Muxton Primary School How to use the bar model

Bar Models 9 + 7 = ? 16 9 7

Visualising Concepts Adding 9 + 7 = ? ? 9 7

Visualising Concepts Number Bonds 10 10 10 6 4 3 7 10 10 10 5 5 2 8 10 9

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

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

Using One Bar

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

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

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

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

Using Two Equal Bars

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

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 + 2 = 8 a a 6 8 -2 -2 a = 6

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 ÷4 a = 5

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 = 8 a 4 8 -4 -4 2a = 4 ÷2 ÷2 a = 4

Using Two or More Unequal Bars

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

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

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

Solving Problems

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 300 - 50 = 250 Group A 50 10 250 ÷ 2 = 125 300 250 50 Group B ? 125

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 3000 - 10 = 2990 1st Pile 10 10 2990 ÷ 5 = 598 2nd Pile 3000 2990 3rd Pile ? 598

Now you try!

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 410 - 100 = 310 10 Jon £100 £310 £410 310 ÷ 2 = 155 £100 Sally ? £155

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 53 + 3 = 56 Adam 56 ÷ 4 = 14 Barry 56 53 14 ? 3 Charlie

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

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