📚 Year 8 WJEC Maths: Cross-Curricular Integrated Problem-Solving Training | Year 8 WJEC 数学：跨学科综合题型训练
In Year 8, WJEC Mathematics encourages pupils to apply numerical, algebraic and statistical skills to real-world contexts. This article explores cross-curricular problem types, showing how maths underpins science, geography, design, business, sport and the arts.
在 Year 8 阶段，WJEC 数学课程鼓励学生将数字、代数和统计技能应用于现实情境。本文探讨跨学科问题类型，展示数学如何支撑科学、地理、设计、商科、体育和艺术。
1. Ratios and Proportions in Science Experiments | 科学实验中的比例关系
In chemistry and biology, mixing solutions or feeding plants often requires precise ratios. For example, a nutrient solution may need to be diluted in the ratio 1:4 of concentrate to water. Understanding equivalent ratios and simplifying them is essential.
在化学和生物学科中，混合溶液或给植物施肥常需精确配比。例如，营养液可能需要以浓缩液与水 1:4 的比例稀释。理解等效比率及其化简至关重要。
technician needs 2.5 litres of diluted solution, how much concentrate and water are needed? l = 500 ml, water = 2000 ml. Proportions can also be represented as fractions or decimals.
Year 8 题型：若实验员需要 2.5 升稀释溶液，需多少浓缩液和水？利用比例 1:4，总份数 = 5。浓缩液 = (1/5) × 2500 ml = 500 ml，水 = 2000 ml。比例还可用分数或小数表示。
Another common task involves scaling up a recipe for an experiment—using multiplication to maintain the ratio while increasing quantities.
另一常见任务涉及在实验中按比例扩大配方——使用乘法在增加量的同时保持比例不变。
2. Statistical Graphs in Geography | 地理学中的统计图表
Geographers use bar charts, line graphs and pie charts to present climate data, population structures and resource distribution. Year 8 pupils must interpret these graphs, calculating averages, ranges and percentages from them.
地理学家用条形图、折线图和饼图展示气候数据、人口结构和资源分布。Year 8 学生需解读这些图表，并从中计算平均数、极差和百分比。
A typical task: Given a climate graph for Cardiff, find the total annual rainfall, mean monthly temperature, and the difference between the highest and lowest temperatures. Units must be read accurately from axes.
典型任务：给定卡迪夫的气候图，求年总降雨量、月平均气温以及最高与最低气温的差值。必须从坐标轴上准确读取单位。
Interpreting population pyramids involves percentages of age groups. Pupils may calculate the proportion of working-age population and express it as a fraction or percentage of the total. Cross-curricular skills include labeling axes and choosing suitable scales for discrete or continuous data.
解读人口金字塔涉及各年龄组的百分比。学生需计算劳动年龄人口比例，并用分数或百分数表示。跨学科技能包括坐标轴标注，以及为离散或连续数据选择合适的刻度。
3. Rearranging Simple Formulae in Physics | 物理中的简单公式变形
mass ÷ volume. In Year 8, pupils learn to substitute values and rearrange these equations to find any unknown.
物理引入了速度 = 距离 ÷ 时间，力 = 质量 × 加速度 (F = m × a) 以及密度 = 质量 ÷ 体积等方程。在 Year 8，学生学会代入数值并变形方程以求未知量。
For example, a problem: 'A car travels 210 km in 3 hours. What is its average speed? If the speed limit is 60 km/h, has it exceeded it?' 210 ÷ 3 = 70 km/h, so yes. Rearranging: distance = speed × time, time = distance ÷ speed.
例如问题：“一辆汽车 3 小时行驶 210 km，平均速度是多少？若限速 60 km/h，是否超速？”解：速度 = 210 ÷ 3 = 70 km/h，超速。公式变形：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。
Cross-curricular problems often combine unit conversions, e.g. changing minutes to hours or metres per second to kilometres per hour. Pupils use algebraic balance methods: divide both sides, multiply both sides.
跨学科题目常结合单位换算，如将分钟转为小时，或米每秒转为千米每小时。学生运用代数平衡法：两边同除、同乘。
4. Perimeter, Area and Volume in Design Technology | 设计技术中的周长、面积与体积
In design and technology, calculating material quantities requires perimeter, area and volume skills. For a wooden picture frame, pupils find the perimeter of the frame and the area of the glass. For a storage box, they calculate the volume and surface area.
在设计技术中，计算材料用量需周长、面积和体积技能。对于木质画框，学生求边框周长和玻璃面积；对于储物盒，计算体积和表面积。
e of soil = 2 × 0.9 × 0.4 = 0.72 m³. If soil is sold in 50-litre bags, how many are needed? (1 m³ = 1000 litres. 0.72 m³ = 720 litres; 720 ÷ 50 = 14.4, so 15 bags.)
示例：一个长方形种植床尺寸为 2 m × 0.9 m，填土深度 0.4 m。土的体积 = 2 × 0.9 × 0.4 = 0.72 m³。若土以 50 升装出售，需多少袋？（1 m³ = 1000 L。0.72 m³ = 720 L；720 ÷ 50 = 14.4，故需 15 袋。）
Surface area calculations are vital for painting or covering objects. Year 8 problems often involve composite shapes that can be split into rectangles and triangles.
表面积计算对于涂漆或包裹物体至关重要。Year 8 问题常涉及可分解为矩形和三角形的组合图形。
5. Percentages and Finance in Business Studies | 商科中的百分比与金融计算
Pupils apply percentage change formula: percentage change = (difference ÷ original) × 100%.
商业场景涉及百分比增减、利润率、折扣和增值税。学生应用百分比变化公式：百分比变化 = (差值 ÷ 原值) × 100%。
A typical task: 'A shop buys a jacket for £45 and sells it for £63. Calculate the percentage profit.' Profit = £18, percentage profit = (18 ÷ 45) × 100% = 40%. Reverse percentages are also common: after a 20% discount the price is £56; find original price.
典型任务：“一家商店以 £45 购入一件夹克，以 £63 出售。计算利润百分比。”利润 = £18，利润百分比 = (18 ÷ 45) × 100% = 40%。逆向百分比也很常见：打八折后价格为 £56，求原价。
Cross-curricular links with citizenship: understanding interest rates on savings and loans, using simple interest formula. Calculations reinforce decimal multiplication and division.
与公民教育跨学科联系：理解储蓄和贷款利率，使用单利公式。计算加强小数乘除能力。
6. Speed, Distance and Time in Physical Education |
Published by TutorHao | Year 8 Mathematics Revision Series | aleveler.com
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