📚 Year 7 Cambridge Maths: Practical and Experimental Assessment Guide | 剑桥七年级数学：实验与实践考核指南
Practical and experimental tasks form a vital part of the Year 7 Cambridge maths curriculum. They help you apply mathematical ideas to real-world situations, develop measurement skills, and learn to collect and analyse data accurately. This guide outlines the key principles for succeeding in practical and experimental assessments.
实践与实验任务是七年级剑桥数学课程的重要组成部分。它们帮助你运用数学思想解决实际问题，培养测量技能，并学会准确地收集和分析数据。本指南概述了在实践和实验考核中取得成功的要点。
1. Understanding Practical Maths Tasks | 理解数学实践任务
Practical tasks in Year 7 maths require you to use equipment, take measurements, and explore patterns. These tasks test your ability to apply knowledge rather than just recall facts. Common examples include measuring angles, drawing shapes, conducting probability experiments, and designing surveys. Your teacher will assess how carefully you carry out the task and how well you interpret the results.
七年级数学的实践任务要求你使用工具、进行测量并探索规律。这类任务考查的是你运用知识的能力，而不仅仅是背诵事实。常见的例子包括测量角度、绘制图形、进行概率实验以及设计调查。老师会评估你完成任务时的细心程度以及对结果的解读能力。
2. Accurate Measurement Skills | 精确测量技能
Using a ruler correctly means aligning the zero mark with one end of the object and reading the scale at eye level. When measuring angles, place the centre of the protractor exactly on the vertex and the baseline along one arm. Read the correct scale – inner or outer – depending on which direction the angle opens. For compass constructions, keep the radius fixed until you finish drawing the arc.
正确使用直尺时，要将零刻度对准物体的一端，并在视线水平处读取刻度。测量角度时，将量角器的中心点精确对准角的顶点，基线紧贴角的一条边。根据角的开口方向读取正确的刻度——内圈或外圈。用圆规作图时，半径固定不动，直到画完弧线为止。
| 1 cm = 10 mm | 1 厘米 = 10 毫米 |
| 1 m = 100 cm | 1 米 = 100 厘米 |
| 1 km = 1000 m | 1 千米 = 1000 米 |
Always include the correct unit when recording measurements. Common mistakes include forgetting to convert mm to cm before calculating area, or misreading the protractor by 180°. Double-check your reading if the result doesn’t make sense.
记录测量结果时一定要写上正确的单位。常见的错误包括计算面积时忘记将毫米换算成厘米，或把量角器的读数弄错180°。如果结果看起来不合理，要重新检查读数。
3. Constructing Geometric Figures | 绘制几何图形
You must be able to draw lines of a given length, angles of a given size, and shapes such as triangles using a ruler and protractor. For a triangle given two sides and the included angle (SAS), draw the first side, construct the angle at one endpoint, mark the second side along the new ray, then join the remaining points. Always label vertices A, B, C and measure the third side as a check.
你必须能够用直尺和量角器画出给定长度的线段、给定大小的角以及三角形等图形。对于已知两边及其夹角（边角边）的三角形，先画出第一条边，在一个端点处作角，沿新射线截出第二条边，再连接剩余点。始终标注顶点 A、B、C，并测量第三条边作为检验。
When constructing a perpendicular bisector, set your compass to more than half the length of the segment. Draw arcs from both endpoints that intersect above and below the line. Connect the two intersection points to obtain the bisector. Similar care is needed for angle bisectors – ensure arcs have equal radii.
作垂直平分线时，将圆规开口设为大于线段长度的一半。从线段的两个端点分别画弧，使上下各有一个交点。连接两个交点即得到平分线。作角平分线也需要同样小心——确保所有弧线的半径相等。
4. Collecting and Recording Data | 收集和记录数据
Before starting an experiment, design a data table with clear headings. Columns should include the trial number, the measured value, and any repeated observations. Use tally marks when counting frequencies. Record raw data immediately – do not rely on memory. If you collect 30 lengths, write each one before moving on.
开始实验之前，先设计一个表格，表头要清晰。栏位应包括试验编号、实测值以及任何重复观测。计数频率时可以使用画“正”字的方法。原始数据要立即记录——不要凭记忆。如果收集了30个长度数据，要逐一写下再继续。
| Trial | Length (cm) | Tally of items > 5 cm |
| 1 | 6.2 | | |
Strive for consistency: if you measure to the nearest mm, all your readings should reflect that precision. Data recorded as 5, 5.0, and 5.00 imply different accuracy levels, so stick to one format.
力求一致：如果测量精确到最接近的毫米，则所有读数都应体现这一精度。记录为5、5.0和5.00暗示不同的准确度，所以要坚持使用一种格式。
5. Experimental Probability | 实验概率
An experiment such as tossing a coin 50 times gives an experimental probability: number of heads divided by total tosses. The more trials you perform, the closer the experimental probability tends to get to the theoretical value (0.5 for a fair coin). Record keeps every outcome, and calculate the relative frequency after each 10 trials to see how it changes.
像抛硬币50次这样的实验会得到一个实验概率：正面朝上的次数除以总抛掷次数。试验次数越多，实验概率往往越接近理论值（公平硬币为0.5）。记录每一次结果，每做完10次试验就计算一次相对频率，观察其变化。
Use the formula: Experimental probability = Number of successful outcomes ÷ Total number of trials. Never assume a small number of trials is enough – Year 7 tasks often require at least 30 or 50 repetitions to show a clear pattern. When comparing with a theoretical probability, discuss whether the difference is due to chance.
使用公式：实验概率 = 成功结果的次数 ÷ 总试验次数。千万不要以为少量试验就够了——七年级的任务通常要求至少30或50次重复才能显示出清晰的规律。与理论概率比较时，要讨论出现的差异是否源于偶然。
6. Drawing and Interpreting Graphs | 绘制与解读图表
Bar charts, pictograms, and line graphs are common practical outputs. For a bar chart, bars must be evenly spaced and of uniform width. The frequency axis should start at 0 and increase in equal steps. Label both axes clearly, including the unit of measurement. For a line graph, plot points accurately and join them with a ruler – only connect points when the horizontal axis shows ordered categories or time.
条形图、象形图和折线图是常见的实践产出。条形图中的长条应等距且宽度一致。频率轴应从0开始，并以等步长递增。两个坐标轴都要清晰地标记，包括测量单位。对于折线图，要精确描点，用直尺连接——只有当水平轴表示有序类别或时间时才连接各点。
When interpreting a graph, describe the general trend, identify the highest and lowest values, and check for any unusual features such as gaps or clusters. Always put a title on every graph you produce. A good title includes what data is shown and where it came from, e.g. “Length of leaves collected from the school garden”.
解读图表时，要描述整体趋势，找出最高和最低值，并检查是否存在间隙或集中等异常特征。你制作的每一张图表都要有标题。好的标题应包含所显示的数据及其来源，例如“校园花园采集的叶片长度”。
7. Measuring and Calculating Perimeter, Area & Volume | 测量与计算周长、面积和体积
In a practical task, you might be asked to measure the sides of a rectangular table and calculate its perimeter and area. Perimeter is the distance around a shape: add all side lengths. Area of a rectangle = length × width. If you measure in cm, the area will be in cm². For a compound shape, divide it into smaller rectangles and triangles, find their areas separately, then add them.
在实践任务中，你可能需要测量矩形桌子的边长，然后计算其周长和面积。周长是围绕图形的总长度：将所有边长相加。矩形面积 = 长 × 宽。如果用厘米测量，面积单位就是 cm²。对于组合图形，把它分割成较小的矩形和三角形，分别求出面积，再相加。
Volume of a cuboid can be found by measuring length, width and height, then multiplying: V = l × w × h. For a small box measured in cm, the volume will be in cm³. When measuring inside a container to find its capacity, you may need to convert cm³ to ml (1 cm³ = 1 ml). Be thorough – measure each dimension twice to catch mistakes.
长方体的体积可通过测量长、宽、高，然后相乘得到：V = l × w × h。对于一个以厘米为单位测量的小盒子，体积单位是 cm³。测量容器内部尺寸求容量时，可能需要将 cm³ 换算为 ml（1 cm³ = 1 ml）。要仔细——每个维度测量两次，以便发现错误。
8. Symmetry and Transformations | 对称与变换
Practical symmetry tasks often involve folding paper to check line symmetry or using a mirror. When drawing the reflection of a shape in a mirror line, measure the perpendicular distance from each vertex to the line, and plot the image point at the same distance on the opposite side. Use a ruler and a set square to ensure the construction is accurate.
对称的实践任务通常包括通过折纸或使用镜子来检查线对称。绘制图形在镜线中的反射时，要测量每个顶点到镜线的垂直距离，然后在镜线的另一侧相同距离处标出镜像点。使用直尺和三角板以保证作图精确。
Rotational symmetry can be tested by tracing a shape onto transparent paper, placing the centre on the likely centre of rotation, and rotating to see if the shape matches itself within a full 360° turn. Note the order of rotational symmetry – for example, an equilateral triangle has order 3. Write a short sentence to describe the symmetry of any shape you draw.
旋转对称可以将图形描摹在透明纸上，把中心点对准可能的旋转中心，然后旋转纸张，查看在360°范围内图形是否与自身重合。要注意旋转对称的阶数——例如，等边三角形的旋转对称阶数为3。用简短的一句话描述你所画图形的对称性。
9. Designing a Mathematical Investigation | 设计数学调查
A strong mathematical investigation begins with a clear question, such as “Do taller students have larger hands?” or “Is there a pattern in multiples of 3 on a hundred square?” Plan how you will collect data: who you will measure, what tools you will use, and how many samples you need. A prediction or hypothesis makes the investigation purposeful.
一项优秀的数学调查始于一个明确的问题，例如“个子高的学生手是否也更大？”或“百数表中3的倍数是否有规律？”要计划如何收集数据：测量谁，使用什么工具，需要多少样本。做出预测或假设会让调查更有目的性。
Once data is collected, organise it and look for patterns. Use calculations such as mean, median, mode or range if appropriate. Draw a graph to visualise relationships. Finally, write a conclusion that answers the original question and refers to the data. Mention any surprising findings or limitations, like “only 20 students were measured, so results may not be true for all Year 7 students”.
收集数据后，进行整理并寻找规律。酌情计算平均数、中位数、众数或极差。绘制图表以直观呈现关系。最后，写出结论来回答最初的问题，并引证数据。提及任何令人意外的发现或局限性，如“仅测量了20名学生，因此结果未必适用于所有七年级学生”。
10. Evaluating and Improving Your Practical Work | 评估和改进实验工作
Evaluation means reflecting on how well the experiment worked. Ask yourself: Were my measurements as accurate as they could be? Did I have enough trials? Could the experiment be repeated by someone else using my written plan? Identifying a weakness, like not holding the ruler steady, shows mature mathematical thinking.
评估意味着反思实验的完成情况。问问自己：测量是否做到了尽可能准确？试验次数是否足够？他人能否按照我写的计划重复这个实验？指出一个弱点，比如没能拿稳直尺，体现了成熟的数学思维。
Suggest specific improvements, for instance: “Next time, I would measure each leaf to the nearest millimetre and take three readings to average.” Evaluations are not about blaming yourself; they show you understand how to make your mathematical work stronger. In an assessment, a good evaluation can raise your overall mark.
提出具体的改进建议，例如：“下次我会将每片叶子测量到最接近的毫米，并读取三次取平均值。”评估不是为了责备自己；它表明你明白如何提高数学工作的质量。在考核中，出色的评估能提升你的整体分数。
11. Common Pitfalls in Practical Assessments | 实用考核常见误区
One major pitfall is forgetting to zero the scale. When measuring length, check that the ruler’s edge starts at 0, not at the edge of the ruler itself. For a protractor, ensure you are reading from the baseline, not the straight edge, because some protractors have a small gap. Another mistake is using units incorrectly: mixing mm and cm in an area calculation leads to errors of factor 100.
一个主要误区是忘记将刻度归零。测量长度时，检查直尺的刻度起点是0，而不是直尺的物理边缘。使用量角器时要确保是从基线读取，而非直边，因为有些量角器有一小段空隙。另一个错误是单位使用不当：在面积计算中混用毫米和厘米会导致100倍的误差。
In data tasks, students often forget to label graph axes or use uneven scales. A bar chart with bars of different widths, or a line graph where points are connected out of sequence, will lose marks. Always read the task instructions carefully – if it asks for a bar chart, don’t draw a pictogram. Rushing leads to these easily avoidable mistakes.
在数据任务中，学生经常忘记给图表坐标轴贴标签，或者使用不均匀的刻度。条形图中长条宽度不一，或折线图连接顺序错误都会扣分。务必仔细阅读任务说明——如果要求画条形图，就不要画象形图。仓促行事会导致这些本可轻松避免的错误。
12. Presenting Your Findings | 展示发现结果
When communicating results, structure your report clearly: title, aim, equipment list, method, results (in tables and graphs), analysis, and conclusion. Use full sentences and accurate mathematical vocabulary, such as “the experimental probability tends towards…”, not just “it gets close”. Include diagrams where helpful, and label them.
在交流结果时，报告结构要清晰：标题、目的、器材清单、方法、结果（含表格和图表）、分析以及结论。使用完整的句子和准确的数学词汇，如“实验概率趋近于……”，而不只是“它接近了”。必要时附上图示并加以标注。
In many practical assessments, you will be asked to present your findings orally or as a poster. Practise explaining what you did and why. A well-presented piece of work with neat tables, sharp graphs, and tidy handwriting creates a strong impression. Remember: the process is as important as the final answer, so show every step of your thinking.
在许多实践考核中，你可能需要以口头形式或海报形式展示你的发现。练习解释你做了什么以及为什么这样做。一份呈现精美的作品——整洁的表格、清晰的图表和工整的字迹——会留下深刻的印象。记住：过程与最终答案同等重要，因此要展示你思考的每一个步骤。
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