Enrichment • Series
Lines In-Context: Using y=mx+b as an Introduction to Advanced Mathematical Concepts.
BL
RS
Riley S
This series ended on March 24, 2023. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
This series relies upon knowledge from previous sessions, so please ensure you are able to come to almost every session. While the content may seem too difficult, this session is designed to be accessible and helpful to those on different parts of their math journey.
Often, we learn math in isolation. We learn about variables, then lines, then exponents, then angles, then vectors -- all without being taught how it connects to past and future topics. This course aims to help bridge this gap by using existing knowledge about lines to seamlessly introduce complicated mathematical concepts in an easily-understandable way.
This series is designed for students who know the basics of linear equations, usually taught in pre-algebra. While we will be covering it again, it will be from a different perspective from how it’s usually taught. Familiarity with Slope-Intercept Form and finding the intersection of two lines will help you greatly. We will create connections between lines and more advanced areas of math like trigonometry and linear algebra by exploring topics such as polar coordinates, Voronoi diagrams, systems of equations as a matrix, applications in word problems, and basic Calculus concepts. So, this course should be helpful for recent pre-algebra students and calculus students alike.
Tutor Qualifications
The Art of Problem Solving's AP Calc BC
International Baccalaureate's Math Applications and Interpretations Higher Level
I do a lot of math-based programming, and have self-studied the basics of Linear Algebra. This means I am very comfortable with lines and have experience with how they are used in various areas.
✋ ATTENDANCE POLICY
You will be withdrawn from the series if you miss 1 session without contacting the tutor within a week.
Dates
January 20 - March 24
Learners
12 / 20
Total Sessions
9
About the Tutor
BL
RS
International Baccalaureate student in QLD, Australia. Also lived in England, Kansas, and Tasmania. Learning to program 3D Rendering Engines.
View Riley S's Profile
Upcoming Sessions
0
Past Sessions
9
20
Jan
O
Session 1
Orientation
SESSION 0: Orientation
Please note that this session is 1 hour long, whereas the rest are 1.5 hours long.
We will start with a short introduction and a group activity. After, we will do other activities so I can understand everyone's current math level. Next, we will have an overview of the course content. If time permits, we will start the course content.
27
Jan
EM
Session 2
Even More Math
SESSION 1: Line Basics
Attending this session is crucial, since all following lessons rely on this knowledge!
We will cover familiar content in a more rigorous manner. We will start by introducing lines. We will explore the limitations of the slope-intercept form of the line, y=mx+b. Next, we will derive and understand some other common forms of a line, such as the point-slope form, point-point form, and the general form. We will then explore the three standard ways of solving linear systems of equations: Graphing, Substitution, and Elimination.
After this session, you should have through intuition behind the foundations of lines!
3
Feb
EM
Session 3
Even More Math
SESSION 2: Polar Coordinates
We will start with a short review. Next, we will explore exactly what information is needed to create a line. We will extend these conclusions to a very important part of math closely related to trigonometry: Polar Coordinates. We will connect this to a new concept of "different-sized infinities." Now, we will use polar coordinates to define a line. This will lead us to some important geometric problems, including perpendicular bisectors and parallel lines.
10
Feb
EM
Session 4
Even More Math
SESSION 3: Vonori Diagrams + Review
Generalizing our understanding of perpendicular bisectors to rectangular coordinates, we will explore a powerful system: Vonori Diagrams. This will encourage exploration of the midpoints of line segments. We will be exposed to the basics of graph theory which will demonstrate the power of these diagrams.
At the end, we will complete a collection of review problems to consolidate our understanding of lines. From hereon out, we will be uncovering advanced mathematical concepts which require a deep understanding of lines.
17
Feb
EM
Session 5
Even More Math
SESSION 4: Dimensionality, Geometry, and Infinity
Using our understanding of vectors, we will start by generalizing lines to the 3rd dimension, then to the nth dimension. After, we will distinguish between euclidean and non-euclidean spaces. By extending polar form into the 3rd dimension, we will show how spherical spaces break our foundational understanding of lines. This will lead into a continuation of our discussion about different-sized infinities. We will briefly talk about hyperbolic geometric spaces, and then tie everything back to our generalizations to the nth dimension.
24
Feb
EM
Session 6
Even More Math
SESSION 5: Linear Algebra
Welcome to the number line! We will go right back to basic arithmetic, viewing it from a new perspective. Taking this to the Cartesian plane, we will introduce an uncommon method of representing lines which exposes a foundational idea in linear algebra. Next, we will combining vectors to create a matrix and discus how this represents an alteration of the coordinate plane. Finally, we will go back to lesson one and learn how to solve systems of linear equations using matrices and gain some intuition.
If time permits, we can extend this into the 3rd dimension.
3
Mar
EM
Session 7
Even More Math
SESSION 6: Physics and Calculus
The session many of you have been waiting for!
We will use the quirks of lines to introduce some ideas behind integration and differentiation. After a brief chat about quadratics, we will complete a typical introduction to calculus. We will explore how the quirks of lines are closely related to calculus concepts like limits and continuity. To help everything make sense, we will use these calculus concepts to explore acceleration, velocity, and distance.
17
Mar
EM
Session 8
Even More Math
SESSION 7: Options Day
We will talk more about this during our sessions. We can take another session to expand on your favorite topic, we can explore applications, do practice questions, or discover something completely new! You get to pick what we cover.
24
Mar
R
Session 9
Review
SESSION 8: Review / Options Day
We can take another session to expand on your favorite topic, we can explore applications, do practice questions, or discover something completely new! You get to pick what we cover.