Singapore Maths at Harris Workshop 3

Using Bar Model to Solve Word Problems involving whole numbers, fractions, ratios and

algebra H a r r i s F e d e r a t i o n , L o n d o n O c t o b e r 2 0 1 2

Yeap Ban Har

Marshall Cavendish Institute Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

Mathematics is “an excellent vehicle for the

development and improvement of a person’s

intellectual competence”. Ministry of Education Singapore 2006

Larry

Maria

4 units = $300

1 units = $300 4 = $75

3 units = 3 x $75 = $300 - $75 = $225

Maria gets $225.

Ratio Example 1

King Solomon Academy, London

Edgewood Elementary School, New York

John

Mary

$100 - $34 = $66

Whole Numbers Example 2

John has $34 more than Mary.

Together, they have $100.

How much money does each of them have? Royston Primary School, London

$34

$66 2 = $33

Mary has ….

John has ….

John

Mary

$34 x

x

2x + 34 = 100

2x = 100 – 34 = 66

x = 66 2 = 33

Royston Primary School, London

Learning Activity Example 3

4

1

84

1

104

1

204

1

GCSE Example 4

Last year Jora spent

30% of his salary on rent

of his salary on entertainment

of his salary on living expenses.

He saved the rest of his salary.

Jora spent £3600 on living expenses.

Work out how much money he saved.

5

2

4

1

10

3%30

10

4

5

2

20

5

4

1

20

8

20

6

4 x £3600 = £12000 + £2400 = £14400

20

19

20

5

20

8

20

6Jora spent:

Jora saved: 20

1

20

191

£14400 20 = £1440 2 = £…..

GCSE Example 4

Last year Jora spent

30% of his salary on rent

of his salary on entertainment

of his salary on living expenses.

He saved the rest of his salary.

Jora spent £3600 on living expenses.

Work out how much money he saved.

5

2

4

1

5 units =£3600

1 unit = £3600 5 = £360 x 2

= £720

PSLE Example 5

Peili

Nurul

After …

Peili

Nurul

Before …

7

7

7

GCSE Example 5

Additional Example on Using Bar

Model and Number Line to Solve

Linear Equations

Solve 7 – 3y = 1 . 7

3y 1

3y + 1 = 2

3y = 2 – 1

3y = 1

Equations Example 6

Solve 7 – 3y = 1 .

7

3y = 6

3y

1

GlobeAcademy, London

emphasis visualization