Year 10 WJEC Maths: Practical Assessment Key Points | Year 10 WJEC 数学：实践考核要点

📚 Year 10 WJEC Maths: Practical Assessment Key Points | Year 10 WJEC 数学：实践考核要点

Practical assessment in WJEC Mathematics is designed to test how well you can apply your knowledge to real situations. Instead of simply recalling formulas, you will be expected to model problems, handle data, measure accurately, and interpret your findings. This guide walks you through the main skills and key points you need to master for the practical tasks in Year 10.

WJEC数学中的实践考核旨在检验你将知识应用于真实情境的能力。你不仅要记住公式，还要会建立模型、处理数据、精确测量并解释结果。本指南将带你梳理Year 10实践任务中需要掌握的主要技能和关键点。

1. Understanding Practical Assessment in WJEC Maths | 理解WJEC数学实践考核

Practical assessment tasks in WJEC Maths usually take the form of structured investigations or problem-solving activities carried out in class. You may be asked to plan a journey, analyse the results of a survey, or construct a geometric design.

WJEC数学的实践考核任务通常以结构化探究或问题解决活动的形式在课堂上进行。你可能会被要求规划一次旅程、分析调查结果或构建一个几何图形。

These tasks are assessed not only on the final answer but on your method, reasoning, and how clearly you present your work. Marks are awarded for each stage of the process.

这些任务的评估标准不仅看最终答案，还包括你的方法、推理过程以及展示作品的清晰程度。过程中每个步骤都可以得分。

2. Key Skills Assessed in Practical Tasks | 实践任务评估的关键技能

WJEC practical tasks test a combination of skills. These include mathematical modelling, data handling, measurement, estimation, and communication of findings.

WJEC实践任务考查多项技能的组合，包括数学建模、数据处理、测量、估算和结果表达。

The core skills you need to demonstrate are: identifying the problem and breaking it down, selecting appropriate mathematics, performing accurate calculations, and interpreting results in context.

你需要展示的核心技能是：识别问题并分解问题、选择合适的数学方法、进行准确的计算，并结合情境解释结果。

Problem solving – devising a strategy to tackle a real scenario.

问题解决 – 制定策略处理真实场景。
Reasoning – justifying choices and conclusions.

推理 – 为你的选择和结论提供合理性说明。
Communication – using correct mathematical language, graphs, and diagrams.

沟通 – 使用正确的数学语言、图表和示意图。
Application – linking different areas of maths such as number, algebra, geometry, and statistics.

应用 – 连接不同数学领域，如数、代数、几何和统计。

3. Real-World Problem Solving | 真实世界问题解决

Many practical tasks start with a real-world scenario: planning a school trip on a budget, calculating the amount of paint for a room, or comparing mobile phone tariffs.

许多实践任务从真实场景出发：在预算内规划学校旅行、计算房间需要多少油漆，或比较手机资费方案。

You need to identify the relevant numbers, discard unnecessary information, and create a step-by-step plan. Formulating an equation or simple algebraic model can help, such as total cost = fixed charge + unit cost × number of items.

你需要找出相关数字，抛弃无关信息，并制定分步计划。建立一个方程或简单的代数模型会有帮助，例如总费用 = 固定费用 + 单位成本 × 数量。

Always check your answer against the context: does your final price make sense? Would you actually have enough money or material?

始终结合情境检查答案：最终价格合理吗？你的钱或材料真的够用吗？

4. Data Collection and Handling | 数据收集与处理

Practical assessments often involve collecting primary data or using given secondary data. You might conduct a class survey on favourite sports, measure hand spans, or record temperature changes.

实践考核常涉及收集一手数据或使用给定的二手数据。你可能会在班里做最喜欢的运动调查、测量手掌宽度，或记录温度变化。

Designing a fair survey means choosing a suitable sample, writing unbiased questions, and recording results in a frequency table. You should be able to calculate the mean, median, mode, and range from grouped or ungrouped data.

设计公正的调查意味着选择合适的样本、编写无偏问题，并用频数表记录结果。你应能从分组或未分组数据中计算平均数、中位数、众数和极差。

When working with averages, show your method clearly: for mean, sum the values and divide by the number of values; for median, list in order and find the middle.

处理平均数时清晰展示方法：计算平均数时，将所有值求和除以个数；计算中位数时，排序后找出中间值。

5. Graphical Representation | 图表表示

Choosing the right graph is essential. Bar charts are used for discrete categories, line graphs for trends over time, pie charts for proportions, and scatter graphs for correlation between two variables.

选择正确的图表至关重要。条形图用于离散类别，折线图用于随时间变化的趋势，饼图用于比例，散点图用于两个变量之间的相关性。

When drawing a graph by hand, always use a sharp pencil, label axes, include a title, and use a sensible scale. For scatter graphs, draw a line of best fit if there is a clear correlation, and be prepared to use it for estimation.

手绘图表时，始终使用削尖的铅笔、标注坐标轴、加上标题并使用合理的刻度。对于散点图，若存在明显相关性就画一条最佳拟合线，并准备用它进行估算。

A common task is to interpret a graph: describe what it shows, identify peaks or trends, and read values accurately. Remember that a steep line on a distance-time graph means faster speed.

常见的任务是解读图表：描述它显示的信息，找出峰值或趋势，并准确读取数值。记住，距离-时间图上陡峭的线意味着速度更快。

6. Estimation and Approximation | 估算与近似

In practical tasks, exact calculations are not always possible or necessary. You need to estimate quantities, check the reasonableness of answers, and round values to a given degree of accuracy.

在实践任务中，精确计算并不总是可行或必要。你需要估算数量、检查答案的合理性，并将数值舍入到指定的精确度。

Estimation techniques include rounding numbers to one significant figure, using known reference points (e.g. an A4 paper is about 30 cm long), and approximating π as 3.14 or 22/7 for area calculations.

估算技巧包括将数字四舍五入到一位有效数字，使用已知参照物（例如一张A4纸长约30 cm），以及将π近似为3.14或22/7进行面积计算。

For example, if a wall area is 4.8 m × 2.9 m, round to 5 m × 3 m = 15 m² to quickly check that a detailed calculation of 13.92 m² is sensible. Always state your assumptions.

例如，若墙面积为4.8 m × 2.9 m，四舍五入得到5 m × 3 m = 15 m²，可以快速验证详细计算结果13.92 m²是否合理。务必说明你的假设。

7. Units of Measurement and Conversion | 测量单位与换算

Practical tasks frequently involve measuring length, mass, capacity, and time, then converting between units. You must be confident with both metric and common imperial units.

实践任务经常涉及测量长度、质量、容量和时间，然后在单位之间进行换算。你必须熟练掌握公制和常见英制单位。

Key conversions: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 litre = 1000 ml. For area, 1 m² = 10 000 cm². For volume, 1 m³ = 1 000 000 cm³.

关键换算：1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, 1 litre = 1000 ml。面积方面，1 m² = 10 000 cm²。体积方面，1 m³ = 1 000 000 cm³。

In WJEC contexts you might also need to work with miles, gallons, and pints. Learn approximate equivalents: 1 mile ≈ 1.6 km, 1 gallon ≈ 4.5 litres, 1 pint ≈ 0.57 litres.

在WJEC的情境中，你可能还需要使用英里、加仑和品脱。记住近似换算关系：1 mile ≈ 1.6 km, 1 gallon ≈ 4.5 litres, 1 pint ≈ 0.57 litres。

Always write the unit after every measurement. Omitting units can lose marks in practical write-ups.

始终在每个测量值后面写上单位。在实践报告里遗漏单位会丢分。

8. Probability Experiments | 概率实验

Probability experiments help link theoretical probability with actual outcomes. You might be asked to roll dice, spin spinners, or toss coins a set number of times and record results.

概率实验有助于将理论概率与实际结果联系起来。你可能会被要求多次掷骰子、旋转转盘或抛硬币，并记录结果。

The experimental probability of an event is: number of times event occurs ÷ total number of trials. As the number of trials increases, the experimental probability should stabilise close to the theoretical probability – this is the law of large numbers.

一个事件的实验概率为：事件发生次数 ÷ 总试验次数。随着试验次数增加，实验概率应稳定在理论概率附近——这是大数定律。

In your report, compare experimental and theoretical probabilities, discuss possible reasons for differences, and comment on sample size. A table like the one below can be used to organise results.

在报告中，要比较实验概率和理论概率，讨论差异的可能原因，并评价样本容量。可以使用类似下面的表格组织结果。

Outcome

结果

Frequency

频数

Experimental Probability

实验概率

Theoretical Probability

理论概率

Head / 正面

0.48

0.5

9. Geometry and Construction | 几何与作图

Practical geometry tasks require accurate use of a ruler, protractor, and compasses. Typical constructions include drawing a triangle given side lengths, bisecting an angle, or constructing a perpendicular bisector.

实践几何任务要求准确使用直尺、量角器和圆规。典型的作图包括根据边长画三角形、平分一个角或作垂直平分线。

When measuring angles, place the crosshairs of the protractor exactly on the vertex. Read the correct scale from 0°. When drawing lines, mark the exact length clearly and leave your construction arcs visible.

测量角度时，将量角器的中心对准顶点。从0°读取正确的刻度。画线时，清晰标出准确长度并保留作图弧线。

In problems involving loci, you may need to construct a path that is a fixed distance from a point or line. Always label your construction and describe what the locus means in practical terms.

在涉及轨迹的问题中，你可能需要作出与一个点或线段保持固定距离的路径。务必标注作图并描述该轨迹的实际意义。

10. Accuracy and Error | 精度与误差

All measurements contain a degree of uncertainty. When you record a length as 6.4 cm, the true value lies between 6.35 cm and 6.45 cm. You should know how to find upper and lower bounds.

所有测量都含有一定的不确定性。当你记录长度为6.4 cm时，真实值在6.35 cm到6.45 cm之间。你应知道如何求上界和下界。

In practical tasks, use appropriate accuracy: a ruler gives ±0.5 mm, a protractor ±1°. When combining measurements, propagate errors by finding the maximum possible value and minimum possible value of a calculation.

在实践任务中，使用适当的精度：直尺误差±0.5 mm，量角器误差±1°。当组合测量时，通过找出计算结果的最大可能值和最小可能值来传播误差。

Report answers with sensible rounding. For example, if you calculate an area as 3.256 m² using inputs with 2 significant figures, round your answer to 3.3 m².

用合理的舍入报告答案。例如，如果使用2位有效数字的输入计算出面积为3.256 m²，则答案应四舍五入为3.3 m²。

11. Assessment Criteria and Marking | 考核标准与评分

WJEC practical tasks are typically marked against criteria that value planning, implementing, and reviewing. Marks are allocated for: stating a clear aim, selecting a method, carrying out accurate calculations, presenting results, and drawing conclusions.

WJEC实践任务通常按重视计划、执行和反思的标准评分。分数分配给：陈述清晰的目标、选择方法、进行准确计算、展示结果以及得出结论。

Communication is a key part – you must use correct units, label graphs, and explain every step. Even if your final answer is wrong, you can still gain marks for correct reasoning.

沟通是关键部分——你必须使用正确单位、标注图表并解释每一步。即使最终答案错误，正确的推理仍可获得分数。

Review your work by asking: Is my method logical? Have I shown all working? Does my conclusion match the data? Can I suggest improvements?

通过以下问题检查你的作品：我的方法逻辑合理吗？我展示了所有计算过程吗？结论与数据匹配吗？我能提出改进建议吗？

12. Tips for Success | 成功秘诀

Read the task carefully and underline the key information you need before you start. Plan your approach on scrap paper.

仔细阅读任务，动手前划出你需要的关键信息。在草稿纸上规划你的方法。
Show every calculation, even simple ones, because marks come from working. If you use a calculator, write down the sums you are entering.

展示每一步计算，即使是简单的，因为分数来自过程。如果使用计算器，写下你输入的算式。
Use proper mathematical vocabulary – words like ‘estimate’, ‘mean’, ‘correlation’ show understanding. Draw diagrams with ruler and pencil, and never freehand graphs.

使用恰当的数学词汇——“estimate”、“mean”、“correlation”等词能体现理解。用直尺和铅笔绘图，绝不要徒手画图表。
Manage your time: leave a few minutes at the end to check units, rounding, and conclusion. Practise past paper practical tasks so you become quicker.

管理时间：最后留几分钟检查单位、舍入和结论。练习往年的实践任务真题，提高速度。
Stay calm and methodical. Practical tasks are designed to be tackled step by step – breaking a big problem into smaller pieces always works.

保持冷静且有条理。实践任务就是为了分步解决而设计的——把大问题分解成小块总是有效的。

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Year 10 WJEC Maths: Practical Assessment Key Points | Year 10 WJEC 数学：实践考核要点