Transcript Slide 1

Problem-Solving
Pupils’ Version
Bridging the Gap
Note to Pupils
Do you know the difference between
Area and Perimeter?
Do you have problems knowing how to get started on tricky
maths problems?
This resource will help you to…
- Learn about the area and perimeter of rectangles
- and shapes made from them
- and become an expert at cracking problems!
- Using a simple 4-step guide to problem-solving!
Contents
A.
Learning Area
(Start here to revise your learning)
B.
Test Yourself: Now It’s Your Turn!
(Start here if you just want to test yourself)
C.
Where To Next?
(Suggestions for main menu)
(TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE)
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Slide Show > View Show
Which One Are You ???
R U a Problem-Coward ?
… or …
PROBLEM!
R U a Problem-Cracker?
R U PC?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now you’re
How to become aready to try
out some
PROBLEM-CRACKER
problems!
in 4 Easy Steps!
RU PC?
Read it! … what’s it about?
But first …
Underline it! … find the clues
Check out the
Picture it! … add? subtract? multiply? divide?
basics about
… use a number line to help
Calculate it! … work it out !
areas and
perimeters of
rectangles …
The Area of a Rectangle …
means …
the amount of
surface
How
doinside
you
and measured by … the number of squares inside
find area?
(eg: square centimetres, square metres, square feet, square yards)
COUNT THE SQUARES
1, 2, 3, … 59, 60
The area is 60 square metres
- Or ROWS X COLUMNS
6 rows of 10 squares = 60
The area is 60 square metres
- Or LENGTH X WIDTH
= 10 X 6 = 60
The area is 60 square metres
Here are
10 m
some ways
you might
have met …
But
which way
is best?
6m
Area Example 1
What is the area of this
rectangle? …
HOW MANY SQUARES?
METHOD 1: COUNT THE SQUARES
Easy! Just count the 12 squares
USEFUL METHOD WHEN …
see thecentimetres
squares
Area -=You
12 can
squares
AND
-there’s not too many to count!
Area Example 2
What is the area of this
rectangle? …
HOW MANY SQUARES?
METHOD
2: AREA
Too many
squares=toROWS
count! X COLUMNS
Is there
an
easier
way?
USEFUL METHOD WHEN …
- You can see the squares
You can see there are 6 rows with 10
BUT
in each row
-there’s
too many to count!
=
60 squares
Area Example 3
7 cm
What is the area of this
rectangle? …
5 cm
HOW MANY SQUARES?
No squares to count
METHOD 3: AREA = LENGTH X WIDTH
BUT
USEFUL METHOD WHEN …
7cm means 7 squares fit in each row
- You can’t see the squares
5 cm means 5 squares fit in each column
AND
2
Number of squares = length
x width
It’s very
fast
= 7 x 5 = 35 square centimetres
Area: Test Yourself 1
AREA = COUNT
THE SQUARES
3 cm
Which
method
best suits
AREA =
each
ROWS X COLUMNS problem?
AREA =
LENGTH X WIDTH
9 cm
Area: Test Yourself 1
9 cm
AREA =
3 cm
=9x3
= 27 cm²
LENGTH X WIDTH
=4x2
= 8 cm²
AND
which way
works for
ALL 3?
= 11 x 5
= 55 cm²
Area: Test Yourself 2
Too many to
count!
But it’s easy to
see there are 6
rows of 7
Match the
method to
the problem
8 cm
5 cm
No squares.
Use
length x width
Easy to
count - only a
few squares
COUNT THE
SQUARES
ROWS X
COLUMNS
LENGTH X
WIDTH
Area Test Yourself 2
=7x5
= 35 cm²
AREA =
LENGTH X WIDTH
8 cm
=8x5
= 40 cm²
5 cm
=3x4
= 12 cm²
AND
which way
works for
ALL 3?
Area– General Rule for all
Rectangles
General Rule:
The area of a rectangle = Length x Width
Or if you like shorthand …
A=LxW
Area
The school grounds has 6 fields, each 1 kilometre square.
Its area is:
6 kilometre
Units
of squares
area:
6 kilometre squared
6 square kilometres
6 km ²
A classroom floor can
ALWAYS IN SQUARES!
A small chess board
fit in 20 carpet tiles,
contains 64 centimetre
each 1 metre square.
squares.
3
Egs
Its area is:
40 centimetre squares
40 centimetre squared
40 square centimetres
40 cm ²
The floor area is:
20 metre squares
20 metre squared
20 square metres
20 m ²
The Perimeter of a Rectangle
…
There’s
lots
Which way
means the distance aroundof
theways
outside
to
do
you
and is measured by - the sum of the lengths
of the
find
the4 sides
prefer?
perimeter…
(eg: millimetres, centimetres, metres, kilometres, feet, yards)
ADD 4 LENGTHS IN ORDER
10 + 6 + 10 + 6 = 32 m
10m
ADD 1 LENGTH + 1 WIDTH
THEN DOUBLE IT
10 + 6 = 16m
2 X 16 = 32m
6m
6m
2 LENGTHS + 2 WIDTHS
= 2 X 10
= 20
+ 2X6
+ 12 = 32m
10m
Perimeter
Units of perimeter:
Any units of length
METRIC UNITS
IMPERIAL UNITS
Millimetres mm
Miles
Centimetres cm
Yards
Kilometres km
Feet
Inches
Perimeter
The school grounds has 6 fields,
each 1 kilometre square.
The length of the perimeter fencing is:
10 kilometre
10 km
A classroom floor can
A small chess board
fit in 20 carpet tiles,
contains 64 centimetre
each 1 metre square.
squares.
3
Egs
The perimeter has a
brown edging:
64 centimetres long
64 cm long
The classroom
perimeter is:
20 metres
20m
Example 1
STEP 1
Read it !
- What do
I know?
- What do
I want to
find out?
… I’ll read this again
so I’m sure I get it …
Example 1
STEP 1
Read it !
KEY NUMBER!
KEY NUMBER!
WORD CLUE! area
STEP 2
Underline it !
… and …
LOOK FOR
KEY
NUMBERS!
The history
classroom is 10m
long and 4m wide.
PERIMETER CLUES
… and
WORD
CLUES –
area or
perimeter?
edge
edging
How much carpet
is needed for the
outside distance
floor?
perimeter fencing
outside length
total outside length
external length
AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
Some word clues
to watch out for…
PERIMETER CLUES
edge
edging
outside distance
AREA CLUES
outside length
surface
perimeter fencing
cover
total outside length
coverage
external length
amount of carpet
how much carpet
STEP 1 Read it !
Example 1
STEP 3 Picture It! !
STEP 2 Underline It !
KEY NUMBER!
KEY NUMBER!
WORD CLUE! area
10m
4m
The history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?
This means
AREA
2 Steps so far …
CLICK for Step 3!
STEP 1 Read it !
Example 1
STEP 3 Picture It! !
10m
STEP 2 Underline It !
4m
The history
classroom is 10m
long and 4m wide.
How much carpet
is needed for the
floor?
STEP 4 Calculate It !
3 steps
done
Area of a rectangle = length
x width
1 to go …
= 10 x 40
= 40
CLICK for
An area of 40m ² carpet is needed.
Step 4!
The 4 Steps
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Example 2
STEP 1
Read it !
- What do
I know?
- What do
I want to
find out?
… I’ll read this again
so I’m sure I get it …
Example 2
STEP 1
Read it !
KEY NUMBER!
KEY NUMBER!
WORD CLUE!
perimeter
… and …
LOOK FOR
KEY
NUMBERS!
STEP 2
Underline it !
The history
classroom is 10m
long and 4m wide.
How much
edging strip is
needed
for the classroom
floor?
PERIMETER CLUES
… and
WORD
CLUES –
area or
perimeter?
edge
edging
outside distance
outside length
perimeter fencing
total outside length
external length
AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
STEP 1 Read it !
Example 2
STEP 3 Picture It! !
10m
STEP 2 Underline It !
The history
classroom is 10m
long and 4m wide.
How much
edging strip is
needed
to go around the
classroom floor?
4m
4m
10m
This means
PERIMETER
2 Steps so far …
CLICK for Step 3!
STEP 1 Read it !
Example 2
STEP 3 Picture It! !
Remember – there’s lots of
ways to do this!
STEP 2 Underline It !
For example:
10 + 4 + 10 + 4 = 28
10m
The history
OR
10classroom
+ 4 = 14
2 X 14 = 28
10m
is 10m
long and 4m wide.
OR
10 X 2 =
20 and
4X2=8
How
much
20 + 8 = 28
edging strip is
needed
to go around the
classroom floor?
4m
4m
STEP 4 Calculate It !
3 steps done
Perimeter of a rectangle
= sum of the lengths of the
sides
1 to4go
…
= 10 + 4 + 10 + 4
= 28
CLICK for
Step
4!
A 28 m length of edging strip
is needed.
The 4 Steps
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Example 3
STEP 1
Read it !
- What do
I know?
- What do
I want to
find out?
… I’ll read this again
so I’m sure I get it …
Example 3
STEP 1
Read it !
STEP 2
Underline it !
… and …
LOOK FOR
KEY
NUMBERS!
The history room floor
is 12m by 6m.
KEY NUMBERS!
KEY NUMBER!
The project corner is a
1m by 3m rectangle.
The rest is tiled.
How much of the
floor surface is tiled?
WORD CLUE! area
PERIMETER CLUES
LOOK FOR
WORD
CLUES –
area or
perimeter?
edge
edging
outside distance
outside length
perimeter fencing
total outside length
external length
AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
STEP 1 Read it !
Example 3
STEP 3 Picture It! !
6m
STEP 2 Underline It !
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?
3m
1m
3m
SURFACE MEANS AREA!
But the shape you’re interested in is not
a rectangle!
2 Steps so far …
One way is to PICTURE IT AS 2
RECTANGLES JOINED TOGETHER.
CLICK for Step 3!
Work out each area and ADD.
STEP 1 Read it !
Example 3
STEP 3 Picture It! !
6m
STEP 2 Underline It !
The history room floor
is 12m by 6m
The project corner is a
1m by 3m rectangle.
2m
?m
= 3Area?
x2
= 6m²
= 3Area?
x3
= 9m²
3m
1m
3m
?m
3m
STEP 4 Calculate It !
The rest is tiled.
How much of the
floor surface is tiled?
Total
Area
6 +
9 =each
15m²
3 steps
done
Work
out=area
of
to go …
rectangle and 1add!
The tiled area is 15m ²
CLICK for
Can you think of any other ways you
could work this out?
Step 4!
The 4 Steps
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Example 4
STEP 1
Read it !
- What do
I know?
- What do
I want to
find out?
… I’ll read this again
so I’m sure I get it …
Example 4
STEP 1
Read it !
STEP 2
Underline it !
… and …
LOOK FOR
KEY
NUMBERS!
The history room floor
is 12m by 6m.
KEY NUMBERS!
KEY NUMBER!
WORD CLUE!
perimeter
The project corner is a
1m by 3m rectangle.
The rest is tiled and
surrounded by
wooden edging.
What length of
edging is needed?
PERIMETER CLUES
… and
WORD
CLUES –
area or
perimeter?
edge
edging
outside distance
outside length
perimeter fencing
total outside length
external length
AREA CLUES
surface
cover
coverage
amount of carpet
how much carpet
STEP 1 Read it !
Example 4
STEP 3 Picture It! !
6m
STEP 2 Underline It !
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?
3m
1m
3m
EDGING MEANS PERIMETER
But the shape you’re interested in is not
a rectangle!
2 Steps so far …
One way is to start at the top
left-hand corner and write down each
for Step 3!
length around the CLICK
perimeter.
Then ADD.
STEP 1 Read it !
Example 4
STEP 3 Picture It! !
6m
STEP 2 Underline It !
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?
2m
?m
3m
1m
3m
?m
3m
STEP 4 Calculate It !
Work out the length
of each
3 steps done
side and add!
1 to go …
6 + 3 + 3 + 1 + 3 + 2 = 18
CLICK for
18m of edging is needed.
Step 4!
The 4 Steps
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now Your Turn! 1
Problem 1
The history classroom is 9m
6m
long and 5m wide.
How carpet is needed 1.5m
to cover
2m floor?
the
4m
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
An
area of
Click
45m²
for
carpet is
solution
needed
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 2
Problem 2
The history classroom is 9m
long and 5m wide.
How edging tape is needed for
the carpet perimeter?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
AClick
length of
28m
for
edging
solution
strip
to is
needed
problem
STEP 4
Calculate It !
?
Now Your Turn! 3
Problem 3
The history classroom is 15m
long and6m
6m wide.
How carpet is needed 1.5m
to cover
2m floor?
the
4m
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
An
area of
Click
90m²
for
carpet is
solution
needed
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 4
Problem 4
The history classroom is 15m
long and 6m wide.
How edging tape is needed for
the carpet perimeter?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
AClick
length of
42m
for
edging
solution
strip
to is
needed
problem
STEP 4
Calculate It !
?
Now Your Turn! 5
Problem 5
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?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
An
area of
Click
68m²
for
carpet is
solution
needed
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 6
Problem 6
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?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
The
Click
perimeter
for
border is
solution
36m
to long
problem
STEP 4
Calculate It !
?
Now Your Turn! 7
Problem 7
The history classroom floor is
a 15m and 7m rectangle.
The computer corner is 3m x
3m square. How much floor
space is left?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
An
area of
Click
96m²
for
carpet is
solution
needed
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 8
Problem 8
The history classroom floor is a
15m by 7m rectangle.
The computer corner is 3m x 3m
square. A tiled border marks the
perimeter of the remaining floor.
How long is the border?
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
The
Click
perimeter
for
border is
solution
44m
to long
problem
STEP 4
Calculate It !
?
Now Your Turn! 9
Problem 9
How much floor space is there
in this classroom?
15m
7m
6m
11m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(0.5m wide)
STEP 3
Picture
? It! !
The
Clickfloor
area is
for
81m²
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 10
Problem 10
What length of skirting board
is needed this classroom?
(Remember to allow for the door!)
15m
7m
6m
11m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(0.5m wide)
STEP 3
Picture
? It! !
An
area of
Click
43.5m²
for
carpet is
solution
needed
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 11
Problem 11
How much floor space is there
in this classroom?
14m
10m
0.5m
17m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(0.5m wide)
STEP 3
Picture
? It! !
The
Clickfloor
area is
for
141.5m²
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 12
Problem 12
What length of skirting board
is needed this classroom?
(Remember to allow for the door!)
14m
10m
0.5m
17m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(0.5m wide)
STEP 3
Picture
? It! !
53.5m
Click of
skirting
for
board is
solution
needed.
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 13
Problem 13
How much floor space is there
in this classroom?
10m
7m
5.5m
8m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(1/2 m wide)
STEP 3
Picture
? It! !
The
Clickfloor
area is
for
59m²
solution
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 14
Problem 14
What length of skirting board
is needed this classroom?
(Remember to allow for the door!)
10m
7m
5.5m
4m
8m
STEP 1
Read
? it !
STEP 2
Underline It !
?
KEY
Door
(1/2 m wide)
STEP 3
Picture
? It! !
33.5m
Click of
skirting
for
board is
solution
needed.
to
problem
STEP 4
Calculate It !
?
Now Your Turn! 15
Problem 15
The ceiling is going to have new tiles.
Each tile is 1 square metre.
How many tiles are needed?
for
So 81 of the
solution
1m² tiles are
to
needed.
problem
1.5m
11m
10m
6m
STEP 1
Read
? it !
STEP 2
Underline It !
?
The
ceiling area
Click
is 81m².
STEP 3
Picture
? It! !
STEP 4
Calculate It !
?
Now Your Turn! 16
Problem 16
The ceiling tiles are enclosed by metal
strip.
How much strip is needed?
1.5m
11m
10m
6m
STEP 1
Read
? it !
STEP 2
Underline It !
?
STEP 3
Picture
? It! !
45m of
Click
metal
for strip
is needed.
solution
to
problem
STEP 4
Calculate It !
?
Now U R PC with Area and
Perimeter …
Are you ready to try …
THE FIENDISH SPANISH CLASSROOM PROBLEMS ?
- about Money with Area and Perimeter
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