📚 Problem Solving: Make a Table and Look for a Pattern | 解题策略：列表与找规律
Problem solving in mathematics often feels challenging because the path to an answer is not always visible. Making a table and looking for a pattern is one of the most powerful strategies for organising information, spotting relationships, and extending a sequence to solve problems efficiently.
数学解题常常让人觉得有挑战性，因为解题路径并非总是一目了然。列表并寻找规律是最强有力的策略之一，它可以帮助我们整理信息、发现关系，并扩展数列，从而高效地解决问题。
1. Why Make a Table? | 为什么要列表？
When a problem gives several changing values, writing them in an organised table turns messy data into a clear picture. The table helps you compare the input, output, and the change from one row to the next.
当一道题给出多个变化的值时，把数据写在有序的表格中，可以把杂乱的信息变成清晰的图像。表格能帮助你比较输入、输出以及每一行到下一行的变化。
For IGCSE questions, making a table is especially useful in sequences, number patterns, and real-life contexts such as costs, distances, and shapes. It reduces mental load and reveals the structure behind the problem.
在 IGCSE 题目中，列表策略在数列、数字规律以及成本、距离、图形等实际情境中尤其有用。它能减轻大脑负担，并揭示问题背后的结构。
A table is not just a place to store answers. It is a thinking tool. When you see the numbers lined up, you can often notice whether they increase by the same amount, multiply by the same factor, or follow a more complex rule.
表格不只是存放答案的地方。它是一种思维工具。当你看到数字排列在一起时，往往能发现它们是否按同样的数量增加、按同样的倍数变化，或者遵循更复杂的规则。
2. What Is a Pattern? | 什么是规律？
A pattern is a repeated or predictable change. In a number sequence, a pattern can tell you how to get from one term to the next. For example, 5, 8, 11, 14, ... adds 3 each time.
规律就是一种重复出现或可以预测的变化。在数列中，规律可以告诉你如何从一项得到下一项。例如：5、8、11、14、…… 每次都加 3。
Sometimes the pattern is not in the numbers alone but in the structure of a real situation, such as the number of chairs needed as more tables are joined. A table helps expose these hidden relationships.
有时规律不只是数字本身的变化，还藏在现实情境的结构中，例如增加桌子数量时所需椅子的数量。列表有助于暴露这些隐藏的关系。
Patterns can be numerical, geometric, or practical. A sequence of matchstick shapes, a train of connected tables, or a series of bus fares can all be understood by building a simple table and observing what changes.
规律可以是数字的、图形的，也可以是实际生活中的。火柴棒图形序列、连接起来的桌子、一系列公交车票价，都可以通过建立简单的表格并观察变化来理解。
3. Reading the Problem Carefully | 仔细审题
Before making a table, identify the variable that changes and the quantity you are asked to predict. Underline the known values, the question, and any repeating unit.
在列表之前，先确定变化的变量以及需要预测的量。划出已知数值、问题以及重复出现的单位。
Ask yourself: What is the first term? What changes from one stage to the next? Is the change constant or increasing? These answers guide your columns.
问问自己：第一项是多少？从一步到下一步发生了什么变化？变化是固定的还是在增加？这些问题的答案将指导你
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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