中学受験算数｜究極の平面図形＜相似・面積比＞

The fourth installment in the definitive junior high school entrance exam prep series, brought to you by the developers of the educational app "ThinkThink," boasting 3 million users!

- 100 frequently asked questions on "Similarity and Area Ratios" were carefully selected based on an analysis of 10 years' worth of past exam questions from top schools!
- Organize geometric properties into "eight techniques" to naturally reveal the underlying logic.
- Intuitive puzzle-like operation provides a new learning experience that sparks inspiration.

◆What kind of learning material is "Ultimate Plane Geometry "?

When it comes to similarity and area ratio problems, the key to success is being able to see the underlying logic. With this app, you'll naturally grasp the flow of thought by repeatedly experiencing simple solutions.

Even complex problems are actually a combination of geometric properties and the laws of similarity. This app organizes these concepts into eight "techniques" designed for gradual learning.

Problems that are difficult to solve with paper and pencil can be solved intuitively with tapping. Enjoy the thrill of inspiration as you see the next step, just like completing a game, and your understanding will naturally solidify.

◆Why are "Similarities and Area Ratios" important?

- The cornerstone of plane geometry and a star of entrance exam math.
Similarities and area ratios are one of the most frequently appearing and crucial units in junior high school entrance exams. While skilled students instantly figure out how to solve them, less skilled students often get lost and lose track of the process. These problems are often presented as large-scale questions, and the key to mastering them lies in how you perceive the entire shape and the order in which you consider it.

- Only with an app can you experience the "process of thinking"

No matter how much you practice, even a slight change in shape can make the "similarities" disappear, which is the difficulty of this unit. By intentionally limiting the controls to simple, this app allows you to experientially learn the optimal timing to use your "techniques."
As you solve the puzzles, you'll hone your flow of thought and your sense for choosing your first move.

Mastering these techniques will give you a huge advantage!

Because this is an area where many test-takers struggle, deepening your understanding can make a big difference.

Solving similarity and area ratio problems, often considered a matter of "innate ability," can be tackled by anyone with eight techniques and strategic thinking. Mastering these crucial areas of plane geometry will lead to both confidence and a higher score.

◆How to Use
- Select the problem you want to play from the problem selection screen.
- Select the appropriate technique from the eight buttons (eight techniques) on the right of the play screen that fit the square at the bottom of the screen.

- Select the location where you want to apply the technique from the options provided.
- Complete the test when all squares are filled.
- After solving a problem, the next problem becomes available for play.

◆Message from Kei Kawashima, CEO of WonderFi, Head of Materials Development

Japan's junior high school entrance exams for mathematics feature many excellent problems whose true essence emerges through careful analysis. Engaging in these problems is a valuable experience, allowing students to enjoy the act of thinking itself. However, when learning with paper and pencil, it can be difficult to know what to focus on, and students may find themselves relying on their "intuition."

Similarities and area ratios are particularly common among plane figures and are an important part of entrance exams. The idea of ​​finding similar shapes or triangles with the same height and combining them to derive length and area ratios is inherently fascinating, like a puzzle. However, this can be a demanding subject for many students, as it requires identifying multiple similar shapes simultaneously, drawing auxiliary lines, and requiring numerous steps.

This app organizes the concepts of similarity and area ratios into eight techniques extracted from an analysis of entrance exam questions from the past 10 years. The app is designed to minimize operations so that key structures naturally come to the user's attention, eliminating unnecessary overhead and allowing students to follow the flow of thought. Students can experience the process of organizing similarity relationships and ratios, and forming a flowchart for solving them—that is, a strategy for tackling problems—in their own mind, much like solving a puzzle.

We also believe that the "ability to combine evidence and reach a conclusion" acquired in this field will be useful for geometry and proof studies in junior high school and beyond. Before learning formal notation, the experience of exploring for oneself what the evidence is and how it connects forms an important foundation for learning mathematics.

Similarities and area ratios are areas where understanding greatly advances once students grasp the tricks and become able to see the "pathway to thinking." We developed this program with the aim of using children's limited learning time to achieve solid understanding and positive feedback.

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