)]: Homotopy Handouts: ProblemsAMC10/12 Training: Recursion https://docs.google.com/presentation/d/1Q7yFZVRIrwzQDi4PCRmGgZ7n7CXdl_E9FBUKeBc97us/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 18 Roman Numerals, The Skipped Rule Beginners 1B [gr.2-3 (Vivian)]: Lesson 18 Roman Numerals, The Skipped Rule Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) This week, we'll finish up the final challenge problem in the first part of our exploration of sets and afterward, begin exploring the connection between sets and Venn DIagrams.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) This week, we'll finish up the final challenge problem in the first part of our exploration of sets and afterward, begin exploring the connection between sets and Venn DIagrams.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Probability II Back to the basics: how can we describe probability for rolling dice and flipping coins? Today we tackle pages 5-10 of our probability worksheet.Handouts: Handout | KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Probability II Back to the basics: how can we describe probability for rolling dice and flipping coins? Today we tackle pages 5-10 of our probability worksheet.Handouts: Handout | KeyIntermediate 2A [gr.7-8 (Preston/Richard)]: Math Kangaroo - Mini Competition We go into our breakout rooms to do some problem solving. Intermediate 2B [gr.7-8 (Kyle)]: Area Approximation This week we introduce some ideas about area approximation, which is very useful in calculus. After this week we will have at least two handouts on one my favorite topics in math: graph theory!Handouts: HandoutOlympiads 1: Geometric Transformations Handouts: Handout 5/9/2021 Advanced 1A [gr.9-10 (Nikita)]: Stars and Bars II We continue our studies in combinatorics.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Combinatorics stars and bars II We continue solving problems using the stars and bars method.Handouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Competition!!! Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Competition I Handouts: Competition ProblemsAdvanced 3 [gr. 12 (Aaron/Harris)]: Quantum Information Handouts: ProblemsAMC10/12 Training: Special Functions https://docs.google.com/presentation/d/1vo2BFKE05-AOGGAuPw6h5FLi8wwllcyPnPY96H1BN34/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 19 Balance Scale Beginners 1B [gr.2-3 (Vivian)]: Lesson 19 Balance Scale Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) This week, we'll continue with our exploration of sets and incorporate the ideas and concepts we've learned so far into Venn Diagrams. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) This week, we'll continue with our exploration of sets and incorporate the ideas and concepts we've learned so far into Venn Diagrams. Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Probability III Today, we will complete the probability packet and explore set notation.Handouts: Handout | KeyIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Probability III Today, we will complete the probability packet and explore set notation.Handouts: Handout | KeyIntermediate 2A [gr.7-8 (Preston/Richard)]: Graphs and Geometry Handouts: HandoutIntermediate 2B [gr.7-8 (Kyle)]: Graph Theory Intro This Sunday we are working on some graph theory and geometry problems, with a bit of area approximation remaining from last week. As a friendly reminder please change your zoom profile name to your actual ORMC registered name (this will help us identify you at the beginning of class)!Handouts: WorksheetOlympiads 1: Geometric Transformations, Part II Handouts: HandoutOlympiads 2: Double summations and Root of Unity Filters A few tricks for sums on olympiadsHandouts: 5/16/2021 Advanced 1A [gr.9-10 (Nikita)]: Game 2 Handouts: GameAdvanced 1B [gr.9-10 (Hunter)]: Game 2 We play another midquarter gameAdvanced 2A [gr.11-12 (Eilon/Yan)]: Sequences Sequences are a fundamental part of advanced mathematics. We continue our study of metric spaces from last quarter by using them to define and study sequences.Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Convergence in Metric Spaces I We will define what it means for a sequence to converge in different metric spaces. We will explore many different examples like convergence with the taxicab metric or the discrete metric.Handouts: Convergence in Metric Spaces IAdvanced 3 [gr. 12 (Aaron/Harris)]: Primes and Counting Handouts: ProblemsAMC10/12 Training: Squeezing https://docs.google.com/presentation/d/18iNIzBPqQ0R65gpMm-ZIxQwQ5pn91AiPpFQScuYWCwA/edit#slide=id.gd170f84eb4_0_10Beginners 1A [gr.2-3 (Vivian)]: Lesson 20 Balance Scale and Binary Numbers Beginners 1B [gr.2-3 (Vivian)]: Lesson 20 Balance Scale and Binary Numbers Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) + Quiz This week we'll go through the challenge problems in the second sets handout and then take a short quiz on everything we've learned so far. If we have extra time, we'll work on some Math Kangaroo problems and Futoshiki puzzles.Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Sets and Venn Diagrams P2 (Continued) + Quiz This week we'll go through the challenge problems in the second sets handout and then take a short quiz on everything we've learned so far. If we have extra time, we'll work on some Math Kangaroo problems and Futoshiki puzzles.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Genetics How can probability be applied to more than dartboards, dice, and coins? Genetics! Today we will explore how we can use probability in biological applications to figure out blood types, hair colors, nose shapes, and more!Handouts: HandoutIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Genetics How can probability be applied to more than dartboards, dice, and coins? Genetics! Today we will explore how we can use probability in biological applications to figure out blood types, hair colors, nose shapes, and more!Handouts: HandoutIntermediate 2A [gr.7-8 (Preston/Richard)]: Graph Theory II We visit bipartite graphs!Handouts: Bipartite graphsIntermediate 2B [gr.7-8 (Kyle)]: Taxi-Cab Metric This week we are starting to look at the Taxi-cab metric: an awesome part of analysisHandouts: HandoutOlympiads 1: Inversion Handouts: Handout 5/23/2021 Advanced 1A [gr.9-10 (Nikita)]: Combinatorics VI (Young Diagrams) We introduce a new method to encode partitions of positive integers -- Young diagrams, and use them to prove some beautiful bijections on partitions.Handouts: HandoutAdvanced 1B [gr.9-10 (Hunter)]: Young Tableau We will continue with combinatorics and in particular, the method of using a Young tableauHandouts: HandoutAdvanced 2A [gr.11-12 (Eilon/Yan)]: Sequences II Handouts: HandoutAdvanced 2B [gr.11-12 (Matt/Glenn)]: Convergence in Metric Spaces II We define the notion of a continuous function using limits in arbitrary metric spaces. We apply the Intermediate Value Theorem to a range of functions on the real line.Handouts: Convergence in Metric Spaces IIAdvanced 3 [gr. 12 (Aaron/Harris)]: Primes and Counting 2 Handouts: With extra problemsAMC10/12 Training: Venn Diagrams & Intro to Sets https://docs.google.com/presentation/d/1QJVrmny8BNaV9ZIywmfFKkUITCwH7IOYbmCughXH0O4/edit?usp=sharingBeginners 1A [gr.2-3 (Vivian)]: Lesson 21 More Binary Numbers Beginners 1B [gr.2-3 (Vivian)]: Lesson 21 More Binary Numbers Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Quiz Review + Additional Problems This week, we'll review the quiz problems and work on some additional Venn diagram problems. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Quiz Review + Additional Problems This week, we'll review the quiz problems and work on some additional Venn diagram problems.Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: Genetics and Herd Immunity We will finish our genetics worksheet from last week and then start with a new topic: herd immunity! What needs to happen in a population to reach herd immunity? How can we approach it mathematically?Handouts: Handout | Key | Herd Immunity NotesIntermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: Genetics and Herd Immunity We will finish our genetics worksheet from last week and then start with a new topic: herd immunity! What needs to happen in a population to reach herd immunity? How can we approach it mathematically?Handouts: Handout | Key | Herd Immunity NotesIntermediate 2A [gr.7-8 (Preston/Richard)]: Propositional Logic Today we study some ideas in propositional logic. Handouts: Logic1Intermediate 2B [gr.7-8 (Kyle)]: Invariant I This week we are studying invariants!Handouts: Worksheet | Worksheet IIOlympiads 1: Linear Transformations Handouts: HandoutOlympiads 2: Dirichlet Characters Also discussion of finite abelian groupsHandouts: 5/30/2021 AMC10/12 Training: No Class Today! Memorial Day Beginners 2A [gr.3-4 (Ashin/Cassandra)]: No Class (Memorial Day Weekend) There is no class today due to Memorial Day weekend. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: No Class (Memorial Day Weekend) There is no class today due to Memorial Day weekend! Intermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: No class. Enjoy Memorial Day Weekend! Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: No class. Enjoy Memorial Day Weekend! 6/6/2021 Advanced 1A [gr.9-10 (Nikita)]: Math game for end of quarter! Advanced 1A [gr.9-10 (Nikita)]: Final game Game!Handouts: Advanced 1B [gr.9-10 (Hunter)]: Game We play an end of quarter game.Advanced 2A [gr.11-12 (Eilon/Yan)]: Final Competition! Handouts: CompetitionAdvanced 2B [gr.11-12 (Matt/Glenn)]: Competition II Handouts: Competition ProblemsAdvanced 3 [gr. 12 (Aaron/Harris)]: Competition Handouts: Competition_problems.pdfAMC10/12 Training: Mixed Review Beginners 1A [gr.2-3 (Vivian)]: Quiz #6 Balance Scale and Binary Numbers Beginners 1B [gr.2-3 (Vivian)]: Quiz #6 Balance Scale and Binary Numbers Beginners 2A [gr.3-4 (Ashin/Cassandra)]: Russian Math Exam This Sunday, we'll experience some Russian Math. Beginners 2B [gr.3-4 (Ashin/Cassandra)]: Russian Math Exam This Sunday, we'll explore some Russian MathIntermediate 1A [gr.5-6 (Doug Lichtman/Chynna Swift)]: The Greatest Hits For our last class, we will review all of the best problems and topics from the school year.Intermediate 1B [gr.5-6 (Chynna Swift/Doug Lichtman)]: The Greatest Hits For our last class, we will review all of the best problems and topics from the school year.Intermediate 2A [gr.7-8 (Preston/Richard)]: Math Dominos We have math dominoes problems by Nikita Gladkov.Handouts: Math Dominos Game with solutionsOlympiads 1: Linear Transformations -- Part II Handouts: HandoutOlympiads 2: Dirichlet's Theorem on primes Dirichlet's theorem on arithmetic progressions, an comprehensive outline thereofThis involves many standard manipulations of sums, complex numbers, and bounding argumentsHandouts: 6/13/2021 Advanced 2 Comp Handouts: Total | Measurement Errors | Smart Codes | Sequences Summer 2021 quarter // Filter groups by: AdvancedBeginners 1ABeginners 1BBeginners 2ABeginners 2BIntermediate 1Intermediate 2 6/27/2021 Beginners 1A [enter grade 2-3 in Fall]: Squares on a Chessboard Beginners 1B [enter grade 2-3 in Fall]: Squares on a Chessboard Beginners 2A [entering grades 4-5 in Fall]: Ciphers 1 Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!Handouts: Ceasar DiskBeginners 2B [entering grades 4-5 in Fall]: Ciphers 1 Welcome to Summer ORMC! This Sunday, we will start by exploring various exciting ciphers!Handouts: Ceasar DiskIntermediate 1 [grades 6-7 in Fall 2021]: Introduction to Modular Arithmetic For our first class we work on problems involving modular arithmetic.Handouts: Modular ArithmeticIntermediate 2 [grades 8-9 in Fall ]: Sets and Set Algebra Handouts: Week 1 Solutions | Week 1 Handout | Week 1 Hw 7/4/2021 Beginners 1A [enter grade 2-3 in Fall]: No Class: Happy Fourth of July! Beginners 1B [enter grade 2-3 in Fall]: No Class: Happy Fourth of July! Beginners 2A [entering grades 4-5 in Fall]: No Class (Independence Day) Beginners 2B [entering grades 4-5 in Fall]: No Class (Independence Day) Intermediate 1 [grades 6-7 in Fall 2021]: No Class (Independence Day) We will resume our selection of topics next week. We have a few problems for you to solve if you didn't complete them with your instructor last week.Handouts: Homework 7/11/2021 Beginners 1A [enter grade 2-3 in Fall]: Chessboard Games Beginners 1B [enter grade 2-3 in Fall]: Chessboard Games Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher. Handouts: Rail Fence Cipher TemplateBeginners 2B [entering grades 4-5 in Fall]: Ciphers 2 This week, we'll continue with our exploration of ciphers by reviewing the reverse, Caesar, and Polybius Ciphers. We'll also learn about the Pigpen and Rail Fence Cipher. Handouts: Rail Fence Cipher TemplateIntermediate 1 [grades 6-7 in Fall 2021]: Introduction to Graph Theory! This Sunday we introduce ourselves to ideas in graph theory. We also include solutions to those general problems from the 27th of June.Intermediate 2 [grades 8-9 in Fall ]: Power Set and Cartesian Product Handouts: Week 3 Solutions | Week 3 Handout | Week 3 Hw 7/18/2021 Beginners 1A [enter grade 2-3 in Fall]: Chessboard Games Part 2 Beginners 1B [enter grade 2-3 in Fall]: Chessboard Games Part 2 Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 (Continued) We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.Handouts: Rail Fence Cipher TemplateBeginners 2B [entering grades 4-5 in Fall]: Ciphers 2 (Continued) We'll work through the student-generated codes and learn about the Pigpen and Rail Fence Cipher.Handouts: Rail Fence Cipher TemplateIntermediate 1 [grades 6-7 in Fall 2021]: Knights and Knaves (and Finishing Graph Theory) We finish our graph theory handout from last week, and begin with knights and knaves.Handouts: knights and knavesIntermediate 2 [grades 8-9 in Fall ]: Functions Between Sets Handouts: Week 4 Handout | Week 4 Solutions | Week 4 Hw 7/25/2021 Beginners 1A [enter grade 2-3 in Fall]: Digits and Numbers Beginners 1B [enter grade 2-3 in Fall]: Digits and Numbers Beginners 2A [entering grades 4-5 in Fall]: Ciphers 2 (Continued) + Lesson 3 Recap This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far. Beginners 2B [entering grades 4-5 in Fall]: Ciphers 2 (Continued) + Lesson 3 Recap This week, we'll finish lesson 2 by practicing with the Rail Fence Ciphers. Afterward, we'll begin Lesson 3 by doing a recap of everything we've learned so far. Intermediate 1 [grades 6-7 in Fall 2021]: Introduction to Probability We introduce some ideas in probability! Handouts: Probability1_2Intermediate 2 [grades 8-9 in Fall ]: Review Handouts: Week 5 Handout | Week 5 Solutions 8/1/2021 Beginners 1A [enter grade 2-3 in Fall]: Coordinates Beginners 1B [enter grade 2-3 in Fall]: Coordinates Beginners 2A [entering grades 4-5 in Fall]: Lesson 3 + Knights and Liars This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars. Beginners 2B [entering grades 4-5 in Fall]: Lesson 3 + Knights and Liars This Sunday, we'll review the problems from the quiz, finish up Lesson 3, and, if we have extra time, jump over to Lesson 10 to explore the puzzling island of Knights and Liars. Intermediate 1 [grades 6-7 in Fall 2021]: Probability Continued This Sunday we continue our introduction in probability.Handouts: Probability IIIntermediate 2 [grades 8-9 in Fall ]: Compostion of Functions, Inverse Images, and Inverse Functions Handouts: Week 6 Handout | Week 6 Solutions | Week 6 Hw 8/8/2021 Beginners 1A [enter grade 2-3 in Fall]: How to Fight a Dragon Beginners 1B [enter grade 2-3 in Fall]: How to Fight a Dragon Beginners 2A [entering grades 4-5 in Fall]: Lesson 10: Knights and Liars This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.Beginners 2B [entering grades 4-5 in Fall]: Lesson 10: Knights and Liars This week, we'll review the homework problems from Lesson 3 and begin Lesson 10, which focuses on Knights and Liars.Intermediate 1 [grades 6-7 in Fall 2021]: Fractions and Decimals We work on some fractions and decimals problems this Sunday.Handouts: FractionsDecimalsIntermediate 2 [grades 8-9 in Fall ]: Cardinality of Sets Handouts: Week 7 Handout | Week 7 Solutions | Week 7 Hw 8/15/2021 Beginners 1A [enter grade 2-3 in Fall]: How to Fight a Dragon Part 2 Beginners 1B [enter grade 2-3 in Fall]: How to Fight a Dragon Part 2 Beginners 2A [entering grades 4-5 in Fall]: Logic Puzzles: Knights and Liars (Continued) This Sunday, we'll work through the final problems in Lesson 10: Knights and LiarsHandouts: Solutions_Math_KangarooBeginners 2B [entering grades 4-5 in Fall]: Logic Puzzles: Knights and Liars (Continued) This Sunday, we'll work through the final problems in Lesson 10: Knights and Liars.Handouts: Solutions_Math_KangarooIntermediate 1 [grades 6-7 in Fall 2021]: Math Dominoes! We will have a math dominoes competition based on what we've learned this season. Intermediate 2 [grades 8-9 in Fall ]: Game Week! Handouts: Game Problems | Game Answers