📚 Year 7 WJEC Maths Case Study: Hands‑On Practical Problem Solving | 七年级 WJEC 数学案例分析实战演练
Welcome to your Year 7 WJEC Maths case study challenge! In this article, we will work through a real‑life situation – planning a school summer fête – and use the mathematics you have learned this year to solve each problem. You will practise working with money, measurements, ratios, charts, probability and more. This hands‑on approach shows how classroom maths appears in everyday decisions, helping you build confidence and skill for your assessments.
欢迎来到七年级 WJEC 数学案例分析挑战！本文中，我们将通过一个真实的情境——策划学校夏日嘉年华——并用你今年学过的数学知识解决每一个问题。你将练习运用货币、测量、比和比例、图表、概率等内容。这种动手实践的方式展示了课堂数学如何出现在日常决策中，帮助你建立信心并提升应试技能。
1. Setting the Scene: The School Fête Planning Committee | 场景设定：学校嘉年华筹委会
Imagine your class has been asked to help organise the annual school summer fête. The headteacher has given you a budget of £300 to cover stalls, prizes and decorations. You need to decide which activities to run, how much food to order, and how to set up the field. Every choice involves maths – from adding costs to measuring spaces – so let’s begin by listing the key numbers we already know.
想象一下，你的班级被邀请协助组织一年一度的学校夏日嘉年华。校长给了你们 300 英镑的预算，用于摊位、奖品和装饰。你需要决定开展哪些活动、订购多少食物以及如何布置场地。每个选择都涉及数学——从相加成本到测量空间——所以让我们从列出已知的关键数字开始。
Key data: Budget = £ eld size = 50 m by 30 m; expected visitors ≈ 200 people; event duration = 4 hours (1:00 pm – 5:00 pm).
关键数据： 预算 = 300 英镑；场地大小 = 50 米 × 30 米；预计游客约 200 人；活动时长 = 4 小时（下午 1:00 – 5:00）。
2. Budget Breakdown: Adding and Subtracting Money | 预算分解：货币的加与减
prizes. You research prices and write down the following estimates: a bouncy castle hire = £85, a face‑painting kit = £22, a popcorn machine rental = £45, ingredients for homemade lemonade = £18, and assorted prizes = £60. Calculate the total cost so far.
你的第一个任务是估算三个主要类别的费用：摊位和活动、食品饮料以及奖品。你研究价格后写下以下估算：充气城堡租金 = 85 英镑，面部彩绘工具包 = 22 英镑，爆米花机租金 = 45 英镑，自制柠檬水原料 = 18 英镑，杂项奖品 = 60 英镑。计算到目前为止的总费用。
: 85 + 22 = 107; 107 + 45 = 152; 152 + 18 = 170; 170 + 60 = 230. So the estimated total is £230. Subtracting this from the £300 budget leaves £ corations. Always check your working by adding in a different order to confirm the result.
总费用 = 85 + 22 + 45 + 18 + 60。我们可以逐步相加：85 + 22 = 107；107 + 45 = 152；152 + 18 = 170；170 + 60 = 230。因此估算总计为 230 英镑。用 300 英镑预算减去这个数，剩余 70 英镑。这笔余钱可以用于意外开支或额外装饰。始终通过改变相加顺序来验算，以确认结果。
3. Scaling Recipes: Ratio and Proportion | 调整食谱：比和比例
f lemonade (1 cup = 250 ml). How many jugs do you need, and what quantities of ingredients must you buy?
你决定售卖自制柠檬水。一份制作 1 壶（供 8 人饮用）的食谱使用：4 个柠檬，200 克糖，1.5 升水。你预计供应大约 160 杯柠檬水（1 杯 = 250 毫升）。你需要多少壶？以及必须购买多少食材？
.5 litres. Number of jugs = 40 ÷ 1.5 = 26.666..., so you need 27 jugs (you cannot make two‑ Sugar: 200 g × 27 = 5400 g = 5.4 kg. Water: 1.5 L × 27 = 40.5 L. Proportions are used here – the ratio of lemons to sugar to water remains the same for every jug.
首先，计算总体积：160 杯 × 250 毫升 = 40 000 毫升 = 40 升。一壶提供 1.5 升。所需壶数 = 40 ÷ 1.5 = 26.666…，因此你需要 27 壶（现实中你不可能只做三分之二壶）。现在按比例调整食材：做 1 壶需要 4 个柠檬，所以 27 壶需要：4 × 27 = 108 个柠檬。糖：200 克 × 27 = 5400 克 = 5.4 千克。水：1.5 升 × 27 = 40.5 升。这里使用了比例——每一壶中柠檬、糖和水的比是保持不变的。
4. Area and Perimeter: Laying Out the Field | 面积与周长：布置场地
h space each stall takes. Perimeter of a rectangle = 2 × (length + width). Area = length × width.
场地是长方形，长 50 米，宽 30 米。你需要计算周长以订购安全警戒带，并计算面积来规划每个摊位占用的空间。长方形的周长 = 2 ×（长 + 宽）。面积 = 长 × 宽。
cy castle, that area = 1500 ÷ 10 = 150 m². This is a large square of about 12.25 m × 12.25 m. Having a clear layout drawn to scale helps everyone know where to set up.
周长 = 2 ×（50 + 30）= 2 × 80 = 160 米。因此你至少需要 160 米警戒带。面积 = 50 × 30 = 1500 平方米。如果你将场地的十分之一分配给充气城堡，该面积 = 1500 ÷ 10 = 150 平方米。这大约是一个 12.25 米 × 12.25 米大的正方形。绘制一个按比例的清晰布局图有助于每个人知道在哪里搭建。
5. Collecting Data: Survey on Favourite Activities | 收集数据：关于最喜爱活动的调查
To make sure visitors enjoy the fête, you survey 50 students asking: "Which activity would you most like to try?" Options: Bouncy castle, Face painting, Tombola, Penalty shoot‑out, Cake stall. The results: Bouncy castle – 20, Face painting – 10, Tombola – 8, Penalty shoot‑out – 7, Cake stall – 5. What fraction of the surveyed students chose the bouncy castle? And what percentage chose face painting?
为了确保游客喜欢嘉年华，你调查了 50 名学生，提问：“你最想参与哪个活动？”选项为：充气城堡、面部彩绘、抽奖转盘、点球射门、蛋糕摊位。结果：充气城堡——20，面部彩绘——10，抽奖转盘——8，点球射门——7，蛋糕摊位——5。选择充气城堡的学生占调查人数的几分之几？选择面部彩绘的百分比是多少？
le = 20 out of 50 = 20/50 = 2/5 simplified. Percentage for face painting = (10 ÷ 50) × 100% = 20% elps you decide which activities to prioritise and where to allocate more space or prizes.
充气城堡的分数 = 50 人中的 20 人 = 20/50，化简为 2/5。面部彩绘的百分比 =（10 ÷ 50）× 100% = 20%。调查数据帮助你决定哪些活动优先，以及在哪里分配更多空间或奖品。
6. Presenting Data: Bar Chart and Pie Chart | 数据展示：条形图与饼图
e proportions of the total each activity represents using a pie chart. For a pie chart, each frequency can be turned into a sector angle: (frequency ÷ total) × 360°.
将调查结果用条形图展示，横轴为活动，纵轴为频数。同时，假设你想用饼图展示每个活动占总体的比例。对于饼图，每个频数可以转换成扇区角度：（频数 ÷ 总人数）× 360°。
= 144°. Face painting: (10/50) × 360° = 72°. Tombola: (8/50) × 360° = 57.6°. Penalty shoot‑ 57.6 + 50.4 + 36 = 360°. When drawing, use a protractor to measure each angle accurately.
充气城堡：（20/50）× 360° = 144°。面部彩绘：（10/50）× 360° = 72°。抽奖转盘：（8/50）× 360° = 57.6°。点球射门：（7/50）× 360° = 50.4°。蛋糕摊位：（5/50）× 360° = 36°。检查角度总和：144 + 72 + 57.6 + 50.4 + 36 = 360°。绘图时，使用量角器准确测量每个角度。
7. Time Management: Creating a Schedule | 时间管理：制定时间表
The fête runs from 1:00 pm to 5:00 pm. You want to schedule the penalty shoot‑out competition in 15‑minute slots, with 5 minutes between each game for setup. If you plan 8 games, what time does the competition finish? And can you fit it within the event?
嘉年华从下午 1:00 持续到下午 5:00。你计划将点球射门比赛安排为 15 分钟一场，每场之间留 5 分钟布置。如果安排 8 场比赛，比赛会在几点结束？能在活动时间内完成吗？
, finishing time = 1:00 + 2 h 40 min = 3:40 pm. Since the event ends at 5:00 pm, there is plenty of time. However, note that the last 5‑ game isn’t needed, so you might finish slightly earlier or use that time for prize giving.
每场比赛加上间隔的总时间 = 15 + 5 = 20 分钟。8 场比赛总时长 = 8 × 20 = 160 分钟 = 2 小时 40 分钟。如果第一场比赛下午 1:00 开始，结束时间 = 1:00 + 2 小时 40 分 = 下午 3:40。由于活动在下午 5:00 结束，时间很充裕。不过请注意，第 8 场比赛后的 5 分钟间隔并无必要，所以你可以稍微提前结束，或者利用那段时间颁奖。
8. Money and Change: Running a Tombola | 货币与找零：运营抽奖转盘
At the tombola, tickets cost 50p each or 3 tickets for £1. A customer gives you a £5 note and says "As many tickets as possible, please." How many tickets do they get, and how much change? The best value is the bundle: 3 tickets for £1. £5 can buy five bundles of 3 tickets = 5 × 3 = 15 tickets. But 5 bundles cost 5 × £1 = £5 exactly, so no change. If they bought single tickets at 50p each, £ ed multiplication and division with money, always converting pounds to pence where needed: £ , 50p ticket → 500 ÷ 50 = 10; bundle: 100p ÷ 3 ≈ 33.3p per ticket, so more for your money.
在抽奖转盘摊位，每张票 50 便士，或者 3 张票 1 英镑。一位顾客给你一张 5 英镑纸币，说：“请给我尽可能多的票。”他能得到多少张票，以及找零多少？最划算的是套餐：3 张票 1 英镑。5 英镑可以买 5 份 3 张票的套餐 = 5 × 3 = 15 张票。但 5 份套餐花费 5 × 1 英镑 = 正好 5 英镑，所以没有找零。如果他们以每张 50 便士的价格单买，5 英镑可以买 10 张票，也没有找零。因此明智的选择是套餐，得到 15 张票。我们应用了货币的乘法和除法，始终在必要时将英镑转换为便士：5 英镑 = 500 便士，50 便士一张票 → 500 ÷ 50 = 10；套餐：100 便士 ÷ 3 ≈ 33.3 便士每张，所以你的钱更划算。
9. Symmetry and Pattern: Designing Bunting | 对称与图案：设计彩旗
You want to make triangular bunting flags. Each flag is an isosceles triangle with a base of 20 cm and a height of 30 cm. You plan to draw a line of symmetry down the middle and decorate one half, then reflect the pattern to the other half. This uses reflective symmetry. How many lines of symmetry does an isosceles triangle have? Only one – the vertical line from the apex to the midpoint of the base. If you instead used equilateral triangles (all sides equal), there would be 3 lines of symmetry. Understanding symmetry helps you design attractive, balanced decorations efficiently.
你想制作三角彩旗。每面旗是底边 20 厘米、高 30 厘米的等腰三角形。你计划沿中线画一条对称轴，装饰一半，然后将图案反射到另一半。这利用了反射对称。等腰三角形有多少条对称轴？仅一条——从顶点到底边中点的垂直线。如果你改用等边三角形（各边相等），则会有 3 条对称轴。理解对称性有助于你高效地设计出漂亮、平衡的装饰。
10. Converting Units: Buying Materials | 单位换算：采购材料
0 cm. The shop sells ribbon in metres, and each roll has 25 m. How many rolls must you buy? you cannot buy 0.8 of a roll, you need 2 full rolls. This gives you 50 m of ribbon, leaving 5 m spare. Converting between units – centimetres, metres, grams, kilograms – is crucial for accurate ordering and cost calculation.
你需要为彩旗购买丝带。所需总长度为 4500 厘米。商店按米出售丝带，每卷 25 米。你需要购买多少卷？首先，将 4500 厘米转换为米：因为 100 厘米 = 1 米，所以 4500 厘米 = 4500 ÷ 100 = 45 米。卷数 = 45 ÷ 25 = 1.8。因为你不能购买 0.8 卷，所以你需要 2 整卷。这将给你 50 米丝带，剩余 5 米。在厘米、米、克、千克等不同单位之间进行换算是准确订购和成本计算的关键。
11. Probability in Games: Spinner Design | 游戏中的概率：转盘设计
blue (win a small prize), and 1 sector gold (win a mystery prize). What is the probability of landing on red? f red sectors) ÷ (total sectors) = 3/8. As a decimal, 3 ÷ 8 = 0.375. As a percentage, 37.5%. Probability of not winning a big prize = 1 – 3/8 = 5/8. This helps you balance the game so it’s fun but not too easy.
你决定为游戏制作一个奖品转盘。转盘是一个圆，被分成 8 个相等的扇形。你将 3 个扇形涂成红色（赢得大奖），4 个涂成蓝色（赢得小奖），1 个涂成金色（赢得神秘奖品）。落在红色上的概率是多少？概率 =（红色扇形数量）÷（总扇形数）= 3/8。转换为小数，3 ÷ 8 = 0.375。转换为百分比，37.5%。没有赢得大奖的概率 = 1 – 3/8 = 5/8。这有助于你平衡游戏，使其有趣但不太容易。
12. Final Check: Using Estimation and Inverse Operations | 最终检查：使用估算与逆运算
u decide to quickly check your budget total using rounding and estimation. Original costs: £85, £22, £45, £18, £ g: 85 → 90, 22 → 20, 45 → 50, 18 → 20, 60 → 60. Estimated total ≈ 90 + 20 + 50 + 20 + 60 = £240. The exact total was £ verse operations: total minus some costs should give you the remaining cost. For instance, £230 – £60 – £18 – £45 = £107, and 85 + 22 = £107. This confirms everything adds up correctly.
在向校长提交计划之前，你决定通过四舍五入和估算快速检查预算总额。原始费用：85 英镑、22 英镑、45 英镑、18 英镑、60 英镑。取整：85 → 90，22 → 20，45 → 50，18 → 20，60 → 60。估算总额 ≈ 90 + 20 + 50 + 20 + 60 = 240 英镑。精确总额是 230 英镑，所以估算结果相近，这让你确信计算是合理的。你还可以使用逆运算：总额减去部分费用应得出剩余费用。例如，230 – 60 – 18 – 45 = 107，而 85 + 22 = 107 英镑。这证实所有加总都是正确的。
This case study has taken you through a realistic event‑planning scenario, using the core topics from the Year 7 WJEC Maths curriculum: number operations, ratios, geometry, data handling, units, and probability. Every decision involved a mathematical skill, just as in many jobs and everyday tasks. Practice by creating your own scenarios, such as planning a party or a school trip, and apply the same problem‑solving steps.
本案例分析带你经历了一个真实的活动策划场景，运用了七年级 WJEC 数学课程的核心主题：数的运算、比和比例、几何、数据处理、单位以及概率。每个决定都涉及数学技能，正如许多工作和日常任务一样。你可以通过创造自己的场景来练习，例如策划派对或学校旅行，并应用同样的问题解决步骤。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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