📚 Interdisciplinary Problem Solving in Year 7 Cambridge Maths | 跨学科综合题型训练
In Year 7 Cambridge Maths, you will often meet word problems that connect numbers, geometry and algebra with topics from science, geography and daily life. These cross-curricular questions train you to apply mathematics beyond routine exercises, building logical reasoning and practical problem-solving skills.
在剑桥七年级数学中，你经常会遇到将数字、几何和代数与科学、地理及日常生活相联系的文字题。这些跨学科题目训练你把数学运用到日常练习之外，锻炼逻辑推理和实际解决问题的能力。
1. What Are Interdisciplinary Problems? | 什么是跨学科问题？
Interdisciplinary problems ask you to use maths in a real-world context, pulling in ideas from other subjects. Instead of a plain ‘solve 3 × 4’, you might find ‘A box holds 3 rows of 4 apples. How many apples altogether?’ – blending counting with a simple science or shopping scenario.
跨学科问题要求你在现实世界的情境中使用数学，并吸收其他学科的概念。不再是一个简单的“计算 3 × 4”，你可能会见到“一个盒子装有 3 排苹果，每排 4 个，共有多少个苹果？” ——这就把计数与简单的科学或购物场景结合起来了。
Such questions prepare you for tasks like reading timetables, scaling a recipe, or planning a budget. They help you see that maths is not just abstract symbols but a tool for everyday thinking.
这类题目为你将来阅读时刻表、缩放食谱或规划预算做好准备。它们让你明白，数学不只是一堆抽象的符号，更是日常思考的工具。
2. Speed, Distance and Time in Travel | 旅行中的速度、距离与时间
When we describe how fast something moves, we use speed. The core relationship is:
当我们描述物体移动的快慢时，我们用到速度。核心关系是：
Speed = Distance ÷ Time
Using this formula, we can also find distance (Distance = Speed × Time) and time (Time = Distance ÷ Speed).
利用这个公式，我们还可以求出距离（距离 = 速度 × 时间）和时间（时间 = 距离 ÷ 速度）。
Example 1: A cyclist rides 36 km in 2 hours. What is the average speed?
Solution: Speed = 36 km ÷ 2 h = 18 km/h.
示例 1：一名骑行者 2 小时骑行了 36 公里。平均速度是多少？
解答：速度 = 36 km ÷ 2 h = 18 km/h。
Example 2: A car travels at 60 km/h for 1.5 hours. How far does it go?
Distance = 60 km/h × 1.5 h = 90 km.
示例 2：一辆汽车以 60 km/h 的速度行驶 1.5 小时。它行驶了多远？
距离 = 60 km/h × 1.5 h = 90 km。
Always check that units match: if speed is in km/h, time must be in hours. If time is given in minutes, convert it first (e.g., 30 min = 0.5 h).
务必检查单位一致：如果速度单位是 km/h，时间就必须是小时。如果题目给的是分钟，要先换算（例如 30 分钟 = 0.5 小时）。
3. Map Scales and Real Distances | 地图比例尺与实际距离
A map scale tells you how much the real world has been shrunk. A scale of 1 : 50 000 means 1 cm on the map stands for 50 000 cm in real life. To find the true distance, multiply the map measurement by the scale factor.
地图比例尺告诉你真实世界被缩小了多少。比例尺 1 : 50 000 表示地图上 1 厘米代表现实中 50 000 厘米。要计算实际距离，就把地图上的测量值乘以比例因子。
Example: On a 1 : 25 000 map, two villages are 8 cm apart. How far apart are they in kilometres?
Real distance = 8 cm × 25 000 = 200 000 cm.
Convert cm to km: 200 000 cm = 2 000 m = 2 km.
示例：在一幅 1 : 25 000 的地图上，两个村庄相距 8 厘米。它们实际相距多少千米？
实际距离 = 8 cm × 25 000 = 200 000 cm。
将厘米转换为千米：200 000 cm = 2 000 m = 2 km。
Remember that 100 cm = 1 m and 1 000 m = 1 km. Drawing your own scale diagrams also helps you plan rooms, gardens or playgrounds.
记住 100 厘米 = 1 米，1000 米 = 1 千米。自己绘制比例图也有助于规划房间、花园或运动场。
4. Converting Temperatures: Celsius and Fahrenheit | 温度转换：摄氏与华氏
Temperature scales often appear in science and geography. To change Celsius (°C) to Fahrenheit (°F), use the formula:
温标经常出现在科学和地理中。要把摄氏度（°C）转换为华氏度（°F），使用公式：
°F = (°C × 9/5) + 32
To reverse the conversion: °C = (°F − 32) × 5/9.
反向转换的公式是：°C = (°F − 32) × 5/9。
Example: Convert 25 °C to °F.
°F = (25 × 9 ÷ 5) + 32 = 45 + 32 = 77 °F.
示例：把 25 °C 转换为 °F。
°F = (25 × 9 ÷ 5) + 32 = 45 + 32 = 77 °F。
Look at the table showing average July temperatures for three cities:
请看三个城市七月的平均气温表：
| City | Temperature (°C) | Temperature (°F) |
| London | 18 | 64.4 |
| Sydney | 13 | 55.4 |
| Tokyo | 26 | 78.8 |
Which city is the warmest? Compare both scales and check your conversions using the formula.
哪个城市最热？比较两种温标，并用公式核对你的转换结果。
5. Budgeting a School Event | 学校活动预算
Planning an event involves addition, multiplication and subtraction with money. Suppose your class organises a film night. Each ticket costs £3.50, and you expect 80 people to attend. The income from tickets would be 80 × £3.50 = £280.
策划活动会用到与金钱有关的加法、乘法和减法。假设你们班组织一次电影之夜。每张门票 £3.50，预计 80 人参加。门票收入就是 80 × £3.50 = £280。
Now list the costs: venue hire £65, snacks £48.50, decorations £22.75. Total costs = £65 + £48.50 + £22.75 = £136.25. The profit = income − costs = £280 − £136.25 = £143.75.
现在列出成本：场地租用 £65，零食 £48.50，装饰 £22.75。总成本 = £65 + £48.50 + £22.75 = £136.25。利润 = 收入 − 成本 = £280 − £136.25 = £143.75。
If you want to share the profit equally among 25 classmates, each gets £143.75 ÷ 25 = £5.75. This kind of problem improves your financial literacy.
如果你想把利润平均分给 25 位同学，每人得到 £143.75 ÷ 25 = £5.75。这类问题可以提升你的财商。
6. Area and Perimeter in Floor Plans | 平面图中的面积与周长
Imagine designing a rectangular classroom that is 5.2 m long and 3.8 m wide. The area of the floor is length × width = 5.2 m × 3.8 m = 19.76 m². The perimeter (the length of the skirting board needed) is 2 × (5.2 + 3.8) = 18 m.
假设你要设计一个长方形的教室，长 5.2 米，宽 3.8 米。地板的面积 = 长 × 宽 = 5.2 m × 3.8 m = 19.76 m²。周长（所需踢脚线的长度）为 2 × (5.2 + 3.8) = 18 m。
To tile the floor, you pick square tiles of side 0.5 m. Each tile covers 0.5 m × 0.5 m = 0.25 m². Number of tiles needed = total area ÷ area per tile = 19.76 ÷ 0.25 = 79.04, so you must buy 80 tiles (rounding up).
要铺设地砖，你选择了边长 0.5 米的正方形瓷砖。每块瓷砖覆盖 0.5 m × 0.5 m = 0.25 m²。所需瓷砖数量 = 总面积 ÷ 单块面积 = 19.76 ÷ 0.25 = 79.04，因此你必须购买 80 块（向上取整）。
Working with measurements and area links closely with design technology and geography fieldwork.
尺寸与面积的计算与设计技术和地理实地考察密切相关。
7. Ratios in Recipes and Mixtures | 食谱与混合物的比例
Ratios appear whenever you mix ingredients. A fruit punch uses orange juice and apple juice in the ratio 2 : 3. If you make 20 litres of punch, the total number of parts is 2 + 3 = 5. One part = 20 ÷ 5 = 4 litres. So orange juice = 2 × 4 = 8 litres and apple juice = 3 × 4 = 12 litres.
只要你混合食材，就会用到比例。一种水果宾治用橙汁和苹果汁按 2 : 3 的比例调配。如果你制作 20 升宾治，总份数 = 2 + 3 = 5。一份 = 20 ÷ 5 = 4 升。所以橙汁需要 2 × 4 = 8 升，苹果汁需要 3 × 4 = 12 升。
When scaling a recipe, the same idea applies. A cake recipe for 6 people needs 240 g of flour. How much flour for 10 people? The ratio is 6 : 10 = 3 : 5, so multiply 240 g by 10/6 (or 5/3) to get 400 g.
缩放食谱时，原理相同。一份供 6 人食用的蛋糕食谱需要 240 克面粉。10 人份需要多少面粉？人数比为 6 : 10 = 3 : 5，因此用 240 g 乘以 10/6（或 5/3）得到 400 g。
This skill is useful in chemistry when preparing solutions and in art when mixing paints.
这项技能在化学制备溶液和美术调配颜料时都非常有用。
8. Reading Timetables and Planning Journeys | 阅读时刻表与规划行程
Timetables test your ability to read tables and calculate elapsed time. Below is part of a bus timetable from the city centre to a museum.
时刻表考验你阅读表格和计算时间间隔的能力。下面是从市中心到博物馆的公交时刻表的一部分。
| Bus stop | Bus A | Bus B |
| City Centre | 09:20 | 10:05 |
| Park Road | 09:35 | 10:18 |
| Museum | 09:55 | 10:38 |
How long does Bus A take from City Centre to the Museum? 09:55 − 09:20 = 35 minutes. How long is the journey from Park Road to the Museum on Bus B? 10:38 − 10:18 = 20 minutes.
公交车 A 从市中心到博物馆需要多长时间？09:55 − 09:20 = 35 分钟。乘坐公交车 B 从公园路到博物馆的行程是多少分钟？10:38 − 10:18 = 20 分钟。
Always write times in 24-hour format if needed, and remember that when the minute subtraction needs borrowing, 1 hour = 60 minutes.
如有需要，始终使用 24 小时制书写时间，并记住当分钟减法需要借位时，1 小时 = 60 分钟。
9. Interpreting Graphs from Science Experiments | 解读科学实验图表
Data in graphs lets you link maths with scientific observations. Suppose you heat water and record its temperature every minute:
图表数据可以让你把数学和科学观察联系起来。假设你加热水并每分钟记录一次温度：
| Time (min) | 0 | 1 | 2 | 3 | 4 |
| Temp (°C) | 20 | 28 | 36 | 44 | 52 |
Plot these points on a line graph. By looking at the graph, you can see the temperature rises steadily. The rise in temperature per minute is the gradient: (52 − 20) ÷ 4 = 32 ÷ 4 = 8 °C per minute.
把这些点描在折线图上。观察图表可以看到温度稳步上升。每分钟的温度升幅就是斜率：(52 − 20) ÷ 4 = 32 ÷ 4 = 每分钟 8 °C。
If the trend continues, you can predict the temperature after 6 minutes: 20 °C + 6 × 8 °C = 68 °C. This kind of prediction is used in many real-world experiments.
如果趋势延续，你可以预测 6 分钟后的温度：20 °C + 6 × 8 °C = 68 °C。这种预测方法在许多真实实验中都得到应用。
10. Mixed Practice and Key Skills Summary | 综合练习与关键技能总结
Let’s put several skills together. Problem A: A school garden is a rectangle 15 m by 10 m. A path 1 m wide is built around the garden. Find the area of the path.
我们来综合运用几项技能。问题 A：一个学校花园是一个长 15 米、宽 10 米
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