Number System Case Study Class 8 PDF
The number system case study class 8 PDF offers detailed explanations of whole numbers, integers, and rational numbers. It includes real-life examples to make learning interactive and engaging. Moreover, students can easily download the PDF to revise key mathematical concepts anytime.
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Case Study 1: Class 8 Number System
A meteorological research team established a weather monitoring station in the Himalayan region to study temperature patterns at high altitudes. Over a seven-day period, they recorded precise temperature readings every six hours. The minimum daily temperatures (in °C) recorded were: Monday: 3, Tuesday: -2, Wednesday: -5, Thursday: 1, Friday: -1, Saturday: 4, Sunday: -3. The researchers observed fascinating patterns in how these integers behaved under various mathematical operations. They noted that the temperature fluctuations created a perfect scenario to study integer operations, rational number formations, and number line representations. The team also analyzed cumulative temperature effects and daily variations to understand closure properties and associative patterns in real-world integer applications. This data became crucial for predicting frost conditions and understanding thermal inertia in mountain ecosystems, providing valuable insights into climate patterns at high altitudes where integer mathematics plays a vital role in accurate weather forecasting and environmental monitoring.
Solution: Highest temperature = 4°C, Lowest temperature = -5°C. Range = 4 – (-5) = 4 + 5 = 9°C.
Solution: -1 and 1 are both exactly 1 unit away from zero on the number line, making them equidistant.
Solution: Positive temperature days: Monday (3), Thursday (1), Saturday (4) = 3 days. Negative temperature days: Tuesday (-2), Wednesday (-5), Friday (-1), Sunday (-3) = 4 days. Ratio = 3/4.
Solution: The equation shows that the grouping of numbers in addition doesn’t change the sum, which is the associative property of addition.
Solution: Sum of temperatures = 3 + (-2) + (-5) + 1 + (-1) + 4 + (-3) = -3. Mean = -3 ÷ 7 = -0.428… ≈ -0.5°C (rounded to one decimal place).