Parents Seminar on PSLE Mathematics

Problem Solving in

PSLE Mathematics

Yeap Ban Har Marshall Cavendish Institute

Singapore

[email protected]

Slides are available at

www.banhar.blogspot.com

Paper 1 (50 min) Paper 2 (1 hr 40 min)

Type Mark Value

Number

MCQ 1 mark 10 (10%)

MCQ 2 marks 5 (10%)

SAQ 1 mark 10 (10%)

SAQ 2 marks 5 (10%)

Type Mark Value

Number

SAQ 2 marks 5 (10%)

LAQ

3 marks 4 marks 5 marks

13 (50%)

Paper 1 (1 hr) Paper 2 (1 hr 15 min)

Type Mark Value

Number

MCQ 1 mark 10 (10%)

MCQ 2 marks 10 (20%)

SAQ 2 marks 10 (20%)

Type Mark Value

Number

SAQ 2 marks 10 (20%)

LAQ

3 marks 4 marks 5 marks

8 (30%)

The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a

person’s intellectual competence”.

Ministry of Education 2006

Find the value of 12.2 ÷ 4 .

Example 1

Answer : 3.05 [B1]

12.20 4

3

12

0.20

.05

0.20

0

12.20

12 20 hundredths

Number Bond Method

Long Division Method

A show started at 10.55 a.m. and ended

at 1.30 p.m. How long was the show in

hours and minutes?

Example 2

11 a.m. 1.30 p.m.

2 h 30 min

Answer : 2 h 35 min [B1]

Find <y in the figure below.

360o – 210o = 150o

70 o

70 o

70 o

y

Example 3

The height of the classroom door is about __.

(1) 1 m

(2) 2 m

(3) 10 m

(4) 20 m

Example 4


Cup cakes are sold at 40 cents each.

What is the greatest number of cup cakes that can be bought with $95?

$95 ÷ 40 cents = 237.5

Answer: 237 cupcakes

Example 5

From January to August last year, Mr

Tang sold an average of 4.5 cars per

month, He did not sell any car in the

next 4 months. On average, how many

cars did he sell per month last year?

Example 6

4.5 x 8 =

36 ÷ 12 = 3

Answer: 3 cars / month

Mr Tan rented a car for 3 days. He was

charged $155 per day and 60 cents for

every km that he travelled. He paid

$767.40. What was the total distance

that he travelled for the 3 days?

Example 7

$767.40 – 3 x $155 = $302.40

$302.40 ÷ 60 cents per km = 504 km

Mr Tan rented a car for 3 days. He was

charged $155 per day and 60 cents for

every km that he travelled. He paid

$767.40. What was the total distance

that he travelled for the 3 days?

Example 7

767.40 – 3 x 155 = 302.40

302.40 ÷ 0.60 = 504

He travelled 504 km.



Parents Up In Arms

Over PSLE

Mathematics Paper TODAY’S 10 OCT 2009

SINGAPORE: The first thing her son did when he came out from

the Primary School Leaving Examination (PSLE) maths paper on

Thursday this week was to gesture as if he was "slitting his

throat".

"One look at his face and I thought 'oh no'. I could see that he felt

he was condemned," said Mrs Karen Sng. "When he was telling

me about how he couldn't answer some of the questions, he got

very emotional and started crying. He said his hopes of getting

(an) A* are dashed."

Not for the first time, parents are up in arms over the PSLE

Mathematics paper, which some have described as "unbelievably

tough" this year. As recently as two years ago, the PSLE

Mathematics paper had also caused a similar uproar.

The reason for Thursday's tough paper, opined the seven parents

whom MediaCorp spoke to, was because Primary 6 students were

allowed to use calculators while solving Paper 2 for the first time.

…

Said Mrs Vivian Weng: "I think the setters

feel it'll be faster for them to compute with a

calculator. So the problems they set are much

more complex; there are more values, more

steps. But it's unfair because this is the first

time they can do so and they do not know

what to expect!"

…

"The introduction of the use of calculators

does not have any bearing on the difficulty of

paper. The use of calculators has been

introduced into the primary maths curriculum

so as to enhance the teaching and learning of

maths by expanding the repertoire of learning

activities, to achieve a better balance between

the time and effort spent developing problem

solving skills and computation skills.

Calculators can also help to reduce

computational errors."

…

Another common gripe: There was not

enough time for them to complete the paper.

A private tutor, who declined to be named,

told MediaCorp she concurred with parents'

opinions. "This year's paper demanded more

from students. It required them to read and

understand more complex questions, and go

through more steps, so time constraints would

have been a concern," the 28-year-old said.

Students in the highest international benchmark are able

to apply their knowledge in a variety of situations and able to explain themselves.


1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

Problem 4

Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic

frame that covers exactly 9 squares of Table 1 with the centre square

darkened.

(a) Kay puts the frame on 9 squares as shown in the figure below.

3 4 5

11 13

19 20 21

What is the average of the 8 numbers that can

be seen in the frame?

Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic

frame that covers exactly 9 squares of Table 1 with the centre square

darkened.

(a) Kay puts the frame on 9 squares as shown in the figure below.

3 4 5

11 13

19 20 21

What is the average of the 8 numbers that can

be seen in the frame?

Alternate Method

4 x 24 = 96

96 ÷ 8 = 12

3+4+5+11+13+19+20 = 96

96 ÷ 8 = 12

(b) Lin puts the frame on some other 9 squares.

The sum of the 8 numbers that can be seen in the frame is 272.

What is the largest number that can be seen in the frame?

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32

33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56

34

A figure is formed by arranging equilateral triangles pieces of sides 3 cm in a line. The figure has a perimeter of 93 cm. How many pieces of the equilateral triangles are used?

93 cm ÷ 3 cm = 31

31 – 2 = 29

29 pieces are used. Problem 2

Problem 3

40 cm x 30 cm x 60 cm = 72 000 cm3

72 000 cm3 ÷ 5 x 3 = 43 200 cm3

43 200 cm3 ÷ 1800 cm2 = 24 cm

Problem 3

40 cm x 30 cm x 60 cm = 72 000 cm3

72 000 cm3 ÷ 5 x 2 = 28 800 cm3

28 800 cm3 ÷ 1200 cm2 = 24 cm

Rena used stickers of four different shapes

to make a pattern. The first 12 stickers are

shown below. What was the shape of the

47th sticker?

………? 1st 12th 47th

Problem 4

Weiyang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20-cent or 50-cent coin. His mother also puts in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90.

(a) How many coins were there altogether?

(b) How many of the coins were 50-cent coins?

Problem 5




Problem 5

182 7 = 20 + 6 = 26

182 x 2 + 26 = 364 + 26 = 390

There were 390 coins altogether.




$133.90 - $26 = $107.90

There were 50-cent coins.

50-cent 20-cent

Suppose each day he put in one 20-cent and

one 50-cent coins, the total is $127.40

But he only put in $107.90 ..

to reduce this by $19.50, exchange 50-cent

for 20-cent coins

$19.50 $0.30 = 65

There were 182 – 65 = 117 fifty-cent coins.

Visualization

John had 1.5 m of copper

wire. He cut some of the

wire to bend into the

shape shown in the figure

below. In the figure, there

are 6 equilateral triangles

and the length of XY is 19

cm. How much of the

copper wire was left?

Problem 5








cm. How much of the









cm. How much of the









cm. How much of the









cm. How much of the


19 cm x 5 = 95 cm

150 cm – 95 cm = 55 cm

55 cm was left.

Problem 7

Problem 7

9

2

4

1

Number Sense

Patterns

Visualization

Communication

Metacognition

Try to do as you read the problems. Do not wait till the end of the question to try to do something.

Try to draw when you do not get what the question is getting at. Diagrams such as models are very useful.

Do more mental computation when practising Paper 1.

Documents

Parents Seminar on PSLE Mathematics