helping students with psle mathematics_6 february 2010

A Seminar for Parents & Tutors

Helping Students withPSLE Mathematics

6 February 2010

SINGAPOTE TEACHERS’ UNION

Yeap Ban HarNational Institute of Education

Nanyang Technological University Singapore

banhar.yeap@nie.edu.sg

Paper 1 (50 min)

Type Mark Value

Number

MCQ 1 mark 10

MCQ 2 marks 5

SAQ 1 mark 10

SAQ 2 marks 5

Paper 2 (1 hr 40 min)

Type Mark Value

Number

SAQ 2 marks 5

LAQ3 marks4 marks5 marks

13

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

improvement of a person’s intellectual competence”.

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.

12.204

3

12

0.20

3.05

0.20

0

12.20

12 0.20

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?

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

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.

1100 1330

Find <y in the figure below.

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

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

70 o

70 o

70 o

y

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.

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 Skills ItemBasic Skills Item

Non-Calculator Item Calculator Item

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?

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?

Non-Calculator Item Calculator Item

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?

 4.5 x 8 = 36 36 ÷ 12 = 3

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?

$155 x 3 = $465 $767.40 - $465 = $302.40 $302.40 ÷ 60 cents/km

= 504 km

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

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

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

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.

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

Challenging Items: Challenging Items: VisualizationVisualization

Challenging Items: Challenging Items: VisualizationVisualization

40 x 30 x 60 = 72 000

72 000 ÷ 5 x 2 = 14 400 x 2 = 28 800

28 800 ÷ 1200 = 24

The height is 24 cm

Challenging Items: Challenging Items: VisualizationVisualization

40 x 30 x 60 ÷ 5 x 2 ÷ (40 x 30) = 24

The height is 24 cm. 40 x 30 x 60 ÷ 5 x 3 ÷ (40 x 45) = 24

The height is Tank B is 24 cm.It is the same for Tank A.

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

It is so basic, students doing It is so basic, students doing Foundation Mathematics are Foundation Mathematics are expected to have the ability …expected to have the ability …

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

18

12

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

12

12

12

12

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

David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 minutes earlier than Michael. However, Michael reached Town B 50 minutes earlier than David. When Michael reached Town B, David had travelled 4/5 of the journey and was 75 km away from Town B.

David and Michael drove from Town A to Town B at different speeds. Both did not change their speeds throughout their journeys. David started his journey 30 minutes earlier than Michael. However, Michael reached Town B 50 minutes earlier than David. When Michael reached Town B, David had travelled 4/5 of the journey and was 75 km away from Town B.

Michael

David

75 km4/5

4 x 75 km = 300 km

(a) Town A to Town B is 375 km.

(b) 50 min 75 km

10 min 15 km

1 h 6 x 15 km = 90 km

(c) 50 min 1/5 of the journey250 min whole journey

Michael took 80 min less.He took 170 min.

Emphasis on Visualization is not Emphasis on Visualization is not new.new.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?

Emphasis on Visualization is not Emphasis on Visualization is not new.new.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?

Emphasis on Visualization is not Emphasis on Visualization is not new.new.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?

Emphasis on Visualization is not Emphasis on Visualization is not new.new.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?

Emphasis on Visualization is not Emphasis on Visualization is not new.new.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?

19 cm x 5 = 95 cm

150 cm – 95 cm = 55 cm

55 cm was left.

180o – 2 x 21o – 2 x 28o = …

Siti packs her clothes into a suitcase and it weighs 29 kg. Rahim packs his clothes into an identical suitcase and it weighs 11 kg. Siti’s clothes are three times as heavy as Rahim’s clothes. What is the mass of Rahim’s clothes?What is the mass of the suitcase?

11 kg

29 kg

11 kg

29 kg

11 kg

18 kg11 kg

18 kg

9 kg

9 kg

27 kg

Every minute Machine A prints 12 pages more than Machine B. Machine A and Machine B together print a total of 528 pages in 3 minutes. At this rate, how many pages does Machine B print in 1 minute?

Every minute, A and B print 528 ÷ 3 = 176 pages.

12

176

B prints 82 pages per minutes

Siti started saving some money on Monday. On each day from Tuesday to Friday, she saved 20 cents more than the amount she saved the day before. She saved a total of $6 from Monday to Friday. How much money did she save on Monday?

20

20 20

20 20

20 20

20

20 20

$6$6 – 10 x 20 cents = $4

$4 ÷ 5 = 80 cents

She saved 80 cents on Monday.

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

B

A

156

72

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

B

A

156

72

At first Shop A had 156 kg of rice and Shop B had 72 kg of rice. After each shop sold the same quantity of rice, the amount of rice that Shop A had was 4 times that of Shop B. How many kilograms of rice did Shop A sell?

B

A

3 units 156 – 72 = 84 = 60 + 24

1 unit 28

Shop A sells (156 – 4 x 28) kg = 44 kg.

Alternatively Shop B sells (72 – 28) kg = 44 kg.So does Shop A.

88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day?

34

88

54

34

54 – 34 = 2034 – 20 = 14

3 x 7 = 21 girls wear goggles

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?

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?

$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?

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?

Chongfu

Azman

Bala

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?

60Chongfu

Azman

Bala

60

100

100

100

40

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?

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?

An Example from Textbook