📚 Draw a Picture and Write an Equation | 画图列式解应用题
Many IGCSE Foundation word problems become much easier when you first draw a simple picture and then write an equation from that picture.
许多 IGCSE 基础阶段的文字题，在你先画出一个简单示意图并据此列出方程后，会变得容易得多。
This strategy turns sentences into visual structures, so you can see which operation to use. It works for one-step questions and for longer multi-step questions, and it is fully accepted in the exam - examiners want to see correct method, not a perfect drawing.
这个策略把句子转化为视觉结构，让你能够看出该用哪种运算。它既适用于一步计算题，也适用于更长的多步题，而且在考试中完全被接受——考官想看的是正确的方法，而不是一幅漂亮的图。
1. What Is the Draw a Picture Strategy? | 什么是画图策略？
Drawing a picture means turning words into bars, number lines, arrays, or part-whole diagrams before doing any calculation.
画图策略是指在计算之前，先把文字转化为条形图、数线、阵列图或部分-整体图。
It is not about making an artistic drawing. It is about making the mathematical relationship visible.
它不是为了画出好看的图画，而是为了让数学关系变得清晰可见。
A clear picture helps you decide whether to add, subtract, multiply, or divide.
清晰的图画能帮助你决定该用加法、减法、乘法还是除法。
The second half of the strategy matters just as much: you must write an equation that matches the picture, then solve it.
这个策略的后半部分同样重要：你必须写出与图画相符的方程，然后求解它。
2. Why Drawing Helps in IGCSE Maths | 为什么画图对 IGCSE 数学有帮助
Word problems contain information in sentences, which can be hard to hold in working memory.
文字题中的信息以句子呈现，在工作记忆中很难全部保持。
A bar model or number line turns that hidden information into a structure you can see.
条形图或数线能把隐藏的信息变成你可以看到的结构。
Once the structure is visible, choosing the correct operation becomes much easier.
一旦结构清晰可见，选择正确的运算就会容易得多。
This skill is especially useful for multi-step IGCSE questions where two or more operations are needed.
对于需要两步或更多运算的 IGCSE 题目，这一技能尤其有用。
It also gives you a quick way to check whether your final answer is reasonable.
它还为你提供了一种快速检验最终答案是否合理的方法。
3. Step 1: Read the Problem Twice | 第一步：把题目读两遍
First, read for the story: who or what is involved and what is happening.
第一遍，为了了解大意：涉及谁或什么，以及发生了什么事。
Second, read for the numbers and the question: underline the quantities, the comparison words, and the final question.
第二遍，关注数字和问题：在数量、比较词语和最后的问题下面画线。
Ask yourself: "What do I know?" and "What do I need to find?"
问自己："我知道什么？"和"我需要求什么？"
This two-read method prevents you from jumping to a calculation too quickly.
这种读两遍的方法可以防止你过快地开始计算。
Comparison words such as "more than", "less than", "times as many" and "altogether" tell you which model to choose.
像 "more than"（多）、"less than"（少）、"times as many"（几倍）和 "altogether"（总共）这样的比较词，会提示你该选哪种模型。
4. Step 2: Choose the Right Picture | 第二步：选择合适的图
Different problems call for different visual models.
不同的问题需要不同的图示模型。
| Problem type | 问题类型 | Useful picture | 常用图示 | Key question | 关键问题 |
|---|---|---|
| Part-whole addition or subtraction | One long bar split into named parts | Which part is the whole? 哪一段是整体？ |
| Comparison: more than, less than, times as many | Two or three bars aligned at one end | Which bar is longer, and by how much? 哪条更长，多多少？ |
| Change, difference, temperature, sequences | Number line with arrows | Which direction do I move? 我往哪个方向移动？ |
| Multiplication, division, equal groups | Array or rectangle (area model) | How many equal groups and how many in each? 有几组、每组多少？ |
| Fractions, ratio, percentage | Fraction bar cut into equal parts | How many equal parts in the whole? 整体被分成几等份？ |
Label every part with its value or its unknown letter, such as x. A picture without labels is only decoration.
要把每一部分都标上数值或未知字母（例如 x）。没有标注的图只是装饰。
5. Bar Models for Part-Whole Problems | 部分-整体问题的条形图
In a part-whole model, the longest bar stands for the whole amount, and it is divided into smaller bars that represent the parts.
在部分-整体模型中，最长的那条代表整体量，它被分成若干较短的条，代表各个部分。
The relationship is always the same.
这个关系始终如一。
Whole = Part + Part, so Part = Whole − Part
llars, the whole is 75 and the known part is 28. The unknown part is 75 − 28 = 47 dollars.
如果一个男孩从 75 元中花掉 28 元，整体是 75，已知部分是 28，未知部分是 75 − 28 = 47 元。
The picture makes it obvious that subtraction finds the missing part, so you will not accidentally add.
图画让"用减法求缺失部分"这一点一目了然，你就不会误用加法。
6. Bar Models for Comparison Problems | 比较问题的条形图
Comparison problems use two or more bars drawn underneath each other and lined up on the left.
比较问题要画两条或更多条，上下排列，并且左边对齐。
The bar that sticks out shows the difference between the two amounts.
多出来的那一段就表示两个数量之间的差。
If Ann has 3 times as many as Ben, draw one short bar for Ben and three equal bars for Ann.
如果安的数目是本的三倍，就给本画一条短条，给安画三条等长的条。
If together they have 96, then all four equal bars make 96, so one bar is 96 ÷ 4 = 24.
如果他们合计有 96，那么四条等长的条合起来是 96，所以一条是 96 ÷ 4 = 24。
Notice how the picture turns a confusing sentence about "times as many" into a simple division.
可以看到，图画把一个关于"几倍"的难懂句子变成了一个简单的除法。
7. Number Lines: Change, Difference and Negative Numbers | 数线：变化、差与负数
A number line is the best model when something increases, decreases or crosses zero.
当某个量增加、减少或跨越零时，数线是最好的模型。
Draw a line, mark the starting value, and use an arrow to show the change.
画一条线，标出起始值，再用箭头表示变化。
A move to the right is an increase, and a move to the left is a decrease.
向右移动表示增加，向左移动表示减少。
For a temperature that falls from 6 °C to −4 °C, the drop is 6 − (−4) = 10 °C.
若气温从 6 °C 降到 −4 °C，下降量为 6 − (−4) = 10 °C。
On the number line you can literally count the 10 steps between the two marks, which stops sign errors.
在数线上你可以直接数出两个刻度之间的 10 格，这能避免符号错误。
8. Arrays and Area Models for Multiplication | 乘法中的阵列图与面积模型
When a problem involves equal groups, draw an array: rows and columns of dots or squares.
当题目涉及等量组时，画一个阵列：用点或方格排成行与列。
contains 7 × 8 = 56 items, and it shows clearly that multiplication is repeated addition.
一个 7 行 8 列的阵列包含 7 × 8 = 56 个元素，它清楚地显示乘法就是重复相加。
The same diagram becomes an area model for rectangles, where area = length × width.
同一个图在矩形问题中就是面积模型，其中面积 = 长 × 宽。
Area of a rectangle = length × width
vision, you already know the total and one side, so you find the missing side: 56 ÷ 8 = 7.
做除法时，你已知总数和一条边，于是求缺失的那条边：56 ÷ 8 = 7。
9. Step 3: Turn the Picture into an Equation | 第三步：把图变成方程
An equation is a sentence that says two things are equal, and the equals sign must sit between them.
方程就是一句话，说明两件事相等，等号必须写在它们之间。
Read your picture and write down exactly what it shows, using a letter for the unknown.
读你的图，用字母表示未知量，把图上显示的内容原样写下来。
For the sticker problem in section 6, the picture gives 3x + x = 96.
对于第 6 节的贴纸问题，图给出的是 3x + x = 96。
3x + x = 96 → 4x = 96 → x = 24
Always simplify the left-hand side before dividing, and keep each line of working on its own line.
在除以系数之前，一定要先化简左边，并且每一步运算单独写一行。
10. Step 4: Solve, Check and Answer in Words | 第四步：求解、检验并用文字作答
Solve the equation using inverse operations, working backwards until the letter stands alone.
用逆运算解方程，一步步倒推，直到字母单独留在一边。
Then substitute your answer back into the original sentence to check that it fits.
然后把答案代回原句，检验它是否成立。
For x = 24, check that 3 × 24 + 24 = 72 + 24 = 96, which matches the question.
当 x = 24 时，检验 3 × 24 + 24 = 72 + 24 = 96，与题目相符。
Finally, write the answer as a full sentence with units, because a bare number may not earn the last mark.
最后，用带单位的完整句子写出答案，因为只写一个数字可能拿不到最后那一分。
11. Common Mistakes and Exam Technique | 常见错误与考试技巧
The most common mistake is drawing bars without labelling them, which makes the picture useless.
最常见的错误是画了条却不标注，结果这张图毫无用处。
Another is treating the difference as the whole, or adding when the question asks for a missing part.
另一个错误是把"差"当成整体，或者在题目要求求缺失部分时用了加法。
Students also forget to answer the actual question, for example finding one part when the question asks for the total.
学生也常忘记回答真正的提问，例如题目问总数，却只求出了某一部分。
- Use a pencil and a ruler; keep the diagram small but neat. 用铅笔和直尺，图要小但整洁。
- Write the equation as a separate line of working. 把方程单独写成一行。
- Keep units in every line of working. 每一行运算都带上单位。
- If time is short, still draw the model - it saves time overall. 时间紧也要画图，总体反而省时。
12. Worked Example and Practice | 完整例题与练习
Problem: Maya has 3 times as many stickers as Leo, and together they have 96 stickers. How many does Leo have?
题目：玛雅的贴纸数量是利奥的 3 倍，两人合计有 96 张贴纸。利奥有多少张？
bar for Leo and three equal bars for Maya, then write 3x + x = 96 and solve to get x = 24.
给利奥画一条，给玛雅画三条等长的条，然后写出 3x + x = 96，解得 x = 24。
Answer: Leo has 24 stickers. 答：利奥有 24 张贴纸。
Now try these two on your own, using the same four steps.
现在用同样的四个步骤，自己尝试下面两题。
- A shop sells 148 pens in the morning and 96 in the afternoon. How many more in the morning? 某店上午卖出 148 支笔，下午卖出 96 支，上午多卖多少支？
- The perimeter of a rectangle is 34 cm and its length is 5 cm more than its width. Find the width. 一个矩形的周长是 34 cm，长比宽多 5 cm，求宽。
Draw, label, write the equation, solve, check, and finish with a sentence - that is the whole method.
画图、标注、列式、求解、检验，最后写一句答语——这就是完整的方法。
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