2010 PSLE Mathematics Seminar for Parents

A Seminar for Parents

Helping Students withPSLE Mathematics

February 2010

www.askyeapbanhar.blogspot.com

Yeap Ban HarNational Institute of Education

Nanyang Technological University Singapore

[email protected]

What is PSLE Mathematics?

PSLE Mathematics

Paper 1 (50 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%)

Paper 2 (1 hr 40 min)

Type Mark Value

Number

SAQ 2 marks 5 (10%)

LAQ3 marks4 marks5 marks

13 (50%)

PSLE Foundation Mathematics

Paper 1 (1 hr)

Type Mark Value

Number

MCQ 1 mark 10 (10%)

MCQ 2 marks 10 (20%)

SAQ 2 marks 10 (20%)

Paper 2 (1 hr 15 min)

Type Mark Value

Number

SAQ 2 marks 10 (20%)

LAQ3 marks4 marks5 marks

8 (30%)

Challenging MCQsfor problems that are difficult for students to

communicate solution methods

Ann, Beng and Siti each had some money at first. Ann gave Beng $0.50. Beng then gave Siti $0.75. Siti spent $0.25 on a ruler. At the end, they had $3 each. What is the difference between the amount of money that Ann and Siti had at first?

(1) $1.00

(2) $0.50

(3) $0.75

(4) $1.25

Ann $3

Beng $3

Siti $3 $3.25 $2.50

$3.75 $3.25

$3.50

What kind of curriculum is it based

on?

rationale of the curriculum

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

improvement of a person’s intellectual competence”.

Visualization – an intellectual competence - is one of the most

important ability in solving problems

Basic Skillsemphasis on visualization in the learning

process

Basic Skillsmental strategies strengthen visualization

ability

Find the value of 12.2 ÷ 4 .

It is not expected that P6 students need to perform written working to do it.

P4 students may need to perform written working as their ability in mental strategies is not as developed as that of P6 students.

Basic Skills Items

12.204

3

12

0.20

3.05

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?


P3 students may need to draw a time line as their ability in using mental strategies is not as developed as that of P6 students.

Basic Skills Items

1100 1330

Prawns are sold at $1.35 per 100 g at a market.What is the price of 1.5 kg of prawns?

Basic Skills Items

$13.50 + $6.75 = $ …

Answer: $_________

Find <y in the figure below.


P5 students may need to perform written working 360o – 210o as the content is new to them.

Basic Skills Items

70 o

70 o

70 o

y

Basic Skillscomputation and procedures is not

everything

The height of the classroom door is about __.

1. 1 m2. 2 m3.10 m4.20 m

Some tasks simply do not require written working.

Basic Skills Items

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

Basic Skill Item

Basic Application Item

Basic Skillsmental computation is an important part of

the curriculum

Find the value of(a) 99 + 97(b) 56 ÷ 8

Find the value of(a) 200 – 53 (b) 9 x 9

Find the value of(a) 73 – 15 (b) 42 ÷ 7

Find the value of(a) 169 + 34(b) 8 x 7

Challenging Problemswhat makes them challenging

1 + 2 + 3 + 4 + 5 + … + 95 + 96 + 97The first 97 whole numbers are added up.What is the ones digit in the total?

Challenging Items: Novel






The method is difficult to communicate in written form. Hence, the problem is presented in the MCQ format where credit is not given for written method.


Challenging Problem: Connection

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

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 Method4 x 24 = 9696 ÷ 8 = 12

3+4+5+11+13+19+20 = 9696 ÷ 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

New Emphasis on Looking for Pattern (Item from 2006)

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


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? ………?1 5 9


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? ………? 4 8 12

rationale of the curriculum

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

improvement of a person’s intellectual competence”.

3 cm 5 cm

3 cm

7 cm

With visualization, one does not need to know a formula to calculate the area of a trapezium.

9 cm2

6 cm2

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.

chocolates

Jim

Ken

sweets

12

12

3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22

Half of the sweets Jim bought = 22 + 12 = 34So Jim bought 68 sweets.`

18

12

12

12

12

180o – 2 x 21o – 2 x 28o = …

The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets available is 1.5 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all the five-dollar tickets were sold. The ticket sales amounted to $5 600. How much more would have been collected if all the tickets were sold?

FMPS

The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets available is 1.5 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all the five-dollar tickets were sold. The ticket sales amounted to $5 600. How much more would have been collected if all the tickets were sold?

FMPS

$10

$57 units $5600

1 units $800

This amount would have been collected: $5600 + $800 = $6400

Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first?

FMPS


FMPS

Chongfu

Azman

Bala


FMPS

60Chongfu

Azman

Bala

60

100

100

100

40


FMPS

60Chongfu

Azman

Bala

60

100

100

100

40

780 – 380 = 300

Some stamps were placed in Album A and Album B. If 30 stamps were removed from Album A, the ratio of the number of stamps in Album A to the number of stamps in Album B would be 1 : 4. If 60 stamps were removed from Album B, the ratio would be 5 : 2. How many stamps were there in Album B?

FMPS