How to Ace PSLE Maths

How to Ace the PSLE Mathematics

Yeap Ban HarNational Institute of Education

Nanyang Technological University

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%)

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”.

“… over-emphasising procedural skills without understanding the

underlying mathematical principles should be avoided.”

Ministry of Education 2006

Find the value of (a) 11.98 – 2.6 (b) 43 ÷ 10

Example 0

Find the value of 12.2 ÷ 4 .

Basic Skills Items

Example 1

12.204

3

12

0.20

3.05

0.20

0

12.20

12 20 hundredths

Number Bond Method

Long Division Method

Find <y in the figure below.

360o – 210o = 150o

70 o

70 o

70 o

y

Example 2

The height of the classroom door is about __.

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

Example 3

“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 4

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 5

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 6

$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 7

295 ÷ 9 = 32 remainder 7

7 eggs are left over

295

270 25

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

Example 8

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 9

$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 9

767.40 – 3 x 155 = 302.40

302.40 ÷ 0.60 = 504

He travelled 504 km.

“Mathematical problem solving is central to

mathematics learning.”

Ministry of Education 2006

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

problems.”

Ministry of Education 2006

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

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

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

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

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 Items: Novel

- = n where n is a whole numberThe difference between a 2-digit wholenumber and a 1-digit whole number is n. Find all the possible subtraction sentences

when n = 4. Describe in words how the number of

possible subtraction sentences depends on the value of n.

Challenging Items: Novel

Example 10

10 - 6 = 411 - 7 = 412 - 8 = 413 - 9 = 4

10 – 7 = 311 – 8 = 312 – 9 = 3

Challenging Items: Novel

Example 10

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

Example 11

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

Example 13

Example 14

“Skill proficiencies include the ability to use technology

confidently, where appropriate, for exploration and problem solving.”

Ministry of Education 2006

32 x 46 = 23 x 6423 is obtained when the digits in 32 are

reversed. 64 is obtained when the digits in 46 are

reversed.   Find three other pairs of 2-digit numbers

where AB x CD = BA x DC.

Example 15

Example 16

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 17

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.

Five Core Competencies 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.

Some Strategies

Shop A

Shop B

After

Example 18

Shop A

Shop B

Before 156 kg

72kg

156 kg – 72 kg = 84 kg

3 units = 84 kg

1 unit = 84 kg ÷ 3 = 28 kg72 kg – 28 kg = 44 kg

Shop B sold 44 kg of rice.

Shop A sold 44 kg of rice.

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?

(Teck Whye Primary School, Grade 6)

Album A

Album B

Album C

Example 19

The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?

(Teck Whye Primary School, Grade 6)

Album A

Album B

Album C

13 units 444 + 24 = 4681 unit 468 ÷ 13 = 36

468

390 78

7 units ?7 units 36 x 7 = 210 + 42 = 252There were 252 more stamps in Album C than Album A in the end.

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