Middle school common “Rectangle Folding Model” classification and problem solving exploration
初中常见“矩形翻折模型”分类与解题探究

摘要

新课标将几何直观和空间观念确立为初中数学核心素养的重要组成部分. 在这一背景下, 翻折问题作为几何领域的经典内容, 凭借其独特的综合性特征, 已成为中考数学命题中几何部分的重点考查方向. 本文基于课标要求, 系统研究了初中数学中的翻折问题的本质; 进而对初中阶段常见的矩形翻折模型进行了科学分类, 包括顶点落在图形边上、图形外部以及图形内部三种基本类型; 最后, 通过2024年江苏无锡中考真题为案例, 完整呈现了多知识点融合应用的解题策略, 目的在于使读者通过该类题型的理解完善自身的几何核心素养.

Abstract

The new curriculum establishes geometric intuition and spatial conception as an important part of the core literacy in junior high school mathematics. In this context, the folding problem, as a classic content in geometry, has become the key examination direction of geometry in the middle school mathematics examination by virtue of its unique comprehensive characteristics. Based on the requirements of the curriculum standard, this paper systematically studies the nature of the folding problems in junior high school mathematics, and then scientifically classifies the common rectangular folding models in junior high school, including three basic types of the vertices falling on the edges of the graphs, the outside of the graphs and the inside of the graphs; finally, through the case of the real exam of the Wuxi, Jiangsu Province, in 2024, the problem solving strategy of integrating and applying the multi-knowledge is presented, which is aimed at improving the understanding of this type of problems by the readers. Finally, through the case of the 2024 Wuxi, Jiangsu, China, exam, a complete presentation of multi-knowledge integration and application of problem-solving strategies is presented, with the aim of enabling readers to improve their own core geometric literacy through the understanding of this type of problem.