Maths and Numeracy CLPL Bar Modelling Part 1 - Count On Us · Count the number of smiley faces 13 =...
Transcript of Maths and Numeracy CLPL Bar Modelling Part 1 - Count On Us · Count the number of smiley faces 13 =...
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?
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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?
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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
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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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3, 6, 9, 12,15,18,21,24,27,30 3, 6, 9, 12,15,18,21
30 21
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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.