1. Use the hats to explain how you change from FDP
÷ 100
2/5
Equivalent fractions (out of 100)
40%
Copy and complete:
Fraction
Decimal
Percentage
1/10
0.25
34%
1/3
0.125
Numerator
0.40

2. I am going to UNPACK these Maths Problems!
UNderline important information in the question.
UNderstand what the question is asking me.
What maths/ Processes will I be using?
My Answer to the question.
I Know my answer makes sense.

3. I am going to UNPACK these Maths Problems!
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
3 4 kg of sand will be put into each bag.
(a) Write as a percentage.
(b) How many bags can be filled with sand from the container? ?

4. UNderline important information in the question.
Thinking Hat UN
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
UNderline important information in the question.

5. UNderstand what the question is asking me.
Thinking Hat UN
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
UNderstand what the question is asking me.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can
be filled with sand?

6. Fractions, Percentages, Divide, Factors, Multiply
Thinking Hat P
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
What maths/ Processes will I be using?
Fractions, Percentages, Divide, Factors, Multiply

7. My Answer to the question.
Thinking Hat A
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
My Answer to the question.
(a) 𝟑 𝟒 × 100 = 75%
(b) 𝟑 𝟒 is 0.75
8 ÷ 0.75 = 10.6…g
10 full bags of sand.

8. C Example: ¾ kg of sand will be put into each bag.
Thinking Hat C
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
(a) 75% = 𝟕𝟓 𝟏𝟎𝟎 = 𝟑 𝟒
(b) 10 x 0.75 = 7.5kg

9. Is your writing readable? Does your answer make sense?
Example:
There are 8kg of sand in a container.
The sand is going to be put into bags.
¾ kg of sand will be put into each bag.
(a) Write 𝟑 𝟒 as a percentage.
(b) How many bags can be filled with sand from the container?
Thinking Hat K
I Know my answer makes sense.
Is your writing readable?
Is your method in order?
Does your answer make sense?

10. I am going to UNPACK these Maths Problems!
Now you try:
3 8 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
I am going to UNPACK these Maths Problems! ?

11. UNderline important information in the question.
Thinking Hat UN
Now you try:
𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
UNderline important information in the question.

12. What percentage of the people are children?
Thinking Hat UN
Now you try:
𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
UNderstand what the question is asking me.
What percentage of the people are children?

13. Fractions, Percentages, Multiply, Subtract, Addition
Thinking Hat P
Now you try:
𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
What maths/ Processes will I be using?
Fractions, Percentages, Multiply, Subtract, Addition

14. My Answer to the question.
Thinking Hat A
Now you try:
𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
My Answer to the question.
Men 𝟑 𝟖 × 100 = 37.5%
Women are 27%
= 64.5 %
100 – 64.5 = 35.5%
35.5% are children

15. C Now you try: 𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
Thinking Hat C
= 62.5
100 – 62.5 = 37.5
37.5 ÷ 100 = 𝟑 𝟖

16. Is your writing readable? Does your answer make sense?
Thinking Hat K
Now you try:
𝟑 𝟖 of the people at a football match are men.
27% of the people at the match are women.
The rest of the people at the match are children.
Work out what percentage of the people at the match are children.
I Know my answer makes sense.
Is your writing readable?
Is your method in order?
Does your answer make sense?

17. I am going to UNPACK these Maths Problems!
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
3 5 of the boys walk to school.
2 3 of the girls walk to school. 
Work out how many pupils walk to school.
I am going to UNPACK these Maths Problems! ?

18. UNderline important information in the question.
Thinking Hat UN
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
UNderline important information in the question.

19. How many pupils in total walk to school?
Thinking Hat UN
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
UNderstand what the question is asking me.
How many pupils in total walk to school?

20. Fractions, Divide, Multiply, Subtract, Addition
Thinking Hat P
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
What maths/ Processes will I be using?
Fractions, Divide, Multiply, Subtract, Addition

21. 120 + 117 = 237 pupils walk to school
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
Thinking Hat A
My Answer to the question.
375 – 195 = 180 girls
𝟑 𝟓 × 195 = 117
𝟐 𝟑 × 180 = 120
= 237 pupils walk to school

22. C Now you try: Thinking Hat There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
Thinking Hat C
𝟐 𝟓 × 195 = 78
𝟏 𝟑 × 180 = 60
= 138
= 375

23. Is your writing readable? Does your answer make sense?
Thinking Hat K
Now you try:
There are 375 pupils at a school.
195 of the pupils are boys.
𝟑 𝟓 of the boys walk to school.
𝟐 𝟑 of the girls walk to school. 
Work out how many pupils walk to school.
I Know my answer makes sense.
Is your writing readable?
Is your method in order?
Does your answer make sense?

24. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q1. There are 24 passengers on a bus.
1 4 of the passengers are men.
1 3 of the passengers are women.
The rest of the passengers are children.
How many passengers are children?
(3 Marks)
Q2. There are 60 beads in a bag. The beads are red, yellow or blue.
40% of the beads are blue.
of the beads are red.
How many beads are yellow?
I am going to UNPACK these Maths Problems! ?

25. Q1. There are 24 passengers on a bus. 1 4 of the passengers are men.
Stretch & Challenge Questions
Q1. There are 24 passengers on a bus.
1 4 of the passengers are men.
1 3 of the passengers are women.
The rest of the passengers are children.
How many passengers are children?
(3 Marks)
Q2. There are 60 beads in a bag. The beads are red, yellow or blue.
40% of the beads are blue.
of the beads are red.
How many beads are yellow?
Answers
Q ÷ 4 = 6 M1
24 ÷ 3 = 8 M1
8+ 6 = 14
24 – 14 = 10 A1
(3 Marks)
Q2. 60 × 𝟒𝟎 𝟏𝟎𝟎 = 24 M1
𝟓 𝟏𝟐 × 60 = 25 M1
= 49
60 – 49 = 11 A1

26. Stretch & Challenge Questions
Q3. £54 inheritance money is split between Abi, Babs and Caz in the ratio 1:3:2.
Abi gives 80% of her money to charity.
Babs gives 0.25 of her money to the same charity.
Caz also gives of her money to the charity.
(a) How much money in total do the girls donate to charity?
(6)
(b) Express the amount of money they give to charity as a percentage of the
inherited amount to 1 decimal place.
(2)
(8 Marks)
Stretch & Challenge Questions
Q4. At the Redbridge School, of pupils have a pet dog, have a cat and have a hamster.
The rest have no pets.
(a) What fraction of the children have no pets? Write this in its simplest form.
(3)
(b) There are 250 pupils at the Redbridge School. How many children have no pets?
(2)
(c) At the Bluebell School, 23% have no pets. What percentage increase of pupils at the Bluebell School have no pets compared to the Redbridge School?
(7 Marks)

27. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q3. £54 inheritance money is split between Abi, Babs and Caz in the ratio 1:3:2.
Abi gives 80% of her money to charity.
Babs gives 0.25 of her money to the same charity.
Caz also gives of her money to the charity.
(a) How much money in total do the girls donate to charity?
(6)
(b) Express the amount of money they give to charity as a percentage of the
inherited amount to 1 decimal place.
(2)
(8 Marks)
I am going to UNPACK these Maths Problems! ?

28. Stretch & Challenge Questions
Q3. £54 inheritance money is split between Abi, Babs and Caz in the ratio 1:3:2.
Abi gives 80% of her money to charity.
Babs gives 0.25 of her money to the same charity.
Caz also gives of her money to the charity.
(a) How much money in total do the girls donate to charity?
(6)
(b) Express the amount of money they give to charity as a percentage of the
inherited amount to 1 decimal place.
(2)
(8 Marks)
Answers
Q3.
(a) = 6 M1
54 ÷ 6 = 9 1 part M1
Abi 1 × 9 = £9
Babs 3 × 9 = £27
Caz 2 × 9 = £18 A1
Abi 9 × 𝟖𝟎 𝟏𝟎𝟎 = £ M1
Babs 27 ÷ 4 = £6.75
Caz 𝟐 𝟗 × 18 = £4 A1
= £ A1
(6)
(b) 𝟏𝟕.𝟗𝟓 𝟓𝟒 M1
𝟏𝟕.𝟗𝟓 𝟓𝟒 × 100 = 33.2% A1
(2)
(8 Marks)

29. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q4. At the Redbridge School, of pupils have a pet dog, have a cat and have a hamster.
The rest have no pets.
(a) What fraction of the children have no pets? Write this in its simplest form.
(3)
(b) There are 250 pupils at the Redbridge School. How many children have no pets?
(2)
(c) At the Bluebell School, 23% have no pets. What percentage increase of pupils at the Bluebell School have no pets compared to the Redbridge School?
(7 Marks)
I am going to UNPACK these Maths Problems! ?

30. Stretch & Challenge Questions
Q4. At the Redbridge School, of pupils have a pet dog, have a cat and have a hamster.
The rest have no pets.
(a) What fraction of the children have no pets? Write this in its simplest form.
(3)
(b) There are 250 pupils at the Redbridge School. How many children have no pets?
(2)
(c) At the Bluebell School, 23% have no pets. What percentage increase of pupils at the Bluebell School have no pets compared to the Redbridge School?
(7 Marks)
Answers
Q3.
(a) 𝟏 𝟑 + 𝟐 𝟓 + 𝟏 𝟏𝟓 = 𝟓+𝟔+𝟏 𝟏𝟓 = 𝟏𝟐 𝟏𝟓 M2
1 - 𝟏𝟐 𝟏𝟓 = 𝟑 𝟏𝟓 = 𝟏 𝟓 A1
(3)
(b) 𝟏 𝟓 × 250 = 50 M1; A1
(2)
(c) 𝟓𝟎 𝟐𝟓𝟎 × 100 = 20% M1
23 – 20 = 3% A1
(7 Marks)