1. Week 3 Understanding and using numbers
MATHS
Week 3
Understanding and using numbers

2. To warm up…….
Can you answer all 10 questions on this weeks number?

3. Today’s plan: Understand, use and calculate using number
Calculate using +, -, x and ÷
Rounding
Negative numbers
Part 2 of your diagnostic (Measure, shape and space section)

4. What did we do last week?

5. Why are they misleading?
Misleading graphs
Why are they misleading?

6. 1. Which is the better graph – and why. 2
1. Which is the better graph – and why? 2. Where is the spelling mistake – and why?

7. Although the vertical scale starts at 0, it does not go up in even steps. This distorts the graph, and makes it look as though the biggest jump is between 1 and 2, rather than 3 and 4.
Also, there are no labels on the axes, so we have no idea what this graph represents!

8. On this pictogram, there is no category for people who do not own a pet. The pictures are different sizes, and it appears that more people own a horse than any other animal.
An improvement would be to redraw the pictogram, with each of the animals the same size and aligned with one another.

9. True or False: Twice as many people like Thrillers than Romance films.
150
120
100 60
Number of People 40 25
The scale on the vertical axis is not linear, so even though the green bar is twice as big as the purple bar, it does not represent twice as many people. 20 5
Horror
Comedy
Action
Romance
Thriller
Favourite Films

10. Summary of points Scale doesn’t start at zero
Scale made very small to make graph look very big
Scale values or labels missing from the graph
Incorrect scale placed on the graph
Size of images used in pictograms are different for the different categories

11. Understand and use very large numbers
Give me a number….let’s look at the place value

12. Here are some annual salaries
Here are some annual salaries. Write them out in order from largest to smallest. Can you say the figures in words? (talk about place value)
£25,740,030
£51,931,640
£40,100,000
£51,750,000
£34,621,093
£9,600,000
£149,440
£143,789
£25,216,800
£27,847,401 £0
£43,500,000

13. The order should look like this:
£51,931,640 £51,750,000 £43,500,00 £40,100,000 £34,621,093 £27,847,401 £25,740,030 £25,216,800 £9,600,000 £149,440 £143,789 £0

14. Who am I?
Write down the name of the celebrity next to the amount of money you think they earn in a year.
Good luck!
(Source:

15. Who am I? How much money do I earn per year?
Usain Bolt

16. Who am I? How much money do I earn per year?
Theresa May

17. Who am I? How much money do I earn per year?
Boris Johnson

18. Who am I? How much money do I earn per year?
Lewis Hamilton

19. Who am I? How much money do I earn per year?
Adele

20. Who am I? How much money do I earn per year?
Jeremy Clarkson

21. Who am I? How much money do I earn per year?
Daniel Radcliffe

22. Who am I? How much money do I earn per year?
Pope Francis

23. Who am I? How much money do I earn per year?
Queen Elizabeth II

24. Who am I? How much money do I earn per year?
Jose Mourinho

25. Who am I? How much money do I earn per year?
Ed Sheeran

26. Who am I? How much money do I earn per year?
Simon Cowell

27. The wealthiest is….
correct them as you go

28. The wealthiest is….
£51,931,640

29. Next wealthiest is….
£51,750,000

30. Next wealthiest is….
£43,500,000

31. Next wealthiest is….
£40,100,000

32. Next wealthiest is….
£34,621,093

33. Next wealthiest is…..
£27,847,401

34. Next wealthiest is….
£25,740,030

35. Next wealthiest is….
£25,216,800

36. Next wealthiest is….
£9,600,000

37. Next wealthiest is….
£149,440

38. Next wealthiest is….
£143,789

39. And the least wealthy is….£0

40. The order should look like this:
Adele £51,931,640 Daniel Radcliffe £51,750,000 Simon Cowell £43,500,00 The Queen £40,100,000 Lewis Hamilton £34,621,093 Ed Sheeran £27,847,401 Usain Bolt £25,740,030 Jose Mourinho £25,216,800 Jeremy Clarkson £9,600,000 Theresa May £149,440 Boris Johnson £143,789 The Pope £0

41. Addition and Subtraction problems
Sum
Total
Add
Plus
Increase
Subtract
Take Away
Minus
Less
Decrease

42. Addition and subtraction problems

43. Addition and subtraction problems
1099 – 875 = £224

44. Multiplication and division problems
159 ÷ 30 = 5.3
So they would need 6 coaches
1079 ÷ 8 =
So Jarred would need 135 boxes

45. Multiplication and division problems
5 x 9 = 45 chips
45 ÷ 7 = 6.428
So 6 chips each as you can’t divide the rest up equally
24 x 19 = 456
456 ÷ 8 = 57 carrots for each rabbit

46. Rounding
Nearest 10, 100, 1000

47. DISCUSS!!! What is ROUNDING?
What do we mean by ‘round up’ and ‘round down’?
Can you think of some examples of when you have seen rounding before?

48. We do not need to know the exact number for everything.
Why do we use rounding?
THINK!
We do not need to know the exact number for everything.
Can you think of any other examples of numbers from everyday that have probably been rounded?
Why not just 7 billion…
There are exactly
6,970,442,289 people on
planet Earth
Teacher Notes:
Class discussion – pupils may have more ideas but key point here is that rounded values are easier to work with in practical contexts.

49. What sorts of things do we round?
Teacher Notes:
The globe with the people represents population.
This slide can be used as a brainstorming activity, using the triggers after students have come up with their own ideas.

50. 50 40 43 Rounding to the nearest 10
43 is closer to 40 than to 50.
Which two TENS does the number 43 lie between?
Where would you place 43 on the washing line?
Teacher Notes:
Discuss rounding UP and DOWN as rounding to the ten, hundred or thousand closest to the original number.
Language of ROUNDING DOWN can be confusing – what does this actually mean?
So, 43 rounded to the nearest 10 is 40.

51. Rounding to the nearest 10
180
190
186
186 is closer to 190 than to 180.
Teacher Notes:
Even though our number now includes place value column of HUNDREDS, we are only rounding to nearest TEN.
Which two TENS does the number 186 lie between?
Where would you place 186 on the washing line?
So, 186 rounded to the nearest 10 is 190.

52. But the rule is… 5 or more, round up
Rounding to the nearest 10 10 20 15
15 is exactly halfway!
But the rule is… 5 or more, round up
Teacher Notes:
Discuss convention of rounding – even though 5 represents half-way, we round UP.
Which two TENS does the number 15 lie between?
Where would you place 15 on the washing line?
So, 15 rounded to the nearest 10 is 20.

53. APPLY 81
Round

54. APPLY 75
Round

55. APPLY 51
Round

56. APPLY 23
Round
Use this slide to discuss the fact that 23 to the nearest 100 is 0!

57. APPLY 97
Round
Use this slide to discuss the fact that 97 to the nearest 10 is 100.

58. APPLY
412
Round

59. APPLY
673
Round

60. APPLY
845
Round

61. APPLY
312
Round

62. APPLY
755
Round

63. Which of these numbers round to 60 to the nearest 10?
ANALYSE
Which of these numbers round to 60 to the nearest 10?
157, 56, 61, 66, 55

64. Which of these numbers round to 90 to the nearest 10?
ANALYSE
Which of these numbers round to 90 to the nearest 10?
98, 92, 87, 84, 95

65. Rounding to the nearest 100
600
700
629
629 is closer to 600 than to 700.
Which two HUNDREDS does the number 629 lie between?
Where would you place 629 on the washing line?
So, 629 rounded to the nearest 100 is 600.

66. 9000 8000 8711 Rounding to the nearest 1000
8711 is closer to 9000 than to 8000.
Which two THOUSANDS does the number 8711 lie between?
Where would you place 8711 on the washing line?
So, 8711 rounded to the nearest 1000 is 9000.

67. Split your scrap paper into three columns.
nearest 1000
nearest 100
nearest 10
Split your scrap paper into three columns.
Round each number to…
Nearest 10
Nearest 100
Nearest 1000
APPLY

68. APPLY
342
Round

69. APPLY
864
Round

70. APPLY
192
Round

71. APPLY
196
Round
Use this slide to discuss the fact that 196 to the nearest 10 is 200.

72. APPLY
107
Round

73. APPLY
Round
4629

74. APPLY
Round
1811

75. APPLY
Round
3815

76. APPLY
Round
7489

77. APPLY
Round
9615
Use this slide to discuss the fact that 9615 to the nearest 1000 is

78. Positive and negative numbers

79. Positive and negative numbers

80. Positive and negative numbers
The Number Line

81. Positive and negative numbers

82. Positive and negative numbers
Look at the number line on the wall if you want a clue!

83. Positive and negative numbers
Extension Questions…
What is the highest / lowest temperature?
What is 100C cooler than 30C?
It is -150C in Moscow (Russia) and 230C in Florida. What is the difference in temperatures?

84. Diagnostic
Please complete the second part of the diagnostic (Measure, shape and space section)
You will have 30 minutes to complete as much as you can