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 boundUpper bound 1.) 320315325 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 4.) 9.39.259.35 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 4.) 9.39.259.35 5.) 970965975 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 4.) 9.39.259.35 5.) 970965975 6.) 6.96.856.95 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 4.) 9.39.259.35 5.) 970965975 6.) 6.96.856.95 7.) 1110.511.5 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 boundUpper bound 1.) 320315325 2.) 5150.551.5 3.) 850084508550 4.) 9.39.259.35 5.) 970965975 6.) 6.96.856.95 7.) 1110.511.5 8.) 280002750028500

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 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? L L WW

12. 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? Perimeter = 2L + 2W L L WW

13. 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? Perimeter = 2L + 2W Area = LW L L WW

14. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55

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

16. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55

17. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55 Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m

18. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55 Max perimeter = (2 x 6.85) + (2 x 7.55) = 28.8m Min perimeter = (2 x 6.75) + (2 x 7.45) = 28.4m

19. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55 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

20. 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? Perimeter = 2L + 2W Area = LW L L WW L/boundU/bound 6.86.756.85 7.57.457.55 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