1. Find the area of the below circle:
Group the words to the left and use them to work out the question below
Area
Circumference Pi
cm2
Find the area of the below circle:
Radius
Diameter

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:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures. ?

4. UNderline important information in the question.
Thinking Hat UN
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
UNderline important information in the question.

5. Find the area of the shaded part of the shape.
Thinking Hat UN
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
UNderstand what the question is asking me.
Find the area of the shaded part of the shape.

6. πr2, Substitution, Addition, Subtraction, Multiply
Thinking Hat P
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
What maths/ Processes will I be using?
πr2, Substitution, Addition, Subtraction, Multiply

7. Area of small circle: π52 = 25π Area of big circle: r is 5 + 1 = 6m
Thinking Hat A
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
My Answer to the question.
Area of small circle: π52 = 25π
Area of big circle: r is = 6m
π62 = 36π
Area of shaded region:
36π - 25π = 11π
= m2
= 34.6m2

8. C Example: Have I used the correct radii?
Thinking Hat C
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
Have I used the correct radii?
Is my answer smaller than area of both circles?
11π + 25π = 36π

9. Is your writing readable? Does your answer make sense?
Example:
The diagram shows a circular pond with a path around it.
The pond has a radius of 5m.
The path has a width of 1m.
Work out the area of the path.
Give your answer correct to 3 significant figures.
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:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
I am going to UNPACK these Maths Problems! ?

11. UNderline important information in the question.
Now you try:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat UN
UNderline important information in the question.

12. What is the area of the shaded region?
Now you try:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat UN
UNderstand what the question is asking me.
What is the area of the shaded region?

13. πr2, Substitution, Addition, Subtraction, Multiply
Now you try:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat P
What maths/ Processes will I be using?
πr2, Substitution, Addition, Subtraction, Multiply

14. Area of small circle: π22 = 4π Area of two small circles = 8π
Now you try:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat A
My Answer to the question.
Area of small circle: π22 = 4π
Area of two small circles = 8π
Area of big circle: π82 = 64π
Area of shaded region:
64π - 8π = 56π
= cm2
= 175.9cm2

15. C Now you try: Have I used the correct radii?
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat C
Have I used the correct radii?
Is my answer smaller than area of big circle?
56π + 8π = 64π

16. Is your writing readable? Does your answer make sense?
Now you try:
The diagram shows two small circles inside a large circle.
The large circle has a radius of 8cm.
Work out the area of the shaded region.
Give your answer to one decimal place.
Thinking Hat K
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:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
I am going to UNPACK these Maths Problems! ?

18. UNderline important information in the question.
Now you try:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat UN
UNderline important information in the question.

19. How many cm of ribbon is needed to go round the cake?
Now you try:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat UN
UNderstand what the question is asking me.
How many cm of ribbon is needed to go round the cake?

20. πd, Substitution, Multiply
Now you try:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat P
What maths/ Processes will I be using?
πd, Substitution, Multiply

21. Circumference of circle:
Now you try:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat A
My Answer to the question.
Circumference of circle:
π20 =
= 62.8cm

22. C 62.8 ÷ π = 19.98 = 20cm Now you try: Thinking Hat
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat C
62.8 ÷ π = 19.98
= 20cm

23. Is your writing readable? Does your answer make sense?
Now you try:
Susan has a round cake.
The cake has a diameter of 20cm.
Susan wants to put ribbon around the cake.
What is the least length of ribbon she can use?
Give your answer to one decimal place.
Thinking Hat K
I Know my answer makes sense.
Is your writing readable?
Is your method in order?
Does your answer make sense?

24. Part of the roller is a cylinder.
Stretch & Challenge Questions
Q1. Jerry has a new garden roller.
Part of the roller is a cylinder.
The diameter of the cylinder is 0.7m.
Jerry pushes the roller along.
The cylinder goes around exactly 16 times.
Work out how far the roller moves.
Give your answer to 3 significant figures.
(3 Marks)
Stretch & Challenge Questions
Q2. The diagram shows the region inside a running track.
The groundsman is going to cover the region with grass seed.
One sack of grass seed will cover 250m2.
How many sacks of grass seed dose the groundsman need?
You must show all your working out.
(5 Marks)

25. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q1. Jerry has a new garden roller.
Part of the roller is a cylinder.
The diameter of the cylinder is 0.7m.
Jerry pushes the roller along.
The cylinder goes around exactly 16 times.
Work out how far the roller moves.
Give your answer to 3 significant figures.
(3 Marks)
I am going to UNPACK these Maths Problems! ?

26. Part of the roller is a cylinder.
Stretch & Challenge Questions
Q1. Jerry has a new garden roller.
Part of the roller is a cylinder.
The diameter of the cylinder is 0.7m.
Jerry pushes the roller along.
The cylinder goes around exactly 16 times.
Work out how far the roller moves.
Give your answer to 3 significant figures.
(3 Marks)
Answers
Q1. Circumference of circle
π0.7 = m M1
× 16 = m A1
35.2m A1
(3 Marks)

27. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q2. The diagram shows the region inside a running track.
The groundsman is going to cover the region with grass seed.
One sack of grass seed will cover 250m2.
How many sacks of grass seed dose the groundsman need?
You must show all your working out.
(5 Marks)
I am going to UNPACK these Maths Problems! ?

28. Q2. The diagram shows the region inside a running track.
Stretch & Challenge Questions
Q2. The diagram shows the region inside a running track.
The groundsman is going to cover the region with grass seed.
One sack of grass seed will cover 250m2.
How many sacks of grass seed dose the groundsman need?
You must show all your working out.
(5 Marks)
Answers
Q2. Area of semi circles:
π322 ÷ 2 = 512π m2
512π × 2 = 1024π m2 M1
Area of rectangle :
105 × 64 = 6720m2 M1
Area of total shape:
π = m2 M1
÷ 250 = A1
The groundsman will need 40 sacks of grass seed to cover the whole running track. C1
(5 Marks)

29. Work out the shaded area. Give your answer in terms of π.
Stretch & Challenge Questions
Q3. The diagram shows a circle drawn inside a square.
Work out the shaded area.
Give your answer in terms of π.
(4 Marks)
Stretch & Challenge Questions
Q4. Mr Weaver’s garden is in the shape of a rectangle.
Mr Weaver is going to spread fertilizer over all the grass.
One box of fertilizer will cover 25m2 of grass.
How many boxes of fertiliser does Mr Weaver need?
You must show all your working out.
(5 Marks)

30. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q3. The diagram shows a circle drawn inside a square.
Work out the shaded area.
Give your answer in terms of π.
(4 Marks)
I am going to UNPACK these Maths Problems! ?

31. Work out the shaded area. Give your answer in terms of π.
Stretch & Challenge Questions
Q3. The diagram shows a circle drawn inside a square.
Work out the shaded area.
Give your answer in terms of π.
(4 Marks)
Answers
Q3. Area of square
12 × 12 = 144 cm2 M1
Area of circle
π62 = 36π cm2 M1
Area of shaded region
144 – 36π M1
(144 – 36π) ÷ 4 A1
(4 Marks)

32. I am going to UNPACK these Maths Problems!
Stretch & Challenge Questions
Q4. Mr Weaver’s garden is in the shape of a rectangle.
Mr Weaver is going to spread fertilizer over all the grass.
One box of fertilizer will cover 25m2 of grass.
How many boxes of fertiliser does Mr Weaver need?
You must show all your working out.
(5 Marks)
I am going to UNPACK these Maths Problems! ?

33. Mr Weaver is going to spread fertilizer over all the grass.
Stretch & Challenge Questions
Q4. Mr Weaver’s garden is in the shape of a rectangle.
Mr Weaver is going to spread fertilizer over all the grass.
One box of fertilizer will cover 25m2 of grass.
How many boxes of fertiliser does Mr Weaver need?
You must show all your working out.
(5 Marks)
Answers
Q4. Area of rectangle
17 – 2.8 = 14.2m
14.2 × 9.5 = 134.9m2 M1
Area of pond
radius is 3.8 ÷ 2 = 1.9
π1.92 = M1
× 2 =
= m2 M1
÷ 25 = A1
Mr Weaver will need 5 boxes of fertiliser to cover all the grass. C1
(5 Marks)