Middle School Competition Math Classes
This class series is for middle school students who love math and are interested in learning more beyond the normal school curriculum. It will also provide a solid foundation for those going into competition math. Targeted toward 5th-8th grade students, the course started in Oct. 2022 and will last until the summer of 2023, covering the following two materials..
Algebra Unit
Geometry Unit
Combinatorics Unit
Number Theory Unit
Competition Math Workshop Session 1 Summary (11/11/2022)
We first reviewed problems students found hard on last week’s homework. Then, we did a timed practice test to see people’s baseline experience with competition math. Finally, we looked at some important ideas in counting, such as casework and permutations.
Competition Math Workshop Session 2 Summary (11/18/2022)
First, we reviewed hard problems from last week’s homework. After that, we looked at the important idea of probability, and how to solve for it using counting techniques learned in the workshop so far such as casework. We then practiced probability problems and continued to practice our casework. For homework, students should try the 2001 AMC 8 and come to class with any questions
Competition Math Workshop Session 3 Summary (12/2/2022)
Today, we did a lot of practice with counting problems. Many of the problems we looked at were types of problems that will show up often in math competitions. We focused on techniques such as casework, permutations, and combinations.
Competition Math Workshop Session 4 Summary (12/09/2022)
We first went over tough problems from last week’s homework. Next, we continued our practice of permutations and combinations. We reviewed factorials, kept practicing common problems such as letter-arrangement, and continued to practice casework.
Competition Math Workshop Session 5 Summary (12/16/2022)
We first reviewed frequently missed problems on last week’s quiz. Next, we continued our review of permutations and combinations, emphasizing which types of problems would use permutations and which would use combinations. We also continued practicing other concepts, like casework.
Competition Math Workshop Session 6 Summary (1/13/2023)
This week, we finally moved onto our next unit, Number Theory! But because of our 3-week break, we did some Counting & Probability review first. We first reviewed hard homework problems, then did some combinations review by introducing the common competition math problem of counting paths on a grid. We then played a fun Gimkit game with Counting & Probability questions.After that, we started some Number Theory by looking at factors, prime factorization, and counting the number of factors a number has.
NOTE: There is a correction that should be made for a Gimkit question. For the question ‘Tommy has a die that can roll a 3 on 3 of the sides and a 5 on the other 3 sides. Beatrice has a die that can roll a 2 on 4 of the sides and a 6 on the other 2 sides. What is the probability of Tommy winning?’ The answer should be 1/2×4/6+1/2×4/6=2/3, not 1/2.
Competition Math Workshop Session 6 Summary (1/13/2023)
This week, we finally moved onto our next unit, Number Theory! But because of our 3-week break, we did some Counting & Probability review first. We first reviewed hard homework problems, then did some combinations review by introducing the common competition math problem of counting paths on a grid. We then played a fun Gimkit game with Counting & Probability questions.After that, we started some Number Theory by looking at factors, prime factorization, and counting the number of factors a number has.
NOTE: There is a correction that should be made for a Gimkit question. For the question ‘Tommy has a die that can roll a 3 on 3 of the sides and a 5 on the other 3 sides. Beatrice has a die that can roll a 2 on 4 of the sides and a 6 on the other 2 sides. What is the probability of Tommy winning?’ The answer should be 1/2×4/6+1/2×4/6=2/3, not 1/2.
Competition Math Workshop Session 7 Summary (1/21/2023)
This week, we continued our new unit on Number Theory. We first reviewed divisibility rules, which we learned last week. We then looked at factorization, including how to find prime factorizations with factor trees and how to count the number of factors a number has. We then started to look at GCF and LCM. For each concept, we went over some practice problems and applications of the concept you might see on competitions.
Competition Math Workshop Session 8 Summary (1/27/2023)
This week, we did a review of the 2023 AMC 8. We went over problems and solutions to the last ten problems, #16-25.
Competition Math Workshop Session 9 Summary (2/3/2023)
This week, we continued our Number Theory unit. First, we went over difficult homework problems. Then we looked at number theory problems involving prime factorization, including how to find the number of factors of a number, and the product of the factors of any number.
Competition Math Workshop Session 10 Summary (2/10/2023)
This week, we continued our Number Theory unit. We kept practicing number theory problems involving prime factorization, including how to find the number of factors of a number, the product of the factors of a number, and the sum of the factors of any number. We looked at several variations of such problems, including a few challenge problems.
Competition Math Workshop Session 11 Summary (2/24/2023)
This week, we continued our Number Theory unit. We first reviewed prime factorization and how to easily find the number of factors of a number. We then introduced some new concepts, such as different number bases and modular arithmetic. We also looked at problems involving the units digit of numbers, an important idea for math competitions.
Competition Math Workshop Session 12 Summary (3/3/2023)
This week, we finished our Number Theory unit. We first reviewed all the concepts we covered, including: divisibility rules, prime factoring, finding the number of factors, sum of factors, and product of factors, factorials, and bases. We then had a quiz on the Number Theory unit. Next week, we will be starting our Geometry unit!
13 Summary (3/10/2023)
This week, we started our Geometry unit. We first reviewed frequently missed problems from the Number Theory quiz. Then we started looking at beginning geometry concepts, such as angles, parallel lines, and triangles. We solved several practice problems involving these concepts.
Competition Math Workshop Session 14 Summary (3/17/2023)
This week, we first reviewed the material about polygons and their angles from the first lesson. Then, we went straight into learning about different types of quadrilaterals and their properties, later applying the knowledge to some practice problems. Afterward, we learned about similar triangles and the Pythagorean Theorem, some important concepts that really form the basis for competition math in Geometry.
Competition Math Workshop Session 15 Summary (4/07/2023)
This week, we continued our Geometry unit by looking at circle problems. We talked about chords, tangents, secants, arcs, inscribed angles, cyclic quadrilaterals, and more. Then we looked at several practice problems involving these concepts.
Competition Math Workshop Session 16 Summary (4/14/2023)
This week, we continued our geometry unit and practiced solving many types of problems. We first reviewed some concepts from last week, such as inscribed angles and arcs. We then practiced several problems involving finding the perimeter or area of unusual shapes. In this week we also introduced the Pythagorean theorem.
Competition Math Workshop Session 17 Summary (4/23/2023)
This week, we continued with our geometry unit and practiced solving various types of problems. We began by attempting to prove the Pythagorean theorem and then applied it to solve problems related to distance and 3D shape geometry. We also reviewed two types of special right triangles, namely the 45-45-90 and 30-60-90 triangles, and practiced solving several problems related to them.
Competition Math Workshop Session 18 Summary (4/28/2023)
This week, we continued our geometry unit and practiced solving many problems. We started by reviewing special right triangles, such as 30-60-90 triangles and 45-45-90 triangles. We practiced many problems involving these triangles, as well as problems involving the Pythagorean Theorem and/or Area formulas
Competition Math Workshop Session 19 Summary (05/05/2023)
A guest speaker, Jerry Zhang, joined us this week! We continued our geometry unit, looking at 3D topics in geometry. We practiced problems involving Polyhedron, Prisms, and Pyramids. We also looked at problems with spheres, cones, and cylinders. There is no homework this week!
Competition Math Workshop Session 20 Summary (05/12/2023)
A new teacher, Peter Bai, joined us this week! We continued our geometry unit, finishing up 3D geometry and getting into similarity. We practiced a lot of problems involving similar triangles especially. We also reviewed ideas such as inscribed angles.
Competition Math Workshop Session 21 Summary (05/21/2023)
This week, we finished up looking at similar triangle relationships. We also learned the angle bisector theorem. We then did a huge review of all the concepts we’ve learned throughout this unit. Next week is our Geometry unit quiz!
Extra note: We actually made a mistake for the practice problem 1 that we discussed- because the sides that are staying constant are the 17 and 8 lengths of the triangle, the x length will actually get smaller as the angle increases. So, x must be greater than 10 and below sqrt(226), so there are only 5 possible choices for x.
Competition Math Workshop Session 22 Summary (05/26/2023)
This is the last class of our geometry unit, we tried couple of review practices at first, then had a fun Kahoot game. We concluded our Geometry unit with a comprehensive Quiz. If anyone was not able to finish it in the class, here is the link https://forms.gle/dMUpdYePQJPjW1kU8, Please time it for 45 minutes.
We will start our Algebra Unit Next week. In addition, I would greatly appreciate if you could fill out this short survey! https://forms.gle/2ze7W7Gwo2VbuEXm6
Competition Math Workshop Session 23 Summary (06/04/2023)
This week, we began our algebra unit! We first looked at the basics of what variables were, and how to solve linear equations. We then looked at how to do some common types of problems. We finished off with many review problems.
Competition Math Workshop Session 24 Summary (06/11/2023)
This week, we continued our algebra unit! We first looked at frequently missed questions of the Geometry unit quiz. Then we reviewed common problem types from last weeks. We then looked at the 3 main forms of linear equations can be written into: slope-intercept form, point-slope form, and standard form.
Competition Math Workshop Session 25 Summary (06/18/2023)
This week, we continued our algebra unit. We first reviewed the ideas of linear equations from last week. Then we began learning about systems of equations and the 2 ways to solve them: substitution and elimination. Throughout, we practiced many common problem types.
Competition Math Workshop Session 26 Summary (06/25/2023)
This week, we started off class with an algebra riddle. Then, we continued where we left off from last class, solving problems involving systems of equations. We also started discussing about ratios, proportions, and percents, ending with a small review of everything we have learned so far. The problems ranged from the most recent material, such as proportions and percents of change, to earlier class material, such as speed, distance, and time.
Competition Math Workshop Session 27 Summary (07/11/2023)
This week, we continued our algebra unit. We went over ways to factor equations, such as the distributive property and differences of squares. Throughout, we practiced many common problems involving such concepts. We also looked at exponents and got into some sequences and series.
Competition Math Workshop Session 28 Summary (07/16/2023)
This week, we started off with a review of the arithmetic sequence and went on to learn about the methods to solve arithmetic series, the geometric sequence, and the geometric series (both finite and infinite) problems. Later, we practiced using the formulas on various word problems and later started the review for the algebra unit.
Competition Math Workshop Session 29 Summary (07/23/2023)
This week, we finished up our algebra unit, and also our very last class! We first did some review of the algebra unit, before moving on to a 45-minute algebra quiz. We finished off with a fun Blooket that covered problems from over all 4 units. Thanks to all of you for joining us in learning and practicing math!