PSLE Mathematics Seminar

Association of Mathematics Educators

http://math.nie.edu.sg/ame

Yeap Ban HarNational Institute of Education

Nanyang Technological University

banhar.yeap@nie.edu.sg

Part 1This section explains the PSLE format.

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%)

Part 2This section explains the curriculum that

the PSLE is based on.

PSLE Mathematics is Based on a Problem-Solving Curriculum

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”.

Part 3This section explains that problem solving

is a basic ability in the PSLE.

“Mathematical problem solving is central to

mathematics learning.”

Ministry of Education 2006

Ali paid for a 85-cent pen with a $5 note.How much change should he get?

Example 1

Answer: $__________

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

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

Example 3

$13.50 + $6.75 = $20.25

During a sale, mugs are sold in sets of 3 for $1.45. How much must Bala pay for buying 15 mugs during the sale?

Example 4

$1.45 x 5 = $14.50 ÷ 2 = $7.25

Sam had 295 eggs. He packed all the eggs into boxes of 9 with some left over. How many eggs are left over?

Example 5

295 ÷ 9 = (30 + 2) remainder 7

7 eggs are left over

295

270 25

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 5

$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 5

767.40 – 3 x 155 = 302.40

302.40 ÷ 0.60 = 504

He travelled 504 km.

Find <y in the figure below.

360o – 210o = 150o

70 o

70 o

70 o

y

Example 6

“Mathematical problem solving is central to

mathematics learning.”

Ministry of Education 2006

Part 4This section explains that there are other

competencies in mathematics learning e.g. practical skills.

Basic Skillscomputation and procedures is not

everything

The height of the classroom door is about __.

(1) 1 m(2) 2 m(3) 10 m(4) 20 m

Example 7

Practical Skillswritten examinations may include bits of

practical tasks

Possibilities

ExampleFind the area of the cover page of the examination paper.

Part 5This section explains the key competencies

in solving challenging problems.

““… including non-routine, open-ended and real-world

problems.”

Ministry of Education 2006

Example 8

Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.

How many cookies did Mrs Hoon sell?

Example 10

chocolate cookies

almond cookies

210

1/5

5/83/8

3/8 – 1/5 = 7/40 210

1/40 30

32/40 960

She sold 960 cookies.

Example 11

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 Ken bought = 22 + 12 = 34So Ken bought 68 sweets.

18

12

12

12

12

18

Visualization – an intellectual competence - is one of the most

important ability in solving problems

Learning Basic Skillsemphasis on visualization in the learning

process

My Pals Are Here! Mathematics 4A

Shaping Maths 2A

Shaping Maths 4B

Catholic High School (Primary)

visualization

Wellington Primary School

Move 3 sticks to make 2 squares.

Task

Move 3 sticks to make 2 squares.

Task

Move 3 sticks to make 2 squares.

Photo: Princess Elizabeth Primary School

Division

My Pals Are Here! Mathematics 1B

visualization

Scarsdale Middle School New York

Primary Mathematics Standards Edition Grade 6

Primary Mathematics Standards Edition Grade 6

How to make sure the butterfly cannot fly

How do you get a butterfly?

First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.

When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.

If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.

The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.

If the butterfly is not left to struggle to come out of the cocoon, it will never fly.

We can learn an important lesson from the butterfly.

Lim Siong Guan Head, Civil Service

How to make sure the butterfly cannot fly

How do you get a butterfly?

First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.

When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.

If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out

easily but it will never fly. Your "help" has destroyed the butterfly.

The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.

If the butterfly is not left to struggle to come out of the cocoon, it will never fly.

We can learn an important lesson from the butterfly.

Lim Siong Guan Head, Civil Service

Part 6The ability to monitor thinking as students read – metacognition as well as the ability to show working – communication are the

other important competencies.

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

Part 7This section explains the importance of

number sense and the role of mental computations in developing number sense.

“Although students should become competent in the various mathematical skills,

over-emphasising procedural skills without understanding the underlying mathematical

principles should be avoided.”

Ministry of Education 2006

Find the value of 12.2 ÷ 4 .

Example 5

Find the value of 6005 – 1947 .

Example 5

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

Basic Skillsmental computation is an important part of

the curriculum

Basic Skillsmental strategies strengthen visualization

ability

Part 8This section explains the role of the

calculator – it is just a computing device. Thinking is still what students need to do.

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

Part 9This section summarizes the five key

competencies in mathematics.

Five Key Competencies Visualization Number Sense Metacognition Communication Patterns – this is shown on the next slide

Part 10Must one knows a formula to calculate the

area of a trapezium.

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