📚 Year 7 SQA Maths: Case Study Practice | Year 7 SQA 数学：案例分析实战演练
Welcome to a real-world case study designed for Year 7 SQA Maths. In this article, you will follow a practical scenario – planning a school trip to a science museum – to revise key numeracy skills such as budgeting, measurement, ratio and data handling. Each section pairs an English explanation with a Chinese translation, so you can master both the language and the mathematics.
欢迎来到为 Year 7 SQA 数学设计的真实世界案例分析。本文将跟随一个实践场景——策划学校去科学博物馆的旅行——来复习预算、测量、比和数据处理等关键算术技能。每个部分都配有英文解释和中文翻译，让你同时掌握语言和数学。
1. Case Study Overview | 案例概述
Your class of 28 students and 2 teachers is planning an educational visit to the City Science Museum. The school has given a total budget of £350. You need to research entry fees, work out transport costs, plan a lunch menu and collect opinions from classmates on which exhibition to visit first.
你们班有 28 名学生和 2 名教师，正计划前往城市科学博物馆进行教育参观。学校提供了 £350 的总预算。你需要研究门票价格、计算交通费用、规划午餐菜单，并收集同学们对于先参观哪个展览的意见。
The case study is broken down into several tasks: calculating total cost, comparing coach hire quotes, sharing food fairly, reading a timetable and creating a bar chart of survey results. Each task mirrors the skills tested in SQA assessments.
该案例被分解为若干任务：计算总花费、比较巴士租赁报价、公平分配食物、阅读时间表以及为调查结果绘制条形图。每项任务都对应 SQA 评估中考查的技能。
2. Understanding the Problem | 理解问题
Before doing any maths, read the entire case study description twice. Underline all numbers and units, such as ’28 students’, ‘£350 budget’ and ‘entrance fee £4.50 per child’. Identify the exact questions being asked: you may need to find the total cost, determine whether the budget is enough or suggest adjustments.
在进行任何数学计算之前，请把整个案例描述读两遍。在所有的数字和单位下面划线，例如“28 名学生”、“预算 £350”和“儿童门票费 £4.50”。确定被问到的确切问题：你可能需要算出总花费、判断预算是否足够，或提出调整建议。
Write down a list of the mathematical topics involved. In this scenario you will use addition, subtraction, multiplication, division, ratio, reading timetables and drawing graphs. Checking the topic list helps you choose the correct operation for each step.
写下所涉及的数学主题列表。本情境中你将用到加法、减法、乘法、除法、比、阅读时间表和绘制图表。检查主题列表可帮助你为每一步选择正确的运算。
3. Extracting Key Information | 提取关键信息
Create a simple table to organise the data. The entrance ticket costs £4.50 per pupil and £6.80 per adult. A coach for 30 people is quoted at £120, and lunch ingredients cost £1.75 per person. The journey takes 55 minutes each way.
制作一张简单的表格来整理数据。门票对学生每人 £4.50，对成人每人 £6.80。一辆载 30 人的巴士报价 £120，午餐原料人均 £1.75。单程旅行时间为 55 分钟。
| Item | Quantity / Unit Cost |
|---|---|
| Pupils | 28 |
| Teachers | 2 |
| Pupil ticket | £4.50 |
| Adult ticket | £6.80 |
| Coach hire | £120 |
| Lunch per person | £1.75 |
Now double-check the numbers: 28 + 2 = 30 people in total. The coach fits exactly 30, which is perfect. You must also consider whether any discounts apply – the museum offers a free adult ticket for every 10 paying pupils, so you can save on teacher tickets.
现在复核数字：28 + 2 = 总共 30 人。巴士恰好可以坐 30 人，非常完美。你也必须考虑是否有折扣——博物馆为每 10 名付费学生提供一张免费成人票，因此你可以在教师门票上省钱。
4. Budget Calculations | 预算计算
First, calculate the total entrance cost without discounts. Pupil tickets: 28 × £4.50 = £126. Adult tickets: 2 × £6.80 = £13.60. So the combined ticket cost would be £126 + £13.60 = £139.60.
首先，计算没有折扣时的总门票费。学生票：28 × £4.50 = £126。成人票：2 × £6.80 = £13.60。因此门票总花费为 £126 + £13.60 = £139.60。
However, the museum policy gives 2 free adult tickets because 28 pupils qualify for two multiples of 10. That means the actual adult ticket cost becomes £0. The adjusted entrance total is £126.
然而，博物馆的政策提供 2 张免费成人票，因为 28 名学生符合两个 10 的倍数。这意味着实际成人票花费变为 £0。调整后的门票总额为 £126。
Now add the coach hire: £126 + £120 = £246. Then add the lunch cost for 30 people: 30 × £1.75 = £52.50. The overall trip cost is £246 + £52.50 = £298.50.
现在加上巴士租赁费：£126 + £120 = £246。然后加上 30 人的午餐费：30 × £1.75 = £52.50。旅行总花费为 £246 + £52.50 = £298.50。
Total cost = (28 × £4.50) + £120 + (30 × £1.75) = £298.50
Since the budget is £350, the surplus is £350 – £298.50 = £51.50. The trip is well within budget.
既然预算为 £350，结余为 £350 – £298.50 = £51.50。这次旅行的花费远低于预算。
5. Transport and Distances | 交通与距离
The direct route from school to the museum is 42 km. The coach travels at an average speed of 56 km/h on motorways. How long will the journey take in minutes? Use the formula time = distance ÷ speed.
从学校到博物馆的直接路线为 42 公里。巴士在高速公路上的平均速度为 56 公里/小时。行程将花费多少分钟？使用公式 时间 = 距离 ÷ 速度。
Time = 42 km ÷ 56 km/h = 0.75 h
Convert 0.75 hours to minutes: 0.75 × 60 = 45 minutes. However, the itinerary includes a 10-minute comfort break, so total travel time per direction is 55 minutes. The round trip takes 110 minutes, or 1 hour 50 minutes.
把 0.75 小时转换为分钟：0.75 × 60 = 45 分钟。然而行程中包含 10 分钟的休息时间，因此单程总旅行时间为 55 分钟。往返共需 110 分钟，即 1 小时 50 分钟。
Use a ratio to share the travel cost if another class joins later and contributes £40. Your class covered the original £120, so your contribution fraction is 120/(120+40) = 120/160 = 3/4. You should receive 3/4 of any future refund.
如果另一个班级稍后加入并出资 £40，请用比来分摊旅行费用。你们班级支付了原来的 £120，因此你们的出资比例为 120/(120+40) = 120/160 = 3/4。将来若有退款，你们应获得 3/4。
6. Food and Drink Allocation | 食物与饮料分配
A sandwich platter contains 40 sandwiches. You need to feed 30 people, with the rule that each person gets at least 1.5 sandwiches on average. How many platters must you order? 30 × 1.5 = 45 sandwiches. Since one platter has 40, you need 2 platters, giving 80 sandwiches.
一个三明治拼盘包含 40 块三明治。你需要供 30 人食用，规定每人平均至少 1.5 块三明治。你必须订购多少拼盘？30 × 1.5 = 45 块三明治。因一个拼盘有 40 块，你需要 2 个拼盘，提供 80 块三明治。
The leftover sandwiches can be expressed as a fraction: (80 – 45) / 80 = 35/80 = 7/16. So 7/16 of the sandwiches remain for the journey back. Share the drink bottles similarly: if you have 48 bottles, the ratio of bottles to people is 48:30, which simplifies to 8:5.
剩余的三明治可表示为一个分数：(80 – 45) / 80 = 35/80 = 7/16。因此返程时还剩下 7/16 的三明治。类似地分配饮料瓶：如果你有 48 瓶，饮料瓶与人的比为 48:30，化简为 8:5。
Create a shopping list with quantities scaled to 30 people. For example, if a recipe for 6 people needs 12 slices of cheese, for 30 people you need (12 ÷ 6) × 30 = 60 slices. Always write the working step by step.
制作一份按 30 人缩放数量的购物清单。例如，如果一份 6 人食谱需要 12 片奶酪，那么 30 人需要 (12 ÷ 6) × 30 = 60 片。务必逐步写出计算过程。
7. Timetable Planning | 时间表规划
The museum opens at 09:30 and closes at 16:00. You plan to arrive at 10:15 and leave at 14:30. How much time do you have inside the museum?
博物馆 09:30 开门，16:00 闭馆。你计划 10:15 到达，14:30 离开。你在博物馆内有多少时间？
14:30 – 10:15 = 4 hours 15 minutes
Use a number line to break the day into segments: travel 55 min, exhibition A 50 min, lunch 40 min, exhibition B 55 min, gift shop 25 min, return travel 55 min. Check the total time and ensure you are back at school by 15:45.
使用数轴将一天分割为若干段：旅行 55 分钟，展览 A 50 分钟，午餐 40 分钟，展览 B 55 分钟，礼品店 25 分钟，返程 55 分钟。核查总时间并确保在 15:45 之前回到学校。
Now complete a 24-hour clock timeline. Depart school at 09:00, arrive museum 09:55 (including break). Start first activity at 10:10. If each activity runs exactly to plan, draw a table showing the finish time of each stage. Remember to convert minutes correctly.
现在完成一个 24 小时制时间线。09:00 从学校出发，09:55 到达博物馆（含休息）。10:10 开始第一项活动。如果每项活动严格按计划进行，绘制一个表格显示每个阶段的结束时间。记住正确转换分钟。
| Activity | Start | Duration | Finish |
|---|---|---|---|
| Travel to museum | 09:00 | 55 min | 09:55 |
| Comfort break | 09:55 | 10 min | 10:05 |
| Exhibition A | 10:10 | 50 min | 11:00 |
| Lunch | 11:10 | 40 min | 11:50 |
8. Data Handling: Survey Results | 数据处理：调查结果
You survey the class on their favourite science topic: Space, Dinosaurs, Robotics or Human Body. The votes are 8, 7, 5 and 8 respectively. How many students voted in total? 8 + 7 + 5 + 8 = 28, matching the class size.
你调查了班级同学最喜爱的科学主题：太空、恐龙、机器人或人体。票数分别为 8、7、5 和 8。总共有多少学生参与了投票？8 + 7 + 5 + 8 = 28，与班级人数相符。
Represent this data in a frequency table and calculate the fraction of students who chose Space. The fraction is 8/28, which simplifies to 2/7. You can also express it as a percentage: (8 ÷ 28) × 100 ≈ 28.6%.
用频数表表示这些数据，并计算选择太空的学生所占的分数。分数为 8/28，化简为 2/7。你也可以用百分数表示：(8 ÷ 28) × 100 ≈ 28.6%。
Now draw a bar chart with labelled axes. The horizontal axis shows the topic, the vertical axis shows the frequency. Use a scale where one square equals one vote. Draw the bars and add a title: ‘Favourite Science Topics in Year 7’.
现在绘制一个带轴标签的条形图。横轴表示主题，纵轴表示频数。使用每个格子代表一票的刻度。画出长条并添加标题：”Year 7 最喜爱的科学主题”。
Extension: calculate the mean number of votes if a new student joins and chooses Robotics. New votes: 8, 7, 6, 8. Mean = (8+7+6+8) ÷ 4 = 29 ÷ 4 = 7.25. The mode remains 8, and the range is 8 – 6 = 2.
拓展：如果一名新同学加入并选择了机器人，计算平均票数。新票数：8, 7, 6, 8。平均值 = (8+7+6+8) ÷ 4 = 29 ÷ 4 = 7.25。众数仍为 8，极差为 8 – 6 = 2。
9. Presenting Your Solution | 呈现你的解决方案
A strong case study response uses clear headings, step-by-step working and final summary statements. Start with a brief paragraph outlining your approach, then show each calculation on a new line.
一份出色的案例分析回答会使用清晰的标题、逐步运算和总结陈述。先用一个简短段落概述你的方法，然后在新的行中展示每个计算。
For money questions, always include the £ sign and check that your final total is less than or equal to the budget. Write a conclusion: ‘The total cost of the trip is £298.50, which is within the £350 budget, leaving a surplus of £51.50. The plan is financially viable.’
对于涉及金钱的问题，务必包含 £ 符号并检查最终总额是否小于或等于预算。写出结论：”本次旅行的总花费为 £298.50，在 £350 预算之内，剩余 £51.50。该计划财务可行。”
Use checklists to ensure you have answered every part. For example, tick off: entrance cost, transport, lunch, timetable and survey graph. This mirrors the SQA marking scheme and helps you spot missing elements.
使用检查清单以确保你回答了每个部分。例如，勾选：门票费用、交通、午餐、时间表和调查图表。这样做符合 SQA 评分方案，并帮助你发现遗漏项。
10. Reflection and Extension | 反思与拓展
After completing the case study, reflect on which part you found most challenging. Was it the ratio, the timetable or the percentage? Spend extra revision time on that topic. You can also swap roles and design your own small case study for a friend.
完成案例分析后，反思你觉得最有挑战的部分。是比、时间表还是百分数？在该主题上多花些复习时间。你也可以互换角色，为朋友设计一个你自己的小型案例。
Extension questions: What if the coach cost rises by 15%? New coach cost = £120 × 1.15 = £138. Then total becomes £126 + £138 + £52.50 = £316.50. The surplus shrinks to £350 – £316.50 = £33.50. Discuss whether to shorten the gift shop time to save money.
拓展问答：如果巴士费用上涨 15%会怎样？新巴士费用 = £120 × 1.15 = £138。那么总额变为 £126 + £138 + £52.50 = £316.50。结余缩小至 £350 – £316.50 = £33.50。讨论是否缩短礼品店时间来省钱。
Another extension: The museum introduces a ½ price offer for pupils during October. Recalculate the entrance fee: 28 × (£4.50 × ½) = 28 × £2.25 = £63. The new trip total becomes £63 + £120 + £52.50 = £235.50. This saves £63 compared to the original plan.
另一个拓展：博物馆在十月份推出学生半价优惠。重新计算门票费：28 × (£4.50 × ½) = 28 × £2.25 = £63。新旅行总额变为 £63 + £120 + £52.50 = £235.50。这比原计划节省了 £63。
Finally, practise explaining your reasoning aloud in English and Chinese. This dual-language skill is valuable for international assessments and builds confidence.
最后，练习用英文和中文大声解释你的推理。这种双语技能对国际评估很有价值，也能建立信心。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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