--- *ZIMSEC O Level Pure Mathematics Project* *Title:* *Determining the Number of Tiles Required to Tile a Classroom Floor* --- *Stage 1: Problem Identification* *Problem Statement:* In our school, several classrooms have dusty and uneven floors, leading to health concerns and discomfort for students and teachers. The administration plans to renovate these floors by installing tiles. However, there is uncertainty about the exact number of tiles required for each classroom, considering variations in tile sizes and classroom dimensions. *Statement of Intent:* This project aims to calculate the precise number of tiles needed to cover a specific classroom floor. By measuring the classroom dimensions and analyzing different tile sizes, the project will provide accurate estimates to assist in procurement and budgeting for the renovation. --- *Stage 2: Investigation of Related Ideas* *Background Research:* - Understanding the concepts of area measurement and unit conversions. - Exploring different tile sizes commonly available in the market. Reviewing methods to calculate the area of rectangular spaces. *Data Collection Methods:* - Measuring the length and width of the selected classroom using measuring tapes. - Researching standard tile sizes from local hardware suppliers. - Consulting with the school maintenance team regarding any additional space considerations (e.g., gaps between tiles, wastage). --- *Stage 3: Generation of Ideas* *Hypothesis:* By accurately measuring the classroom dimensions and selecting appropriate tile sizes, we can determine the exact number of tiles required, minimizing wastage and ensuring cost-effectiveness. *Experimental Design:* - Measure the classroom's length and width to calculate its total area. - Select a tile size and calculate the area of a single tile. - Divide the classroom area by the tile area to estimate the number of tiles needed. - Account for additional tiles to cover potential wastage or cutting errors. --- *Stage 4: Development of Ideas* *Implementation Plan:* 1. *Materials Needed:* - Measuring tape - Calculator - Notebook and pen for recordings - Access to tile samples or specifications 2. *Procedure:* - Measure the length and width of the classroom floor in meters. Calculate the area of the classroom (Area = length × width). - Obtain the dimensions of the chosen tile and calculate its area. - Divide the classroom area by the tile area to determine the number of tiles required. - Add an additional percentage (e.g., 10%) to account for wastage and cutting. --- *Stage 5: Presentation of Results* *Findings:* - Classroom dimensions: Length = 8 meters, Width = 6 meters - Classroom area: 8 m × 6 m = 48 m² - Selected tile size: 0.5 m × 0.5 m = 0.25 m² per tile - Number of tiles needed: 48 m² ÷ 0.25 m² = 192 tiles - Adding 10% for wastage: 192 × 0.10 = 19.2 ≈ 20 tiles - Total tiles required: 192 + 20 = 212 tiles *Analysis:* The calculation indicates that 212 tiles of size 0.5 m × 0.5 m are needed to cover the classroom floor, including an allowance for wastage. This estimation ensures efficient resource planning and cost management for the renovation project. --- *Stage 6: Evaluation and Recommendations* *Evaluation:* - The methodology provided accurate estimations based on precise measurements and standard calculations. - Potential limitations include irregularities in room shape or obstacles that may require custom tile cutting. *Recommendations:* Conduct similar assessments for other classrooms to facilitate comprehensive renovation planning. - Consider using software tools for more complex room layouts to enhance accuracy. - Engage with professional tilers for insights on best practices and potential challenges during installation. --- - Local hardware supplier catalogs for tile specifications.