“Enhancing Understanding and Mastery

of P3 and P4 Mathematics”

P3 and P4 Parent Workshop

3 April 2020, Friday

Math Sharing

Use of Model Drawing for Effective Problem-Solving

Use of Heuristics

PSLE Questions involving P3 or P4 Concepts

P3 and P4 Syllabus

• The P3 and P4 syllabus cover many important fundamental concepts. (eg. types of angles, fraction of a set)

• Based on our Spiral Curriculum, students will learn certain topics in greater depth at P5 and P6. Hence, if their foundation in P3 and P4 is weak, they will face challenges in mastering more difficult concepts at higher levels.

• Certain topics covered in P3 and P4 will not be taught again but they will still be tested at PSLE. (eg. length, mass, factors and multiples, 8-point compass, multiplication and long division)

Spiral Curriculum from P3 to P4 Topics P3 P4

Whole

Numbers

Numbers up to 10 000 Numbers up to 100 000

Four Operations

(up to 2-step word problems)

Four Operations

(up to 3-step word problems)

Factors and Multiples

Fractions Proper Fractions and

Equivalent Fractions

Mixed Numbers and Improper

Fractions

Fraction of a whole Fraction of a set of objects

Addition and Subtraction Addition and Subtraction

(up to 2-step word problems)

Decimals Money in decimal notation

(2 decimal places)

Decimals up to 3 decimal places

Addition and Subtraction of

money in decimal notation

Four Operations

(up to 2-step word problems)

Step 1: Understanding the Problem

Step 2: Devising a Plan

Step 3: Carrying out the plan

Step 4: Looking back

George Polya’s 4-step Problem-Solving Process

What makes a good model?

Help learner ‘see’ the question

Clearly labelled with names,

numbers

Indicate where is to guide

thinking

?

Basic Models

Part-Whole model

Understand the relationship between the parts that make the whole

Words such as ‘altogether’, ‘in all’, ‘total’, ‘left’ appear in the problem

Whole = Part + Part

Part = Whole - Part

Ravi’s family ate dinner at a restaurant.

The bill was $68.50.

Ravi’s father paid the waiter $100.

How much change should he get?

[Change = Paid - Spent]

Money (WB 3A p. 183)

$100 - $68.50 = $31.50

Ans: $31.50

$68.50

Spent? ?

Paid $100

Change

Basic Models

Comparison model

Students must have a good understanding of

comparatives such as ‘more/less than’, heavier/lighter

than, longer/shorter than and the meaning of

difference [How much more/less…?]

Annotation: Help students better understand the

question

Decimals (WB 4B p.62)

A wire 36 m long is cut into two pieces.

One of the pieces is 15.42 m long.

How much longer is the other piece of wire?

Ans: 5.16 m

36first

second

15.42

36 - 15.42 = 20.58

20.58 - 15.42 = 5.16

?

?

Basic Models Unitary model

A

B

1 unit

5 units

total

Use of the term ‘unit/s’

Use of = sign

Words such as ‘twice’, ‘times’ e.g. ‘5 times’ appear in

the problem

Whole Numbers (WB 3A p.144)

In a school gymnasium, there are 25 basketballs and 6 times as many

tennis balls.

(a) How many tennis balls are there?

(b) How many tennis balls and basketballs are there altogether?

25

Basketball

Tennis ball

(b) ?

(a) 1 unit = 25

6 units = 6 x 25

= 150

1 u 6 u

(a) ? (b) 7 units = 7 x 25

= 175

Ans: (a) 150

(b) 175

Use of other Heuristics for Effective Problem-solving

• Guess and Check

• Making Suppositions

When do we use Heuristics?

• Not all problems require the use of heuristic(s) to solve, especially when the problem is simple and straight forward.

• The use of heuristics enhances the chancesof achieving a solution.

• Guess and Check and Making Suppositions are methods to make a calculated guess.

Guess and Check

• This is also called ‘trial and error’.

• We make a guess of the answer and checkwhether it satisfies all the conditions given.We repeat this process with reasonableguesses until we reach an answer that satisfiesall the conditions.

• Students can also use this heuristics whenthey are ‘stuck’ at a problem and have no ideahow to proceed.

MTS 2020 P4 Problem-Solving Booklet

There are 50 cars and motorcycles at a car park. Given that

the total number of tyres was 136, how many cars are there at

the car park?

Number of cars

Tyres that the cars have

Number of motorcycles

Tyres that the motorcycles

have

Total number of tyres

Check

25 25 x 4 = 100 25 25 x 2 = 50 100 + 50 = 150 No

24 24 x 4 = 96 26 26 x 2 = 52 96 + 52 = 148 No

18 18 x 4 = 72 32 32 x 2 = 64 72 + 64 = 136 Yes

Ans: 18 carsFor every decrease in the number of cars,

the total number of tyres decreases by 2.

150 – 136 = 14

14 ÷ 2 = 7

25 – 7 = 18

Guess and Check

Making Suppositions

• We suppose a statement about a givenproblem situation is true (even though it is notgiven by the problem or it is untrue)

• When we make such suppositions, we usuallyadd element(s) or remove element(s) from theproblem to see how the other element(s) fromthe problem are affected.

MTS 2020 P4 Problem-Solving Booklet

There are 50 cars and motorcycles at a car park. Given that

the total number of tyres was 136, how many cars are there at

the car park?

Making Supposition

Assume all were motorcycles,Total number of tyres = 50 x 2 = 100Difference in total number of tyres= 136 – 100 = 36 (need to add another 36 tyres)

Difference between the number of tyres of a car and a motorcycle = 4 – 2 = 2

36 ÷ 2 = 18

Ans: 18

Check:18 x 4 = 7232 x 2 = 6472 + 64 = 136

Importance of mastering a repertoire of heuristics

Question

There are 50 cars and motorcycles at a car park. Given that the total number of tyres was 136, how many cars are there at the car park?

• It is faster to use ‘making suppositions’ than ‘guess and check’ in most cases.

Another example using Guess & Check

During a competition, 5 points were awarded for each gold medal and 2 points were awarded for each silver medal. A team won 25 medals and was awarded 74 points. How many gold medals did the team win?

Number

of gold

medals

Points

awarded for

gold medals

Number of

silver

medals

Points

awarded for

silver medals

Total number

of points

Check

13 13 x 5 = 65 12 12 x 2 = 24 65 + 24 = 89 No

12 12 x 5 = 60 13 13 x 2 = 26 60 + 26 = 86 No

8 8 x 5 = 40 17 17 x 2 = 34 40 + 34 = 74 Yes

Ans: 8 gold medalsFor every decrease in the number of gold

medals, the total number of points decreases

by 3.

89 – 74 = 15

15 ÷ 3 = 5

13 – 5 = 8

Assume that all were silver medals.

Total points = 25 x 2 = 50

Difference in total number of points = 74 – 50 = 24

Difference between points awarded = 5 – 2 = 3

24 ÷ 3 = 8

Ans: 8

Another example using Guess & Check

During a competition, 5 points were awarded for each gold medal and 2 points were awarded for each silver medal. A team won 25 medals and was awarded 74 points. How many gold medals did the team win?

Check:12 x 4 = 4813 x 2 = 2648 + 26 = 74

In the number 43.21, which digit is in the tens place?

(1) 1

(2) 2

(3) 3

(4) 4

PSLE 2019 Booklet A Question 1 P4 (Decimals – Place Value System)

Place Value ChartTens

(T)

Ones

(O)

. Tenths (t) Hundredths

(th)

4 3 . 2 1

PSLE Questions involving P3 or P4 Concepts

Which of the following is the same as 50 kg 80 g?

(1) 5080 g

(2) 5800 g

(3) 50 080 g

(4) 50 800 g

PSLE 2019 Booklet A Question 2

1 kg = 1000 g

50 kg = 50 000 g

50 kg 80 g = 50 000 g + 80 g= 50 080 g

P3 (Measurement - Mass)

P4 (Numbers to 100 000)

Conversion of Measurement

Which pair of lines are parallel?

(1) AB and BC

(2) CD and FE

(3) ED and AB

(4) FE and AF

PSLE 2019 Booklet A Question 4P3 (Perpendicular and Parallel lines)

2 lines that will never meet as they have a constant distance between them.

Jill baked some muffins to sell at a funfair. Figure 1 shows the number of muffins that was sold. Figure 2 shows the number of muffins left unsold at the end of the funfair.

PSLE 2019 Booklet A Question 5 and 6P3 (Bar Graphs)

Infer each marking = 2 muffins

What was the number of chocolate muffins Jill baked?

(1) 10

(2) 28

(3) 34

(4) 38

PSLE 2019 Booklet A Question 5P3 (Bar Graphs)

28 (sold) + 10 (left) = 38 (total chocolate muffins)

Altogether, how many apple and banana muffins were left unsold after the funfair?

(1) 27

(2) 34

(3) 44

(4) 54

PSLE 2019 Booklet A Question 6P3 (Bar Graphs)

18 (apple left) + 16 (banana left) = 34 (total left)

Express 9 1

50as a decimal.

(1) 9.1

(2) 9.2

(3) 9.02

(4) 9.15

PSLE 2019 Booklet A Question 7P4 (Decimals - Conversion)

Change the denominator

to 100.

1

50=

2

100

= 0.02

9 1

50= 9 +

1

50

= 9 + 0.02

= 9.02

At first, Ali and Bala were facing the same direction. Then Ali turned 135° clockwise to face West and Bala turned 90°anti-clockwise.

Which direction did Bala face in the end?

(1) North-East

(2) North-West

(3) South-East

(4) South-West

PSLE 2019 Booklet A Question 11P4 (8 - point compass)

N

S

EW

NE

SESW

NW

Start

Ali

Bala

Work backwards by turning 135° anti-

clockwise to get

starting point.

Find the value of 230 x 16

Ans: _______________

PSLE 2019 Booklet B Question 17P4 (Whole Numbers – Multiplication)

2 3 0

x 1 6

1 3 8 0

+ 2 3 0 0

3 6 8 0

1

3680

Alternatively:

16 groups = 10 groups + 6 groups230 x 10 = 2300230 x 6 = 13802300 + 1380 = 3680

Amy bought some packets of stickers. Each packet contained 9 stickers. The total number of stickers Amy bought was fewer than 60.

Amy kept 3 stickers for herself and gave the rest equally to her 7 cousins.

(a) How many stickers did Amy buy?

(b) How many stickers did Amy give to each cousin?

+3: 10, 17, 24, 31,38, 45, 52, 57…

Ans: (a) _____________

(b) _____________

PSLE 2019 Booklet B Question 28P4 (Factors and Multiples)

(a) Multiples of 9: 9, 18, 27, 36, 45, 54…(fewer than 60)

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56…(fewer than 60)

6(b) 45 – 3 = 42

42 ÷ 7 = 6

45

Find the value of 3.47 + 6.8

Ans: _______________

PSLE 2019 Booklet B Question 18P4 (Decimals - Addition)

Place Value ChartTens

(T)

Ones

(O)

. Tenths (t) Hundredths

(th)

3 . 4 7

+ 6 . 8

1 0 . 2 7

1

The decimal points must be aligned so that addition can be performed correctly.

10.27

Write down

(a) the first common multiple of 4 and 10.

(b) all the common factors of 18 and 81.

Ans: (a) _____________

(b) _____________

PSLE 2019 Paper 2 Question 1P4 (Factors and Multiples)

(a) Multiples of 4: 4, 8, 12, 16, 20…

Multiples of 10: 10, 20…

20

(b) 1 x 18 1 x 81

2 x 9 3 x 27

3 x 6 9 x 9

1, 3, 9

Siti had a rectangular piece of paper, 35 cm by 24.6 cm. She cut out as many squares as possible from the paper. The side of each square was 5 cm.

(a) What area of the paper was left?

(b) How many squares did Siti cut out?

Ans: (a) ___________cm

(b) _____________

PSLE 2019 Paper 2 Question 4P4 (Area and Perimeter)

(b) 35 ÷ 5 = 7

20 ÷ 5 = 4

4 x 7 = 28

161

(a) 24.6 – 20 = 4.6 (multiples of 5)

35 x 4.6 = 161

28

2

Note: Use of calculator is allowed for this question. Similar question could be tested at P4 with manageable numbers and steps.

How can I help my child in Mathematics?

1) Revise Times Table (Factual Fluency)

eg. Verbal testing; Times Table Challenge;

playing computer games (https://www.arcademics.com/games)

BUT supervision is necessary.

6

4

10

2

How can I help my child in Mathematics?

2) Create learning experienceseg. Walk 1 km taking note of the time and landmark buildings; visit

supermarket to carry 1 kg and 5 kg of rice; budgeting for party etc.

3) Distributed and Inter-leaved revisioneg. Practise questions on a regular basis from different topics to help

them reinforce conceptual understanding and hone factual and

procedural fluency.

4) Ask questions to guide them in their thinkingeg. What information is given? What is the unknown? Why did you

add? What can we find out first? What strategy comes to your

mind?

Thank you