Intuition Series
I am writing a series of blog posts about how to build intuition for junior high math concepts.
Intuition - Quadratic Formula
6 May 2024
Last class, we learned about the quadratic formula and the discriminant (I am talking about math!).
Intuition: Completing the Square
2 May 2024
Today we learned about completing the square. This is essential to finding the quadratic formula, and can be used to solve quadratic equations on its own. The important part of this is that these methods have a 100% success rate, meaning that you don’t have to guess to solve a quadratic.
Intuition - Radicals Chapter
30 April 2024
This chapter was about radicals. I decided to do one intuition post for the whole chapter. I will first show how to find radicals, introduce some vocab, and then show how to do problems with radicals.
Intuition - Trig Functions
19 April 2024
Today, we learned the basic trig functions. This is actually part of the radicals unit. If you are wondering why there hasn’t been many posts lately, it’s because I wanted to do all of radicals in one post.
Intuition - Proportions
11 March 2024
Today, we learned to solve some proportion-related problems.
Intuition - Update
26 February 2024
Sorry for not posting.
We had a lot of review days, a test day, and a whole break, so there wasn’t anything to go over.
Intuition - Factoring Part 4
9 February 2024
These past 3 classes, we didn’t do much except for review and take quizzes.
We learned: Solving non-linear equations, finding x-intercepts and y-intercepts of a quadratic graph, finding the vertex of a quadratic graph, and factoring sum and difference of cubes.
Intuition: Factoring Part 3
1 February 2024
Today, we learned another way of factoring when \(a\) isn’t \(1\). We also learned how to identify and factor perfect squares.
Also, I forgot about a very intuitive way to distribute 2 binomials, so I’ll include that here.
Intuition: Factoring Part 2
31 January 2024
Today we learned about factoring quadratic trinomials and factoring difference of squares.
Intuition - Factoring Part 1
28 January 2024
In this class, they (not including me, I wasn’t there) learned about factoring. This most likely isn’t the factoring you’re thinking about.
We learned three things: factoring a GCF out of a list of terms, factoring a GCF out of polynomials, and factoring 4-termed polynomials.
Intuition: Polynomial Division
19 January 2024
In this class (well, technically last class), we learned to do polynomial division. Polynomial division is when you divide one polynomial by another. An example of polynomial division would be: \(\frac{x^2+2x+1}{x+1}\).
Here’s a one-line strategy to solve the problem: Pretend those are two numbers in base x, and then divide regularly.
Intuition: Multiplying Polynomials
12 January 2024
Today, we learned about multiplying polynomials together with each other. What we learned looks like:
\((a_1x+a_0)(b_1x+b_0)\),
\((a_2x^2+a_1x+a_0)(b_1x+b_0)\),
or sometimes, \((a_1x+a_0y)(b_1x+b_0y)\),
but really, this can apply to any degree of polynomial, with as many polynomials multiplied together as you want, with as many variables as you want in each polynomial.
There isn’t much intuition for expanding stuff, even though it’s kind of hard sometimes, so I’ll try to add exercises to test your intuition.
Intuition: Operations with Polynomials
10 January 2024
Today, we learned about some operations with polynomials. Specifically, we learned how to do:
\(polynomial + other \hspace{0.15 cm} polynomial\),
\(constant \cdot polynomial\),
\(monomial \cdot polynomial\),
as well as some vocabulary.
There isn’t much intuition to go through today, as it’s mostly just distributing. I’ll still go through all of the stuff, just in case anybody is using this to learn.
Also, I'll teach you how to not panic when faced with a gigantic math thing.
Intuition - Exponential Interest
12 December 2023
Today, we learned about exponential interest. The formulas are:
\(f(t)=a(1+r)^t\),
and \(g(t)=a(1-r)^t\).
We’ll also go into finding \(e\).
Intuition - Exponent Graphs
12 December 2023
This class, we learned about graphing exponents, as well as translating them and dilating them. I’ll go through everything that we learned, but I think that translation of functions and asymptotes of graphs are much more worthwile to study deeply than the others.
Things we learned:
Graphing exponential functions
Exponential growth/decay
Range and domain of exponential functions
Asymptotes of exponential functions
Translating exponential functions
Intuition - Exponent Rules
8 December 2023
I want to write this post to help people gain a bit of intuition for some math formulas we are learning at school. Specifically, I noticed that my classmates often memorize all the formulas without actually learning why they work. I will try to make this series go along with what is taught in class right now.
Formulas we memorized this class:
\(x^{-a} = \frac{1}{x^a}\),
\(x^a \cdot x^b = x^{a+b}\),
\(\frac{x^a}{x^b} = x^{a-b}\),
and \((x^a)^b = x^{a \cdot b}\).