Bridging the Gap Problem-Solving Teachers’ Version

Bridging the Gap Bridging the Gap

Problem-SolvingProblem-SolvingTeachers’ VersionTeachers’ Version

Teacher NotesTeacher NotesThis resource is …This resource is …

A simple guide to problem-solving - using an easy 4-step approach to solving tricky problems about area and perimeter:

1. Read it! 2. Underline it! 3. Picture it! 4. Calculate it!

The 4 steps are reinforced throughout, both in this activity and the other problem-solving activities. The aim is that pupils will feel confident in applying the four steps when trying out problems independently, regardless of mathematical topic.

Flexible- suitable both for whole-class teaching and individual pupil revision. The mouse-activated steps allow time for whole-class interactions or individual thinking time.

User-friendlyThe activity introduces the concepts of area and perimeter alongside the 4-step strategy, R U PC? using stepwise examples for interactive teaching.

A Test Yourself Section follows with 8 problems to test your pupils’ learning.

More problems are available in the pupils version (see Main Menu).

How to use this resourceHow to use this resourceYou can control how fast or slow you go using:

FORWARD: OR OR Enter OR Left-hand mouse

BACK: OR OR Back Space

TO START POWERPOINT: F5 OR Slide Show > View Show

TO RETURN TO MENU: Escape

ContentContentSlide 4 Learn to solve problems about area and perimeterSlides 4-19 Intro: Solving Problems, area and perimeterSlides 20 – S40 4 Examples

Slide 41 Test YourselfSlides 41 – 49 Now Your Turn: 8 Problems

Slide 50 Where To Next?(TO GO TO LINK, HOLD DOWN CONTROL AND CLICK ON YOUR CHOICE)

Which One Are You ???Which One Are You ???

R UR U a a PProblemroblem-C-Coward oward ??… … or …or …

R UR U a a PProblemroblem-C-Crackerracker??

PROBLEM!

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Read it ! Underline It !

Picture It! !

Calculate It !

R U PC?R U PC?

R U P CR U P C ? ?RRead it! ead it! … what’s it about?… what’s it about?

UUnderline it! nderline it! … find the clues… find the clues

PPicture it! icture it! … add?… add? subtract? multiply? divide? subtract? multiply? divide?

… … use a number line to helpuse a number line to help

CCalculate it! alculate it! … work… work it out ! it out ! But first …

Check out the basics

about areas and perimeters

of rectangles

…

How to become How to become aa PROBLEM-CRACKERPROBLEM-CRACKER

inin 4 Easy Steps! 4 Easy Steps!

Now you’re ready to try out some

problems!

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


COUNT THE SQUARESCOUNT THE SQUARES

1, 2, 3, … 59, 601, 2, 3, … 59, 60


10 m

6 m

But which way

is best?

But which way

is best?

How do you find area?

Here are some ways you might

have met …

How do you find area?

Here are some ways you might

have met …

Area Example 1 Area Example 1

What is the area of this rectangle? …

HOW MANY SQUARES?


HOW MANY SQUARES?

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

-there’s not too many to count!there’s not too many to count!


HOW MANY SQUARES?


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


- You can see the squares - You can see the squares

BUT BUT

-there’s too many to count!there’s too many to count!

Area Example 2Area Example 2

Area Example 3 Area Example 3


HOW MANY SQUARES?


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


- You can’t see the squares - You can’t see the squares

ANDAND

It’s very fastIt’s 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 =


Area: Test Yourself 1Area: Test Yourself 19 cm

3 cm

ANDwhich way works for

ALL 3?


ALL 3?

= 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

LENGTH X LENGTH X WIDTHWIDTH

COUNT THE COUNT THE SQUARES SQUARES

ROWS X ROWS X COLUMNSCOLUMNS

Area: Test Yourself 2Area: Test Yourself 2

Easy to count - only a few squares

Easy to count - only a few squares

No squares.Use

length x width

No squares.Use

length x width

8 cm

5 cm

Too many to count!

But it’s easy to see there are 6

rows of 7

Too many to count!

But it’s easy to see there are 6

rows of 7

Match the method to

the problem

Match the method to

the problem

AREA = AREA =


Area Test Yourself 2Area Test Yourself 2


ALL 3?


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

3 3 Egs Egs

AreaArea

Units of area: Units of area:

ALWAYS IN SQUARES!ALWAYS IN SQUARES!A small chess board A small chess board contains 64 centimetre contains 64 centimetre

squares.squares.

Its area is:Its area is:40 centimetre squares 40 centimetre squares 40 centimetre squared 40 centimetre squared 40 square centimetres 40 square centimetres

40 cm 40 cm ²²

The school grounds has 6 fields, each 1 kilometre square.The school grounds has 6 fields, each 1 kilometre square.

Its area is:Its area is:6 kilometre squares 6 kilometre squares 6 kilometre squared 6 kilometre squared 6 square kilometres 6 square kilometres

6 km 6 km ²²A classroom floor can A classroom floor can

fit in 20 carpet tiles, fit in 20 carpet tiles, each 1 metre square.each 1 metre square.

The floor area is:The floor area is:20 metre squares 20 metre squares 20 metre squared 20 metre squared 20 square metres 20 square metres

20 m 20 m ²²

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

Which way do you prefer?

Which way do you prefer?

There’s lots of ways to

find the perimeter…

There’s lots of ways to

find the perimeter…

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

PerimeterPerimeter

3 3 Egs Egs

The school grounds has 6 fields, The school grounds has 6 fields, each 1 kilometre square.each 1 kilometre square.

The length of the perimeter fencing is:The length of the perimeter fencing is:10 kilometre10 kilometre

10 km10 km

A small chess board A small chess board contains 64 centimetre contains 64 centimetre

squares.squares.

The perimeter has a The perimeter has a brown edging:brown edging:

64 centimetres long64 centimetres long64 cm long64 cm long

A classroom floor can A classroom floor can fit in 20 carpet tiles, fit in 20 carpet tiles,

each 1 metre square.each 1 metre square.

The classroom The classroom perimeter is:perimeter is:20 metres 20 metres

20m20m

Example 1Example 1- What do I know?

STEP 1

Read it !

- What do I want to find out?

… I’ll read this again so I’m sure I

get it …

STEP 1

Read it !

STEP 2 Underline

it !

… and …LOOK FOR

KEY NUMBERS

!

Example 1Example 1

The history

classroom is 10m

long and 4m wide.

How much carpet

is needed for the

floor?

WORD CLUE! area

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?

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


external length

Example 1Example 1STEP 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

2 Steps so far …

CLICK for Step 3!

This means AREA




STEP 4 Calculate It !

Area of a rectangle = length x width

= 10 x 40

= 40

An area of 40m ²² carpet is needed.

3 steps done

1 to go …

CLICK for

Step 4!

10m

4mThe history

classroom is 10m

long and 4m wide.

How much carpet

is needed for the

floor?

The 4 StepsThe 4 Steps

STEP 1

?

STEP 2

?

STEP 3


Picture It! !STEP 4

?Calculate It !

Example 2Example 2STEP 1

Read it !



get it …

- What do I know?

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


external length

… and WORD

CLUES – area or

perimeter?

Example 2Example 2

STEP 1 Read it !



2 Steps so far …

CLICK for Step 3!

Example 2Example 2

10m

4m

10m

4mThe history

classroom is 10m

long and 4m wide.


needed to go around the classroom floor?

This means PERIMETER

STEP 1 Read it !




Perimeter of a rectangle = sum of the lengths of the 4 sides

= 10 + 4 + 10 + 4

= 28

A 28 m length of edging strip is needed.

3 steps done

1 to go …

CLICK for

Step 4!

Example 2Example 2

10m

4m

10m

4mThe history

classroom is 10m

long and 4m wide.


needed to go around the classroom floor?

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


STEP 1

?

STEP 2

?

STEP 3


Picture It! !STEP 4

?Calculate It !


STEP 1

Read it !



get it …

STEP 1

Read it !

STEP 2 Underline

it !

… and …LOOK FOR

KEY NUMBERS

!

Example 3Example 3

AREA CLUES

surface

cover

coverage

amount of carpet

how much carpet

PERIMETER CLUES

edge

edging

outside distance

outside length

perimeter fencing


external length

LOOK FOR WORD

CLUES – area or

perimeter?

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!

1m

6m

3m

3m




2 Steps so far …

CLICK for Step 3!

SURFACE MEANS AREA!But the shape you’re interested in is not a rectangle!

One way is to PICTURE IT AS 2 RECTANGLES JOINED TOGETHER.

Work out each area and ADD.


is 12m by 6m.


1m by 3m rectangle.

The rest is tiled.


tiled?

1m

6m

3m

3m


is 12m by 6m


1m by 3m rectangle.

The rest is tiled.


tiled?




?m2m

?m3m

Area?Area? = 3 x 2 = 6m²

= 3 x 3 = 9m²


3 steps done

1 to go …

CLICK for

Step 4!

Work out area of each rectangle and add!

Total Area = 6 + 9 = 15m²

The tiled area is 15m ²

Can you think of any other ways you could work this out?


STEP 1

?

STEP 2

?

STEP 3


Picture It! !STEP 4

?Calculate It !


STEP 1

Read it !



get it …

STEP 1

Read it !

STEP 2 Underline

it !

… and …LOOK FOR

KEY NUMBERS

!

Example 4Example 4

AREA CLUES

surface

cover

coverage

amount of carpet

how much carpet

PERIMETER CLUES

edge

edging

outside distance

outside length

perimeter fencing


external length

… and WORD

CLUES – area or

perimeter?


is 12m by 6m.


1m by 3m rectangle.

The rest is tiled and surrounded by

wooden edging.

What length of edging is needed?

WORD CLUE! perimeter

KEY NUMBER!

KEY NUMBERS!

1m

6m

3m

3m




2 Steps so far …

CLICK for Step 3!


is 12m by 6m.

The carpeted area in the corner is a

1m by 3m rectangle.


wooden edging.


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.

1m

6m

3m

3m




?m2m

?m3m


3 steps done

1 to go …

CLICK for

Step 4!

Work out the length of each side and add!

6 + 3 + 3 + 1+ 3 + 2 = 18

18m of edging is needed.


is 12m by 6m.

The carpeted area in the corner is a

1m by 3m rectangle.


wooden edging.



STEP 1

?

STEP 2

?

STEP 3


Picture It! !STEP 4

?Calculate It !

Now Your Turn! 1Now Your Turn! 1

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !

Picture It! ! Calculate It !

Read it !

An area of 45m² carpet is needed

Click for

solution to

problem

6m

1.5m2m

4m

Problem 1Problem 1 The history classroom is The history classroom is 9m long and 5m wide.9m long and 5m wide.

How carpet is needed to How carpet is needed to cover the floor?cover the floor?


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

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

Click for

solution to

problem


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline 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?

An area of 68m² carpet is needed

Click for

solution to

problem


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

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?

The perimeter border is 36m long

Click for

solution to

problem


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 5Problem 5How much floor space is How much floor space is there in this classroom? there in this classroom? The floor

area is 81m²

Click for

solution to

problemKEY

Door

(0.5m wide)

15m

7m 6m

11m


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

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!)

43.5m of skirting board is needed.

Click for

solution to

problemKEY

Door

(0.5m wide)

15m

7m 6m

11m


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 7Problem 7How much floor space is How much floor space is there in this classroom? there in this classroom? The floor

area is 59m²

Click for

solution to

problemKEY

Door (1/2 m wide)

10m

7m5.5m

8m


STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !


Read it !

Problem 8Problem 8What 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!)

33.5m of skirting board is needed.

Click for

solution to

problem4m

KEY

Door (1/2 m wide)

10m

7m5.5m

8m

Now U R PC with Area and Now U R PC with Area and Perimeter …Perimeter …

Why not have a go on your own Why not have a go on your own withwith

THE PUPIL VERSION IN THE HISTORY THE PUPIL VERSION IN THE HISTORY CLASSROOM?CLASSROOM?

Or are you ready to try …Or are you ready to try … THE FIENDISH SPANISH CLASSROOM PROBLEMS THE FIENDISH SPANISH CLASSROOM PROBLEMS

?? - about Money with Area and Perimeter - about Money with Area and Perimeter

PRESS ESCAPE TO RETURN TO MENUPRESS ESCAPE TO RETURN TO MENU

Documents

Bridging the Gap Problem-Solving Teachers’ Version