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Understanding Upper and Lower Boundaries in Measurements

This resource provides a comprehensive guide to finding upper and lower boundaries for given values, particularly when measurements are represented to two significant figures. It includes practical examples, such as calculating the minimum and maximum perimeter and area of a rectangular garden based on accurately measured side lengths. This educational tool is ideal for students and professionals who seek to apply boundary concepts in real-world applications.

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Understanding Upper and Lower Boundaries in Measurements

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  1. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: 1.) 320 2.) 51 3.) 8500 4.) 9.3 5.) 970 6.) 6.9 7.) 11 8.) 28000

  2. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 3.) 8500 4.) 9.3 5.) 970 6.) 6.9 7.) 11 8.) 28000

  3. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 4.) 9.3 5.) 970 6.) 6.9 7.) 11 8.) 28000

  4. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 5.) 970 6.) 6.9 7.) 11 8.) 28000

  5. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 9.25 9.35 5.) 970 6.) 6.9 7.) 11 8.) 28000

  6. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 9.25 9.35 5.) 970 965 975 6.) 6.9 7.) 11 8.) 28000

  7. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 9.25 9.35 5.) 970 965 975 6.) 6.9 6.85 6.95 7.) 11 8.) 28000

  8. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 9.25 9.35 5.) 970 965 975 6.) 6.9 6.85 6.95 7.) 11 10.5 11.5 8.) 28000

  9. Starter: Recap finding upper and lower boundaries Write the upper and lower boundaries of the following values which are written to 2 s.f: Lower bound Upper bound 1.) 320 315 325 2.) 51 50.5 51.5 3.) 8500 8450 8550 4.) 9.3 9.25 9.35 5.) 970 965 975 6.) 6.9 6.85 6.95 7.) 11 10.5 11.5 8.) 28000 27500 28500

  10. Objective: Use upper and lower boundaries to answer practical questions Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area?

  11. Objective: Use upper and lower boundaries to answer practical questions L Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? W W L

  12. Objective: Use upper and lower boundaries to answer practical questions L Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W W W L

  13. Objective: Use upper and lower boundaries to answer practical questions L Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W L

  14. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W L

  15. Objective: Use upper and lower boundaries to answer practical questions To get answers using boundaries For maximum answer For minimum answer When multiplying: u/bound X u/bound l/bound X l/bound When dividing: u/bound l/bound l/bound u/bound When adding: u/bound + u/bound l/bound + l/bound When subtracting: u/bound – l/bound l/bound – u/bound

  16. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W L

  17. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m L

  18. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m Min perimeter = (2 x 6.75) + (2 x 7.45) = 28.4m L

  19. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m Min perimeter = (2 x 6.75) + (2 x 7.45) = 28.4m Max area = 6.85 x 7.55 = 51.7 to 1 d.p L

  20. Objective: Use upper and lower boundaries to answer practical questions L L/bound U/bound 6.8 6.75 6.85 7.5 7.45 7.55 Example A rectangular garden has sides of length 6.8m and 7.5m measured to 1d.p. 1.) What are the minimum and maximum values of the perimeter? 2.) What are the minimum and maximum values of the area? Perimeter = 2L + 2W Area = LW W W Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m Min perimeter = (2 x 6.75) + (2 x 7.45) = 28.4m Max area = 6.85 x 7.55 = 51.7 to 1 d.p Min area = 6.75 x 7.45 = 50.3 to 1 d.p L

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