Complex numbers are an area where algebraic and geometric perspectives provide very different strengths and intuitions. Having a firm grasp of both perspectives and being able to switch from one … Read More
Category: Lessons (Page 2 of 3)
What does it mean to raise a number to a power?
What if the power is whole number? An integer? A rational number? A real number?
For a specific example, … Read More
Polynomials and their roots
What are the polynomials? They are a particular collection of functions.… Read More
Why do we spend so much time studying quadratic functions, but relatively little time on cubic functions, quartic functions, quintic functions, and so on?
Putting together our work from yesterday, can we answer the following?… Read More
Definition. A parabola is the set of points equidistant from a given point $P$ and a given line $L$ (not containing the given point).
Definition. A quadratic function
How do we define the slope of a line?
The coordinate plane
The coordinate plane, labelling each point in the plane with a pair of numbers (coordinates), allows us to … Read More
What does it mean for two line segments OR triangles OR other subsets of the plane to be “the same shape”?
The concept of “shape”, the concept of “similarity”… Read More
The main issues [with TSMs treatment of geometry] may be summarized as follows:
- The high school geometry course cannot be the only place in the K–12 curriculum where definitions, theorems,
Every fraction has a unique reduced form, and there is a sequence of explicit steps to obtain the reduced form.
This section proves that every fraction has a unique reduced … Read More