The Algebra+ class will be aligned with the Algebra I standard curriculum, but will seek to be different in a few important ways.
1) The Set Up: When it comes to word problems, many students struggle with creating the correct equations to set up the problem. The same issues exist with Geometry - most of the hard work is creating the algebraic set-up. Our program will spend significant time practicing setting up problems.
2) Desmos: Our program will spend significant time using Desmos (a powerful online graphing tool) to bring algebra to life. In Desmos, we can create a range of geometric 'targets,' from the simple to the very complex and beautiful. Students (and adults) love Desmos. It enables them to be creative explorers, and in this class will give them a real sense of the power of algebra.
3) Gaps: We will fill in important gaps. As an example, in this class students will memorize the quadratic formula and know how to use it. They will also understand the derivation both from an algebraic and geometric point of view. Students will also be introduced to Viete’s Formulas, a beautiful piece of mathematics that relates the coefficients of a polynomial to its roots.
4) Creative Problem Solving: Problems from the CMMS textbook (chapter 1) will be incorporated into the Algebra+ curriculum, along with additional competition questions for those students who want an additional challenge.
Because many students enrolled in MSM II will be enrolled in Algebra I in school as 7th or 8th graders, we view Algebra+ and MSM II as companion courses.
All of our Advanced Topics seminars are being offered online through Zoom. The maximum enrollment for each seminar is 10. Students will work closely with their coach and collaborate in pairs and small groups. Due to the small class size, they will have many opportunities to present solutions to the entire group.
Counting and Probability
Counting and Probability is a fun and challenging area of mathematics. We are looking forward to sharing some visual approaches that are both powerful and efficient. The program will work through 2 chapters from the CMMS textbook, supplemented by additional problems from a wide range of sources. We will also go into more depth on Pascal's Triangle, P.I.E, as well as some special types of “numbers that count,” including Fibonacci, Tribonacci, and Catalan numbers.
While some of the fundamental concepts in this class are accessible to younger students, some of the more challenging questions often require more mathematical maturity. As a result, we view this as a companion course to the MSM III class, typically attended by 8th graders. Veterans of MSM II are encouraged to consider taking both classes. We expect a handful of talented / motivated students from lower grades will join us as well.
I have found that many - if not most - of the Middle-School-Mathletes have a tough time solving the geometry questions that typically show up on competitions. The Geometry chapter in the textbook that we will use has hard problems. We will also use other textbooks and competitions to provide a rich landscape of questions.
This program will provide very good exposure for students who will take Geometry now, or in the future. While the class will not focus on proof writing, I will provide proofs of some of my favorite results. We will likely touch on all of the main theorems covered in a typical high school geometry class *and more.* It turns out, creative problem solving is often similar to doing proofs - I encourage students to justify their steps as they solve. Students will make - and share - presentations of some of their solutions. I have found students rise to the occasion when given this opportunity, and often exceed by expectations.
In this class there will be a small amount of homework. If you want to get good at something, you have to practice more than 1x a week (!).
I absolutely love geometry. I think these problems are fun, and I’d like to get our MSMs to the point where they actually LOOK for the geometry problems on competitions because it plays to their strength. It will take time and hard work. But I know they can do it.