Miracle Middle School Arithmetic 1A - Factorization, Integers, and Rational Numbers
Ⅰ.
factorization
01. Prime numbers and factorization
02.
The relationship between prime factorization and divisors
03.
Greatest common divisor and least common multiple
Ⅱ.
Integers and rational numbers
04.
Number system
Ⅲ.
Calculation of integers and rational numbers
05.
Four arithmetic operations with fractions
06.
Addition and subtraction of integers and rational numbers
07.
Multiplication and division of integers and rational numbers
Ⅳ.
Mixed calculations with integers and rational numbers
08.
Mixed calculations with integers and rational numbers

▶ Why does math fall apart when you enter middle school?
Middle school mathematics is based on the elementary school curriculum, but is distinctly different from elementary school mathematics.
In elementary school, problems are dealt with that can be solved intuitively using concrete objects or numbers, whereas in middle school, problems are dealt with that require abstract and logical thinking using unknown numbers or letters.
That is, fourteen is the age when mathematics begins to change to logical thinking, so mathematics is bound to be unfamiliar and difficult.
It requires preparation for fundamentally different mathematics.
You must go through a process of training to understand the concepts accurately, express them in mathematical language, and apply them directly to problems.
To overcome the barriers of middle school math, you must develop your ability to apply concepts.

▶ Build a solid foundation in math with the three-stage, multi-faceted learning of [Miracle Middle School Math].
Through a three-stage, multi-faceted learning process of seeing with your eyes, learning with your hands, and applying with your head, you can build a solid foundation in middle school mathematics by expressing and practicing concepts you intuitively understand in mathematical language.

STEP1.
With your eyes! Intuitive concept formation
To form concrete and rich concepts, you need to be able to recall not only the mathematical definitions but also the intuitive images of academic terms.
Think of it as seeing the forest, not the trees, and take the whole picture in your mind to create your own image.
By linking visualized concepts to abstract, logical, linguistic concepts, we can form a three-dimensional knowledge network.

STEP2.
Establishing mathematical concepts with your hands!
A concept understood only with the eyes is not perfect.
Even if you think you understand a concept well, if you don't cover it repeatedly, it's easy for misconceptions to form.
This is because a single piece of knowledge needs to be engraved multiple times before it becomes established in the brain.
Let them remember the principle with their hands.
If you solve problems repeatedly by hand, you can easily understand and master the principles.

STEP3.
With your head! Applying and utilizing the concept
You will practice the process of deciding for yourself how to apply the intuitive and mathematical concepts you have learned previously to problems and solving them.

Many of the questions on actual exams require you to go through a single step using a concept to find the answer.
If you have a proper understanding of the concept, you can find out which concept is needed when you encounter a problem and apply it to solve it.
Develop your ability to apply principles through a variety of problems.