parents seminar on psle mathematics
DESCRIPTION
This was held in Henry Park PrimarTRANSCRIPT
![Page 1: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/1.jpg)
Problem Solving in
PSLE Mathematics
Yeap Ban Har Marshall Cavendish Institute
Singapore
Slides are available at
www.banhar.blogspot.com
![Page 2: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/2.jpg)
![Page 3: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/3.jpg)
![Page 4: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/4.jpg)
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%)
![Page 5: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/5.jpg)
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%)
![Page 6: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/6.jpg)
![Page 7: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/7.jpg)
![Page 8: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/8.jpg)
![Page 9: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/9.jpg)
![Page 10: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/10.jpg)
The rationale of teaching mathematics is that it is “a good vehicle for the development and improvement of a
person’s intellectual competence”.
![Page 11: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/11.jpg)
Ministry of Education 2006
![Page 12: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/12.jpg)
Find the value of 12.2 ÷ 4 .
Example 1
Answer : 3.05 [B1]
![Page 13: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/13.jpg)
12.20 4
3
12
0.20
.05
0.20
0
12.20
12 20 hundredths
Number Bond Method
Long Division Method
![Page 14: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/14.jpg)
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]
![Page 15: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/15.jpg)
Find <y in the figure below.
360o – 210o = 150o
70 o
70 o
70 o
y
Example 3
![Page 16: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/16.jpg)
The height of the classroom door is about __.
(1) 1 m
(2) 2 m
(3) 10 m
(4) 20 m
Example 4
![Page 17: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/17.jpg)
Ministry of Education 2006
![Page 18: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/18.jpg)
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
![Page 19: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/19.jpg)
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
![Page 20: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/20.jpg)
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
![Page 21: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/21.jpg)
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.
![Page 22: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/22.jpg)
Ministry of Education 2006
![Page 23: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/23.jpg)
Ministry of Education 2006
![Page 24: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/24.jpg)
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.
![Page 25: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/25.jpg)
Students in the highest international benchmark are able
to apply their knowledge in a variety of situations and able to explain themselves.
![Page 26: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/26.jpg)
![Page 27: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/27.jpg)
![Page 28: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/28.jpg)
![Page 29: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/29.jpg)
![Page 30: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/30.jpg)
![Page 31: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/31.jpg)
![Page 32: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/32.jpg)
![Page 33: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/33.jpg)
![Page 34: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/34.jpg)
Ministry of Education 2006
![Page 35: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/35.jpg)
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
![Page 36: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/36.jpg)
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?
![Page 37: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/37.jpg)
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
![Page 38: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/38.jpg)
(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
![Page 39: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/39.jpg)
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
![Page 40: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/40.jpg)
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
![Page 41: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/41.jpg)
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
![Page 42: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/42.jpg)
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
![Page 43: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/43.jpg)
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
![Page 44: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/44.jpg)
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
182 7 = 20 + 6 = 26
182 x 2 + 26 = 364 + 26 = 390
There were 390 coins altogether.
![Page 45: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/45.jpg)
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?
$133.90 - $26 = $107.90
There were 50-cent coins.
50-cent 20-cent
![Page 46: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/46.jpg)
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.
![Page 47: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/47.jpg)
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
![Page 48: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/48.jpg)
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?
![Page 49: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/49.jpg)
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?
![Page 50: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/50.jpg)
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?
![Page 51: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/51.jpg)
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.
![Page 52: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/52.jpg)
Problem 7
![Page 53: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/53.jpg)
Problem 7
9
2
4
1
![Page 54: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/54.jpg)
Number Sense
Patterns
Visualization
Communication
Metacognition
![Page 55: Parents Seminar on PSLE Mathematics](https://reader034.vdocuments.net/reader034/viewer/2022042700/554efc03b4c90580698b4ac1/html5/thumbnails/55.jpg)
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.