Problem-SolvingProblem-Solving
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 How to become aa PROBLEM-CRACKERPROBLEM-CRACKER
inin 4 Easy Steps! 4 Easy Steps!
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 The area is 60 square metresmetres
- Or ROWS X COLUMNS- Or ROWS X COLUMNS
6 rows of 10 squares = 60
The area is 60 square The area is 60 square metresmetres
COUNT THE SQUARESCOUNT THE SQUARES
1, 2, 3, … 59, 601, 2, 3, … 59, 60
The area is 60 square The area is 60 square metresmetres
10 m
6 m
Area Example 1 Area 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!
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 You can see there are 6 rows with 10 in each row 10 in each row = 60 squares= 60 squares
METHOD 2: AREA = ROWS X METHOD 2: AREA = ROWS X COLUMNSCOLUMNS
USEFUL METHOD WHEN …USEFUL METHOD WHEN …
- You can see the squares - You can see the squares
BUT BUT
-therethere’’s too many to count!s too many to count!
Area Example 2Area Example 2
Area Example 3 Area 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 column 5 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 squares t see the squares
ANDAND
ItIt’’s very fasts very fast
7 cm
5 cm
9 cm
3 cm
AREA = AREA =
LENGTH X WIDTHLENGTH X WIDTH
AREA = COUNT AREA = COUNT THE SQUARES THE 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?
AREA = AREA =
LENGTH X WIDTHLENGTH X WIDTH
Area: Test Yourself 1Area: Test Yourself 19 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
AREA = AREA =
LENGTH X WIDTHLENGTH X WIDTH
Area Test Yourself 2Area Test Yourself 2
ANDwhich way works for
ALL 3?
ANDwhich 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
Area– General Rule for all Area– General Rule for all RectanglesRectangles
General Rule:General Rule:
The area of a rectangle = Length x The area of a rectangle = Length x WidthWidth
Or if you like shorthand …Or if you like shorthand …
A = L x WA = L x W
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 WIDTHS 2 LENGTHS + 2 WIDTHS
= 2 X 10 + 2 X 6= 2 X 10 + 2 X 6
= 20 + 12 = 32m
ADD 1 LENGTH + 1 ADD 1 LENGTH + 1 WIDTH THEN DOUBLE ITWIDTH THEN DOUBLE IT
10 + 6 = 16m10 + 6 = 16m
2 X 16 = 32m2 X 16 = 32m
ADD 4 LENGTHS IN ADD 4 LENGTHS IN ORDERORDER
10 + 6 + 10 + 6 = 32 m10 + 6 + 10 + 6 = 32 m10m
6m
10m
6m
PerimeterPerimeterUnits 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
Miles Miles
YardsYards
FeetFeet
InchesInches
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?
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
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
Example 1STEP 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
4mThe history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?
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?
STEP 1 Read it !
STEP 2 Underline It !
STEP 3 Picture It! !
Example 2Example 2
10m
4m
10m
4mThe history
classroom is 10m
long and 4m wide.
How much edging strip is
needed to go around the classroom floor?
This means PERIMETER
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
The history room floor
is 12m by 6m.
The project corner is a
1m by 3m rectangle.
The rest is tiled.
How much of thefloor surface is
tiled?
WORD CLUE! area
KEY NUMBER!
KEY NUMBERS!
Total Area = 6 + 9 = 15m²
The tiled area is 15m ²
1m
6m
3m
3m
Example 4STEP 1 Read
it !
STEP 2 Underline It !
STEP 3 Picture It! !
2 Steps so far …
CLICK for Step 3!
EDGING MEANS PERIMETERBut 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.
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?
Work out the length of each side and add!
18m of edging is needed
STEP 1
?
STEP 2
?
STEP 3
?
STEP 4
?Underline It !
Picture It! ! Calculate It !
Read it !
6m
1.5m2m
4m
Problem 1Problem 1 The history classroom is 9m long The history classroom is 9m long
and 5m wide.and 5m wide.
How carpet is needed to cover the How carpet is needed to cover the floor?floor?
Problem 2Problem 2 The history classroom is The history classroom is 9m long and 5m wide.9m long and 5m wide.
How edging tape is needed How edging tape is needed for the carpet perimeter?for the carpet perimeter?
A length of 28m edging strip is needed
STEP 1
?
STEP 2
?
STEP 3
?
STEP 4
?Underline It !
Picture It! ! Calculate It !
Read it !
Problem 3Problem 3
The history classroom floor The history classroom floor is a 12m and 6m rectangle.is a 12m and 6m rectangle.
The resource corner is 2m The resource corner is 2m x 2m square. How much x 2m square. How much floor space is still free?floor space is still free?
Problem 4Problem 4
The history classroom floor is a The history classroom floor is a 12m by 6m rectangle.12m by 6m rectangle.
The resource corner is 2m x The resource corner is 2m x 2m square. A tiled border 2m square. A tiled border
marks the perimeter of the marks the perimeter of the remaining floor. How long is remaining floor. How long is
the border?the border?
An area of 68m² carpet is needed
Problem 6Problem 6What length of skirting What length of skirting
board is needed this board is needed this classroom?classroom?
(Remember to allow for the door!)(Remember to allow for the door!)KEY
Door
(0.5m wide)
15m
7m 6m
11m
43.5m of skirting board is needed.
Problem 7Problem 7How much floor space is How much floor space is there in this classroom? there in this classroom?
KEY
Door (1/2 m wide)
10m
7m5.5m
8m
The floor area is 59m²