📚 Writing Framework and Sample Paper for Year 7 WJEC Maths | Year 7 WJEC 数学：论文写作框架与范文
In the WJEC Year 7 mathematics curriculum, being able to communicate your reasoning clearly is just as important as finding the correct answer. Writing a mini mathematical paper or investigation report helps you structure your thoughts, show your logical process and demonstrate deep understanding. Whether you are exploring number patterns, collecting data or solving a real‑life problem, following a consistent writing framework ensures your reader—and your teacher—can follow every step of your thinking.
在 WJEC 7 年级数学课程中，清晰表达推理想法与找到正确答案同样重要。写一篇数学小论文或调查报告，有助于你组织思路、展示逻辑过程并体现深刻的理解。无论你是在探讨数字规律、收集数据还是解决实际问题，遵循一套稳定的写作框架，能让你的读者——以及你的老师——清晰地跟上你思维的每一个步骤。
1. The Purpose of a Maths Paper at Key Stage 3 | 数学论文在 KS3 的目的
A maths paper in Year 7 is not a long essay; it is a structured report that shows how you approach a problem, what methods you choose and why, and how you interpret your results. In WJEC, such tasks often appear as "investigations" or "rich tasks" where you are asked to explore, hypothesise and draw conclusions. Writing formally about maths builds literacy in the subject and prepares you for the reasoning skills needed in GCSE.
7 年级的数学论文不是长篇作文，而是一份结构化的报告，展示你如何分析问题、选择了什么方法及其理由，以及你如何解读所得结果。在 WJEC 课程中，这类任务常以“探究”或“富问题”形式出现，要求你探索、提出猜想并得出结论。正式地把数学写成文字，能培养你的学科素养，并为 GCSE 所需的推理论证技能打好基础。
2. Core Structure of a Year 7 Maths Paper | 七年级数学论文的基本结构
Every good investigation follows a predictable pattern. Use the table below as a planning checklist before you start writing.
任何好的探究都遵循一个明确的模式。动笔前，先把下表当作你的规划清单。
| Section (English) | 中文 | What to include |
|---|---|---|
| Title & Question | 标题与问题 | A clear, descriptive title and the main question you are investigating. |
| Introduction | 引言 | Why you chose the topic, what you already know and what you predict. |
| Method | 方法 | Step‑by‑step explanation of how you collected information or carried out the task. |
| Results & Data | 结果与数据 | Tables, graphs, calculations presented clearly; raw data in an organised form. |
| Analysis | 分析 | What patterns do you notice? Use mathematical vocabulary to describe them. |
| Conclusion | 结论 | Answer your original question, explain how your findings support the answer. |
| Evaluation & Reflection | 评估与反思 | What went well? What would you improve? Any new questions that arose? |
Sticking to this structure makes your paper logical and easy to mark, which is exactly what WJEC examiners look for in longer tasks.
坚持这个结构能让你的文章逻辑清晰且易于评分，这正是 WJEC 考官在考查长任务时所看重的。
3. Title and Question Statement | 标题与问题陈述
Your title should be specific enough to tell the reader exactly what you investigated. Avoid vague titles like "My Maths Project". Instead, write something like "Investigating the relationship between the height of a ramp and the distance a toy car travels" or "Which supermarket wrap is the best value for money?". Underneath the title, rewrite the main question as a sentence. In WJEC cross‑curricular tasks, the question often comes from a real‑life context.
你的标题应当足够具体，让读者立刻明白你探究的内容。避免用“我的数学项目”之类含糊的题目，而要用类似“探究坡道高度与玩具车行驶距离的关系”或“哪种超市保鲜膜最划算”这样的表述。在标题下方，把核心问题重写成一个完整的句子。在 WJEC 跨学科任务中，题目往往来源于真实生活情境。
4. Introduction: Setting the Scene | 引言：搭建场景
Start the introduction by explaining why you chose this investigation. Mention any background knowledge you already have, perhaps a topic you covered in class, like fractions, averages or angles. Then make a prediction or hypothesis – what do you think the outcome will be? Use the word "because" to give a reason. For example, "I predict that the larger the diameter of a paper plane's wings, the longer it will stay in the air because there is more surface area to catch the air."
引言部分首先要说明你为何选择这个探究。提到你已有的背景知识，也许是在课堂上学过的分数、平均值或角度等内容。然后做出一个预测或假设——你认为结果会是什么？要用“因为”给出理由。例如：“我预测纸飞机的机翼直径越大，它在空中停留的时间越长，因为表面积越大，兜住的空气越多。”
5. Writing a Clear Method | 写出清晰的方法
The method is not a story; it is a set of instructions that someone else could follow to repeat your investigation exactly. Use bullet points or numbered steps. Include details such as the equipment used, how you made measurements, how many trials you completed, and how you ensured the test was fair. Always mention the variables you kept the same (control variables) and the one you changed (independent variable). In WJEC, the idea of a fair test is central to any data‑handling project.
方法部分不是讲故事，而是一套清晰的操作说明，让别人也能完全重复你的探究过程。可以使用项目符号或编号步骤。需说明所用器材、测量方式、测试次数以及如何保证测试的公平性。要始终提及你保持不变的条件（控制变量）和你改变的那个条件（自变量）。在 WJEC 中，公平测试的概念是所有数据处理项目的核心。
6. Presenting Results and Data | 呈现结果与数据
Organise your measurements in a neat table with clear headings and units. For instance, if you measured time in seconds, write "Time (s)" at the top of the column. Use tally charts for counting activities and frequency tables for survey data. When you calculate averages, show the formula in Unicode. For the mean:
Mean = (Σ x) ÷ n
Explain what Σ x and n stand for. Add simple graphs, such as bar charts drawn on squared paper or a digital tool. Every graph needs a title, labelled axes and a key if you have more than one set of data.
把你的测量数据整理成整洁的表格，用清晰的表头并标注单位。例如，如果测量时间以秒为单位，就在列顶部写上“时间 (s)”。计数活动使用频数表，调查数据使用频率表。计算平均数时，用 Unicode 写出公式：
平均数 = (Σ x) ÷ n
解释 Σ x 和 n 分别代表什么。添加简单的图表，比如在方格纸上或通过数字工具绘制的条形图。每张图都需要标题、带标签的坐标轴，如果有多组数据还需要图例。
7. Analysis: Spotting Patterns and Using Numbers | 分析：发现规律并运用数字
In the analysis section, do not simply repeat your results. Describe the trends you see. For a ramp investigation you might write: "As the height of the ramp increased from 10 cm to 50 cm, the distance travelled increased from 1.2 m to 3.8 m. The increase was not perfectly steady, which suggests there may be some experimental error." Use comparative language such as "twice as long", "half the amount", "85% of..." and calculate percentage difference if relevant. WJEC values the use of proportional reasoning in analysis.
在分析部分，不要简单重复结果。要描述你看到的趋势。对于坡道探究，你可以这样写：“随着坡道高度从 10 厘米增加到 50 厘米，行驶距离从 1.2 米增加到 3.8 米。这种增长并非完全匀速，说明可能存在一定的实验误差。”使用比较性语言，如“是……的两倍长”、“数量的一半”、“……的 85%”，并在适当时计算百分比差异。WJEC 重视在分析中运用比例推理。
8. Conclusion: Answering the Question | 结论：回答问题
Begin your conclusion by clearly answering the main investigation question. Then share the evidence that supports your answer, referring back to specific data. If your prediction was correct, say so and explain why the data proved it. If your results surprised you, explain what actually happened and suggest a reason. A strong conclusion never introduces brand‑new information; it sums up what the investigation has revealed.
结论部分开头要明确回答主要探究问题。然后给出支持该答案的证据，并引用具体数据。如果你的预测正确，就明确指出并解释数据如何证实了它。如果结果出乎意料，则说明实际发生了什么并推测原因。一个有力的结论绝不会引入全新信息，而是总结探究所揭示的内容。
9. Sample Paper: Paper Plane Flight Duration | 范文：纸飞机飞行时长探究
Below is a short sample paper written in the WJEC style for a Year 7 investigation. Read it together with the annotations provided in the next section.
以下是一篇采用 WJEC 风格、为 7 年级探究所写的简短范文。请结合下一节的批注阅读。
Title: How does the wing width of a paper plane affect the time it stays in the air?
问题：纸飞机的机翼宽度对它在空中停留的时长有何影响？
Introduction: I chose this investigation because we made paper planes in our STEM club and I noticed some designs flew much longer than others. We have been learning about average speed and distance in maths, and I wanted to see whether a simple change in the wing could make a difference. My prediction is that a plane with wider wings will stay in the air longer because the bigger surface area creates more lift.
引言：我选择这个探究，是因为我们在 STEM 俱乐部制作纸飞机时，我注意到有的设计飞行时间远长于其他。我们在数学课上正在学习平均速率和距离，我想看看机翼的简单改变是否会产生影响。我的预测是：机翼较宽的飞机在空中停留的时间更长，因为更大的表面积能产生更多升力。
Method: I folded three identical planes from A4 paper, changing only the wing width. Plane A had a wing width of 3 cm, Plane B 5 cm, Plane C 7 cm. I threw each plane 5 times from the same height (1.5 m) in the school hall, using the same launch style. A friend measured the flight time with a stopwatch. All windows were closed to avoid draughts — a fair test.
方法：我用 A4 纸折叠了三架相同的飞机，只改变机翼宽度。飞机 A 翼宽 3 厘米，飞机 B 翼宽 5 厘米，飞机 C 翼宽 7 厘米。我在学校礼堂从相同高度（1.5 米）以同样的投掷方式分别投掷每架飞机 5 次。一位朋友用秒表测量飞行时间。所有窗户关闭以避免气流——保证了公平测试。
Results:
| Plane | Trial 1 (s) | Trial 2 (s) | Trial 3 (s) | Trial 4 (s) | Trial 5 (s) | Mean (s) |
|---|---|---|---|---|---|---|
| A (3 cm) | 1.2 | 1.4 | 1.1 | 1.3 | 1.5 | 1.3 |
| B (5 cm) | 1.8 | 2.0 | 1.9 | 1.7 | 2.1 | 1.9 |
| C (7 cm) | 2.5 | 2.3 | 2.6 | 2.4 | 2.7 | 2.5 |
Analysis: The mean flight times show a clear pattern: the wider the wing, the longer the plane stayed in the air. Plane C's average time (2.5 s) is nearly double Plane A's (1.3 s). However, Plane B’s time did not double compared to Plane A, so the relationship might not be directly proportional. The range of results for Plane A was 0.4 s, while for Plane C it was also 0.4 s, showing similar consistency. I think some variation happened because my throws were not exactly identical each time.
分析：平均飞行时间呈现出明显的规律：机翼越宽，飞机在空中停留越久。飞机 C 的平均时长（2.5 秒）几乎是飞机 A（1.3 秒）的两倍。然而，飞机 B 的时间并没有比飞机 A 长一倍，因此这种关系可能不是正比例关系。飞机 A 的结果极差为 0.4 秒，飞机 C 的极差也是 0.4 秒，说明一致程度相近。我认为部分差异是因为我每次的投掷动作并非完全相同。
Conclusion: My prediction was correct — wider wings do keep the plane in the air longer. The data strongly supports this, as every trial of Plane C was longer than every trial of Plane A. In the future, I would like to test even wider wings and also explore the effect of wing length.
结论：我的预测是正确的——更宽的机翼确实能让飞机在空中停留更久。数据有力地支持了这一点，因为飞机 C 的每一次试验时长都超过飞机 A 的任何一次试验。今后，我想测试更宽的机翼，并探究机翼长度的影响。
10. Detailed Annotations on the Sample | 范文详细批注
Look at how the sample paper follows the framework exactly. The title is a clear question. The introduction explains the background, states a prediction and uses "because". The method lists the independent variable (wing width), the control variables (same paper, same height, closed windows) and repeats trials. The results table has proper headings and calculates the mean. The analysis compares means, uses the concept of doubling, mentions range and acknowledges variation. The conclusion answers the question and suggests further work. This is exactly what teachers look for in a WJEC Year 7 investigation.
请观察范文是如何严格遵循框架的。标题是一个清晰的问题。引言部分说明了背景、提出了预测并用到了“因为”。方法部分列出了自变量（翼宽）、控制变量（相同的纸张、相同的高度、关闭的窗户）并做了重复试验。结果表格带有正确表头并计算了平均值。分析部分比较了平均数，运用了加倍的概念，提到了极差并承认了变异。结论回答了问题并提出了进一步研究的建议。这完全符合老师对 WJEC 7 年级探究的要求。
11. Self‑Assessment and Improvement Checklist | 自评与改进清单
Use this checklist before handing in your work. Read each statement aloud and tick when done.
交作业前使用这份清单。大声读出每一条并在完成后打勾。
- Did I write a specific title and the investigation question?
- 我是否写了具体的标题和探究问题？
- Does my introduction explain my prediction with a reason?
- 我的引言是否用理由解释了我的预测？
- Did I describe a fair test and list my variables?
- 我是否描述了公平测试并列出了变量？
- Are my results clear with units and averages?
- 我的结果是否清晰，并带有单位和平均数？
- Did I use mathematical language to describe patterns?
- 我是否用数学语言描述了规律？
- Did I answer the main question in the conclusion?
- 我是否在结论中回答了主要问题？
- Have I checked for spelling and accidental misuse of symbols?
- 我是否检查了拼写和符号的误用？
Practising self‑assessment develops the "reflect and evaluate" skill highlighted in the WJEC Numeracy Framework.
练习自评能培养 WJEC 算术能力框架中强调的“反思与评估”技能。
12. Common Mistakes to Avoid | 需避免的常见误区
Many Year 7 students lose marks by skipping the hypothesis, forgetting units, or drawing conclusions without linking back to data. Another trap is writing "I think it was a good experiment" without saying why. Always be specific: instead of "some results were odd", write "Trial 2 for Plane B was much lower than the others, possibly because the plane hit a table leg." Also, remember that in WJEC, the process is as important as the final answer, so never delete your rough working – include it as an appendix if asked.
许多 7 年级学生因跳过假设、忘记单位或脱离数据做结论而失分。另一个陷阱是只写“我认为这个实验不错”而不说明原因。要始终具体：不要写“有些结果很奇怪”，而应写“飞机 B 的第 2 次试验数据远低于其他各次，可能是因为飞机撞到了桌腿。”还要记住，在 WJEC 中，过程与最终答案同样重要，因此决不要丢弃你的草稿——若要求，可将其作为附录附上。
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