Carry out a project to solve a problem using mathematical skills

1. Identify a Problem

Choose a real problem from your environment that can be solved using mathematics. The problem should be clear and measurable.

2. State the Objective

Write down exactly what you want to achieve. For example: "Determine the most affordable transport option for delivering goods from Dar es Salaam to Mwanza."

3. Gather Data

Collect relevant information. This may include:

• Prices and costs
• Distances and travel times
• Quantities and measurements
• Survey responses

4. Apply Mathematical Skills

Use appropriate mathematical concepts such as:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Percentages and ratios
• Algebraic equations
• Statistics (mean, median, mode)
• Geometry (area, volume)
• Linear programming (for optimization)

5. Analyze and Interpret Results

Perform calculations and explain what the results mean in the context of your problem.

6. Present Your Findings

Write a clear report or present orally, showing your methodology, calculations, and conclusions.

Problem: A vendor at Mwanza Central Market has 24 meters of fencing to create a rectangular display area for vegetables. What dimensions will give the maximum area?

Step 1: Define the variables Let $L$ = length and $W$ = width of the rectangle.

Step 2: Write the constraint The perimeter is 24 meters: $2L + 2W = 24$ Simplifying: $L + W = 12$ $W = 12 - L$

Step 3: Write the area function $A = L \times W = L(12 - L) = 12L - L^2$

Step 4: Find the maximum This is a quadratic function. The maximum occurs at the vertex: $L = -\frac{b}{2a} = -\frac{12}{2(-1)} = 6$

Step 5: Calculate dimensions $L = 6 \text{ meters}$ $W = 12 - 6 = 6 \text{ meters}$

Conclusion: The vendor should make a square stall of 6 m × 6 m to get the maximum area of 36 square meters using 24 meters of fencing.

• Number and Operations: Calculations with money, measurements, quantities
• Algebra: Setting up equations from word problems
• Statistics: Collecting and interpreting data, finding averages
• Geometry: Working with areas, volumes, shapes
• Probability: Assessing likelihood in decision-making
• Mathematical Modeling: Translating real situations into mathematical form

• Choose a problem you understand well
• Keep your data collection simple and accurate
• Show all your working clearly
• Relate your conclusions back to the original problem
• Be honest about any limitations or assumptions

A Form 5 student in Tanzania can use these project skills when helping a family member or neighbor optimize their small business. For example, a student could help a mama lishe (cooked food vendor) at a local masoko determine the best price for her chipsi mayai by calculating the cost of ingredients, estimating daily sales based on customer counts, and using algebra to find the break-even point — ensuring she makes a profit while staying affordable for customers in her community.