📚 School Disco Planning: A Year 8 OCR Maths Case Study | 学校迪斯科策划：八年级OCR数学案例研究
Welcome to a real-world case study where you step into the shoes of a student council member tasked with organising a charity school disco. Throughout this project, you will apply a wide range of Year 8 maths skills — from rounding and percentages to algebra and data handling. Every decision depends on careful calculation, and you will see exactly how the maths you learn in class makes an event like this possible. Let’s begin the planning journey and put your knowledge into action.
欢迎来到一个真实世界的案例研究，你将扮演学生会成员，负责组织一场慈善学校迪斯科舞会。在这个项目过程中，你将运用各种八年级数学技能——从四舍五入和百分比到代数和数据处理。每一个决策都依赖于精确的计算，你会亲眼看到课堂上学到的数学如何让这样的活动成为可能。让我们开始策划之旅，把你的知识付诸实践。
1. Introducing the Case: The School Disco Challenge | 案例导入：学校迪斯科挑战
The student council has set an ambitious target: raise £500 for a local charity by running an end-of-term disco. You have a budget for the venue, a DJ, decorations and refreshments. The goal is not just to cover costs but to generate a clear profit. Your first job is to collect all the real-world numbers and use maths to plan a successful evening. This case study will guide you through every calculation, showing how each topic in your syllabus plays a part.
学生会设定了一个雄心勃勃的目标：通过举办一场期末迪斯科舞会为本地慈善机构筹集 500 英镑。你们有用于场地、DJ、装饰和点心的预算。目标不仅仅是收回成本，还要产生清晰的利润。你的第一项工作是收集所有现实世界的数字，运用数学来规划一个成功的夜晚。这个案例研究将引导你完成每一个计算，展示教学大纲中的每一个知识点如何发挥作用。
2. Estimating the Venue Cost: Rounding and Multiplication | 估算场地费用：四舍五入与乘法
The school hall costs £ nning a budget, it is often convenient to round this figure to the nearest pound. Rounding £127.50 gives £128. If you also need to add a security deposit of £9.75 for the keys, you can round that deposit to £10. An estimated total venue cost is therefore £128 + £10 = £ ep the exact decimals, but rounding helps you check whether your final figures make sense.
学校礼堂租用一个晚上需要 127.50 英镑。在制定预算时，通常将这个数字四舍五入到最接近的英镑会很方便。将 127.50 英镑四舍五入得到 128 英镑。如果还需要为钥匙添加 9.75 英镑的安全押金，你可以将这笔押金四舍五入为 10 英镑。因此，估计的总场地费用是 128 英镑 + 10 英镑 = 138 英镑。在更详细的工作中，你可能会保留精确的小数，但四舍五入有助于你检查最终的数字是否合理。
3. Setting the Ticket Price: Percentages and Profit | 设定门票价格：百分比和利润
t year’s data, you expect around 130 students to attend. You have estimated total costs of £ including the hall, DJ and snacks. To simply break even, the ticket price must be at least £210 ÷ 130 ≈ £1.62. However, you want to make a profit that will contribute to the £500 charity goal. If you increase this base price by 60%, the new price becomes £1.62 × 1.6 = £2.59. For practicality, you round this up to £2.75. This decision uses a percentage increase — a key skill in Year 8.
根据去年的数据，你预计大约有 130 名学生参加。你已估算出总成本为 210 英镑，包括礼堂、DJ 和零食费用。单是为了盈亏平衡，门票价格必须至少为 210 英镑 ÷ 130 ≈ 1.62 英镑。然而，你希望获得利润来为 500 英镑的慈善目标做出贡献。如果你把这个基础价格提高 60%，新的价格将变为 1.62 英镑 × 1.6 = 2.59 英镑。为了实际操作的方便，你将其上调至 2.75 英镑。这个决定运用了百分比增加——这是八年级的一项关键技能。
4. Designing the Dance Floor: Area and Perimeter | 设计舞池：面积与周长
ooring, you need to know the area. The area of a rectangle is given by length × width, so:
Area = 8.5 × 6.2 = 52.7 m²
You also want to put a glow-in-the-dark tape around the edge for safety. The perimeter is the total distance around the shape, calculated as:
Perimeter = 2 × (8.5 + 6.2) = 2 × 14.7 = 29.4 m
This shows how decimal multiplication ties directly to practical measurements in event planning.
舞池是矩形的，长 8.5 米，宽 6.2 米。为了订购足够的防滑地板，你需要知道面积。矩形面积由长 × 宽给出，所以：
面积 = 8.5 × 6.2 = 52.7 平方米
你还需要在边缘贴一圈发光胶带以确保安全。周长是形状周围的总长度，计算为：
周长 = 2 × (8.5 + 6.2) = 2 × 14.7 = 29.4 米
这表明小数乘法如何在活动策划中直接与实际测量相联系。
5. Providing Snacks: Ratio and Proportion | 提供小吃：比例与分配
rts of drink, 3 parts are juice and 2 are water. To find the exact quantities, divide the total into 3 + 2 = 5 shares. One share is 30 ÷ 5 = 6 litres. Therefore, you need juice: 3 × 6 = 18 litres and water: 2 × 6 = 12 litres. Ratios are essential for scaling recipes and mixing ingredients accurately.
你计划总共提供 30 升饮料。一项调查显示，学生们偏好果汁和水的比例为 3 : 2。这个比例意味着每 5 份饮料中，有 3 份是果汁，2 份是水。为了找出准确的量，将总数分成 3 + 2 = 5 份。一份是 30 ÷ 5 = 6 升。因此，你需要 果汁：3 × 6 = 18 升 和 水：2 × 6 = 12 升。比例对于调整食谱份量和精确混合配料至关重要。
6. The DJ’s Playlist: Fractions of Songs | DJ 的播放列表：歌曲的分数
The DJ plans to play 45 songs during the evening. The council decides that 1/3 of the songs should be pop, 1/5 . Rock songs: 45 × 1/5 = 9. The remaining songs are 45 − 15 − 9 = 21 dance tracks. This can also be expressed as a fraction: 21/45 = 7/15 when simplified. Working with fractions helps you keep the music balanced and fair.
DJ 计划在当晚播放 45 首歌曲。委员会决定其中 1/3 的歌曲应为流行乐，1/5 应为摇滚乐，其余为舞曲。要找出每个类别的数量，将总数乘以分数。流行歌曲：45 × 1/3 = 15 首。摇滚歌曲：45 × 1/5 = 9 首。剩下的歌曲是 45 − 15 − 9 = 21 首舞曲。这也可以表示为一个分数：21/45，经简化后为 7/15。运用分数有助于你保持音乐的均衡和公平。
7. Past Ticket Sales Data: Calculating Averages | 过去的票务销售数据：计算平均数
und by adding all the values and dividing by how many there are. So the sum is 120 + 135 + 110 + 145 = 510. There are 4 events, so the mean attendance is 510 ÷ 4 = 127.5. This average gives you a reasonable starting point for predicting how many people will come this time.
为了估算你的迪斯科舞会出席人数，你查看了之前四次学校活动的参加学生人数：120、135、110 和 145。平均数是通过将所有数值相加再除以数值的数量求得的。因此总和为 120 + 135 + 110 + 145 = 510。共有 4 次活动，所以平均出席人数为 510 ÷ 4 = 127.5。这个平均值为你预测这次将会有多少人参加提供了一个合理的起点。
8. Predicting Attendance: Using the Mean and Range | 预测出席人数：使用平均数和范围
The mean you calculated is 127.5, but it is also useful to know the range — means the past attendances do not vary wildly, so the mean is a fairly reliable predictor. You decide to round the mean up to 130 for planning purposes, knowing that real numbers might be slightly higher or lower. In maths, this combination of average and spread helps you make informed decisions.
你计算出的平均数是 127.5，但了解范围也很有用——即最高值与最低值之间的差值。这里，范围是 145 − 110 = 35。一个相对较小的范围意味着过去的出席人数波动不大，因此平均数是一个相当可靠的预测指标。你决定为了规划目的将平均数上调至 130，同时知道实际数字可能会稍高或稍低。在数学中，将平均数和离散程度结合起来有助于你做出明智的决策。
9. Graphing Ticket Sales Over Time: Line Graphs | 绘制随时间变化的门票销售图：折线图
To monitor progress, you record the number of tickets sold each day during the week leading up to the disco: Monday 15, Tuesday 25, Wednesday 40, Thursday 60, Friday 80. When you plot these on a line graph, with days on the horizontal axis and ticket sales on the vertical axis, you see an upward trend. A line graph is perfect for showing how data changes over time; it immediately highlights the sales spike just before the event. Drawing and interpreting such graphs is an important part of the Year 8 curriculum.
为了监控进度，你记录了迪斯科舞会当周每天售出的门票数量：周一 15、周二 25、周三 40、周四 60、周五 80。当你在折线图上描出这些点时，横轴表示日期，纵轴表示门票销售，你会看到一条上升的趋势线。折线图非常适合显示数据随时间如何变化；它能立即突出活动开始前销售猛增的情况。绘制和解读这类图表是八年级课程的重要内容。
10. Breaking Even: Solving Simple Equations | 损益平衡：解简单方程
Now comes the algebra. Let p be the ticket price and n be the number of attendees. Your total income is n × p. The total costs are £210. To raise exactly £500 for charity, you need the profit to be £500, giving the equation:
130p − 210 = 500
en divide by 130: p = 710 ÷ 130 ≈ 5.4615. Rounding up to a reasonable price means charging £ olving equations like this one turns a real-world problem into a simple algebraic process.
现在到了代数部分。设 p 为门票价格，n 为参加人数。你的总收入是 n × p。总成本为 210 英镑。要为慈善机构恰好筹集 500 英镑，你需要利润为 500 英镑，于是得到方程：
130p − 210 = 500
两边同时加 210：130p = 710。然后除以 130：p = 710 ÷ 130 ≈ 5.4615。将其四舍五入为一个合理的价格，即每张门票收取 5.50 英镑。像这样解方程将一个实际问题转化成了简单的代数过程。
11. Discount for Early Birds: Percentage Decrease | 早鸟票折扣：百分比减少
To boost early sales, you offer a 20% discount on tickets bought before Monday. A 20% decrease means customers pay 100% − 20% = 80% of the original price of £5.50. So the early-bird price is £5.50 × 0.8 = £4.40. If you sell 40 early-bird tickets at this price, the revenue from them is 40 × £4.40 = £176. The remaining 90 tickets are sold at the full price, bringing in 90 × £5.50 = £495. This mix of prices uses percentage decrease to solve a practical finance challenge.
为了促进早期销售，你对周一之前购买的门票提供 20% 的折扣。20% 的减少意味着顾客支付原价 5.50 英镑的 100% − 20% = 80%。因此早鸟票价格为 £5.50 × 0.8 = £4.40。如果你以这个价格售出 40 张早鸟票，那么来自它们的收入为 40 × £4.40 = £176。剩下的 90 张门票以全价售出，带来 90 × £5.50 = £495。这种价格组合运用百分比减少解决了实际的财务挑战。
12. Checking Your Work: Rounding and Significant Figures | 检查工作：四舍五入与有效数字
As a final step, review all the numbers you have used. The dance floor area of 52.7 m² is given to one decimal place, which is appropriate for a measurement with a tape measure. The mean attendance of 127.5 rounds to 130 when considering people (since you cannot have half a person). The ticket price of £5.4615... was rounded to £5.50, giving an answer to two decimal places for money. Paying attention to rounding and significant figures ensures that your results are both accurate and realistic. In real life, answers that look too precise often hide uncertainty; as a good mathematician, you always present numbers with a sensible degree of accuracy.
作为最后一步，回顾你使用过的所有数字。舞池面积 52.7 平方米给出了一位小数，这对于用卷尺测量的数据来说是恰当的。平均出席人数 127.5 在考虑人的数量时四舍五入为 130（因为你不能有半个人）。门票价格 5.4615... 英镑被四舍五入为 5.50 英镑，这给出了到两位小数的货币答案。留意四舍五入和有效数字能确保你的结果既准确又符合实际。在现实生活中，看似过于精确的答案往往隐藏着不确定性；作为一名优秀的数学家，你总是用合理的精度来呈现数字。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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