1. Problem-SolvingProblem-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 becomeHow to become aa
PROBLEM-CRACKERPROBLEM-CRACKER
inin 4 Easy Steps!4 Easy Steps!

3. The Area of a Rectangle …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- Or LENGTH X WIDTH
= 10 X 6 = 60
The area is 60 square metresThe area is 60 square metres
- Or ROWS X COLUMNS- Or ROWS X COLUMNS
6 rows of 10 squares = 60
The area is 60 square metresThe area is 60 square metres
COUNT THE SQUARESCOUNT THE SQUARES
1, 2, 3, … 59, 601, 2, 3, … 59, 60
The area is 60 square metresThe area is 60 square metres
10 m
6 m

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

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

6. Area Example 3Area Example 3
What is the area of this
rectangle? …
HOW MANY SQUARES?
What is the area of this
rectangle? …
HOW MANY SQUARES?
No squares to countNo squares to count
BUTBUT
7cm means 7 squares fit in each row7cm means 7 squares fit in each row
5 cm means 5 squares fit in each column5 cm means 5 squares fit in each column
22
Number of squares = length x widthNumber of squares = length x width
= 7 x 5 = 35 square centimetres= 7 x 5 = 35 square centimetres
METHOD 3: AREA = LENGTH X WIDTHMETHOD 3: AREA = LENGTH X WIDTH
USEFUL METHOD WHEN …USEFUL METHOD WHEN …
- You can- You can’’t see the squarest see the squares
ANDAND
ItIt’’s very fasts very fast
7 cm
5 cm

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

8. AREA =AREA =
LENGTH X WIDTHLENGTH X WIDTH
Area: Test Yourself 1Area: Test Yourself 1
9 cm
3 cm
= 9 x 3= 9 x 3
= 27 cm= 27 cm²²
= 4 x 2= 4 x 2
= 8 cm= 8 cm²²
= 11 x 5= 11 x 5
= 55 cm= 55 cm²²

9. AREA =AREA =
LENGTH X WIDTHLENGTH X WIDTH
Area Test Yourself 2Area Test Yourself 2
AND
which way
works for
ALL 3?
AND
which way
works for
ALL 3?
8 cm
5 cm
= 7 x 5= 7 x 5
= 35 cm= 35 cm²²
= 8 x 5= 8 x 5
= 40 cm= 40 cm²²
= 3 x 4= 3 x 4
= 12 cm= 12 cm²²

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

11. The Perimeter of a Rectangle …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 WIDTHS2 LENGTHS + 2 WIDTHS
= 2 X 10 + 2 X 6= 2 X 10 + 2 X 6
= 20 + 12 = 32m
ADD 1 LENGTH + 1 WIDTHADD 1 LENGTH + 1 WIDTH
THEN DOUBLE ITTHEN DOUBLE IT
10 + 6 = 16m10 + 6 = 16m
2 X 16 = 32m2 X 16 = 32m
ADD 4 LENGTHS INADD 4 LENGTHS IN
ORDERORDER
10 + 6 + 10 + 6 = 32 m10 + 6 + 10 + 6 = 32 m
10m
6m
10m
6m

12. PerimeterPerimeter
Units of perimeter:Units of perimeter:
Any units of lengthAny units of length
METRIC UNITSMETRIC UNITS
Millimetres mmMillimetres mm
Centimetres cmCentimetres cm
Kilometres kmKilometres km
IMPERIAL UNITSIMPERIAL UNITS
MilesMiles
YardsYards
FeetFeet
InchesInches

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 ²² 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 2Example 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
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 1Problem 1
The history classroom is 9m long andThe history classroom is 9m long and
5m wide.5m wide.
How carpet is needed to cover theHow carpet is needed to cover the
floor?floor?

26. Problem 2Problem 2
The history classroom is 9mThe history classroom is 9m
long and 5m wide.long and 5m wide.
How edging tape is neededHow edging tape is needed
for the carpet perimeter?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 3Problem 3
The history classroom floorThe history classroom floor
is a 12m and 6m rectangle.is a 12m and 6m rectangle.
The resource corner is 2m xThe resource corner is 2m x
2m square. How much floor2m square. How much floor
space is still free?space is still free?

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

30. An area of 68m² carpet is needed

31. Problem 6Problem 6
What length of skirting boardWhat length of skirting board
is needed this classroom?is needed this classroom?
(Remember to allow for the door!)(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 7Problem 7
How much floor space isHow much floor space is
there in this classroom?there in this classroom?
KEY
Door
(1/2 m
wide)
10m
7m
5.5m
8m

34. The floor area is 59m²