Struggling with teaching or learning High School Math?

Have no fear, Mr. Starzynski is here to guide you through High School Math from grades 9-11 with grade 12 coming during the 24/25 academic year.

Whether you're a fan of math or find it challenging, Mr. Starzynski's lessons will help you see and understand math through the Waldorf approach.

Our math courses provide an academic year-long math track designed to enhance your ability for logical thinking by engaging in and honing math skills. In this way, you may advance your learning,  increase your appreciation for, and improve your overall understanding of the beauty of mathematics.

Additionally, each corse features a 4 week Math Main Lesson block, allowing the student to immerse themselves in a new topic thoroughly. This deep dive ensures proper introduction and exploration of the topic, engaging head, heart, and hands through historical context, artistic expression, and problem-solving activities.

Here's a glimpse into what each corse provides:

• Grade 9 - We will begin this course with a review of prealgebra concepts. We will then dive straight into algebra spending a significant portion of the year on solving linear equations using multiple techniques. Along the way, we will review and deepen basic geometry concepts and begin to look at combining geometry and algebra (a.k.a. graphing). Ultimately, the course will build up to solving 2nd-degree equations (quadratics). During this year, we will also look at several interesting math puzzles.

  
  Permutations, Combinations & Probability Main Lesson: 
  
  “Probability is the very guide of life.” -Cicero"
  
  The Permutations, Combinations & Probability Main Lesson is an exploration into possibilities and chance. We will learn how to find the number of possible outcomes in an event and then use these outcomes to discover the likelihood of a specific outcome occurring. Along the way, we will learn how probability theory developed during the 17th century and we will look at various applications.

• Grade 10 - This course will cover the fundamental concepts of geometry and will lead into Algebra II, Trigonometry and Logarithms. We will begin with an overview of basic geometrical forms such as triangles and quadrilaterals. We will then look more at angles and the relationship these have in and out of circles. As the year progresses, we will go from analyzing the areas of triangles and circles to looking at the volumes of more complex, three-dimensional figures such as cones and spheroids. We will also look at the Pythagorean Theorem, ratios and proportions of geometrical objects, proofs and basic trigonometry. This will continue into the spring semester where we will pick up with an extensive review of solving linear and quadratic equations. The student will learn to simplify complex expressions and solve intricate equations. We will also delve into analytic geometry (graphing).
  
  Greek Geometry Main Lesson: The 10th Grade Greek Geometry Block is an exploration into the Greek mathematical mind. Beginning each day with Pythagoras’s Golden Verses, we ask the questions that the Greeks also asked for the first time in humanity’s history: How do we know what we know? The essence of proof is explored, and, through the well-known Pythagorean Theorem, many different kinds of proofs were experienced. Proof is what brought the Pythagoreans to crisis when they proved that the diagonal and the side of any square were incommensurable! The power of pure thought and the true nature of the perfect circle (as something that resides only in our minds) were explored. , that number defined by a circle, is another mysterious incommensurable number, which nevertheless, Archimedes found a reliable way to approach. Between Pythagoras and Archimedes came Euclid, the Father of Geometry. Understanding the new Greek motivation to know the world through observation and thinking (rather than story and tradition) allows us to see why Euclid devoted his life to the systematic construction of theory after theory, based only on a handful of assumptions (postulates), definitions, and logical presuppositions. Finally, after practicing our hand at the Great Greek Geometric Game using only compass and straightedge, we apply our own formidable powers of thought to understanding Euclid’s own proof of the Pythagorean Theorem.

• Grade 11 - This course will cover topics from Algebra II and Precalculus. We will begin with a thorough introduction (possibly review depending on grade level) of 2D Cartesian coordinates. After that we will move on to reviewing Trigonometry and then go into Complex Numbers. This will be followed by combining all three subjects together along with an extensive review of algebra and an introduction of function terminology. Along the way, the student will look at graphs and roots of polynomials, exponential and logarithmic functions, ambiguous cases in trigonometry and much more.

  
  Projective Geometry Main Lesson:

  “An approach to the secrets of space from the standpoint of artistic and imaginative insights.”- Lawrence Edwards

  The 11th Grade Projective Geometry Block is a challenging, highly imaginative exercise, stretching the limits of our traditional “Euclidean” worldview. Through various geometric constructions first discovered by Pappus, Desargues, Pascal and Brianchon, the student will explore the ways in which mathematicians for 2000 years flirted with the ideas which we now recognize as projective constructions. The effort moved forward when artists in the 15th century began to wonder how to depict scenes on flat paper which appeared to be three dimensional. PG was only recognized and developed in the 19th century. Through these explorations, we will come to appreciate a completely unfamiliar space reality which is just as valid, and in fact more generally true, than the one with which we are more used to dealing.

• Grade 12- This course will cover topics from Precalculus, Statistics and Data Management and Calculus. We will begin with a thorough review of precalculus concepts including simplifying radicals and rational expressions, The Fundamental Theorem of Algebra and Analytic Geometry. We will also review and extend our knowledge of logarithms and trigonometric functions. As the year continues, the student will dive into Statistics and Data Management learning to analyze, organize, and graph large groups of data. There will be projects to undertake and present and the student will look at the current state of statistics in the world. We will then begin our transition into Calculus. The student will begin this journey by thoroughly looking at average rate of change. The student will work on numerous applications from everything involving speed to changes in the pricing of lumber. The next question that will be asked is how fast is something moving at an instant in time? The student will look at estimating what is known as the instantaneous rate of change or the derivative using the average rate of change. It will become apparent that in order to calculate the derivative, we need a new concept to overcome division by zero. What we need is the mathematical concept of a limit. We will look at properties of limits and continuity and then used the average rate of change and the idea of a limit to find the formula for finding the derivative of a power function.

  
  History of Math Main Lesson Block: 
  
  “Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.”
  -Shakuntala Devi
  
  This main lesson will begin at the beginning of time and go through the modern age highlighting the journey humankind took towards the discovery of The Calculus. The student will look at how math developed in each Era and how it developed in different ways in different parts of the world. Themes include the continuous vs. discrete debate, irrational numbers, constructions, developing infinite series and much, much more. The student will look at how mathematical development shaped human thought around the world and they will look at what came after each great mathematical discovery.

Do you want to take live classes with Mr. Starzynski?

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