1. Set Theory Problem: Survey classmates about favorite sports (football, cricket, volleyball), represent with Venn diagrams, and interpret results. 2. Algebra Problem: Design a magic square or puzzle where sums follow an algebraic rule, e.g., $2x + 3$, and show algebraic patterns. 3. Statistics Problem: Collect class data on daily study hours or favorite social media apps, represent via bar graphs and pie charts, calculate mean, median, and mode. 4. Number System Problem: Investigate decimal expansions of fractions $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{7}$, $\frac{1}{11}$; determine which are terminating or recurring decimals and their patterns. 5. Integrated Project: Collect data on ages of 10-15 neighbors, represent in a table, form algebraic expression for total age, calculate average age. Since these are conceptual or data collection tasks without explicit numerical questions or algebraic expressions to solve here, please provide specific numerical data or problems for detailed step-by-step solutions. For example, to analyze $\frac{1}{7}$, note: 1. Divide 1 by 7 to get the decimal expansion. 2. $\frac{1}{7} = 0.142857142857\ldots$ recurring with period 6. Number of distinct problems: 5.