1. Muxton Primary School How to use the bar model

2. Bar Models
9 + 7 = ? 16 9 7

3. Visualising Concepts
Adding
9 + 7 = ? ? 9 7

4. Visualising Concepts Number Bonds 10 10 10 6 4 3 7 10 10 10 5 5 2 8 109

5. Visualising Concepts
Multiplying
4 x 5 = ? ? 4 4 4 4 4

6. Visualising Concepts
Dividing
20 ÷ 5 = ? 20 ? ? ? ? ?

7. Using One Bar

8. Two Equal Bars 3 3 3 3 3 Work out… 3 x 5 = ? Model Calculations ? 15 3
= 15 3 3 3 3 3

9. Two Equal Bars Find of 21 2 7 Model Calculations 21 21 ÷ 7 = 3
3 x 2 = 6 6 ?

10. Two Equal Bars 4 4 4 4 4 4 Now you try! 4 x 6 = ? Model Calculations ?24 4
X 6
= 24 4 4 4 4 4 4

11. Two Equal Bars Now you try! Find of 30 3 5 Model Calculations 30
30 ÷ 5 = 6
6 x 3 = 18 ? 18

12. Using Two Equal Bars

13. Two Equal Bars a a a 5 12 17 Solve… 3a + 5 = 17 Model Calculations 3a-5 -5
3a = 12 12 17
÷ ÷3
a = 4

14. Two Equal Bars a a a 2 a a 6 8 Solve… 3a + 2 = 2a + 8 Model
Calculations 3a
+ 2 =
2a + 8 a a a 2
-2a
-2a
a = a a 6 8
a =

15. Two Equal Bars a a a a 3 20 23 Now you try! 4a + 3 = 23 Model
Calculations 4a
+ 3 = 23 a a a a 3 -3 -3
4a = 20 20 23
÷ ÷4
a = 5

16. Two Equal Bars a a a 4 a 4 8 Now you try! 3a + 4 = a + 8 Model
Calculations 3a
+ 4 =
a + 8 a a a 4 -a -a
2a + 4 = a 4 8
2a =
÷ ÷2
a =

17. Using Two or More Unequal Bars

18. Two Equal Bars
Peter and Jane share £40 in the ratio of 3:5 How much money does each person get?
Model
Calculations
40 ÷ 8 = 5 5
Peter
Peter: 5x3 = 15
£40
Jane: 5x5 = 25
Jane

19. Two Equal Bars
Peter and Jane share £40 in the ratio of 3:5 How much more money does Jane have than Peter?
Model
Calculations
40 ÷ 8 = 5 10 5
Peter
Peter: 3x5 = 15
£40
Jane: 5x5 = 25
Jane
25 – 15 = 10

20. Two Equal Bars
Jessie, Lisa and David share £60 in the ratio of 1:2:3 How much more money does David get than Jessie?
Model
Calculations 20
60 ÷ 6 = 10
Jessie 10
Jessie: 10x1 = 10
Lisa
£60
Lisa: 10x2 = 20
David: 10x3 = 30
David
30 – 10 = 20

21. Solving Problems

22. Problems Model Calculations 300 - 50 = 250 Group A 50 10 250 ÷ 2 = 125
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?
Model
Calculations =
250
Group A 50 10
250 ÷ 2 =
125
300
250 50
Group B ?
125

23. Problems Model Calculations 3000 - 10 = 2990 1st Pile 10 2990 ÷ 5 =
3000 exercise books are arranged into 3 piles. The first pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are in the third pile?
Model
Calculations =
2990
1st Pile 10 10
2990 ÷ 5 =
598
2nd Pile
3000
2990
3rd Pile ?
598

24. Now you try!

25. Problem A Model Calculations 410 - 100 = 310 10 Jon £100 £310 £410
Jon and Sally shared £410 between them. Jon received £100 more than Sally. How much money did Sally receive?
Model
Calculations
= 310 10
Jon
£100
£310
£410
310 ÷ 2 = 155
£100
Sally ?
£155

26. Problem B Model Calculations 53 + 3 = 56 Adam 56 ÷ 4 = 14 Barry 56 53
Adam is twice as old as Barry. Charlie is 3 years younger than Barry. The sum of all their ages is 53. How old is Barry?
Model
Calculations
= 56
Adam
56 ÷ 4 = 14
Barry 56 53 14 ? 3
Charlie

27. Problem C Model Calculations $1000 ? 300 x 2 = 600 $200 $200 $200 $200
Encik Hassan gave of his money to his wife and spent of the remainder. If he had $300 left, how much money did he have at first? 5 2
Model
Calculations
$1000 ?
300 x 2 = 600
Hassan’s money at the start
$200
$200
$200
$200
$200
600 ÷ 3 = 200
$600
Given to his wife
200 x 5 = 1000
Hassan’s money afterwards
$300
$300
Left
Spent

28. Problem D Model Calculations $75 ? 50 ÷ 2 = 25 Raju $25 $25 $25
Raju had 3 times as much money as Gopal. After Raju spent $60 and Gopal spent $10, they each had equal amount of money. How much money did Raju have at first?
Model
Calculations
$10
$50
$75 ?
50 ÷ 2 = 25
Raju
$25
$25
$25
25 x 3 = 75
$60
Gopal
$10