📚 Year 7 CIE Maths Case Study in Action: Fundraising Fair | Year 7 CIE 数学案例分析实战：筹款嘉年华
In this case study, we will step into the shoes of Year 7 students planning a fundraising fair for their school. Throughout the process, we will apply a wide range of mathematical skills, from basic arithmetic to data handling, all in a practical, real-world context. Let’s see how mathematics can help turn a fun idea into a successful event.
在这个案例分析中，我们将扮演一群正在为学校策划筹款嘉年华的七年级学生。在整个过程中，我们会运用从基础算术到数据处理的各种数学技能，全部在真实的实际场景中展开。让我们一起看看数学如何帮助我们将一个有趣的点子变成一场成功的活动。
1. Understanding the Scenario | 理解情景
Our school wants to raise money for new library books. A team of Year 7 students has decided to organise a fundraising fair with games, food stalls, and a raffle. We need to plan everything carefully, keep track of income and expenses, and make sure we reach our target of £500 profit. Mathematics will be our best tool.
学校想为图书馆新书筹集资金。一群七年级学生决定组织一场筹款嘉年华，设有游戏摊位、食品摊位和抽奖活动。我们需要仔细规划每件事，记录收入和支出，并确保达到 500 英镑的盈利目标。数学将是我们最好的工具。
The fair will run on a Saturday for 4 hours. We have a starting budget of £150 provided by the school. We can charge entry, sell tickets for games, and sell drinks and snacks. All money raised after covering costs will be donated. Let’s begin planning!
嘉年华将在某个周六举办，持续 4 小时。学校提供 150 英镑的启动预算。我们可以收取入场费、出售游戏券，并销售饮料和零食。扣除成本后的所有收入都将捐出。让我们开始规划吧！
2. Setting Up a Budget | 制定预算
Our first task is to work out how to spend the £150 budget. We estimate needing tables, decorations, ingredients for bake sale, prizes, and printing for tickets. A rough plan: tables hire £25, decorations £15, baking ingredients £30, small prizes £40, printing £10, and we keep £30 as emergency reserve. Does this add up to exactly £150?
我们的第一项任务是弄清楚如何使用这 150 英镑预算。我们估计需要桌椅租赁、装饰品、烘焙原料、奖品和票券印刷。粗略计划：桌子租赁 25 英镑，装饰 15 英镑，烘焙原料 30 英镑，小奖品 40 英镑，印刷 10 英镑，并预留 30 英镑作为应急储备。这些加起来正好是 150 英镑吗？
Calculation: 25 + 15 = 40; 40 + 30 = 70; 70 + 40 = 110; 110 + 10 = 120; 120 + 30 = 150. Yes, it sums exactly to £150. We must track every pound spent so we do not overspend. Using addition and subtraction, we will update our balance sheet regularly.
计算过程：25 + 15 = 40；40 + 30 = 70；70 + 40 = 110；110 + 10 = 120；120 + 30 = 150。是的，总和正好 150 英镑。我们必须追踪每一英镑的支出，以免超支。通过加法和减法，我们会定期更新资金平衡表。
3. Ordering Supplies: Multiplying and Dividing | 订购物资：乘除运算
For the bake sale, we plan to make 120 cupcakes. A recipe for 12 cupcakes requires 200 g of flour and 3 eggs. How much flour and how many eggs do we need in total? We must multiply: 120 ÷ 12 = 10, so we need 10 times the recipe. Flour: 200 g × 10 = 2000 g, which is 2 kg. Eggs: 3 × 10 = 30 eggs.
烘培义卖计划制作 120 个纸杯蛋糕。一份 12 个蛋糕的配方需要 200 克面粉和 3 个鸡蛋。总共需要多少面粉和鸡蛋？我们必须进行乘法运算：120 ÷ 12 = 10，所以需要 10 倍的配方量。面粉：200 g × 10 = 2000 g，即 2 kg。鸡蛋：3 × 10 = 30 个。
We buy flour in 1.5 kg bags. How many bags are needed for 2 kg? 2 ÷ 1.5 = 1.333…, so we must buy 2 bags to have enough. This decision uses division and rounding up. Similarly, eggs are sold in boxes of 6. 30 ÷ 6 = 5 boxes exactly.
我们购买 1.5 公斤装的面粉。2 公斤需要几袋？2 ÷ 1.5 = 1.333…，因此我们必须买 2 袋才够。这个决策用到了除法和向上取整。同样，鸡蛋每盒 6 个。30 ÷ 6 = 5 盒，恰好。
4. Calculating Discounts with Percentages | 计算百分比折扣
A local shop offers us a 15% discount on all decorations and paper goods because we are a school. The original price of decorations is £15, and printing is £10. Together the original cost is £25. How much do we save? 15% of 25 = 0.15 × 25 = £3.75. The discounted total is £25 − £3.75 = £21.25.
一家本地商店因我们是学校，给予所有装饰品和纸制品 15% 的折扣。装饰原价 15 英镑，印刷 10 英镑，原价合计 25 英镑。我们能节省多少？25 的 15% = 0.15 × 25 = 3.75 英镑。折扣后总价为 25 − 3.75 = 21.25 英镑。
This means we can reallocate the saved £3.75 to other areas or increase our emergency fund. Understanding percentages helps us make smarter purchasing decisions and stretch the budget further.
这意味着我们可以将节省的 3.75 英镑重新分配到其他项目，或增加应急基金。理解百分比能帮助我们在采购时做出更明智的决策，进一步拉长预算。
5. Pricing Items: Using Fractions and Decimals | 商品定价：分数与小数
We decide to sell cupcakes at £0.75 each, or 3 for £2.00. Which offer gives a better price per cupcake? Single price = £0.75. Multipack: £2.00 ÷ 3 ≈ £0.666… per cupcake. The difference is £0.75 − £0.6667 = £0.0833, about 8 pence cheaper per cupcake with the multipack. Customers save by buying more.
我们决定单个纸杯蛋糕售价 0.75 英镑，或者 3 个 2.00 英镑。哪种方案每个蛋糕更便宜？单买价格 = 0.75 英镑。多买套餐：2.00 ÷ 3 ≈ 0.666… 英镑每个。差价为 0.75 − 0.6667 = 0.0833，即套餐每个便宜约 8 便士。顾客多买更省钱。
We also sell juice in cups of 0.3 litres. If we make 15 litres of juice, how many cups can we fill? 15 ÷ 0.3 = 50 cups. Decimals and fractions are essential when measuring and pricing. We set the juice price at £0.50 per cup.
我们还出售每杯 0.3 升的果汁。如果制作 15 升果汁，能装多少杯？15 ÷ 0.3 = 50 杯。小数和分数在计量和定价时至关重要。我们把每杯果汁定价为 0.50 英镑。
6. Estimating Crowd Numbers | 估计参与人数
To plan how many cupcakes and prizes we need, we must estimate attendance. The school has 800 students, but not all will come. We guess 30% of students will attend, plus family members. 30% of 800 = 0.30 × 800 = 240 students. If each student brings 1.5 family members on average, total people ≈ 240 × 2.5 = 600 people.
为了计划需要多少蛋糕和奖品，我们必须估计参加人数。学校有 800 名学生，但不会全部到场。我们估计 30% 的学生会来，再加上家庭成员。800 的 30% = 0.30 × 800 = 240 名学生。如果平均每位学生带 1.5 位家人，总人数约为 240 × 2.5 = 600 人。
However, this is only an estimate. We round it to 600 for planning, but we also prepare for a range between 500 and 700. Estimation and rounding help us handle uncertainty.
然而，这只是一个估计。我们把它取整为 600 用于规划，但也为 500 至 700 人的范围做准备。估计和取整帮助我们应对不确定性。
7. Creating a Timetable: Time Calculations | 制定时间表：时间计算
The fair runs from 10:00 to 14:00. We need to set up before opening. Setup takes 1 hour 20 minutes. What time must we start setting up? 10:00 minus 1 hour 20 minutes = 08:40. We must arrive by 08:40.
嘉年华从上午 10:00 到下午 14:00。我们需要在开门前布置。布置需 1 小时 20 分钟。我们必须在什么时候开始布置？10:00 减去 1 小时 20 分钟 = 08:40。我们必须在 08:40 前到达。
Each game stall will operate in 45-minute slots, with 15 minutes changeover. How many complete slots fit into 4 hours? 4 hours = 240 minutes. Each slot + changeover = 45 + 15 = 60 minutes. So we can have 240 ÷ 60 = 4 slots. A timetable ensures smooth operation.
每个游戏摊位按 45 分钟一个时段运行，中间有 15 分钟轮换时间。4 小时内能安排多少个完整时段？4 小时 = 240 分钟。每个时段加轮换 = 45 + 15 = 60 分钟。因此我们可以安排 240 ÷ 60 = 4 个时段。时间表能确保活动顺利进行。
8. Measuring Spaces: Perimeter and Area | 测量空间：周长与面积
The fair will be held on the school field, a rectangle 50 m long and 30 m wide. What is the perimeter to fence the area? Perimeter = 2 × (50 + 30) = 2 × 80 = 160 m. The area for activities is 50 × 30 = 1500 m². We need to fit stalls and a stage.
嘉年华将在学校操场举行，操场为长 50 米、宽 30 米的长方形。围栏需要多长？周长 = 2 × (50 + 30) = 2 × 80 = 160 米。活动区域面积为 50 × 30 = 1500 平方米。我们需要安排摊位和一个舞台。
If each game stall requires a rectangular space 3 m by 2 m, area per stall = 6 m². How many stalls can fit if we use half the field? Half area = 750 m². Maximum stalls = 750 ÷ 6 = 125 stalls, but we only plan 8 stalls, leaving plenty of room for walking.
假如每个游戏摊位需要一块 3 米 × 2 米的长方形区域，每个摊位面积为 6 平方米。如果我们使用半个操场，能容纳多少个摊位？一半面积 = 750 平方米。最多摊位 = 750 ÷ 6 = 125 个，但我们只规划 8 个摊位，留出大量行走空间。
9. Collecting and Organising Data | 收集与整理数据
During the fair, we record the number of visitors every 30 minutes: 10:00-10:30: 150 people; 10:30-11:00: 210; 11:00-11:30: 190; 11:30-12:00: 230; 12:00-12:30: 250; 12:30-13:00: 220; 13:00-13:30: 180; 13:30-14:00: 140. This data helps us see peak times.
在嘉年华期间，我们每 30 分钟记录一次访客人数：10:00-10:30：150 人；10:30-11:00：210；11:00-11:30：190；11:30-12:00：230；12:00-12:30：250；12:30-13:00：220；13:00-13:30：180；13:30-14:00：140。这些数据帮助我们了解高峰时段。
We can organise the data into a frequency table. It’s useful to calculate the total number of visits, though some people may be counted multiple times. Total raw count = 150+210+190+230+250+220+180+140 = 1570 visits.
我们可以将数据整理成频率表。尽管有些人可能被重复计数，但计算总访问次数仍然有用。原始计数总和 = 150+210+190+230+250+220+180+140 = 1570 次。
10. Presenting Data: Bar Charts and Pictograms | 数据展示：柱状图与象形图
To share our findings with the school, we draw a bar chart showing visitors per half-hour slot. The horizontal axis shows time intervals, and the vertical axis shows number of people, scaled 0 to 300. The tallest bar is at 12:00-12:30 with height 250. This visual clearly indicates the busiest period.
为了向学校展示我们的发现，我们绘制了一张柱状图，显示每半小时的访客数量。横轴表示时间段，纵轴表示人数，刻度从 0 到 300。最高的柱子出现在 12:00-12:30，高度为 250。这张图表清晰地显示了最繁忙的时段。
We could also use a pictogram where each symbol represents 20 visitors. For the 10:00 slot, 150 ÷ 20 = 7.5 symbols, so we draw 7 full and one half symbol. Pictograms are engaging and easy to interpret.
我们还可以使用象形图，每个符号代表 20 名访客。对于 10:00 时段，150 ÷ 20 = 7.5 个符号，因此我们画 7 个完整符号和半个符号。象形图生动有趣，易于解读。
11. Analysing Profit and Loss | 分析利润与亏损
We need to find out if we reached the £500 profit goal. First, total income: entry fees £1 per person, with 600 people, gives £600. Cupcake sales: 120 sold, 40 as singles at £0.75 each = £30, and 80 in multipacks (sold as 26 sets of 3 plus 2 singles) actually let’s simplify: 80 sold in multipacks means 80 cupcakes at £0.666… each, total £53.33. But we can calculate with actual sales: Suppose total cupcake revenue = £85. Juice: 50 cups at £0.50 = £25. Raffle tickets: 200 tickets at £1 each = £200. Game tickets: 300 tickets at £0.50 each = £150. Total income = 600 + 85 + 25 + 200 + 150 = £1060.
我们需要看看是否达到了 500 英镑的利润目标。首先，总收入：入场费每人 1 英镑，600 人，收入 600 英镑。纸杯蛋糕销售：120 个全部售出，其中 40 个按单价 0.75 英镑卖出 = 30 英镑，80 个以套餐形式售出（假设为 26 套三只装再加两个单只）简化计算：80 个按每个 0.666… 英镑计，共 53.33 英镑；实际我们可按总蛋糕收入 85 英镑记录。果汁：50 杯 × 0.50 英镑 = 25 英镑。抽奖券：200 张 × 1 英镑 = 200 英镑。游戏券：300 张 × 0.50 英镑 = 150 英镑。总收入 = 600 + 85 + 25 + 200 + 150 = 1060 英镑。
Next, total costs: budget spent £150 (but we saved £3.75, so actual spend £146.25). Additionally, we used some of the emergency fund, say £20 extra. Total costs = £166.25. Profit = 1060 – 166.25 = £893.75. We far exceeded our target! We can report that we made a profit of £893.75, which is (893.75 ÷ 500) × 100 = 178.75% of the goal.
然后，总成本：预算支出 150 英镑（但我们节省了 3.75 英镑，故实际花费 146.25 英镑）。此外，我们动用了部分应急资金，假设 20 英镑。总成本 = 166.25 英镑。利润 = 1060 − 166.25 = 893.75 英镑。我们远超目标！可以报告实现利润 893.75 英镑，是目标的 (893.75 ÷ 500) × 100 = 178.75%。
12. Review and Reflection | 回顾与反思
This case study showed how we used addition, subtraction, multiplication, division, fractions, decimals, percentages, measurement, time, and data handling to organise a successful fair. Every mathematical skill played a part in real decision-making. Reflecting on our estimates, we see that being flexible with numbers helped us adapt to actual attendance and sales.
本案例展示了我们如何运用加法、减法、乘法、除法、分数、小数、百分比、测量、时间以及数据处理，成功组织了一场嘉年华。每一项数学技能都在真实的决策中发挥了作用。通过回顾我们的估计，我们发现灵活处理数字有助于应对实际到场人数和销售情况。
We can now present our financial results to the headteacher, using clear tables and charts. Mathematics doesn’t just live in textbooks; it’s a powerful tool for solving problems and making events like this possible. Next time we can try a more complex case study, perhaps including ratios for drink mixing or probability for raffle draws.
现在我们可以用清晰的表格和图表向校长展示财务成果。数学不仅存在于课本中；它是解决问题和开展此类活动的强有力工具。下次我们可以尝试一个更复杂的案例分析，或许会涉及调配饮品的比例，或抽奖活动中的概率。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导