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. What are we going to do today?
Recap from last week
Understand and use very large numbers
Use and calculate with the 4 operations - +, -, x and ÷
Identify
Prime numbers
Factors
Multiples
Powers and roots – squares, cubes, square roots, cube roots
Highest common factor
Lowest common multiple
from lists of numbers
Follow BIDMAS – the order of operations

4. For today…

5. What did we do last week?

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

7. True or False: Sales are rising rapidly!
4370
4360
4350
4340
Sales
4330
4320
The graph is misleading because it suggests that sales have increased significantly over a five year period. In reality they have only increased by 70 units, which is not much given that they are selling thousands.
4310
4300
2000
2001
2002
2003
2004
2005
Year

8. This may help to explain the previous slide

9. 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!

10. 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.

11. True or False: There are more 15 year old boys than girls.
18 year olds
18 year olds
15 year olds
15 year olds
17 year olds
17 year olds
16 year olds
False. We cannot make this conclusion from these graphs because we don’t know the totals. There might be 10 boys in total, making roughly 5 aged 15, but 100 girls, 30 of which are 15. It only tells us the proportion of 15 year olds.
16 year olds

12. 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
Information missing from a pie chart
Incorrect scale placed on the graph
Size of images used in pictograms are different for the different categories

13. 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

14. 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

15. 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:

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

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

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

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

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

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

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

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

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

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

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

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

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

29. The wealthiest is….
£51,931,640

30. Next wealthiest is….
£51,750,000

31. Next wealthiest is….
£43,500,000

32. Next wealthiest is….
£40,100,000

33. Next wealthiest is….
£34,621,093

34. Next wealthiest is.…
£27,847,401

35. Next wealthiest is….
£25,740,030

36. Next wealthiest is….
£25,216,800

37. Next wealthiest is….
£9,600,000

38. Next wealthiest is….
£149,440

39. Next wealthiest is….
£143,789

40. And the least wealthy is….£0

41. 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

42. Inequality symbols An inequality shows that two values are not equal.
A < B says that A is less than B
A > B says that A is greater than B

43. Use your amounts of money and your T/F card
True or False?
Use your amounts of money and your T/F card

44. Usain Bolt’s salary > The Queen’s salary
True or False?
Usain Bolt’s salary > The Queen’s salary

45. Lewis Hamilton’s salary > Jeremy Clarkson’s salary
True or False?
Lewis Hamilton’s salary > Jeremy Clarkson’s salary

46. Theresa May’s salary > The Pope’s salary
True or False?
Theresa May’s salary > The Pope’s salary

47. Simon Cowell’s salary > Adele’s salary
True or False?
Simon Cowell’s salary > Adele’s salary

48. True or False?
574 > 121

49. True or False?
1249 < 578

50. Number of days in a week > Number of sides of a nonagon
True or False?
Number of days in a week > Number of sides of a nonagon

51. Number of days in February < Number of days in October
True or False?
Number of days in February < Number of days in October

52. Number of degrees in a circle < Number of months in a year
True or False?
Number of degrees in a circle < Number of months in a year

53. True or False?
Number of planets in the solar system > Number of blind mice in the nursery rhyme

54. Number of Olympic rings > Number of days of Christmas
True or False?
Number of Olympic rings > Number of days of Christmas

55. Addition & Subtraction
Do you all have a method for adding and subtraction WITHOUT a calculator?

56. Addition

57. Subtraction
76 – 23
102 – 78

58. Multiplication
Which method do you use?

59. 3 x 7 12 x 7

60. 45 x 7

61. 468 x 8

62. 39 x 47

63. 156 x 17

64. 41.9 x x x 0.08

65. 2.5 x 4.5 Extension: 0.58 x 126

66. Division

67. 375 ÷ 2

68. 2793 ÷ 4

69. ÷ 8

70. 746 ÷ 3

71. Word of the day - integer
What is an integer?
An integer is a positive or negative whole number, including zero.

72. +, -, x, ÷ positive and negative integers

74. Multiplication
4 x 5
-4 x 5
-4 x -5

75. Divide
20 ÷ 5
20 ÷ -5
-20 ÷ -5

76. Addition
4 + -6
-4 + 6

77. Subtraction
-10 – 2

78. Negative Number BINGO

79. Put one number in each box
Put one number in each box. Pick any numbers from the list but no repeats. 15
-10 3
-21
-13 17 -9 11 18
-12
-15 -2 -4 22 6 25 7 20 -5 24 16 14 8 -3

80. 8 -12

84. - 1 +8

85. -2 x -10

86. -2 -3

88. - 4 x -4

90. 9 – 1

91. 7 -10

93. -40 ÷ 4

94. -9 ÷ -3

95. 7 x -3

96. -26 ÷ 2

97. -17 x -1

98. 3 x -3

101. 6 x -2

104. What is the answer to this question?
2 + 3 x 4

105. 3 + 7 x 6 – 5

106. Bidmas activity:

108. Factors, Multiples and Primes

109. What is a ……..
Factor
Multiple
Prime

110. Prime Numbers A prime number has exactly two factors – one and itself
One is not a prime number because it has only one factor – itself
Two is the first prime number
Two is the only even prime number

111. Give an example of as many of these as possible
Give an example of as many of these as possible. Then put it away - we will revisit this before the end of the lesson.
A factor of 24
A multiple of 5
A prime number
A power of 2
A square number
A cube number
The square root of 100
The cube root of 27

113. On your number grid, cross out the 5 times table, apart from the number 5.

114. Cross out the 6 times table, apart from the number 6.

115. What are we left with? What about the number 1?
Cross out the 2 times table, apart from the number 2.
Cross out the 3 times table, apart from the number 3.
What are we left with?
What about the number 1?

117. What is a ……..
Factor
Multiple
Prime

118. Question
For each of these pairs of numbers, there is just one prime number that lies between them. In each case, write that prime number.
a) b) c)
e) f)
g) h)

119. Factors multiples puzzle

120. Answers

121. From these numbers: 1 3 8 12 16 20 13 15 2 17 24 6 Write down
Write down
4 prime numbers
all the factors of 6
any multiples of 4

122. Square numbers √ Square Square root Square Square root Area = 3 x 3
= 3² 3 9 =9
Square root √
Area =
4 x 4
Square
= 4² 4 16
Square root
= 16

123. cube numbers cube cube Cube root Cube root Volume = 3 x 3 x 3 Volume =
= 3³
= 4³
cube
= 27
cube
= 64 4 64 3 27
Cube root
Cube root

124. Can you answer these questions?
What is the square of 5? What is the square root of 36? Is there another one? What is the cube of 2? What is the cube root of 125? What are the powers of 10?

125. From these numbers: 121 49 20 19 800 1000 5 Find two square numbers
Find
two square numbers
a cube number
the square root of 400
the cube root of 125

126. 90
Prime factors Then with powers Over to you – prime factors of 84?

127. 84

128. Finally - Factors, Multiples and Primes
8 quick questions
Write down your answers

129. 1
Which of the following numbers divides into 49, without remainder?
Divisors
a: 3
b: 4
c: 7
d: 9

130. 2
Including one and itself, how many factors has the number 6?
Factors
a: 2
b: 3
c: 4
d: 6

131. 3
Which of the following is a multiple of 6?
Multiples
a: 1
b: 3
c: 9
d: 12

132. 4 Common Factors a: 2 b: 4 c: 8 d: 36
Which of the following is a common factor of 12 and 18?
Common Factors
a: 2
b: 4
c: 8
d: 36

133. 5 Prime Numbers a: 2 b: 15 c: 17 d: 29
Which of the following is not a prime number?
Prime Numbers
a: 2
b: 15
c: 17
d: 29

134. 6 Prime Numbers a: 51 b: 53 c: 55 d: 57
What is the next prime number after 47?
Prime Numbers
a: 51
b: 53
c: 55
d: 57

135. 7 Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5
Which of the following shows the prime factors of 30?
Prime
Factor
Decomposition
a: 2 x 15
b: 3 x 10
c: 5 x 6
d: 2 x 3 x 5

136. 8 Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5
Which of the following shows the prime factors of 40 (with powers)?
Prime factor
decomposition
a: 23 x 5
b: 22 x 10
c: 2 x 4 x 5
d: 4 x 10

137. Answers

138. 1
Which of the following numbers divides into 49, without remainder?
Divisors
a: 3
b: 4
c: 7
d: 9

139. 2
Including one and itself, how many factors has the number 6?
Factors
a: 2
b: 3
c: 4
d: 6

140. 3
Which of the following is a multiple of 6?
Multiples
a: 1
b: 3
c: 9
d: 12

141. 4 Common Factors a: 2 b: 4 c: 8 d: 36
Which of the following is a common factor of 12 and 18?
Common Factors
a: 2
b: 4
c: 8
d: 36

142. 5 Prime Numbers a: 2 b: 15 c: 17 d: 29
Which of the following is not a prime number?
Prime Numbers
a: 2
b: 15
c: 17
d: 29

143. 6 Prime Numbers a: 51 b: 53 c: 55 d: 57
What is the next prime number after 47?
Prime Numbers
a: 51
b: 53
c: 55
d: 57

144. 7 Prime Factor Decomposition a: 2 x 15 b: 3 x 10 c: 5 x 6 d: 2 x 3 x 5
Which of the following shows the prime factors of 30?
Prime
Factor
Decomposition
a: 2 x 15
b: 3 x 10
c: 5 x 6
d: 2 x 3 x 5

145. 8 Prime factor decomposition a: 23 x 5 b: 22 x 10 c: 2 x 4 x 5
Which of the following shows the prime factors of 40 (with powers)?
Prime factor
decomposition
a: 23 x 5
b: 22 x 10
c: 2 x 4 x 5
d: 4 x 10

146. Add them up! 7 or 8? Brilliant 5 or 6? Jolly good show
3 or 4? Some good, but revision needed
1 or 2? Oh dear, have you been paying attention?
0 Whoops!

147. Plenary - revisit this: can you answer all these now?
A factor of 24
A multiple of 5
A prime number
A power of 2
A square number
A cube number
The square root of 100
The cube root of 27

148. Website of the week Help is at hand

150. Homework
AQA Number Homework sheet