1. Problem-Solving

2. R U P C ?
Read it! … what’s it about?
Underline it! … find the clues
Picture it! … add? subtract? multiply? divide?
… use a number line to help
Calculate it! … work it out !
How to become a
PROBLEM-CRACKER
in 4 Easy Steps!

3. The Area of a Rectangle …
means … the amount of surface inside
and measured by … the number of squares inside
(eg: square centimetres, square metres, square feet, square yards)
- Or LENGTH X WIDTH
= 10 X 6 = 60
The area is 60 square metres
- Or ROWS X COLUMNS
6 rows of 10 squares = 60
The area is 60 square metres
COUNT THE SQUARES
1, 2, 3, … 59, 60
The area is 60 square metres
10 m
6 m

4. Area Example 1
Easy! Just count the 12 squares
Area = 12 squares centimetres
METHOD 1: COUNT THE SQUARES
USEFUL METHOD WHEN …
- You can see the squares
AND
-there’s not too many to count!

5. What is the area of this
rectangle? …
HOW MANY SQUARES?
Too many squares to count!
Is there an easier way?
You can see there are 6 rows with 10
in each row
= 60 squares
METHOD 2: AREA = ROWS X COLUMNS
USEFUL METHOD WHEN …
- You can see the squares
BUT
-there’s too many to count!
Area Example 2

6. Area Example 3
What is the area of this
rectangle? …
HOW MANY SQUARES?
No squares to count
BUT
7cm means 7 squares fit in each row
5 cm means 5 squares fit in each column
2
Number of squares = length x width
= 7 x 5 = 35 square centimetres
METHOD 3: AREA = LENGTH X WIDTH
USEFUL METHOD WHEN …
- You can’t see the squares
AND
It’s very fast
7 cm
5 cm

7. 9 cm
3 cm
AREA =
LENGTH X WIDTH
AREA = COUNT
THE SQUARES
AREA =
ROWS X COLUMNS
Area: Test Yourself 1
Which
method
best suits
each
problem?

8. AREA =
LENGTH X WIDTH
Area: Test Yourself 1
9 cm
3 cm
= 9 x 3
= 27 cm²
= 4 x 2
= 8 cm²
= 11 x 5
= 55 cm²

9. AREA =
LENGTH X WIDTH
Area Test Yourself 2
AND
which way
works for
ALL 3?
8 cm
5 cm
= 7 x 5
= 35 cm²
= 8 x 5
= 40 cm²
= 3 x 4
= 12 cm²

10. Area– General Rule for all
Rectangles
General Rule:
The area of a rectangle = Length x Width
Or if you like shorthand …
A = L x W

11. The Perimeter of a Rectangle …
means - the distance around the outside
and is measured by - the sum of the lengths of the 4 sides
(eg: millimetres, centimetres, metres, kilometres, feet, yards)
2 LENGTHS + 2 WIDTHS
= 2 X 10 + 2 X 6
= 20 + 12 = 32m
ADD 1 LENGTH + 1 WIDTH
THEN DOUBLE IT
10 + 6 = 16m
2 X 16 = 32m
ADD 4 LENGTHS IN ORDER
10 + 6 + 10 + 6 = 32 m
10m
6m
10m
6m

12. Perimeter
Units of perimeter:
Any units of length
METRIC UNITS
Millimetres mm
Centimetres cm
Kilometres km
IMPERIAL UNITS
Miles
Yards
Feet
Inches

13. STEP 1
Read it !
STEP 2
Underline it !
… and …
LOOK FOR
KEY
NUMBERS!
The history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?WORD CLUE! area
KEY NUMBER!
KEY NUMBER!
… and
WORD
CLUES –
area or
perimeter?

14. AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
Some word clues
to watch out for…
PERIMETER CLUES
edge
edging
outside distance
outside length
perimeter fencing
total outside length
external length

15. STEP 1 Read it !
STEP 2 Underline It !
STEP 3 Picture It! !
The history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?WORD CLUE! area
KEY NUMBER!
KEY NUMBER!
10m
4m
This means
AREA

16. Example 1
STEP 1 Read it !
STEP 2 Underline It !
STEP 3 Picture It! !
STEP 4 Calculate It !
Area of a rectangle = length x width
= 10 x 40
= 40
An area of 40m ² carpet is needed.
10m
4m
The history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?

17. STEP 1
Read it !
STEP 2
Underline it !
… and …
LOOK FOR
KEY
NUMBERS!
The history
classroom is 10m
long and 4m wide.
How much
edging strip is
needed
for the classroom
floor?
WORD CLUE!
perimeter
KEY NUMBER!
KEY NUMBER!
AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
PERIMETER CLUES
edge
edging
outside distance
outside length
perimeter fencing
total outside length
external length
… and
WORD
CLUES –
area or
perimeter?

18. STEP 1 Read it !
STEP 2 Underline It !
STEP 3 Picture It! !
Example 2
10m
4m
10m
4m
The history
classroom is 10m
long and 4m wide.
How much
edging strip is
needed
to go around the
classroom floor?
This means
PERIMETER

19. 10m
4m
10m
4m
Remember – there’s lots of
ways to do this!
For example:
10 + 4 + 10 + 4 = 28
OR
10 + 4 = 14
2 X 14 = 28
OR
10 X 2 = 20 and 4 X 2 = 8
20 + 8 = 28

20. The history room floor
is 12m by 6m.
The project corner is a
1m by 3m rectangle.
The rest is tiled.
How much of the
floor surface is tiled?
WORD CLUE! area
KEY NUMBER!
KEY NUMBERS!

21.  Total Area = 6 + 9 = 15m²
 The tiled area is 15m ²

22. 1m
6m
3m
3m
Example 4
STEP 1 Read it !
STEP 2 Underline It !
STEP 3 Picture It! !
2 Steps so far …
CLICK for Step 3!
EDGING MEANS PERIMETER
But the shape you’re interested in is not
a rectangle!
One way is to start at the top
left-hand corner and write down each
length around the perimeter.
Then ADD.

23. The history room floor
is 12m by 6m.
The carpeted area in
the corner is a
1m by 3m rectangle.
The rest is tiled and
surrounded by
wooden edging.
What length of
edging is needed?

24.  Work out the length of each side and add!
 18m of edging is needed

25. STEP 1
?
STEP 2
?
STEP 3
?
STEP 4
?
Underline It ! Picture It! ! Calculate It !Read it !
6m
1.5m
2m
4m
Problem 1
The history classroom is 9m long and
5m wide.
How carpet is needed to cover the floor?

26. Problem 2
The history classroom is 9m
long and 5m wide.
How edging tape is needed for
the carpet perimeter?

27. A length of 28m edging strip is
needed

28. STEP 1
?
STEP 2
?
STEP 3
?
STEP 4
?
Underline It ! Picture It! ! Calculate It !Read it !
Problem 3
The history classroom floor is
a 12m and 6m rectangle.
The resource corner is 2m x
2m square. How much floor
space is still free?

29. Problem 4
The history classroom floor is a
12m by 6m rectangle.
The resource corner is 2m x 2m
square. A tiled border marks the
perimeter of the remaining floor.
How long is the border?

30. An area of 68m² carpet is needed

31. Problem 6
What length of skirting board
is needed this classroom?
(Remember to allow for the door!)
KEY
Door
(0.5m wide)
15m
7m
6m
11m

32. 43.5m of skirting board is needed.

33. Problem 7
How much floor space is there
in this classroom?
KEY
Door
(1/2 m wide)
10m
7m
5.5m
8m

34. The floor area is 59m²