Maths and Numeracy CLPL

Bar ModellingPart 1

What is bar modelling?

Bar modelling is an approach used for teaching and understanding problem solving.

It involves drawing a visual representation to help understand the basis of the problem.

It helps us all to understand which calculations to carry out to solve the problem

It is a part of the “Singapore Maths” teaching approaches.

C – P – ABar Modelling

Concrete – the doing part, hands on physical objectsPictorial – the seeing part, visual representations of the physical problemAbstract – symbolic stage where mathematical notation is introduced

C – P – A

Early Level First Level Second Level Third Level

Concrete Concrete Pictorial Abstract

Pictorial Abstract

Early Level First Level Second Level Third Level

Concrete Concrete Concrete Concrete

Pictorial Pictorial Pictorial Pictorial

Abstract Abstract Abstract Abstract

Count out 3 yellow counters.

Learning objective• Single digit addition within 5• Finding 1 more• Finding 2 more

Abstract part3 + 1 = ?

Concrete Pictorial

How many counters do you have altogether (in total)?

Now add 1 red counter.

Get 3 yellow counters.

Get 1 red counter.

How many counters do you have altogether?

3 1 4 3 1

4 3 + 1 = 4

1 + 3 = 4

LinkTo abstract

Austin has 5 pencils.Scarlett has 2 pencils.

How many pencils are there altogether?

Concrete – use two people and pencils to model the problem

Pictorial – use an image to model the problem

There are 7 pencils altogether

5 2

7

part part

whole

Number bond

Abstract 5 + 2 = 7

Austin has 5 pencils.Scarlett has 2 pencils.

How many pencils are there altogether?

5 2

7

part part

whole

Abstract

5 + 2 = 7

Number bond

Make an 8-train using the same colour of blocks.

8

Make an 8-train using 2 different colour of blocks.

Make a different 8-train using 2 different colour of blocks.

6 2

3 5

3 5

8

part part

whole

6 2

8

part part

whole

Make any 8-train using as many colours as you want.

2

8

part part

whole

3 4

8

part part

whole

part part

222

1part

2 2 22

143

Using the multi link cubes

Red Yellow Blue

Red Yellow Blue

Red Yellow Blue

There are 3 red blocks .There are 8 yellow blocks.There are 5 blue blocks.

There are __ more yellows than blues.

There are __ fewer reds than yellows.

There are __ more blue than reds.

Aiden had 6 rubbers. He gave away 2 rubbers to his friend.

How many rubber does he have left?

4 2

6

part part

whole

Abstract 6 – 2 = 4

Number bond

Aiden has 4 rubbers left.

Aiden had 6 rubbers. He gave 2 rubbers to his friend.

How many rubber does he have now?

Aiden’s rubbers

friendLeft ?

6

part part

whole

2

6

part part

whole

4 2

6

part part

whole

Aiden has 4 rubbers left.

What is 3 less than 8.

8

5 3

8

part part

whole

3 less than 8 is 5

5

Susan has 9 pencils. Kathleen has 7 pencils.

How many more pencils does Susan have than Kathleen

Susan’s pencils

Susan has 2 more pencils than Kathleen

Kathleen’s pencils

There are 7 yellow cubes under the two flags.

How many are under the red flag?

Place ValueCount the number of smiley faces

13 = 1 ten and 3 ones

Tens Ones

1 3

10 3

13

part part

whole

Group 10 faces together

Count out 23 multi link cubes.

Make two 10 trains.Tens Ones

2 3

Count out 23 multi link cubes.

20 3

23

part part

whole

20 + 3 = 23

Make two 10 trains.

Tens Ones

2 3

Count out 23 multi link cubes.

310 10

Nicola has 8 sweets. She eats 3 sweets.How many sweets does she have left?

Twitter : @CountOnUsEd

left?eats

8 sweets

3?

Nicola has 5 sweets left.

Green sweets

Blue sweets

Kevin has some blue and green sweets. He has 3 green sweets. He has 4 more blue sweets than green ones. How many sweets does he have in total?

3

7

Total sweets = 3 + 7 = 10 Kevin has 10 sweets in total.

3

3 4

Green sweets

Blue sweets

Kevin has some blue and green sweets. He has 3 green sweets. He has 4 more blue sweets than green ones. How many sweets does he have in total?

3

7

Total sweets = 3 + 7 = 10 Kevin has 10 sweets in total.

300 children are divided into two groups. There are 50 more children in the first group than in the second group.How many children are there in the second group?

300 children are divided into two groups. There are 50 more children in the first group than in the second group.How many children are there in the second group?

150 150

200 100

180 120

170 130

175 125

Difference = 0

Difference = 100

Difference = 60

Difference = 40

Difference = 50

David and Susan have 13 sweets in total between them. Susan has 3 more sweets than David.How many sweets does David have?

Twitter : @CountOnUsEd

David’s sweets

Susan’s sweets

David and Susan have 13 sweets in total between them. Susan has 3 more sweets than David.How many sweets does David have?

Twitter : @CountOnUsEd

David’s sweets

Susan’s sweets

David has 5 sweets.

? ?

300 children are divided into two groups. There are 50 more children in the first group than in the second group.How many children are there in the second group?

300

250 50

125 50125

125 175

Twitter : @CountOnUsEd

Summary

• Use concrete materials to model problems• Solve problems from visual representations• Use C & P models to build understanding of Abstract

processes.• Use Bar modelling to represent a problem visually to

help understand the basis of the problem. • Answer the specifics of the question in a verbal or

written statement.

Maths and Numeracy CLPL

Bar ModellingPart 2

Addition and subtraction with the multi link cubes

310 10

THINK

TALK

TACKLE

In groups of 2 or 3

THINK about the problem

– no talking allowed

– no touching the resources

TALK about the problem

– no touching the resources

TACKLE the problem

– Now do the problem

Remove 10 cubes

Make a 10 tower with the yellows

Make a 10 tower with the reds

Join them together to make a 20 tower

Make a 9 tower with the blues

Join it to make a 29 towerTHINK

TALK

TACKLE

THINK

TALK

TACKLE

910 10

910

10 9

29 – 10 = 19

Put the 10 back on to make 29 again

Remove 12 counters THINK

TALK

TACKLEHow did you do it?

THINK

TALK

TACKLE

910 10

710

10 7

29 – 12 = 17

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What is 51 divided by 3?

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36912151821

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36912151821

3, 6, 9, 12,15,18,21,24,27,30 3, 6, 9, 12,15,18,21

30 21

Twitter : @CountOnUsEd

51 ÷ 317

3 30 21

10 7

Using the bar modelling strategy for division

51

Maths and Numeracy CLPL

Bar ModellingPart 3

Fiona

Ruby

Tina saves 4 times as much money as Fiona.Ruby saves £20 less than Tina.Fiona saves £30.How much money does Ruby save?

Tina saves £30 x 4 = £120

Ruby saves £120 - £20 = £100

Tina

20

30

30

Ruby saves £100.

30 30 30

Messi

Ronaldo

Messi, Ronaldo and Bale are playing in the CL.Bale and Messi both score the same number of goals. Ronaldo scores three times as many goals as Messi.Ronaldo scored 8 more goals than Messi.How many goals did they all score together?

8 more goals Total goals = 4 + 4 + 4 + 4 + 4 = 20

Bale

4 44

4

4

They scored 20 goals altogether.

Jane

Emma

Jane, Emma and Brian are taking part in a dance competitionJane and Brian both score the same number of pointsEmma scores four times times as many points as Jane.Emma scored 18 more points than Jane.How many points did they all score?

18 more pointsBrian

6 66

6

6

Jane scored 6 pointsBrian scored 6 pointsEmma scored 24 points

6

What is the ratio of blue to red?

Bar modelling and ratio

What is the ratio of blue to red?

Bar modelling and ratio

Using a bar model to demonstrate a ratio of 3:4

A A A B B B B

Robert and Anne share £30 in the ratio 2:3.

Who gets more money and by how much?

Robert and Anne share £30 in the ratio 2:3.

Who gets more money and by how much?

R R R R R

Robert and Anne share £30 in the ratio 2:3.

Who gets more money and by how much?

£6R

£6R

£6A

£6A

£6A

Kevin and Rose share some money in the ratio 2:5. Rose gets £12 more than Kevin. How much money did they share?

Kevin and Rose share some money in the ratio 2:5. Rose gets £12 more than Kevin. How much money did they share?

K K R R R R R

This represents the £12 more

Kevin and Rose share some money in the ratio 2:5. Rose gets £12 more than Kevin. How much money did they share?

K K R R R4

R4

R4

This represents the £12 more

Kevin and Rose share some money in the ratio 2:5. Rose gets £12 more than Kevin. How much money did they share?

K4

K4

R4

R4

R4

R4

R4

Kevin and rose shared £28

Claire spent 3

5of her pocket money on a toy.

The toy cost Claire £6.How much pocket money did Claire get?

Bar modelling and ratio

£6

Toy Toy Toy

Bar modelling and ratio

£6

Toy£2

Toy£2

Toy£2 £2 £2

Bar modelling and ratio

Claire got £10 pocket money

Chris spent 3

8of his birthday money on a computer

game.The game cost Chris £21.How much birthday money did Chris get?

Kevin and Rose share some money in the ratio 3:7. Rose gets £20 more than Kevin. How much money did they share?

London Utd had an equal number of orange footballs and white footballs.They lost 21 orange footballs in 1 training session and as a result they were left with 4 times as many white balls than orange balls.How many footballs did they have at the start of training?

Orange footballs

White footballs

They lost 21 orange footballs in 1 training session.

As a result they were left with 4 times as many white balls than orange balls.

left

21 ÷ 3 =7

Lost 21 footballs

They lost 21 orange footballs in 1 training session.

As a result they were left with 4 times as many white balls than orange balls.

left

7

21

7 7 7

21 ÷ 3 =7

7

At the start of training they had 28 + 28 = 56 footballs

A large box weighs three times as much as a small box. Two large boxes and one small box weigh 35 kg. How much does one large box weigh?

Large SLarge

Large

S S S35 kg

S S S S S S S

35 ÷ 7 = 5kg 5kg × 3 = 15kg

Final Part

The SANGRIA PROBLEM

SANGRIA PROBLEM

There is twice as much orange juice as lemonade

There is twice as much lemonade as brandy.

There is three times as much red wine as brandy.

If there is 80ml of lemonade juice, what is the volume of the Sangria?

Extra Q:If one ice cube is added for every 25ml, how many ice cubes will be added?

Brandy

Orange

lemonade

Red wine

SANGRIA PROBLEMThere is twice as much orange juice as lemonadeThere is twice as much lemonade as brandy.There is three times as much red wine as brandy.If there is 80ml of lemonade juice, what is he volume of the Sangria?

Brandy

Orange

lemonade

Red wine

SANGRIA PROBLEMThere is twice as much orange juice as lemonade There is twice as much lemonade as brandy.There is three times as much red wine as brandy.If there is 80ml of lemonade juice, what is he volume of the Sangria?

There is twice as much orange juice as lemonade and twice as much lemonade as brandy.There is three times as much red wine as brandy.If there is 80ml of lemonade juice, what is he volume of the Sangria?

Brandy

Orange

lemonade

Red wine

There is twice as much orange juice as lemonade and twice as much lemonade as brandy.There is three times as much red wine as brandy.If there is 80ml of lemonade juice, what is the volume of the Sangria?

Extra Q:If one ice cube is added for every 25ml, how many ice cubes will be added?

Brandy

Orange

40 x 10 = 400 ml

80 / 2 = 40ml

lemonade

Red wine

80ml

The volume of sangria is 400ml

16 ice cubes will be added.