📚 Year 7 SQA Maths: Interdisciplinary Problem-Solving Training | S1 数学跨学科综合题型训练
In the Scottish Curriculum for Excellence, Year 7 (S1) mathematics is not just about numbers; it is about applying those numbers to real-world situations across different subjects. Interdisciplinary problem-solving training helps you build confidence and see how maths connects to science, geography, technology, and everyday life. The following exercises are designed to challenge your ability to select and apply the right mathematical skills in mixed contexts – exactly what the SQA expects.
在苏格兰卓越课程中，S1（七年级）数学不仅仅涉及数字，更强调将数学运用于不同学科的真实情境。跨学科问题解决训练有助于建立信心，并让你看到数学如何与科学、地理、技术和日常生活紧密相连。以下练习旨在培养你在混合情境下选择并运用正确数学技能的能力，这正是 SQA 所期望的。
1. What Interdisciplinary Problem-Solving Really Means | 跨学科问题解决到底考什么
Interdisciplinary problem-solving does not mean learning five subjects at once. It means that a single task contains information from more than one context: a map, a budget, a science experiment, a recipe, or a design brief. Your job is to identify which mathematical tool is useful at each step.
跨学科问题解决并不意味着一次学五门学科。它指的是同一道题中包含来自多个情境的信息：一张地图、一份预算、一个科学实验、一份食谱或一份设计说明。你的任务是判断每一步该用哪个数学工具。
A typical S1 interdisciplinary question has three layers. First, you must extract the numbers from the words. Second, you must choose the correct operation or formula. Third, you must interpret the answer in the original context, including the correct unit.
典型的 S1 跨学科题目有三层结构。第一，从文字中提取数字；第二，选择正确的运算或公式；第三，把答案放回原来的情境中解释，并带上正确的单位。
Marks are usually awarded for method as well as for the final answer, so always write down the intermediate step, even if you can do it mentally. A clear method also makes it much easier to spot a mistake when you check your work.
评分通常既给方法分，也给最终答案分，所以即使你能心算，也要写下中间步骤。清晰的过程也能让你在检查时更容易发现错误。
2. Budgeting and Finance | 预算与理财
When organising a school trip, you are given a total budget of £480. The coach hire costs £195, and entry tickets for 30 students cost £7.50 each. You need to calculate the remaining money for lunch and any unplanned expenses.
组织学校旅行时，你的总预算为480英镑。租用大巴花费195英镑，30名学生的门票每人7.5英镑。你需要计算余下的钱用于午餐和意外支出。
First, find the total ticket cost: 30 × £7.50 = £225. Then add the coach hire: £195 + £225 = £420. Subtract from the budget: £480 − £420 = £60. So you have £60 left.
首先，计算门票总费用：30 × 7.5 = 225 英镑。然后加上大巴租金：195 + 225 = 420 英镑。从预算中减去：480 − 420 = 60 英镑。因此还剩下60英镑。
Remaining budget = 480 − (195 + 30 × 7.50) = £60
剩余预算 = 480 − (195 + 30 × 7.50) = 60 英镑
If lunch for each student costs £2.80, can you afford it? 30 × £2.80 = £84, which exceeds the remaining £60, so you would need to find additional funds or reduce costs.
如果每位学生的午餐费用是2.8英镑，负担得起吗？30 × 2.8 = 84 英镑，超出了剩余的60英镑，因此需要额外筹款或降低成本。
This type of question tests three skills at once: multiplication of a decimal by a whole number, addition of money, and comparison of two amounts to reach a decision. Notice that the final sentence is not a calculation but a conclusion – SQA questions often ask you to "decide", "justify" or "comment".
这类题目同时考查三项技能：小数乘整数、金额相加，以及比较两个数量后作出判断。注意最后一句话不是计算，而是结论——SQA 题目经常要求你"作出决定""说明理由"或"给出评论"。
3. Map Scales and Distances | 地图比例尺与距离
A map has a scale of 1:25,000. The distance between two villages on the map is 8.4 cm. What is the actual distance in kilometres?
一张地图的比例尺为1:25000。地图上两个村庄之间的距离是8.4厘米。实际距离是多少公里？
A scale of 1:25,000 means that 1 cm on the map represents 25,000 cm in real life. Multiply the map distance by the scale factor, then convert centimetres into metres and metres into kilometres.
比例尺1:25000表示地图上1厘米代表实际25 000厘米。用图上距离乘以比例尺系数，再把厘米换算成米、把米换算成公里。
8.4 cm × 25 000 = 210 000 cm = 2 100 m = 2.1 km
8.4 厘米 × 25 000 = 210 000 厘米 = 2 100 米 = 2.1 公里
The most common error here is forgetting the unit conversion. An answer of "210,000 km" is clearly unreasonable, because that would be several times around the Earth. Always ask yourself whether your answer is sensible.
这里最常见的错误是忘记换算单位。答案写成"210 000 公里"显然不合理，因为那相当于绕地球好几圈。永远要问自己：这个答案合理吗？
If the same task asked for the distance in metres instead, you would stop at 2,100 m. Reading the question carefully to find the required unit is worth an easy mark.
如果同一道题要求用米作答，那么算到2 100米就停止。仔细读题、看清要求的单位，是很容易拿到的一分。
4. Speed, Distance and Time in Science | 科学中的速度、距离与时间
Speed problems link maths directly to physics. The relationship is simple and appears in almost every S1 science topic, from walking pace to the speed of sound.
速度问题把数学与物理直接联系起来。这个关系很简单，却几乎出现在每一个 S1 科学主题中，从步行速度到声速都用得到。
Distance ÷ Time Distance = Speed × Time Time = Distance ÷ Speed
速度 = 距离 ÷ 时间 距离 = 速度 × 时间 时间 = 距离 ÷ 速度
Because the formula uses hours, convert 45 minutes into 0.75 hours: 2.1 ÷ 0.75 = 2.8 km/h.
假设全班用45分钟走完第3题中的2.1公里路线。由于公式使用小时，先把45分钟换算成0.75小时：2.1 ÷ 0.75 = 2.8 公里/小时。
and 4.2. It is the total distance divided by the total time: 4.2 km ÷ 1.25 h = 3.36 km/h.
如果返程用30分钟，那么整段行程的平均速度并不是2.8和4.2的平均值，而是总距离除以总时间：4.2 公里 ÷ 1.25 小时 = 3.36 公里/小时。
This distinction between average speed and the mean of two speeds is a favourite exam trap. Use the definition, not intuition.
平均速度与"两个速度的平均值"之间的区别是考试中最爱设的陷阱。请用定义，而不要凭直觉。
5. Ratio, Proportion and Rates | 比、比例与比率
Ratio questions appear in home economics, chemistry and design technology. In each case the method is the same: find the value of one part, then multiply.
比例问题出现在家政、化学和设计技术中。方法都一样：先求一份的值，再相乘。
people you need a scale factor of 6 ÷ 4 = 1.5, so the flour required is 300 × 1.5 = 450 g.
一份供4人使用的食谱需要300克面粉。供6人使用时，倍率为6 ÷ 4 = 1.5，所以需要面粉300 × 1.5 = 450克。
In chemistry, a compound might mix two substances in the ratio 2:1 by mass. If you have 90 g in total, there are 3 parts altogether, so one part is 30 g and the mixture contains 60 g and 30 g.
在化学中，某种化合物可能按质量比2:1混合两种物质。若总量为90克，则共有3份，每份30克，因此两种物质分别为60克和30克。
A direct proportion means both quantities grow together; inverse proportion means one grows while the other shrinks, such as more workers taking less time. Spotting which one applies is the key step.
正比例表示两个量同增同减；反比例表示一个增大另一个减小，例如工人越多用时越少。判断属于哪一种，是关键一步。
6. Percentages in Geography and Data Handling | 百分比：地理与数据处理
Percentages connect money, geography and statistics. A 15% discount on £84 is found by calculating 10% (£8.40) plus 5% (£4.20), giving £12.60 off and a final price of £71.40.
百分比把金钱、地理和统计联系起来。84英镑打85折（减15%）可以先算10%（8.40英镑）再加5%（4.20英镑），共优惠12.60英镑，最终价格为71.40英镑。
Breaking a percentage into friendly parts is a reliable non-calculator strategy. 1% is found by dividing by 100, 10% by dividing by 10, and any other percentage can be built from these.
把百分数拆成好算的部分，是不用计算器时最可靠的策略。1%是除以100，10%是除以10，其他百分数都可以由它们组合而成。
In geography, if a town of 12,000 people grows by 4% s 12 000 × 0.04 = 480, giving a new population of 12,480. If the following year brings a 4% does not return to 12,000, because the second percentage is taken from the larger number.
在地理中，若一座12 000人的城镇增长4%，增加量为12 000 × 0.04 = 480，新人口为12 480。如果下一年下降4%，人口并不会回到12 000，因为第二次百分数是从更大的基数上计算的。
d as change ÷ original × 100. Always divide by the original value, never by the new value.
百分变化率的算法是：变化量 ÷ 原值 × 100。永远除以原值，而不是新值。
7. Area, Perimeter and Design Technology | 面积、周长与设计技术
Design technology tasks combine measurement, area and cost. A rectangular school garden measuring 6 m by 4 m has an area of 24 m² and a perimeter of 20 m.
设计技术类题目把测量、面积和成本结合起来。一块6米乘4米的矩形校园花园，面积为24平方米，周长为20米。
If each square metre needs 5 plants, you need 24 × 5 = 120 plants. If fencing costs £8.50 per metre, the fence costs 20 × £8.50 = £170.
如果每平方米需要5株植物，那么需要24 × 5 = 120株。如果围栏每米8.50英镑，围栏费用为20 × £8.50 = 170英镑。
Area and perimeter are constantly confused because both use the same two numbers. Area is measured in square units and covers the inside; perimeter is measured in linear units and goes around the edge.
面积和周长经常被混淆，因为两者都用到同样的两个数字。面积用平方单位，覆盖内部；周长用长度单位，绕边缘一圈。
e Area = ½ × base × height, remembering that the height must be perpendicular to the base.
遇到复合图形时，把它拆成若干个矩形，分别算面积再相加。三角形用面积 = ½ × 底 × 高，注意高必须垂直于底。
8. Statistics and Scientific Enquiry | 统计与科学探究
Science investigations produce data, and maths turns that data into meaning. The mean is the total of all values divided by the number of values; the median is the middle value when the data are arranged in order.
科学探究会产生数据，而数学把数据变成意义。平均数等于全部数值之和除以数值个数；中位数是数据按顺序排列后的中间值。
en one unusually large value appears, the median often describes the group better than the mean.
对于数值12、15、15、18、20，平均数为80 ÷ 5 = 16，中位数为15。当出现一个特别大的数值时，中位数往往比平均数更能代表整体。
llest: 20 − 12 = 8. Range measures spread, so it tells you how consistent the results are.
极差是最大值减最小值：20 − 12 = 8。极差衡量离散程度，因此能说明结果的一致性如何。
In a fair test you should also ask whether the sample is large enough, whether the measurements were repeated, and whether any outliers should be excluded with a stated reason.
在公平实验中，你还应思考：样本是否足够大？测量是否重复过？是否有异常值需要排除，并说明理由。
9. Algebra, Formulae and Coding | 代数、公式与编程
Algebra is the language that links all of the previous sections. Once a situation is written as a formula, any set of numbers can be substituted into it.
代数是把前面各节联系起来的语言。只要把一个情境写成公式，任何一组数字都可以代入求解。
st is C = 195 + 7.5n, where n is the number of students. When n = 30, C = 195 + 225 = 420.
对于旅行预算，总成本可写为 C = 195 + 7.5n，其中 n 为学生人数。当 n = 30 时，C = 195 + 225 = 420。
The same formula answers new questions instantly: with £480 available, how many students can go if lunch is not included? Solve 195 + 7.5n ≤ 480, giving 7.5n ≤ 285 and n ≤ 38.
同一个公式能立刻回答新问题：若可用资金为480英镑，不含午餐时最多能带多少学生？解 195 + 7.5n ≤ 480，得到 7.5n ≤ 285，n ≤ 38。
This is exactly how computer programs work: a variable stores a value, and an expression is evaluated each time the variable changes. Writing code and writing algebra use the same logical structure.
计算机程序正是这样工作的：变量存储数值，每次变量改变时表达式就被重新计算。写代码与写代数使用相同的逻辑结构。
10. Angles, Bearings and Navigation | 角度、方位与导航
Geography and outdoor education use angles and bearings. A bearing is measured clockwise from north and is always written with three digits, so due east is 090° and south-west is 225°.
地理和户外教育会用到角度与方位。方位角从正北开始顺时针测量，并且总是写成三位数，所以正东是090°，西南是225°。
Compass directions, map work and orienteering all rely on the fact that angles on a straight line add to 180° and angles around a point add to 360°.
罗盘方向、地图作业和定向越野都依赖以下事实：同一直线上的角相加为180°，绕一点一周的角相加为360°。
allows you to find a missing bearing or direction. In a right-angled triangle, Pythagoras' theorem gives a² + b² = c², where c is the hypotenuse.
任何三角形的内角和为180°，这可以帮你求出缺失的方位或方向。在直角三角形中，勾股定理给出 a² + b² = c²，其中 c 是斜边。
When solving navigation problems, sketch the situation first, mark north, and label every known angle. A clear diagram prevents most errors before any calculation begins.
解导航题时，先画草图，标出正北，并标注所有已知角。清晰的示意图能在开始计算前就避免大部分错误。
11. Units, Accuracy and Estimation | 单位、精度与估算
Many marks are lost not through weak mathematics but through careless units. Length, area and volume use different powers of ten when converting.
许多失分不是因为数学能力不足，而是因为单位疏忽。长度、面积和体积换算时使用的十的幂次并不相同。
1 m = 100 cm 1 m² = 10 000 cm² 1 m³ = 1 000 000 cm³
1 米 = 100 厘米 1 平方米 = 10 000 平方厘米 1 立方米 = 1 000 000 立方厘米
Estimation is a powerful checking tool. If a map distance of 8.4 cm gives 2.1 km, then roughly 4 cm should give roughly 1 km, and a quick mental check confirms the answer is reasonable.
估算是强有力的检查工具。如果图上8.4厘米对应2.1公里，那么大约4厘米应约对应1公里，心算一下就能确认答案是否合理。
Rounding should be done at the end, not in the middle of a calculation. Rounding early can shift a final answer by several units, especially in multi-step money problems.
四舍五入应放在最后进行，不要放在计算中途。过早取整可能让最终答案偏差好几个单位，在多步骤的金钱问题中尤其明显。
12. Exam Technique and Common Errors | 考试技巧与常见错误
Interdisciplinary questions are longer than routine exercises, so reading strategy matters as much as calculation. Read the whole question once before writing anything, then underline the numbers and the units they are given in.
跨学科题目比常规练习更长，因此阅读策略和计算能力同样重要。动笔前先通读整题，然后划出数字及其单位。
Answer in a full sentence where the question asks for a decision, and always include the unit. "£60" is a complete answer; "60" alone may lose a mark.
当题目要求作出判断时，用完整句子作答，并且一定带上单位。"60英镑"是完整答案，只写"60"可能会丢分。
Check three things at the end: the arithmetic, the units, and whether the answer is realistic in the context of the story. These three checks catch the majority of avoidable errors.
最后检查三件事：运算是否正确、单位是否正确、答案在故事情境中是否合理。这三项检查能拦住大多数本可避免的错误。
Practise mixed-topic questions regularly rather than only single-topic drills. The skill being tested is selection – choosing the right tool from your whole mathematical toolkit.
平时要定期练习混合主题题目，而不是只做单一主题的练习。真正被考查的技能是选择——从你全部的数学工具箱中挑出合适的工具。
Published by TutorHao | Year 7 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图