📚 Cross-Curricular Problem Solving in Year 8 Mathematics | Year 8 数学跨学科综合题型训练
In Year 8, AQA Mathematics encourages students to apply mathematical concepts to real-world situations and other subjects. This article explores cross-curricular problem-solving types, providing strategies and examples that link maths with science, geography, design, and more.
在 Year 8，AQA 数学鼓励学生将数学概念应用于现实世界和其他学科。本文探讨跨学科问题解决题型，提供将数学与科学、地理、设计等联系起来的策略和示例。
1. Introduction to Cross-Curricular Maths | 跨学科数学导览
Cross-curricular problems integrate mathematics with other subjects, requiring you to identify the maths behind a scenario. Common areas include using ratios in recipes, reading scales on maps, calculating speed in science, and managing budgets in citizenship.
跨学科问题将数学与其他学科融合，需要你识别情景背后的数学。常见领域包括在食谱中使用比例、阅读地图比例尺、科学中计算速度以及公民教育中的预算管理。
Approaching these problems: First, extract the mathematical question. Then, decide which operation or formula to apply. Finally, check whether your answer makes sense in the real-world context.
应对这些问题：首先，提取数学问题。然后，决定使用哪种运算或公式。最后，检查你的答案在现实背景下是否合理。
2. Science: Speed, Distance and Time | 科学：速度、距离与时间
In science, the relationship between speed, distance and time is a perfect example of cross-curricular maths. The formula triangle is often used:
在科学中，速度、距离和时间的关系是跨学科数学的完美例子。常使用公式三角形：
Speed = Distance ÷ Time
formula is also common: Distance = Speed × Time, and Time = Distance ÷ Speed.
如果一名骑行者 3 小时骑行 45 公里，平均速度为 45 ÷ 3 = 15 公里/小时。重组公式也很常见：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。
5 = 60 km/h. You might need to convert 24 minutes into hours (24 ÷ 60 = 0.4 hours).
Year 8 题型常要求单位转换：例如，分钟转小时。一列火车 2.5 小时行驶 150 公里；速度 = 150 ÷ 2.5 = 60 公里/小时。你可能需要将 24 分钟转换为小时（24 ÷ 60 = 0.4 小时）。
3. Science: Density and Mass | 科学：密度与质量
Density links mass and volume. The formula is Density = Mass ÷ Volume. In cross-curricular tasks, you may be given mass and volume and asked to calculate density, or rearrange to find mass or volume.
密度将质量和体积联系起来。公式是 密度 = 质量 ÷ 体积。在跨学科题目中，可能会给出质量和体积要求计算密度，或重组求质量或体积。
y of a liquid is 0.8 g/cm³ and you have 200 cm³, mass = 0.8 × 200 = 160 g.
示例：一块木头质量为 300 g，体积为 150 cm³。密度 = 300 ÷ 150 = 2 g/cm³;。如果一种液体密度为 0.8 g/cm³，有 200 cm³，则质量 = 0.8 × 200 = 160 g。
4. Geography: Scale Drawings and Maps | 地理：比例尺绘图与地图
Maps use a scale to represent real distances. A scale such as 1:50000 means 1 cm on the map represents 50000 cm in reality (0.5 km). Understanding scale factors is essential.
地图使用比例尺表示实际距离。像 1:50000 的比例尺意味着地图上 1 cm 代表实际 50000 cm（0.5 km）。理解比例尺因子至关重要。
e = 8 × 25000 = 200000 cm = 2000 m = 2 km. Always convert to sensible units like km.
任务：在 1:25000 的地图上，两镇相距 8 cm。实际距离 = 8 × 25000 = 200000 cm = 2000 m = 2 km。务必转换为合适的单位，如公里。
Sometimes you' of 1:200. You solve proportions: 10 m = 1000 cm, scale length = 1000 ÷ 200 = 5 cm.
有时会要求绘制比例图。例如，用 1:200 比例将 10 m 的墙表示为 5 cm。解比例：10 m = 1000 cm，图上长度 = 1000 ÷ 200 = 5 cm。
5. Geography: Population Data and Graphs | 地理：人口数据与图表
Geography involves interpreting population pyramids, bar charts, and line graphs. You must extract data, compare values, and calculate percentages or changes.
地理学涉及解读人口金字塔、条形图和折线图。必须提取数据、比较数值并计算百分比或变化量。
1.2 million. Percentage increase from A to B = ((3.6 - 2.4) ÷ 2.4) × 100 = 50%.
示例：条形图显示城市人口：A = 240万，B = 360万。差值为 120万。从 A 到 B 的百分比增加 = ((3.6 - 2.4) ÷ 2.4) × 100 = 50%.
You may also need to use line graphs showing temperature change over time, calculating the range (max – min) or mean. These are typical Year 8 statistics skills applied in geography.
你可能还需使用显示温度随时间变化的折线图，计算极差（最大–最小）或平均值。这些都是 Year 8 统计技能在地理中的应用。
6. Design & Technology: Perimeter, Area, and Costing | 设计与技术：周长、面积与成本
In design projects, you often need to calculate the amount of material (area) or the length of framing (perimeter), and then work out costs. This combines geometry with arithmetic.
在设计项目中，常常需要计算材料用量（面积）或框架长度（周长），然后计算成本。这结合了几何和算术。
², number of pots = 9600 ÷ 400 = 24, total cost = 24 × 2.50 = £60.
示例：一块矩形板长 120 cm，宽 80 cm。面积 = 120 × 80 = 9600 cm²;。如果油漆每 400 cm² 花费 £2.50，所需罐数 = 9600 ÷ 400 = 24，总成本 = 24 × 2.50 = £60。
ter = 2 × (15 + 10) = 50 m. If fencing costs £8 per metre, total = £400.
周长问题：给花园围栏。一个 15 m 乘 10 m 的矩形，周长 = 2 × (15 + 10) = 50 m。如果围栏每米 £8，总计 = £400。
7. Food Technology: Ratios and Proportions in Recipes | 食品技术：食谱中的比和比例
Recipes are based on ratios. Scaling a recipe up or down for different numbers of servings tests your
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