📚 Year 7 CCEA Maths: Case Study Practical Exercises | 七年级 CCEA 数学：案例分析实战演练
In Year 7 CCEA Mathematics, case study exercises bring real‑world scenarios into the classroom. These activities ask you to solve multi‑step problems by combining number skills, measurement, data handling, and basic algebra. This article walks you through a complete practical case study, from understanding the brief to checking your final solution. Along the way you will revise decimals, perimeter, area, fractions, time calculations, and graphs — all while planning a school Fun Day.
在七年级 CCEA 数学中，案例分析演练将真实情境带入课堂。这些活动要求你综合运用数字技能、测量、数据处理和基础代数来解决多步骤问题。本文将带你完成一个完整的实战案例，从理解任务要求到检查最终答案。整个过程你将复习小数、周长、面积、分数、时间计算以及图表——所有这些都会在策划学校“趣味日”的过程中用到。
1. Understanding the Case Study Brief | 理解案例任务书
A clear problem statement is the starting point. Our brief: ‘Plan a Year 7 Fun Day in the school playground. You have a budget of £150. You need to design the layout, schedule three activities, run a survey to choose a team game, and calculate how to share leftover money between the charity and the school tuck shop.’
清晰的问题陈述是起点。我们的任务书是：“在学校操场策划一次七年级趣味日。你有 150 英镑预算。需要设计场地布局、安排三项活动的时间表、做一项调查来选择一个团队游戏，并计算剩余资金如何分配给慈善机构和学校小吃店。”
Read the brief twice. Underline the maths words: ‘budget’, ‘design the layout’, ‘schedule’, ‘survey’, ‘share’. Each word points to a specific set of skills you must use.
把任务书读两遍。划出数学关键词：“预算”、“设计布局”、“时间表”、“调查”、“分配”。每个词都指向你必须使用的一组特定技能。
2. Breaking Down the Problem | 拆分问题
Large case studies become manageable when you split them into smaller tasks. Write a list: (1) Budget spending, (2) Measure and sketch the playground, (3) Work out perimeter and areas for stalls, (4) Create a timed schedule, (5) Collect and display survey data, (6) Calculate fractions of the remaining money.
大型案例分析通过拆分为小任务会变得易于处理。写下清单：(1) 预算支出，(2) 测量并画出操场示意图，(3) 计算摊位周边的周长和面积，(4) 制定时间计划表，(5) 收集并展示调查数据，(6) 计算余款的分配分数。
Ticking off each mini-task helps you stay organised and makes sure no maths strand is left out. The order is not fixed — sometimes you may need to budget before measuring, and sometimes survey data affects scheduling.
逐一勾选小任务有助于保持条理，并确保没有遗漏任何数学分支。顺序不固定——有时你可能需要先做预算再测量，而有时调查数据可能会影响时间安排。
3. Handling Money and Decimals | 处理货币与小数
All amounts should be written in pounds to two decimal places, even if the pence ends in zero. Start by listing costs. Example: decorations £23.50, prizes £41.75, drinks £18.00, printing £7.30. Add them using column addition with the decimal points lined up.
所有金额必须以英镑为单位，保留两位小数，即使末尾为零。先列出各项开支。例如：装饰 23.50 英镑、奖品 41.75 英镑、饮料 18.00 英镑、打印 7.30 英镑。用竖式加法将它们相加，确保小数点对齐。
Total = 23.50 + 41.75 + 18.00 + 7.30 = 90.55
Now subtract this from £150: 150.00 – 90.55 = 59.45 remaining. This is your leftover amount that will later be shared. Always check your subtraction by adding the result back to spending — you should get £150.00.
再从 150 英镑中减去总支出：150.00 – 90.55 = 59.45 为剩余金额。这笔钱稍后会用于分配。每次做完减法都要用加法验算：将余款与支出相加，应得到 150.00 英镑。
4. Measuring Lengths and Perimeters | 测量长度与周长
The playground is a rectangle 30 m long and 20 m wide. The perimeter is the distance all the way round. Use the formula:
操场是一个长 30 m、宽 20 m 的长方形。周长是一圈的总长度。使用公式：
Perimeter = 2 × (length + width) = 2 × (30 m + 20 m) = 100 m
You need to mark out a safety border 1.5 m inside the playground edge. The inner rectangle will be 27 m by 17 m. Its perimeter is 2 × (27 + 17) = 88 m. This inner boundary is where the stalls will be placed.
你需要在操场边缘内侧 1.5 m 处标出安全边界。内部矩形将是 27 m × 17 m。其周长为 2 × (27 + 17) = 88 m。这个内部边界就是摆放摊位的地方。
Always write the correct unit: m for metres, cm for centimetres. When converting, remember 1 m = 100 cm, so 1.5 m = 150 cm.
一定要写对单位：m 表示米，cm 表示厘米。换算时要记住 1 m = 100 cm，因此 1.5 m = 150 cm。
5. Calculating Areas for Stalls | 计算摊位面积
Each stall is a square with side length 2 m. The area of one square stall is:
每个摊位是边长为 2 m 的正方形。一个正方形摊位的面积为：
Area = side × side = 2 m × 2 m = 4 m²
You plan to have 6 stalls. The total area taken by stalls is 6 × 4 m² = 24 m². The total area of the inner rectangle is 27 m × 17 m = 459 m². The fraction of the inner space used by stalls is 24/459. Simplify this by dividing numerator and denominator by 3: 8/153.
你计划安排 6 个摊位。摊位总占地面积为 6 × 4 m² = 24 m²。内部矩形的总面积为 27 m × 17 m = 459 m²。摊位占内部空间的比例为 24/459。分子分母同时除以 3 化简：8/153。
Sometimes you are asked for the area of remaining space: 459 m² – 24 m² = 435 m², which is for walking and queuing.
有时题目会要求计算剩余空间面积：459 m² – 24 m² = 435 m²，这部分用于行走和排队。
6. Scheduling Activities Using Time | 用时间规划活动
The Fun Day runs from 09:30 to 12:15. Convert end time to minutes past 09:00 to find total duration. 12:15 is 3 hours 15 minutes after 09:00, so total time is 195 minutes. Split this into three activity slots with 5‑minute breaks between them.
趣味日从 09:30 持续到 12:15。将结束时间转换为 09:00 后经过的分钟数来计算总时长。12:15 是 09:00 后 3 小时 15 分钟，因此总时长为 195 分钟。将其分成三个活动时段，时段之间各有 5 分钟休息。
Let each activity have the same length. Subtract breaks: 2 breaks × 5 min = 10 min. Time for activities = 195 – 10 = 185 min. Divide by 3: each activity lasts 61 minutes with 2 minutes leftover — add those to the final activity or breaks. A tidy schedule would be: Activity 1: 09:30–10:31, Break 10:31–10:36, Activity 2: 10:36–11:37, Break 11:37–11:42, Activity 3: 11:42–12:15 (allowing the extra minute).
假设每个活动时长相同。先减去休息时间：2 次 × 5 分钟 = 10 分钟。活动总时长 = 195 – 10 = 185 分钟。除以 3：每个活动 61 分钟，还剩余 2 分钟——加到最后一个活动或休息中。整洁的时间表可以是：活动一 09:30–10:31，休息 10:31–10:36，活动二 10:36–11:37，休息 11:37–11:42，活动三 11:42–12:15（包含多出的 1 分钟）。
7. Planning a Survey and Collecting Data | 设计调查并收集数据
You need to find out which team game is most popular: Dodgeball, Rounders, or Relay Races. Survey all 84 Year 7 pupils using a tally chart. Each pupil chooses one game.
你需要找出最受欢迎的团队游戏：躲避球、圆场棒球还是接力跑。使用计数表调查全部 84 名七年级学生。每名学生选择一个游戏。
| Game | 游戏 | Tally | 计数 | Frequency | 频数 |
|---|---|---|
| Dodgeball | 卌 卌 卌 卌 III | 23 |
| Rounders | 卌 卌 卌 卌 卌 I | 26 |
| Relay Races | 卌 卌 卌 卌 卌 卌 卌 | 35 |
| Total | 84 |
Check the total matches the number of pupils. From the table, Relay Races has the highest frequency, so that game is chosen for the Fun Day schedule.
检查合计数是否与学生总人数相符。从表格看，接力跑频数最高，因此趣味日当天选择该游戏。
8. Displaying Results in Graphs | 用图表展示结果
Choose a bar chart to display the survey data clearly. Label the horizontal axis ‘Game’, and the vertical axis ‘Number of pupils’. Draw three bars reaching up to 23, 26, and 35. Use a scale where 1 cm on the vertical axis represents 2 pupils, so the tallest bar is 17.5 cm high.
选用条形图清晰地展示调查数据。横轴标记为“游戏”，纵轴标记为“学生人数”。画出三个直条，高度分别达到 23、26 和 35。纵轴刻度定为 1 cm 代表 2 人，那么最高的直条高度为 17.5 cm。
Always give the chart a title: ‘Favourite Team Games in Year 7’. Check that the bars are evenly spaced and the axes are labelled with units.
务必为图表加上标题：“七年级最受欢迎团队游戏”。检查直条间距是否均匀，坐标轴是否标注了单位。
9. Sharing the Leftover Money Using Fractions | 用分数分配余款
From the budget, £59.45 remains. The brief states that 3/5 of the leftover money goes to charity, and the rest to the school tuck shop. First find 1/5 of £59.45:
预算中还剩余 59.45 英镑。任务书规定，余款的 3/5 捐给慈善机构，其余给学校小吃店。先求出 59.45 英镑的 1/5：
1/5 of 59.45 = 59.45 ÷ 5 = 11.89
Then 3/5 is 3 × 11.89 = 35.67. So charity receives £35.67. The tuck shop receives the rest: 59.45 – 35.67 = 23.78. In fraction form, the tuck shop gets 2/5, and 2 × 11.89 = 23.78 confirms accuracy.
那么 3/5 为 3 × 11.89 = 35.67。因此慈善机构收到 35.67 英镑。小吃店得到剩下的部分：59.45 – 35.67 = 23.78。用分数表示，小吃店获得 2/5，用 2 × 11.89 = 23.78 可以验证准确性。
10. Checking Your Work with Reversals and Estimates | 用逆运算和估算进行检查
Go back over each calculation. Add the shared amounts: 35.67 + 23.78 = 59.45 — correct. Estimate the division: 59.45 ÷ 5 ≈ 60 ÷ 5 = 12, which is close to 11.89. Check the area by multiplying 27 × 17: 27 × 10 = 270, 27 × 7 = 189, sum = 459 m².
回头检查每一步计算。将分配金额相加：35.67 + 23.78 = 59.45——正确。除法估算：59.45 ÷ 5 ≈ 60 ÷ 5 = 12，与 11.89 很接近。检查面积：27 × 17，27 × 10 = 270，27 × 7 = 189，合计 459 m²。
In real case studies, small errors can cascade. A quick check using the inverse operation or a sensible estimate stops you from losing marks.
在实际案例分析中，小错误可能引发连锁反应。用逆运算或合理估算快速检查，能避免丢分。
11. Extension: Adding Ratio Thinking | 拓展：融入比的思想
CCEA papers may ask you to express relationships as ratios. In the survey, the ratio of students who chose Relay Races to those who chose Dodgeball is 35:23. Simplify if possible; since 35 and 23 have no common factor except 1, the ratio stays as 35:23.
CCEA 试卷可能会要求用比来表示关系。调查中，选择接力跑与选择躲避球的人数比为 35:23。如果可能就化简；因为 35 和 23 除 1 外没有公因数，比值保持为 35:23。
For the budget, the ratio of spending to total money is 90.55:150. Multiply by 100 to use whole numbers: 9055:15000, then divide by 5: 1811:3000. This shows advanced thinking that impresses examiners.
对于预算，支出与总金额的比为 90.55:150。乘以 100 化为整数：9055:15000，再除以 5 得 1811:3000。这展示出更高阶的思维，能给考官留下好印象。
12. Summary: Your Case Study Toolkit | 总结：你的案例分析工具箱
Every Year 7 CCEA case study can be tackled by reading carefully, listing the maths topics involved, and solving one step at a time. Keep your working neat, label units, and always show your check steps. Use this same structure whenever you practise — it builds confidence and accuracy.
每一个七年级 CCEA 案例分析都可以通过仔细读题、列出涉及的数学主题、按步骤逐一解决来攻克。保持解题过程整洁，标注单位，并始终展示你的检查步骤。每次练习都使用这套结构——它能建立信心、提升准确度。
Practise with your own scenarios: planning a picnic, designing a small garden, or organising a cake sale. The more you connect maths to everyday situations, the stronger your problem‑solving skills become.
用你自己的情境来练习：策划一次野餐、设计一个小花园，或者组织一次蛋糕义卖。你越多地把数学与日常情境联系起来，你的解决问题的能力就会越强。
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