1. GCSE Maths - Higher Lesson 4
Fractions, decimals and percentages
- and finishing off from last week!

2. What do these inequalities say
What do these inequalities say? What integer values satisfy the inequality?

3. Homework was finishing the topic test and the systematic listing one (answers were already on the back)
Also finishing histogram sheet

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

5. +, -, x, ÷ positive and negative integers
Mathswatch Clip 99 (demonstrate Cdrom)

6. Negative number cards

7. Negative Number BINGO

8. 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

9. 8 -12

13. - 1 +8

14. -2 x -10

15. -2 -3

17. - 4 x -4

19. 9 – 1

20. 7 -10

22. -40 ÷ 4

23. -9 ÷ -3

24. 7 x -3

25. -26 ÷ 2

26. -17 x -1

27. 3 x -3

30. 6 x -2

33. Practice
Mr Corbett’s real life negative number questions – for homework?

34. What is the answer to this question? (give out a few basic calculators)
2 + 3 x 4
Now put it in your calculator – what is the answer?

36. Homework - bidmas activity

37. New vocabulary
Factor
Multiple
Prime number
Square
Cube
Root
Power

38. Use this to talk about factors, multiples as well as primes

39. 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

40. 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

41. Factors multiples puzzle

42. Answers

43. 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

44. 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

45. 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?

46. 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

47. For higher, you may need to estimate the values of powers and roots.

48. Estimate the square root of 43
Between which two integers does the square root of 150 lie?
Between which two integers does the cube root of 100 lie?
Estimate the value of
Estimate the value of
Estimate the value of 2x = 40

49. Estimate the square root of 43
Between which two integers does the square root of 150 lie?
Between which two integers does the cube root of 100 lie?
Estimate the value of
Estimate the value of
Estimate the value of 2x = 40

50. Finally - Factors, Multiples and Primes
8 quick questions
Write down your answers on your whiteboard

51. 1
Which of the following numbers divides into 49, without remainder?
Divisors
a: 3
b: 4
c: 7
d: 9

52. 2
Including one and itself, how many factors has the number 6?
Factors
a: 2
b: 3
c: 4
d: 6

53. 3
Which of the following is a multiple of 6?
Multiples
a: 1
b: 3
c: 9
d: 12

54. 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

55. 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

56. 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

57. 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

58. 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 in index form?
Prime factor
decomposition
a: 23 x 5
b: 22 x 10
c: 2 x 4 x 5
d: 4 x 10

59. Answers

60. 1
Which of the following numbers divides into 49, without remainder?
Divisors
a: 3
b: 4
c: 7
d: 9

61. 2
Including one and itself, how many factors has the number 6?
Factors
a: 2
b: 3
c: 4
d: 6

62. 3
Which of the following is a multiple of 6?
Multiples
a: 1
b: 3
c: 9
d: 12

63. 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

64. 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

65. 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

66. 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

67. 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 in index form?
Prime factor
decomposition
a: 23 x 5
b: 22 x 10
c: 2 x 4 x 5
d: 4 x 10

68. 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!

69. For after the break ……

70. What are we going to do now?
Fractions
Order fractions
Find a fraction part of a quantity
The four operations: + - x ÷
Percentages
Find a percentage part of a quantity
Write one value as a percentage of another value
Percentage increase and decrease (simple/compound interest)
Reverse percentages
Decimals
Order decimal numbers
Convert between fractions, decimals and percentages

71. Fractions Finding a fraction part Equivalent fractions & simplifying
Ordering fractions
Adding and Subtracting fractions
Multiplying and Dividing fractions

72. Finding a fraction part of a number
You need to remember the following:
Divide by the bottom
THEN
Times by the top

73. Example:
What is 5/7 of 350 ?
First, divide by the bottom: ÷ 7 = 50
Then, times your answer by the top: x 5 = 250
So 5/7 of 350 is 250.

74. Your Turn…

75. Can you guess which thing One of these things, it doesn’t belong.
3 8 𝑜𝑓 32
1 2 𝑜𝑓 24
Can you guess which thing
One of these things, it doesn’t belong.
Before I finish my soonnnggg.
One of these things is not like the other thing
is not like the other things
2 5 𝑜𝑓 20
6 7 𝑜𝑓 14

76. 3 8 𝑜𝑓 32
1 2 𝑜𝑓 24
2 5 𝑜𝑓 20
6 7 𝑜𝑓 14

77. Simplify the fractions…
Customers have paid the following amounts to begin to pay off their overdraft. Simplify the fractions below.
£300 paid of £450
£50 paid of £600
£400 paid of £1000
£60 paid of £120
£30 paid of £40
£45 paid of £90
£110 paid of £450

78. Equivalent Fractions
Equivalent means equal to, so equivalent fractions are fractions that are the same.
½ = 2/4 = 3/6 = 4/8 = 5/10
(These could all be simplified to ½ therefore they are equivalent)

81. Ordering fractions - together
We use equivalent fractions to put fractions in order: We find the common denominator and use it to place the fractions in order, smallest to largest

82. Your turn
Using the common denominator place the fractions in order, smallest to largest.

83. A fraction problem to solve together
Anna, Bobby and Cheryl order a large 24 piece pizza. Anna eats 1/6 of the pizza. Bobby has 5 pieces and Cheryl eats a quarter. What fraction of the pizza is left?
3/8 is the answer

84. Another fraction problem – “The builder’s day”
A builder works for of a day.
If he sleeps 7 ½ hours per day what fraction of the day does he have left ?
13/48

85. Yet another – “The TV Programme”
A TV programme lasting an hour has ⅖ of it dedicated to adverts.
The rest of the programme is split equally between current affairs and sport.
How long is spent on Sport ?
18 minutes

86. Adding and Subtracting Fractions
To add or subtract fractions, you need to have a common denominator – both fractions need to have the same value on the bottom. =

87. Or you can use the “kiss & smile” method to add and subtract fractions
There’s a really clear handout for this method plus x and ÷ and top-heavy etc.

88. Your turn

89. Multiplying Fractions
Multiplying fractions is nice and easy – you just multiply across!
3 7 x =

90. Your turn

91. Dividing Fractions
To divide fractions, you first need to flip the second fraction and multiply them.
5 8 ÷ 2 3 =

92. Your turn

97. +, -, x and ÷ top heavy fractions and mixed numbers

98. +

99. -

100. x

101. ÷

104. Homework for next 2

112. Percentages Finding a percentage part without a calculator
Finding a percentage part with a calculator
Writing one number as a percentage of the other

113. Without a calculator
Remember how to find the following amounts and you can then work out any percentage:
50% = divide by 2
25% = divide by 2 again
75%?
10% = divide by 10
20%?
5%?
15%?
1% = divide by 100

115. Without a calculator 20% of 400 = 15% of 60 = 90% of 180 =

116. How do you find a percentage with a calculator?
What is 34% of 812?

117. How do you find a percentage with a calculator?
What is 27% of 540?

118. Make some up

119. Writing one number as a percentage of the other
First write it as a fraction and then multiply it by 100 to turn it into a percentage.
Freddie scored 25 out of 40 on his Maths test. What percentage did he get right?

120. Example:
A DVD contains a film and some extra clips. The film lasts 120 mins.
The clips after the main film last an extra 30 mins.
What % of the DVD is taken up with:
(a) the film (b) the clips?

121. Your turn

122. Percentage Increase and Decrease

123. BRITISH GAS INCREASE PRICES BY 15%
Mr and Mrs Jones,
BILL
3 months = £150
BRITISH GAS INCREASE PRICES BY 15%

124. You could do something like “percentages codebreaker” here to practise increase or decrease, or the following slide or something else.

125. Percentage Profit/Loss
If a value has increased or decreased by an amount and the question asks what this would be as a percentage, this is how you would work it out:
actual increase/decrease x 100
original amount

126. Example:

127. Your turn

128. Going for Gold A fractions, decimals & percentages problem to solve together
The times, in seconds for a 400m hurdle race are shown below • The top 15% get a gold award • The bottom two fifths do not get an award. • Twice as many get bronze awards as silver awards

129. Which times get a gold award?
23.405, , 23.5

130. Which times get a silver award?
23.509, 23.56,

131. Which times get a bronze award?
23.585, 23.6, , 23.67, ,

132. So how do we convert between fractions, decimals and percentages?
Fractions to decimals? Top of fraction divided by bottom Decimals to percentages? x 100 Fractions to percentages Both of the above, one after the other Decimals to fractions 1 decimal place – over 10 2 decimal places – over 100 etc Percentages to decimals ÷ 100 Percentages to fractions a fraction of 100 and cancel if you can MAKE YOUR OWN NOTES ON THE HOMEWORK SHEET

133. Match the Fractions and the Percentages
35%
1/50
120%
7/20
24%
4/5 2%
6/5
80%
6/25

134. Please can you complete the equivalencies table showing the fraction, decimal and percentage for each amount.

135. Reverse Percentages

136. There is a 20% sale on in Topshop. The bag I want is now £60.
What was the original cost of my bag? % 60

137. In a sale, everything is reduced by 30%
In a sale, everything is reduced by 30%. If an armchair costs £175 in the sale, how much did it cost before the sale? %
175

138. A mouse increases its body weight by 15%
A mouse increases its body weight by 15%. If it now weighs 368g, what was the mouse’s original weight? %
368

139. Reverse percentage practice – “scaffolded” sheet or exam questions

140. Compound Interest

141. Definition

142. £2000 earning Compound Interest at 5% per year for 3 years
Original Amount = 100%
Compound Interest = 5%
100% + 5% = 105% = 1.05 3
£2000 x
105%
1.05
= £
This is the total amount including interest: £

143. Mathswatch clip 137
This is based on the method on the previous slide

144. Exam practice here – or the questions on the next slide.

145. Compound Interest Questions
£10,000 earning Compound Interest at 1% per year for 3 years
£8,650 earning Compound Interest at 2% per year for 5 years
£5,000 earning Compound Interest at 0.5% per year for 4 years
£10,000 earning Compound Interest at 1.5% per year for 6 years
£8,000 earning Compound Interest at 3% per year for 7 years

146. The formula to calculate compound interest is:
A = P x (1 + i)n

147. Help is at hand
Website of the week

148. Work with general iterative processes
Start with this next week because it’s kind of revision

149. Homework Mr Corbett’s real life negative number questions
The next 2 slides – negative numbers
Bidmas matching
Equivalences table
4 operations for fractions with mixed numbers
Topic test – basic fractions
Look at mathsgenie website

150. The number in the centre equals = -5 + -3
The number that goes in the top right box is 5 less than -5
The number in the bottom left is -3 x -3
The number in the top left is the number in the centre x -1 add -13
The number in the middle of the bottom row is 6 less than the number above it
There is a number 6 in one of the middle row boxes
There is a number equal to -4 x -5 next to the box containing -5
When you add up the numbers in the right hand column you get -27
The number below -5 is -6-10

151. Copy & Complete; subtract the right hand square from the left to get the square below...5 3 -1 6 4 2 4 -9
-33