Criterion D Analysis: School Charity Fun Run Financial Planning

Overview of the Criterion D Charity Fun Run Scenario

The provided exemplar outlines a mathematical problem involving a school planning a charity fun run. The primary objective of this event is to generate financial resources to procure new library books. This scenario serves as a functional application of mathematics to solve real-world organizational and budgeting challenges. Each participating student is required to pay a fixed entry fee of $12\, \text{dollars}$. The problem requires a multi-step analysis to determine if the financial goals of the project can be met given specific variables such as expected registration and potential non-attendance.

Detailed Numerical Data and Financial Objectives

Several key quantitative parameters are established in the scenario. First, the school expects a total registration of $180$ students for the event. However, historical or projected data suggests a attrition variable: approximately $15\%$ of the students who register are expected not to attend the actual event on the day. Finacially, the school has set a strict target based on the cost of the new library stock; they require at least $1800\, \text{dollars}$ to facilitate the purchase. To solve the problem, students are tasked with calculating the expected actual attendance, the resulting total revenue, and evaluating that total against the $1800\, \text{dollars}$ threshold.

Calculation Process for Attendance and Revenue

The solution follows a three-step mathematical process. Step 1 involves identifying the number of students who will likely be absent. This is calculated by taking $15\%$ of the registered student body: $15\% \times 180 = 0.15 \times 180 = 27$. Thus, $27$ students are projected to be absent. Step 2 determines the actual attendance by subtracting the absent students from the registration total: $180 - 27 = 153$. Therefore, $153$ students are expected to participate and pay the fee. Step 3 calculates the total funds raised. With an entry fee of $12\, \text{dollars}$ per person, the calculation is as follows: $153 \times 12 = 18361$. Despite the typo in the calculation string provided in the transcript, the school confirms the expected raise to be $1836\, \text{dollars}$.

Logic and Justification of the Solution

In Step 4, a conclusion must be drawn and justified using the previously calculated figures. The success of the fundraiser depends on meeting or exceeding the minimum requirement of $1800\, \text{dollars}$. Because the calculated revenue of $1836\, \text{dollars}$ is numerically greater than the required $1800\, \text{dollars}$, the school will have sufficient funds. The solution makes sense within the provided context because it accounts for the potential loss of income due to non-attendance and demonstrates that the surplus created by the majority of the students still covers the costs for the library books. This logic satisfies the requirement to justify why the answer is reasonable in a real-world setting.

Evaluation of the Exemplar and Pedagogical Standards

This specific exemplar is categorized as a Level 5–6 response for Criterion D, illustrating the expected format, structure, and style for student submissions. It is important to note that while this specific question may not appear on the formative assessment, it represents the standard for how mathematics should be applied in real-life contexts. The exemplar highlights the necessity for students to justify their reasoning explicitly through step-by-step calculations and to provide narrative explanations regarding the context-sensibility of their answers. High-level detail in both mathematical working and written explanation is essential for meeting these academic standards.