中学受験算数｜究極の平面図形＜角度＞

From the development team behind the 3 million-user educational app "ThinkThink," comes the definitive series for junior high school entrance exam preparation, now in its fifth installment!

* Analyzing 10 years' worth of past exam questions from prestigious schools, we've carefully selected 100 questions focusing on "angles," the key to mastering geometry!

* Organizing geometric properties into "14 techniques," you'll naturally acquire the "essential tips" for logically deriving answers.

* Simple digital operation prevents "thought-lost thinking" and provides a learning experience that allows you to gain experience in identifying the essentials of problem-solving.

◆ What kind of material is the ultimate plane geometry ?

In angle problems, the key to success lies in being able to select the "next move" to the correct answer from among the many properties.

This app allows you to naturally grasp the flow of thought by repeatedly experiencing the refined shortest route.

Even problems that seem complex are actually combinations of "geometric properties."

This app organizes that way of thinking into "14 techniques," designed for gradual learning.

With its intuitive digital interface, you can focus solely on "strategy selection"—identifying the key to solving the problem—allowing you to experience the "satisfaction of insight" like clearing a game, while deepening your fundamental understanding.

◆Why are "angles" so important?

—Actually, this is where the difference lies. The "key" to deciphering complex geometric figures.
Angles are the "first step" in mastering geometry in junior high school entrance exams, and an indispensable unit for determining the direction of the solution.
It goes beyond simple calculations, providing clues to discerning side lengths and similarity in complex figures. This "ability to logically interpret" is the foundation for improving your score in entrance exam mathematics.

—Because it's an app, you can acquire the "essence" of mastering the properties of geometric figures.
The difficulty with angles lies in the fact that even a slight change in the figure can make it difficult to see the path of thought.
This app is designed to allow you to repeatedly experience strategies (how to formulate a thought process) of "which technique to use and when" in a short amount of time by deliberately limiting the operation to simplicity.
This prevents haphazard calculations and naturally instills the "essential techniques" for logically deriving answers.

—The experience of discerning "when to use" these techniques becomes a reliable source of points.
Angles are a common stumbling block in application problems, but opportunities to study them intensively in cram schools, etc., are not frequent.
That's why deepening your understanding here will lay the foundation for raising your overall math score.
Accumulating experience of intuitively mastering "when to use" techniques with the app will cultivate confidence in geometry problems and directly lead to steady points gains in the actual exam.

◆How to Use
- Select the problem you want to play from the problem selection screen.
- Select the appropriate technique from the 14 buttons (14 techniques) on the right side of the play screen to fit into the squares at the bottom of the screen.
- Select the location to apply the technique from the displayed options.
- Clear the problem when all squares are filled and the angle marked "?" is derived.
- After completing one problem, the next problem will become playable.

◆Message from Kei Kawashima, CEO of WonderFi and Head of Curriculum Development
Japanese junior high school entrance exams in mathematics contain many excellent problems whose essence can be seen through careful reading and interpretation. Engaging with such problems is a valuable experience that allows students to enjoy the act of thinking itself.
However, in learning using paper and pencil, it can be difficult to grasp where to focus attention, and there are times when it seems to rely on "intuition."
This series focuses on two units: "similarity and area ratio," which are the core of geometry problems, and "angles," which are the first step in mastering geometry and the foundation of all solution methods.
These are the most important areas in plane geometry, fostering the ability to discern properties from complex figures and logically determine the direction of the solution, rather than simply memorizing calculations and patterns.
On the other hand, even a slight change in the figure can make it difficult to see the path of thought, making it a unit that is "fun once understood, but hard to get started with" for many children.

The "Ultimate Plane Geometry" series thoroughly analyzes entrance exam problems and organizes the properties of eight core techniques (similarity and area ratio) and fourteen core techniques (angles) that form the basis of problem-solving.

The series is designed to allow users to follow the flow of thought directly, minimizing operations and removing unnecessary burdens so that important structures are naturally apparent. Users can experience the process of developing their own strategies—deciding which properties to use and in what order—like solving a puzzle.

Furthermore, we believe that the "attitude of combining evidence to arrive at a conclusion" acquired in these areas will be useful for learning geometry and proofs in middle school and beyond. The experience of verifying for oneself what the evidence is and how it connects, before memorizing formal notation, forms a crucial foundation for learning mathematics.

This series was developed with the aim of ensuring that children's limited learning time leads to solid understanding and a positive sense of accomplishment.