a4/b4 - let's star te way 2 - model drawing_heuristics
DESCRIPTION
Parents' Symposium 2015TRANSCRIPT
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
Fractions - Strategies
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
1 packet of sugar
4
1of the packet of sugar
3
1of the packet of sugar
12
3=
12
4= 12
5
12
71
12
7
12
4
12
3
cakes
biscuits
Fractions - Strategies
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
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
Fractions - Strategies
Jane used of a packet of sugar for baking cakes.
She used of the remainder for baking biscuits.
What fraction of the packet of sugar was left?
4
1
3
1
1 packet of sugar
4
1of the packet of sugar
4
3of the packet of sugar
4
1
4
3
3
1x
2
1
4
3
3
2x
cakes
remainder biscuits
left
2
1
4
1
4
11
2
Method
Fractions - Strategies
Jane used of a packet of sugar for baking cakes.
She used of the remainder for baking biscuits.
What fraction of the packet of sugar was left?
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
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
$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)
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?
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