Year 7 CAIE Maths: Interdisciplinary Problem-Solving Training | 跨学科综合题型训练

📚 Year 7 CAIE Maths: Interdisciplinary Problem-Solving Training | 跨学科综合题型训练

Mathematics in Year 7 does not exist in isolation. Many exam questions blend number skills, algebra basics, and data handling with contexts from science, geography, everyday life, and even art. This article trains you to recognise and solve these interdisciplinary problems with confidence, building the transferable skills that CAIE assessments value.

7年级的数学并非独立存在。许多考题将数字运算、基础代数和数据处理与科学、地理、日常生活甚至艺术情境相融合。本文训练你自信地识别并解决这些跨学科问题，培养 CAIE 评估所看重的可迁移技能。

1. Speed, Distance and Time: Maths in Physics | 速度、距离和时间：物理中的数学

In science you learn that speed is the rate at which an object covers distance. Mathematically, we use the formula linking three quantities. If a car travels 150 km in 3 hours, we can calculate its average speed.

在科学中你学到速度是物体通过距离的速率。数学上我们使用联系三个量的公式。如果一辆汽车在3小时内行驶150公里，我们可以计算其平均速度。

Average speed = Total distance ÷ Total time

平均速度 = 总距离 ÷ 总时间

You can rearrange the formula to find distance (speed × time) or time (distance ÷ speed). Always check that units match: if speed is in m/s, time must be in seconds and distance in metres.

你可以重新整理公式来求距离（速度 × 时间）或时间（距离 ÷ 速度）。务必检查单位是否一致：如果速度单位是米/秒，时间必须是秒，距离必须是米。

Quantity	Common Units
Speed	m/s, km/h, mph
Distance	m, km, miles
Time	seconds, minutes, hours

Train by solving: A cyclist moves at a steady 5 m/s. How far does she travel in 2 minutes? Remember to convert minutes to seconds first.

通过解题来训练：一名自行车手以稳定的5米/秒的速度骑行，她在2分钟内行驶多远？记得先把分钟换算成秒。

2. Density and Mass in Materials | 密度与质量在材料科学中

Density tells us how much mass is packed into a certain volume. It appears in physics and chemistry, but the maths is straightforward proportion work.

密度告诉我们一定体积内含有多少质量。它出现在物理和化学中，但所需的数学就是直接的比例运算。

Density = Mass ÷ Volume

密度 = 质量 ÷ 体积

If a block of metal has a mass of 500 g and a volume of 200 cm³, its density is 2.5 g/cm³. You may be asked to compare materials: a substance with lower density floats on one with higher density.

如果一块金属的质量是500克，体积是200立方厘米，它的密度就是2.5克/立方厘米。你可能会被要求比较材料：密度较小的物质会浮在密度较大的物质上。

To find mass or volume from a known density, multiply or divide accordingly. Keep units consistent: g and cm³, or kg and m³. This skill reinforces algebraic thinking.

要从已知密度求质量或体积，只需相应地进行乘法或除法。保持单位一致：克和立方厘米，或千克和立方米。这一技能会强化代数思维。

3. Map Scales and Real-World Geography | 地图比例尺与现实地理

Geographers use scale drawings and maps. In maths, you interpret a scale such as 1 : 25 000 to calculate actual distances. The scale means 1 cm on the map represents 25 000 cm in reality.

地理学家使用比例图和地图。在数学中，你解读如 1 : 25 000 这样的比例尺来计算实际距离。该比例尺表示地图上1厘米代表实际中的25 000厘米。

Always convert large centimetre measurements into metres or kilometres. For example, 25 000 cm = 250 m. If two towns are 8 cm apart on the map, actual distance = 8 × 250 = 2000 m, or 2 km.

始终将较大的厘米数换算成米或千米。例如，25 000厘米 = 250米。如果两个城镇在地图上相距8厘米，实际距离 = 8 × 250 = 2000米，即2千米。

Scales can also be given as a statement: ‘1 cm represents 5 km’. Use proportion: 1 cm : 5 km = map distance : real distance. Cross-multiplying is an essential numerical skill.

比例尺也可以用文字说明表示：“1厘米代表5公里”。使用比例式：1厘米 : 5公里 = 地图距离 : 实际距离。交叉相乘是一项重要的数值计算技能。

4. Temperature Conversion and Negative Numbers | 温度换算与负数

In science experiments you often record temperatures. Converting between degrees Celsius (°C) and Fahrenheit (°F) practises substituting into a formula and working with negative numbers, a key Year 7 topic.

在科学实验中你经常记录温度。摄氏度与华氏度之间的转换练习了代入公式和负数运算——这也是7年级的重要课题。

°F = (°C × 9/5) + 32

If the temperature is 10°C, first multiply by 9/5 (or 1.8) to get 18, then add 32 to obtain 50°F. When it is −5°C, careful: (−5) × 1.8 = −9; add 32 gives 23°F. This reinforces order of operations and negative number multiplication.

如果温度为10°C，先乘以9/5（或1.8）得18，再加32得到50°F。当温度为−5°C时需小心：（−5）× 1.8 = −9；再加32得23°F。这强化了运算顺序和负数乘法。

You may also need to convert from °F to °C using the inverse: °C = (°F − 32) × 5/9. Always work inside the brackets first.

你也许需要从华氏度转回摄氏度，使用逆运算：°C = (°F − 32) × 5/9。始终先计算括号内的部分。

5. Averages and Statistics in Sport | 体育中的平均数和统计

Sports reports are full of numbers: points per game, batting averages, lap times. In maths you use the mean, median, mode and range to make sense of these performances.

体育报道充满了数字：场均得分、击球率、单圈用时。在数学中你使用平均数、中位数、众数和极差来理解这些表现。

The mean (average) is found by adding all values and dividing by the number of values. If a basketball player’s scores over five games are 12, 15, 10, 18, 15, the mean is (12+15+10+18+15) ÷ 5 = 70 ÷ 5 = 14 points.

平均数（均值）是将所有数值相加再除以数值的个数。如果一名篮球运动员五场比赛的得分是12、15、10、18、15，均值就是（12+15+10+18+15）÷ 5 = 70 ÷ 5 = 14分。

The median is the middle value when data is ordered. For 10, 12, 15, 15, 18, the median is 15. The mode is the most frequent, here also 15. The range (maximum − minimum) shows consistency: 18 − 10 = 8.

中位数是数据排序后中间的那个值。对于10、12、15、15、18，中位数是15。众数是出现最频繁的，这里也是15。极差（最大值 − 最小值）反映稳定性：18 − 10 = 8。

Interdisciplinary questions might ask: ‘A team’s mean score increased. What must have happened?’ This links maths with real interpretation.

跨学科问题可能会问：“一支队伍的场均得分提高了，可能发生了什么？”这将数学与现实解读联系起来。

6. Ratios and Proportions in Cooking | 烹饪中的比例与比

Recipes are essentially ratio problems. If a cake recipe for 4 people requires 200 g of flour, how much flour is needed for 10 people? This is direct proportion.

食谱本质上就是比例问题。如果一个供4人食用的蛋糕食谱需要200克面粉，那么10人需要多少面粉？这是正比例。

Set up equivalent ratios: 200 g : 4 people = x g : 10 people. Cross-multiply: 4x = 200 × 10, so 4x = 2000, x = 500 g. You can also find the unit rate: 200 ÷ 4 = 50 g per person, then multiply by 10.

列出等价比值：200克 : 4人 = x克 : 10人。交叉相乘：4x = 200 × 10，得4x = 2000，x = 500克。你也可以先求单位比率：200 ÷ 4 = 每人50克，再乘以10。

Fraction skills appear when halving or doubling a recipe, or when an ingredient is given as a fraction: ‘Use 3/4 cup of sugar per 6 muffins’. How much for 15 muffins?

当食谱减半或加倍，或者材料用量以分数给出时（如“每6个松饼用3/4杯糖”），就需要运用分数技能。15个松饼用多少糖？

7. Money, Discounts and Simple Interest | 货币、折扣与单利

Personal finance connects percentages and decimals to real decisions. A 15% discount on a £60 bag means you save 0.15 × 60 = £9, and pay £51.

个人理财将百分数和小数与实际决策联系起来。一个原价£60的包打八五折（15%折扣），意味着你节省0.15 × 60 = £9，实付£51。

Simple interest, used in some savings accounts, is calculated as a percentage of the original principal each year. Interest = Principal × Rate × Time. For £400 at 3% per year for 2 years: Interest = £400 × 0.03 × 2 = £24.

某些储蓄账户使用的单利，每年按原始本金的百分数计算。利息 = 本金 × 利率 × 时间。本金£400，年利率3%，存2年：利息 = £400 × 0.03 × 2 = £24。

Currency conversion is another typical task. If £1 = $1.30, how many dollars do you get for £200? Multiply: 200 × 1.30 = $260. Converting back means dividing.

货币兑换是另一典型任务。如果£1 = $1.30，用£200可以换多少美元？相乘：200 × 1.30 = $260。换回英镑则要用除法。

8. Symmetry and Geometric Patterns in Art | 艺术中的对称与几何图案

Art and nature use line symmetry and rotational symmetry. In maths, a shape has line symmetry if a mirror line splits it into two identical halves. A square has 4 lines of symmetry; a rectangle has 2.

艺术与自然利用线对称和旋转对称。数学中，如果一条镜像线将图形分成两个完全相同的部分，该图形就具有线对称。正方形有4条对称轴；长方形有2条。

Rotational symmetry is the number of times a shape looks exactly the same during a full 360° turn. An equilateral triangle has rotational symmetry of order 3.

旋转对称是指一个图形在绕中心旋转360°的过程中，有多少次看起来与原来完全一样。等边三角形的旋转对称阶数为3。

Interdisciplinary tasks might ask you to complete a pattern using reflection or identify the symmetry in a cultural design. Use tracing paper or visual reasoning to count symmetry orders.

跨学科任务可能要求你通过反射补全图案，或识别文化图样中的对称性。运用描图纸或视觉推理来计算对称阶数。

9. Interpreting Line Graphs from Experiments | 解读实验得出的折线图

Science experiments often produce data plotted on line graphs. Your maths skill is to read coordinates, describe trends, and even predict values beyond the data (extrapolation, though Year 7 usually sticks to interpolation).

科学实验常产生以折线图呈现的数据。你的数学技能是读取坐标、描述趋势，甚至预测数据范围之外的值（外推，不过7年级通常限于内插）。

For a cooling curve of water, the temperature drops quickly at first, then more slowly. You should be able to find the temperature at a given time and say how many minutes it took to reach a certain degree.

对于水的冷却曲线，温度起初下降很快，然后变慢。你应当能找出给定时间的温度，并说出达到某一度数需要多少分钟。

Note the scale on each axis. A common mistake is misreading an interval: check if one small square stands for 1 unit, 2 units, or 10 units. The graph title and labels are just as important as the numbers.

注意每条坐标轴上的刻度。常见错误是误读间隔：检查一个小格代表1个单位、2个单位还是10个单位。图表的标题和标签与数字同样重要。

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

Interdisciplinary questions often involve length, mass, capacity and time conversions. You must know the key equivalences: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm; 1 kg = 1000 g; 1 litre = 1000 ml; 1 hour = 60 minutes, 1 minute = 60 seconds.

跨学科题目常涉及长度、质量、容量和时间的换算。你必须掌握关键的等量关系：1千米 = 1000米，1米 = 100厘米，1厘米 = 10毫米；1千克 = 1000克；1升 = 1000毫升；1小时 = 60分钟，1分钟 = 60秒。

For compound units like speed, you may need to convert m/s to km/h. Multiply by 3.6: 10 m/s × 3.6 = 36 km/h. The reasoning: 10 m in one second means 10 × 3600 m in one hour ÷ 1000 = 36 km.

对于复合单位如速度，你可能需要将米/秒换算为千米/时。乘以3.6即可：10米/秒 × 3.6 = 36千米/时。推理过程：每秒10米，意味着每小时10 × 3600米 ÷ 1000 = 36千米。

Always show your conversion factors clearly in working. Multi-step problems may ask, for instance, how many 25 ml doses are in a 1.5 litre bottle. Convert litres to ml first: 1.5 × 1000 = 1500 ml, then 1500 ÷ 25 = 60 doses.

务必在解题步骤中清晰展示换算因子。多步骤问题可能问，例如，一个1.5升的瓶子中有多少个25毫升的剂量。先把升换成毫升：1.5 × 1000 = 1500毫升，然后1500 ÷ 25 = 60剂。

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Year 7 CAIE Maths: Interdisciplinary Problem-Solving Training | 跨学科综合题型训练