1. Percentage of a Quantity – Non-Calculator – Complete Lesson
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2. Starter
A task at the beginning of the lesson that reviews a skill required for the learning.
Knowledge Check
Questions to assess students’ current understanding and to consequently show progress.
Real-Life Example
A ‘hook’ to raise interest and provide a concrete example.
Demonstration
Slides for a teacher to lead students – didactically or via questioning – through a mathematical method.
AFL Questions
Assessment For Learning Questions, used to assess students’ competency for independent tasks/activities.
Plenary
An opportunity for students to prove/evaluate their learning.

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4. 25 -5 ÷4
x10
÷10
+30
÷10 x2 4 x3 +8 ÷5 ??

5. STARTER 30% = 70% = 40% = 25% = 34% = 240 ÷ 2 = 500 ÷ 10 = 460 ÷ 10 =
Change these percentages to fractions.
(The first one has been done for you)
240 ÷ 2 =
30% =
= 3 10
500 ÷ 10 =
460 ÷ 10 =
70% =
220 ÷ 10 =
40% =
160 ÷ 4 =
25% =
60 ÷ 4 =
34% =
70 ÷ 4 =

6. STARTER 30% = 70% = 40% = 25% = 34% = 240 ÷ 2 = 120 500 ÷ 10 = 50
Change these percentages to fractions.
(The first one has been done for you)
240 ÷ 2 =
120
30% =
= 3 10
500 ÷ 10 = 50
460 ÷ 10 = 46
70% =
= 7 10
220 ÷ 10 = 22
40% =
= 4 10 = 2 5
160 ÷ 4 = 40
25% =
= 5 20 = 1 4
60 ÷ 4 = 15
34% =
= 17 50
70 ÷ 4 =
17.5

7. Percentage of a Quantity
27 August 2019
Percentage of a Quantity

8. £500 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 = £150
KNOWLEDGE CHECK
David went on holiday with his family.
He took £500 to pay for everything.
Calculate how the money was divided.
£500
Transport: 25%
= £125
Food: 15%
= £75
Accommodation: 30%
= £150
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
Ice Cream: 3%
= £15
Drinks: 7%
= £35
How much was he left with?

9. £500 £100 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75
KNOWLEDGE CHECK
David went on holiday with his family.
He took £500 to pay for everything.
Calculate how the money was divided.
£500
Transport: 25%
= £125
Food: 15%
= £75
Accommodation: 30%
= £150
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
Ice Cream: 3%
= £15
Drinks: 7%
= £35
How much was he left with?
£100

10. Mortgage: Pension: 20% 10% Tax: Charity: 15% 5% Kids: Car Expenses:
Jenny earns £2000 every month.
She is trying to save for a holiday but she has lots of expenses!
Mortgage:
20%
Pension:
10%
Tax:
15%
Charity: 5%
How much can she
save each month?
Kids:
20%
Car Expenses:
20%
She has 10% leftover to save.
10% = £200

11. Jenny earns £2000 every month.
She is trying to save for a holiday but she has lots of expenses!
The total
is 100%
How much can she
save each month?
A percent is a proportion of a whole.
20% = 20 out of 100 pieces =
Percentages are very useful in real-life:
business, bills, shopping, taxes…
She has 10% leftover to save.
10% = £200

12. 1 2 of 20 = 10 Jenny gives 50% of her chocolate bar to Anna.
There are 20 squares, how many does Anna get?
50% = 50 out of 100 = = = 1 2
1 2 of 20 = 10

13. 1 4 of 20 = 5 Joe gives 25% of his chocolate bar to Pete.
There are 20 squares, how many does Pete get?
25% = 25 out of 100 = = = 1 4
1 4 of 20 = 5

14. 1 10 of 20 = 2 Sheila gives 25% of his chocolate bar to James.
There are 20 squares, how many does James get?
10% = 10 out of 100 = = 1 10
1 10 of 20 = 2

15. £8 £4 £4 Josh has £8. He gives 50% to Tom How much does Tom get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Josh has £8.
He gives 50% to Tom
How much does Tom get? £8 £4 £4
Tom gets £4

16. £3 £12 £3 £3 £3 Sally has £12. She gives 25% to Anna
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Sally has £12.
She gives 25% to Anna
How much does Anna get? £3
£12 £3 £3 £3
Anna gets £3

17. 5 50 Jane had £50. She gave 10% to Joe. How much does Joe get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Jane had £50.
She gave 10% to Joe.
How much does Joe get? 50 5
Joe gets £5

18. 120 12 Sarah had £120. She gave 10% to Sam. How much does Sam get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Sarah had £120.
She gave 10% to Sam.
How much does Sam get?
120 12
Sam gets £12

19. 40 4 Polly had £40. She gave 20% to Mark. How much does Mark get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Polly had £40.
She gave 20% to Mark.
How much does Mark get? 40 4
Mark gets £8

20. 60 6 Anna had £60. She gave 30% to Polly. How much does Polly get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Anna had £60.
She gave 30% to Polly.
How much does Polly get? 60 6
Polly gets £18

21. 20 2 Mary had £20. She gave 60% to Tim. How much does Tim get?
50% = 1 2
25% = 1 4
10% = 1 10
Remember!
Mary had £20.
She gave 60% to Tim.
How much does Tim get? 20 2
Tim gets £12

22. 40 4 Jane had £40. 10% How much is…. How much is…. How can we find 5%?
10%?
50%?
How much is….
20%?
25%?
15%?
40%?
75%?
95%?
60%?
35%?
85%?
70%?
45%?
How can we find 1%?

23. 40 4 Jane had £40. 10% How much is…. How much is…. How can we find 5%?
10%? £4
50%?
£20
How much is….
20%? £8
25%?
£10
15%? £6
40%?
£16
75%?
£30
95%?
£38
60%?
£24
35%?
£14
85%?
£34
70%?
£28
45%?
£18
How can we find 1%?

24. Percentage of a Quantity
Alice had £80.
Complete the boxes showing 50%, 25% and 10%.
Use the bar models to help you answer the questions.
a) 20% = £
100% = £80
b) 30% = £
50% = £40
c) 60% =
25%
£20
d) 40% =
10% £8
e) 75% =
f) 65% =
100% = £140
50% = £70
£35
Tom had £140.
Complete the bar models and
use them to
answer the questions.
a) 20% =
d) 30% =
g) 5% =
b) 40% =
e) 75% =
h) 15% =
c) 70% =
f) 35% =
i) 35% =
Tim had £120.
He gave 30% to Sally, 25% of Tom,
15% to David and £20 to John.
How much did he have left?

25. Percentage of a Quantity
Alice had £80.
Complete the boxes showing 50%, 25% and 10%.
Use the bar models to help you answer the questions.
a) 20% = £16
100% = £80
b) 30% = £24
50% = £40
c) 60% = £48
25%
£20
d) 40% = £32
10% £8
e) 75% = £60
f) 65% = £52
100% = £140
50% = £70 £70
£35
Tom had £140.
Complete the bar models and
use them to
answer the questions. 35 14 7
a) 20% = £28
d) 30% = £42
g) 5% = £7
b) 40% = £56
e) 75% = £105
h) 15% = £21
c) 70% = £98
f) 35% = £49
i) 35% = £49
Tim had £120.
He gave 30% to Sally, 25% of Tom,
15% to David and £20 to John.
How much did he have left?
30% = £36
25% = £30
15% = £18
£20
= £104
Answers
He had
£16 left.

26. Percentage of a Quantity Percentage of a Quantity
Alice had £80.
Complete the boxes showing 50%, 25% and 10%.
Use the bar models to help you answer the questions.
Alice had £80.
Complete the boxes showing 50%, 25% and 10%.
Use the bar models to help you answer the questions.
a) 20% = £
a) 20% = £
100% = £80
100% = £80
b) 30% = £
b) 30% = £
50% = £40
50% = £40
c) 60% =
c) 60% =
25%
£20
25%
£20
d) 40% =
d) 40% =
10% £8
e) 75% =
10% £8
e) 75% =
f) 65% =
f) 65% =
100% = £140
100% = £140
50% = £70
50% = £70
£35
Tom had £140.
Complete the bar models and
use them to
answer the questions.
£35
Tom had £140.
Complete the bar models and
use them to
answer the questions.
a) 20% =
d) 30% =
g) 5% =
a) 20% =
d) 30% =
g) 5% =
b) 40% =
e) 75% =
h) 15% =
b) 40% =
e) 75% =
h) 15% =
c) 70% =
f) 35% =
i) 35% =
c) 70% =
f) 35% =
i) 35% =
Tim had £120.
He gave 30% to Sally, 25% of Tom,
15% to David and £20 to John.
How much did he have left?
Tim had £120.
He gave 30% to Sally, 25% of Tom,
15% to David and £20 to John.
How much did he have left?

27. How can we quickly find 25%?
100%
÷ 2
50%
50%
÷ 2
25%
25%

28. How can we quickly find 5%?
100%
÷ 10
10%
÷ 2 5%

29. How can we quickly find 1%?
100%
÷ 10
10%
÷ 10 1%

30. Sam stole 60% of
the money from the safe!
$400
How can we calculate how much that is?
Addition
Multiplication
50% = $200
10% = $440 +
10% = $240
× 6
× 6
60% = $240
60% = $240
Which method do you prefer?

31. Sam stole 70% of
the money from the safe!
$500
Addition
Multiplication
50% = $250
10% = $450 +
10% = $250
× 7
× 7 +
10% = $250
70% = $350
70% = $350

32. Multiplication & Addition
Sam stole 35% of
the money from the safe!
$300
Addition
Multiplication & Addition
25% = $275
10% = $430 +
10% = $230
× 3
× 3
30% = $090
35% = $105 +
5% = $215
35% = $105

33. Multiplication & Addition
Sam stole 13% of
the money from the safe!
$600
Multiplication & Addition
10% = $460
31% = $436
× 3
× 3
43% = $018
13% = $078

34. Multiplication & Addition
Sam stole 28% of
the money from the safe!
$800
Multiplication & Addition
10% = $480
× 2
× 2
20% = $160
31% = $438
× 8
× 8
48% = $064
28% = $224

35. Use combinations of bags to find:
÷ 2
÷ 2
100%
50%
25%
$800
$400
$200
÷ 2
÷ 10
Use combinations of bags to find:
÷ 2
40%
60%
55%
35%
46%
18%
77%
34.5%
10% 5%
$80
$40
÷ 10 1% $8

36. Use combinations of bags to find:
÷ 2
÷ 2
100%
50%
25%
$800
$400
$200
÷ 2
÷ 10
Use combinations of bags to find:
÷ 2
40%
$320
60%
$480
55%
$440
35%
$280
46%
$368
18%
$144
77%
$616
34.5%
$276
10% 5%
$80
$40
÷ 10 1% $8
Answers

37. How would you calculate the answer?
Find 27%
of $400.
How would you calculate the answer?

38. Find 27% of $400. Todd Anne May Tim Jim Find 25% 1% × 2 = 2%
Add them together!
10% × 2 = 20%
Find 5%
1% × 2 = 2%
Add them together!
Anne
May
Find 27%
of $400.
Find 1% and multiply by 27!
10% × 2 = 20%
1% × 7 = 7%
Add them together!
Tim
Jim
10% × 3 = 30%
1% × 3 = 3%
Subtract 3% from 30%!

39. Use the common percentages to help.
100% = 400
20% =
40% =
55% =
15% =
35% =
11% =
21% =
61% =
50% = 200
10% = 40
5% = ?
1% = ?
100% = 600
100% = 150
30% =
21% =
95% =
938% =
70% =
94% =
35% =
994% =
95% =
99% =
97% =
965% =
15% =
53% =
23% =
123% =
35% =
74% =
66% =
43.5% =

40. Use the common percentages to help.
100% = 400
20% = 80
40% = 160
55% = 220
15% = 60
35% = 140
11% = 44
21% = 84
61% = 244
50% = 200
10% = 40
5% = ?
1% = ?
100% = 600
100% = 150
30% = 180
21% = 126
95% = 7.5
938% = 57
70% = 420
94% = 24
35% = 52.5
994% = 141
95% = 30
99% = 54
97% = 10.5
965% = 97.5
15% = 90
53% = 318
23% = 34.5
123% = 184.5
35% = 210
74% = 444
66% = 99
43.5% = 65.25

41. Use the common percentages to help.
100% = 160
30% =
60% =
65% =
25% =
85% =
12% =
23% =
47% =
50% = 80
10% = 16
5% = ?
1% = ?
100% = 80
100% = 150
40% =
31% =
97% =
138% =
60% =
97% =
38% =
171% =
95% =
19% =
79% =
10.5% =
15% =
58% =
94% =
24.5% =
35% =
67% =
63% =
17.4% =

42. Use the common percentages to help.
100% = 160
30% = 48
60% = 96
65% = 104
25% = 40
85% = 136
12% = 19.2
23% = 36.8
47% = 75.2
50% = 80
10% = 16
5% = ?
1% = ?
100% = 80
100% = 150
40% = 32
31% = 24.8
97% = 10.5
138% = 207
60% = 48
97% = 5.6
38% = 57
171% = 256.5
95% = 4
19% = 15.2
79% = 118.5
10.5% = 15.75
15% = 12
58% = 46.4
94% = 141
24.5% = 36.75
35% = 28
67% = 53.6
63% = 94.5
17.4% = 26.1

43. Percentage of a Quantity
A) Calculate the value of each size bag (the first has been done for you).
Use these percentages to calculate your answers.
$150
$300
50%
10% 5% 1%
How much is…
40%?
25%?
15%?
60%?
8%?
19%?
43%?
6%?
82%?
79%?
5.5%?
57%?
B) Complete the table. Calculate common percentages (10%, 5%, 1%) first.
20%
45%
11%
53%
79%
0.5%
300
4000
160 60
C) All these clothes are on sale.
What is their new price?
Jeans
Were: £60
3% off!
Now:
Hoodie
Was: £76
84% off!
Now:
Shirt
Was: £60
40% off!
Now: £
T-Shirt
Was: £30
15% off!
Now: £
Dress
Was: £55
24% off!
Now:
Underpants
Were: £4.50
37% off!
Now:

44. Percentage of a Quantity
A) Calculate the value of each size bag (the first has been done for you).
Use these percentages to calculate your answers.
$150
$30
$15 $3
$300
50%
10% 5% 1%
$180
How much is…
$18
$171
40%?
25%?
15%?
60%?
8%?
19%?
43%?
6%?
82%?
79%?
5.5%?
57%?
$120
$24
$246
$75
$57
$237
$45
$129
$16.50
B) Complete the table. Calculate common percentages (10%, 5%, 1%) first.
20%
45%
11%
53%
79%
0.5%
300 60
135 33
159
237
1.5
4000
800
1800
440
2120
3160 20
160 32 72
17.6
84.8
126.4
0.8 12 27
6.6
31.8
47.4
0.3
C) All these clothes are on sale.
What is their new price?
Jeans
Were: £60
3% off!
Now:
Hoodie
Was: £76
84% off!
Now:
£58.20
£12.16
Shirt
Was: £60
40% off!
Now: £
T-Shirt
Was: £30
15% off!
Now: £
Dress
Was: £55
24% off!
Now:
Underpants
Were: £4.50
37% off!
Now:
Answers
£36
£25.50
£41.80
£2.84

45. Percentage of a Quantity Percentage of a Quantity
A) Calculate the value of each size bag (the first has been done for you).
Use these percentages to calculate your answers.
A) Calculate the value of each size bag (the first has been done for you).
Use these percentages to calculate your answers.
$150
$150
$300
$300
50%
10% 5% 1%
50%
10% 5% 1%
How much is…
How much is…
40%?
25%?
15%?
60%?
8%?
19%?
43%?
6%?
82%?
79%?
5.5%?
57%?
40%?
25%?
15%?
60%?
8%?
19%?
43%?
6%?
82%?
79%?
5.5%?
57%?
B) Complete the table. Calculate common percentages (10%, 5%, 1%) first.
B) Complete the table. Calculate common percentages (10%, 5%, 1%) first.
20%
45%
11%
53%
79%
0.5%
300
4000
160 60
20%
45%
11%
53%
79%
0.5%
300
4000
160 60
C) All these clothes are on sale.
What is their new price?
Jeans
Were: £60
3% off!
Now:
C) All these clothes are on sale.
What is their new price?
Hoodie
Was: £76
84% off!
Now:
Jeans
Were: £60
3% off!
Now:
Hoodie
Was: £76
84% off!
Now:
Shirt
Was: £60
40% off!
Now: £
Shirt
Was: £60
40% off!
Now: £
T-Shirt
Was: £30
15% off!
Now: £
T-Shirt
Was: £30
15% off!
Now: £
Dress
Was: £55
24% off!
Now:
Underpants
Were: £4.50
37% off!
Now:
Dress
Was: £55
24% off!
Now:
Underpants
Were: £4.50
37% off!
Now:

46. £500 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 = £150
KNOWLEDGE CHECK
David went on holiday with his family.
He took £500 to pay for everything.
Calculate how the money was divided.
£500
Transport: 25%
= £125
Food: 15%
= £75
Accommodation: 30%
= £150
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
Ice Cream: 3%
= £15
Drinks: 7%
= £35
How much was he left with?

47. £500 £100 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75
KNOWLEDGE CHECK
David went on holiday with his family.
He took £500 to pay for everything.
Calculate how the money was divided.
£500
Transport: 25%
= £125
Food: 15%
= £75
Accommodation: 30%
= £150
Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson.
Ice Cream: 3%
= £15
Drinks: 7%
= £35
How much was he left with?
£100

48. £24 60 100 × 40 40 100 ×60 = What is 60% of £40? What is 40% of £60?
What’s interesting about the answers?
Can you explain why?
× 40
×60 =
It works for any percentage!
Try these…
30% of £50 =
£15
24% of £50 =
£12
85% of £20 =
£17
90% of £20 =
£18
18% of £25 =
£4.50
180% of £3 =
£5.40

49. Check your success!
I can calculate 10% and 5% of a quantity and use that to find other percentages.
I can calculate
whole number percentages (13%, 72%).
I can calculate the cost of items on sale.

50. Check your success!
I can calculate 10% and 5% of a quantity and use that to find other percentages.
I can calculate
whole number percentages (13%, 72%).
I can calculate the cost of items on sale.

51. How to calculate 43% of a quantity.
Write a text message to a friend describing…
How to calculate 43% of a quantity.

52. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to