1. Week 13 Rounding & Estimation
MATHS
Week 13
Rounding & Estimation

2. Starter!
Each table has the ‘starting 6’ worksheet on – can your table answer all 6 questions?

5. What did we do last week?

6. Before we begin……

7. Have you done your directed study?
I hope you revised!

8. What are we going to do this week?
Rounding and Estimating
Upper and Lower Bounds
Truncation
Assessment

9. Rounding and estimating

10. Rounding – to the nearest 10
1 9 5
5 or more?
5 or more?
5 or more? No
Yes
Yes
2 0 0

11. Rounding – to the nearest 100
8 9
5 or more?
5 or more?
5 or more? No
Yes
Yes
1 0 0

12. Rounding – to the nearest 1000
5 or more?
5 or more?
5 or more? No
Yes
Yes

13. Rounding to 1 Decimal Place (1DP)
5 or more?
5 or more?
5 or more? No No
Yes
4 . 8
9 . 3
4 . 9
5 or more?
5 or more?
5 or more?
Yes
Yes
Yes
4 . 9
5 . 3
2 . 0

14. Rounding to 2 Decimal Places: 2DP
5 or more?
5 or more?
5 or more? No
Yes
Yes
5 or more?
5 or more?
5 or more? No
Yes
Yes

15. Rounding to Decimal Places: 3DP
5 or more?
5 or more?
5 or more?
Yes No
Yes
5 or more?
5 or more?
5 or more? No
Yes
Yes

16. Significant Figures: Important Zeros in Numbers5 2 a.
Which zeros matter?
Are there any we could get rid of and still have the same value? 5 . 2 b. . 5 c. 2 . 5 d.
When dealing with Significant Figures, you need to keep any zeros that tell us the value of a number

17. Rounding to 1 Significant Figure (1SF)
5 or more?
5 or more?
5 or more?
Yes No No 1
2 4 1
5 8 7
7 5
5 or more?
5 or more?
5 or more? No
Yes
Yes
2 0 0
6 0 0
8 0

18. Rounding to 2 Significant Figures (2SF)
5 or more?
5 or more?
5 or more?
Yes No
Yes
1 . 4
5 or more?
5 or more?
5 or more?
Yes No
Yes

19. Rounding to 3 Significant Figures (3SF)
5 or more?
5 or more?
5 or more? No No No
5 or more?
5 or more?
5 or more?
Yes
Yes
Yes

20. Rounding to Significant Figures
1SF
2SF
3SF
5 or more?
5 or more?
5 or more?
Yes
Yes
Yes

21. The following number could be the population of a country at a particular instant in time.Write this number to 1, 2, 3, 4, 5, 6 and 7 significant figures.

22. Estimation and Rounding
What is… = 79 50 30 + = 80

23. =
179 70
110 + =
180

24. =
278 50
230 + =
280

25. Exam question using rounding

26. Upper & Lower Bounds

27. What are they?

28. Limits of accuracy

29. So to find the bounds……
Upper bound = Add on half of whatever it is rounded to Lower bound = Subtract half of whatever it is rounded to

30. For example
The measurement has been rounded to the nearest metre so I need to find half of this.
1m ÷ 2 = 0.5m
This is the amount I will add and subtract to find the bounds (limits)
UPPER BOUND = 22m + 0.5m = 22.5m
LOWER BOUND = 22m – 0.5m = 21.5m

31. Your turn What is it measured to? Find half of this.
Add this on to find the upper bound
Take this away to find the lower bound

36. Exam Question A small van can take a load of up to 1500 kg.
This van has to take the following to a market:
50 large bags of potatoes, each bag weighing 25kg to the nearest kg,
240 boxes of oranges, each box weighing 3000 g to the nearest 10 g.
Could this load be over the limit?
You must show all your working.

37. Truncation

38. Truncation
Truncation is a way to approximate a number without rounding
You always round down at the given unit
If someone asks ‘how old are you?’ what do you say?

40. Truncation

41. Truncation
Mini Whiteboards
Truncate
To 4 d.p.

42. Truncation
Mini Whiteboards
Truncate
To 1 d.p.
3123.2

43. Truncation
Mini Whiteboards
Truncate
To the whole number
123

44. Truncation
Mini Whiteboards
Truncate
To the hundreds
23900

45. If 5.4 has been truncated to 1 d.p.
Upper and Lower Bounds
How could we describe the Error Interval of a truncated number?
If 5.4 has been truncated to 1 d.p.
what are the values it could have been?
5.3
5.4
5.5
The Error Interval
5.4 ≤ x < 5.5
5.4
5.5

46. Find the error interval of 8.2345 truncated to 4 d.p.
Upper and Lower Bounds
Find the error interval of truncated to 4 d.p.
what are the values it could have been?
8.2344
8.2345
8.2346
The Error Interval
≤ x <
8.2345
8.2346

47. What is the Error Interval of
Truncation
Mini Whiteboards
What is the Error Interval of
24.13
Truncated to 2 d.p.
24.13 ≤ x < 24.14

48. What is the Error Interval of
Truncation
Mini Whiteboards
What is the Error Interval of
14.745
Truncated to 3 d.p.
≤ x <

49. 741 What is the Error Interval of Truncated to a whole number
Truncation
Mini Whiteboards
What is the Error Interval of
741
Truncated to a whole number
741 ≤ x < 742

50. What is the Error Interval of
Truncation
Mini Whiteboards
What is the Error Interval of
7480
Truncated to the tens
7480 ≤ x < 7490

51. Round or Truncate?

52. 2nd lesson Half Term Mini Assessment
You now have one and a half hours to complete the mini assessment.
You are expected to stay for the full time. If you finish the assessment early, use the time wisely to check through your answers.

53. Directed Study

54. Your targets…
Make sure you have worked on your targets as it is time to review them over the next couple of weeks (hint: if you can’t remember them look on pro-portal)!!!