A4/B4 - Let's STAR te Way 2 - Model Drawing_Heuristics

Let’s STAR the way

To better support our children in

learning Mathematics

• Chemistry between 2 people

Using Ratio

Math in everyday life

Concepts Skills

Strategies

Fractions - Concepts

A box contains 3 red apples and 7 green apples.

What fraction of the apples in the box are red?

A fraction can be conceptualised as a numerical figure for comparing the number of items in 2 sets.

of the apples are red. 3 10

Fractions - Concepts

of the apples are red. 3 10

3 10

in discrete form

3 10

in continuous form

Fractions - Skills

Equivalent fractions

1 3

2 6

3 9

4_ 12

1 3

2 6

3 9

4_ 12

= = =

Fractions - Strategies

A specific method to solve a set of similar problems

One strategy for solving fraction problems is the Tree-Diagram Strategy/ Branching Method

Jane used of a packet of sugar for baking cakes.

She used of it for baking biscuits.

What fraction of the packet of sugar was left?

4

1

3

1





4

1

3

1

1 packet of sugar

4

1of the packet of sugar

3


12

3=

12

4= 12

5

12

71

12

7

12

4

12

3

cakes

biscuits





4

1

3

1

Cake

Biscuits Left

1_ 4

3_ 12 =

1_ 3

4_ 12 =

5_ 12

of the packet of sugar was left.

Concepts - 1. fractions

Skills - 1. part-whole method - 2. equivalent fractions - 3. addition and subtraction of fractions

Strategy - Tree-Diagram Strategy/ Branching Strategy/ model



She used of the remainder for baking biscuits.


4

1

3

1

1 packet of sugar

4


4


4

1

4

3

3

1x

2

1

4

3

3

2x

cakes

remainder biscuits

left

2

1

4

1

4

11

2

Method



She used of the remainder for baking biscuits.


4

1

3

1

Cake

Biscuits Left

2_ 4

of the packet of sugar was left.

Remainder

1_ 2

=

Concepts - 1. fractions - 2. remainder of remainder

Skills - 1. part-whole method - 2. multiplying a fraction by another fraction

Strategy - Tree-Diagram Strategy/ Branching Strategy/models

George Polya Steps of Problem Solving

Step 1 Study the question carefully

Step 2 Think of a plan

Step 3 Act on my plan

Step 4 Reflect and check

STAR Math

3. Syed and Nurliena each earned some money during the

school holidays. If Syed spent $40 each week and Nurliena spent

$120 each week, Syed would have $720 left when Nurliena had

spent all her money. If Syed spent $120 each week and Nurliena

spent $40 each week, Syed would have $80 left when Nurliena

had spent all her money. How much did Syed earn?

S

N

S

N

$720

$80

8 units = $720 - $80 = $640

1 unit = $80

Syed had $720 + $80 = $800

4. Miss Tan bought some scarves and dresses from a shop for $4 650.

She paid $150 less for the scarves than dresses. Each dress cost $14

more than each scarf. The number of dresses bought was 60% of the

number of scarves bought. How many scarves did she buy?

D

S

$2 400

$2 250

$4 650

$4 650 - $150 = $4500

$4 500 ÷ 2 = $2 250 ( Paid for scarves)

$2 250 + $150 = $2 400 ( Paid for dresses)

* Must be same number of items to compare prices

D

S

$2 400

$2 250

$4 650

$2 400 ÷ 3 = $800 ( 1 unit of dresses)

$2 250 ÷ 5 = $450 ( 1 unit of scarves)

* Now we can compare the difference in price





D

S

$2 400

$2 250

$4 650

$800 - $450 = $350 ( Big difference in price: 1u of dress vs 1u of scarf)

$14 ( Small difference in price: 1 pc of dress vs 1 pc of scarf)

$350 ÷ 14 = 25 ( No. of pc in 1 unit)

5 x 25 = 125 (No. of scarves bought)





20 20 20 Z

T

1 big part = 2 small units

Zack gives 3 units + 30

Tim will have 11 units + 30

Zack will have 3 units + 30

5. of Zack’s marbles is 20 more than of Tim’s marbles. If Zack

gives half of his marbles to Tim, Tim will have 64 more marbles

than Zack.

a. How many marbles does Zack have at the start?

b. What fraction of Zack’s marbles is Tim’s marbles at the start?

Leave your answer in the simplest form.

31

41

20 20 20 Z

T

(11 units + 30)

- (3 units + 30)

8 units = 64

1 unit = 8

5. of Zack’s marbles is 20 more than of Tim’s marbles. If Zack

gives half of his marbles to Tim, Tim will have 64 more marbles

than Zack.

a. How many marbles does Zack have at the start?

b. What fraction of Zack’s marbles is Tim’s marbles at the start?

Leave your answer in the simplest form.

31

10864

Zack has ( 6 x 8 ) + 60 = 108

Tim has 8 x 8 = 64

41

= 2716

6. An MRT train left Station A with some passengers. At the first stop

Station B, no one alighted while of the original number of passengers

boarded the train. At the next stop, Station C, of the total passengers

alighted and 120 passengers boarded. At the last stop, Station D, all 632

passengers got off. How many passengers were on the train at Station A?

31

51

120

632

632 – 120 = 512

(512 ÷ 4 ) x 5 = 640

(640 ÷ 4 ) x 3 = 480

31

51

? 632

+ 120 54 x

34 x

- 120 34 ÷

632 – 120 = 512

54 ÷

512 ÷ 54

= 512 x

= 640 45

512 640

640 ÷ 34

= 640 x

= 480 43

480

6. An MRT train left Station A with some passengers. At the first stop

Station B, no one alighted while of the original number of passengers

boarded the train. At the next stop, Station C, of the total passengers

alighted and 120 passengers boarded. At the last stop, Station D, all 632

passengers got off. How many passengers were on the train at Station A?

7. A fruit vendor spends a total of $100.80 on papayas, oranges and

mangoes. The number of papayas is the number of oranges. The

number of mango is the number of papayas. The ratio of the price of a

papaya, an orange and a mango is 9 : 2 : 12. If the mango cost $2.40,

what is the total number of fruits bought by the fruit vendor?

31

21

Number of fruits Price

M : P : O

1 : 3

1 : 2

2 : 6

1 : 2 : 6

* 1 basic set has 9 fruits

M : P : O

12 : 9 : 2

$2.40 : ? : ? $1.80 : $0.40

7. Continue. A fruit vendor spends a total of $100.80 on papayas,

oranges and mangoes. …………what is the total number of fruits bought

by the fruit vendor?

Number of fruits

M : P : O

1 : 2 : 6

* 1 basic set has 9 fruits

Price

M : P : O

12 : 9 : 2

$2.40 : ? : ? $1.80 : $0.40

$2.40 x 1 = $2.40

$1.80 x 2 = $3.60

$0.40 x 6 = $2.40

$2.40 + $3.60 + $2.40 = $8.40

* 1 set cost $8.40

$100.80 ÷ $8.40 = 12 sets were bought

12 x 9 = 108 fruits were bought in total

A4/B4 - Let's STAR te Way 2 - Model Drawing_Heuristics

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