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P5 and P6 Parents’ Workshop 2021 “Helping your child to Understand and Solve Word Problems”

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Page 1: P5 and P6 Parents’ Workshop 2021

P5 and P6 Parents’ Workshop 2021

“Helping your child to Understand

and Solve Word Problems”

Page 2: P5 and P6 Parents’ Workshop 2021

• Get students to be familiar with the recall of basic mathematical facts/rules and formulae automatically and without hesitation.

• It has also shown that students who can’t recall number facts automatically often cannot calculate accurately and also struggle with even higher order thinking skills

Factual FluencyImproving Confidence and Achievement in Numeracy (ICAN)

Page 3: P5 and P6 Parents’ Workshop 2021

One of the key structures of ICAN

Time was set aside in Math lesson to practise basic number facts

regularly

Different forms: Speed Test, Class Practice and Games using fact cards

Eases the pupils’ cognitive load when learning new concepts

Factual Fluency

Page 4: P5 and P6 Parents’ Workshop 2021

• Systematic approach to scaffold

students in problem solving

• Students use it as a checklist when they

are solving word problems

• Implemented across levels P1 – P6

STAR Framework

Page 5: P5 and P6 Parents’ Workshop 2021

STAR Framework

CUBA Strategy:• Circle the

numbers• Underline the key

words• Bracket what we

need to find• Draw Arrows to

link data with information

Mathematical Processes:• Thinking skills

and heuristics• Reasoning

Review:• NTUC (Number Transfer, Units, Calculation) check• Check if the answer is reasonable

MEAL Strategy:• Model• Equation• Algorithm• Last Answer

Page 6: P5 and P6 Parents’ Workshop 2021

Four classes A, B, C and D raised money for a charity.

Classes A and B raised a total of $108. Together, classes

B, C and D raised a total of $180. The total amount of

money raised by all 4 classes is 5 times the amount that

class B raised. [How much money] did [class B] raise?

6 units = $108 + $180= $288

1 unit = $288 ÷ 6= $48

STAR Checklist

Stop

Think

Act

Review

A, B, C, D

B

$108 + $180

?

1 unit

1 unit

1 unit

1 unit

1 unit

1 unit

Class B raised $48.#

Page 7: P5 and P6 Parents’ Workshop 2021

Model Drawing

1) Fractions: Remainder Concept

2) Whole Numbers: Before and After

Page 8: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Fractions: Remainder Concept (branching method indicated by arrows)

Firdaus’ stamp

collectionat first

Gave cousin 14

Left with

[1 -14

]

Gave sister 59

Left with 80(in the end)

Fraction:

[1 -59

]

Firdaus gave his cousin 14

of his stamp collection.

He gave his sister 59

of the remainder and had 80 stamps left.

How many stamps did he have at first?

Page 9: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Firdaus gave his cousin 14

of his stamp collection.

He gave his sister 59

of the remainder and had 80 stamps left.

How many stamps did he have at first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Fractions: Remainder Concept Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

Cousin

80

1 unit

9 units = ?

Sister

Page 10: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Fractions: Remainder ConceptStep 3:

I will write out the

steps of my solutions

Firdaus gave his cousin 14

of his stamp collection.

He gave his sister 59

of the remainder and had 80 stamps left.

How many stamps did he have at first?

4 small units = 801 small unit = 80 ÷ 4

= 209 small units = 20 × 9

= 180

3 big units = 1801 big unit = 180 ÷ 3

= 604 big units = 60 × 4

= 240

Firdaus had 240 stamps at first.

Page 11: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Fractions: Remainder Concept Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Firdaus gave his cousin 14

of his stamp collection.

He gave his sister 59

of the remainder and had 80 stamps left.

How many stamps did he have at first?

Alternative method:

Cousin

80

1 unit

Sister

Using a different method to check (when big units can be divided equally):1. Find 1 unit

• 80 ÷ 4 = 202. Find 12 units

• 20 × 12 = 240

Page 12: P5 and P6 Parents’ Workshop 2021

Whole Numbers:Before and After

• 2 things have equal at first or at the end

• Keywords like “after”, “at first” , “in the end” and “equal”

Don’t be confused with Work Backwards Method, where no information of “Before” situation is given at all.

Page 13: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Whole Numbers: Before and After

Paul(same)

- $145

Left with 4 unitsKen

(same)- $64

Left with 1 unit

Paul and Ken had an equal amount of money at first.

Paul spent $145 and Ken spent $64.

After that, Ken had 4 times as much money left as Paul.

How much did each of them have at first?

Page 14: P5 and P6 Parents’ Workshop 2021

Paul and Ken had an equal amount of money at first.

Paul spent $145 and Ken spent $64.

After that, Ken had 4 times as much money left as Paul.

How much did each of them have at first?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Whole Numbers: Before and After Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

1 unit 1unit 1 unit 1 unit

1 unitPaul

Ken $64

$145

$145

After finding the value of 1 unit, we can add $145 to find out how much Paul had at first. That gives us what ‘each of them’ had at first.

1. Find 3 units2. Find 1 unit

Page 15: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Whole Numbers: Before and AfterStep 3:

I will write out the

steps of my solutions

Paul and Ken had an equal amount of money at first.

Paul spent $145 and Ken spent $64.

After that, Ken had 4 times as much money left as Paul.

How much did each of them have at first?

3 units = $145 - $64= $81

1 unit = $81 ÷ 3= $27

Paul at first = $ 145 + $27= $172

Each of them had $172 at first.

Page 16: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Whole Numbers: Before and After Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Paul and Ken had an equal amount of money at first.

Paul spent $145 and Ken spent $64.

After that, Ken had 4 times as much money left as Paul.

How much did each of them have at first?

Alternative method:

Ken should also have $172 at first.

1 unit 1unit 1 unit 1 unitKen $64

$172

Check if the value of 1 unit is the same.4 units = $172 - $64

= $1081 unit = $108 ÷ 4

= $27

Page 17: P5 and P6 Parents’ Workshop 2021

HEURISTIC Framework

Page 18: P5 and P6 Parents’ Workshop 2021

HEURISTIC Framework

Page 19: P5 and P6 Parents’ Workshop 2021

1) Supposition

2) Guess and Check

3) Working Backwards

Heuristic Skills

Page 20: P5 and P6 Parents’ Workshop 2021

Supposition

• Supposition questions usually have the following characteristics:Usually 2 criteria (2 variables found in a question)to fulfilWhen all criteria are fulfilled, answers obtained can be considered correct

• Method: Assume 1 part of the final answer to fulfil 1 of the criteria

Page 21: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Supposition

Number of three-mark questions: 10

Number of five-mark questions: 10

Number of correct answers: 15

Score: 57

What do we need to find?• Number of CORRECT

three-mark questions• Number of CORRECT

five-mark questions

In a test, each pupil had to answer 10 three-mark questions and

10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Page 22: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

Supposition

In a test, each pupil had to answer 10 three-mark questions and

10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Fulfil 2 final answers to achieve the full marks for the question:• Number of correct three-mark questions• Number of correct five-mark questions

Fulfil 2 criteria when answering the question:• 15 correct answers• 57 marks

Choose either:• SuppositionOR• Guess & Check

Page 23: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Step 3:

I will write out the

steps of my solutions

SuppositionIn a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Assume that Ting Ting answered 15 five-marks questions correctly

(1) 15 x 5 = 75 (Number of marks Ting Ting would have scored if she scored 15 five-mark questions correctly)

(3) 5 – 3 = 2 (Difference in marks between a five-mark and three mark question)

(2) 75 – 57 = 18 (Difference in marks between assumed marks and real marks)

(4) 18 ÷ 2 = 9 (number of three-mark questions Ting Ting answered correctly)

(5) 15 – 9 = 6 (number of five-mark questions Ting Ting answered correctly)

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

5 m

- 23 m- 23 m- 23 m

- 23 m - 23 m - 23 m

- 23 m- 23 m- 23 m

Page 24: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Supposition

In a test, each pupil had to answer 10 three-mark questions and

10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Assume that Ting Ting answered 15 three-marks questions correctly

(1) 15 x 3 = 45 (number of marks Ting Ting would have scored if she scored 15 three-mark questions correctly)

(2) 5 – 3 = 2 (Difference in marks between a five-mark and three mark question)

(3) 57 – 45 = 12 (Difference in marks between assumed marks and real marks)

(4) 12 ÷ 2 = 6 (number of five-mark questions Ting Ting answered correctly)

(5) 15 – 6 = 9 (number of three-mark questions Ting Ting answered correctly)

Alternative method:Assume Ting Ting answered 15 three-marks questions correctly.

Page 25: P5 and P6 Parents’ Workshop 2021

Guess and Check

• Guess and Check questions usually have the following characteristics:Usually 2 criteria (2 variables) to be used as a “Check” for “Guesses” of correct/incorrect answersWhen all criteria are fulfilled, answers obtained can be considered correct

Page 26: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Guess and Check

Guess: - How many correct three-mark questions?- How many correct five-mark questions?

Check:- 15 correct answers- 57 marks

Page 27: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Guess and Check

Guess: - How many correct three-mark questions?- How many correct five-mark questions?

Check:- 15 correct answers- 57 marks

Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

We can use Guess and Check to find possible combinations of correct three-mark and five-mark questions in a table

Page 28: P5 and P6 Parents’ Workshop 2021

No. of correct three-mark questions

Marks from three-mark questions

No. of correct five-mark questions

Marks from five-mark questions

Marks scoredNo. of correct

answersCHECK

7 7 x 3 = 21 8 8 x 5 = 40 21 + 40 = 61 15 X

8 8 x 3 = 24 7 7 x 5 = 35 24 + 35 = 59 15 X

9 9 x 3 = 27 6 6 x 5 = 30 27 + 30 = 57 15

STAR Approach to Problem-Solving

In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Guess and CheckStep 3:

I will write out the

steps of my solutions

Page 29: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

In a test, each pupil had to answer 10 three-mark questions and 10 five-mark questions.

Ting Ting had 15 correct answers and scored 57 marks.

How many questions of each kind did she answer correctly?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Guess and Check Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

No. of correct three-mark questions

Marks from three-mark questions

No. of correct five-mark questions

Marks from five-mark questions

Marks scoredNo. of correct

answersCHECK

7 7 x 3 = 21 8 8 x 5 = 40 21 + 40 = 61 15 X

8 8 x 3 = 24 7 7 x 5 = 35 24 + 35 = 59 15 X

9 9 x 3 = 27 6 6 x 5 = 30 27 + 30 = 57 15

Page 30: P5 and P6 Parents’ Workshop 2021

Working Backwards

• Used when no information of ‘Before’ situation is given at all

• All the information is given at the ‘After’ situation

Page 31: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Working Backwards

A shopkeeper had some files for sale.

Jack bought 12

of the files and was given 8 files free.

Rebecca bought 12

of the remaining files and was given 3 files free.

The shopkeeper had 54 files remaining.

How many files did the shopkeeper have at first?

Page 32: P5 and P6 Parents’ Workshop 2021

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Working Backwards

Files in the shop at first

Jack bought 12

and got 8 free

Remainder:12

of the total number – 8 files

Rebecca bought 12

of remainder and got 3 free

Left with 54 files

Page 33: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Working Backwards Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files

free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper

had 54 files remaining. How many files did the shopkeeper have at first?

54 remaining 3 Rebecca’s files

12

of remainder12

of remainder

57 57

114

Page 34: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Working Backwards Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files

free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper

had 54 files remaining. How many files did the shopkeeper have at first?

54 remaining 3 Rebecca’s files

114

Jack’s files8

12

of original12

of original

122 122

Page 35: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Step 3:

I will write out the

steps of my solutions

Working Backwards

A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files

free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper

had 54 files remaining. How many files did the shopkeeper have at first?

54 + 3 = 57

57 × 2 = 114

114 + 8 = 122

122 × 2 = 244

The shopkeeper had 244 files at first.

Page 36: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Working Backwards

A shopkeeper had some files for sale. Jack bought ½ of the files and was given 8 files

free. Rebecca bought ½ of the remaining files and was given 3 files free. The shopkeeper

had 54 files remaining. How many files did the shopkeeper have at first?

Alternative method:

244 ÷ 2 = 122

122 – 8 = 114

114 ÷ 2 = 57

57 – 3 = 54

Alternative method:Checking for calculation errors by counting backwards

Page 37: P5 and P6 Parents’ Workshop 2021

Strategies to solve word problems related to Ratio

Based on these concepts:• Constant Part Concept• Constant Total Concept• Constant Difference Concept

Students need to use their calculator to solve these word problems.

Page 38: P5 and P6 Parents’ Workshop 2021

Topic: Ratio (relative sizes)

How many times one quantity is as large as another given their ratio?

Solve word problems involving 2 pairs of ratios

Page 39: P5 and P6 Parents’ Workshop 2021

Constant Part Concept

• 2 parts (2 quantities) in a word problem.

• There is a change in one part (quantity) while the other part (quantity) remains unchanged.

• Make use of the unchanged part (quantity) to solve the word problem.

Page 40: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the

box was 1:2. When 135 more apples were added into the box, the ratio of the number of

apples to the number of oranges became 9:3. How many apples were in the box at first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question)

The number of oranges is unchanged.

Before ratio-- Apples : oranges 1 : 2

135 more apples were put in the boxAfter ratio -- Apples : oranges

9 : 3

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

Page 41: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the

box was 1:2. When 135 more apples were added into the box, the ratio of the number of

apples to the number of oranges became 9:3. How many apples were in the box at first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question)

Make use of this constant part concept (orange quantity) to solve the word problem.

before ratio-- Apples : oranges 1 : 2

135 more apples were put in the box

after ratio -- Apples : oranges 9 : 3

Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

Page 42: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of oranges. The ratio of the number of apples to the number of oranges in

the box was 1:2. When 135 more apples were added into the box, the ratio of the number

of apples to the number of oranges became 9:3. How many apples were in the box at

first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question)

Make the units of oranges in both ratios the same (Equivalent Ratio)Before AfterA : O A : O1 : 2 9 : 3

3 : 6 18 : 6

Step 3:

I will write out the

steps of my solutions

X 3 X 2

Note: 6 is the first common multiple of 2 and 3

Page 43: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of oranges. The ratio of the number of apples to the number of oranges in

the box was 1:2. When 135 more apples were added into the box, the ratio of the number

of apples to the number of oranges became 9:3. How many apples were in the box at

first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question)

Before AfterA : O A : O1 : 2 9 : 3

3 : 6 18 : 6

Step 3:

I will write out the

steps of my solutions

X 3 X 2

Multiply the units of apples in each ratio by the same number used to multiply the units of oranges in the same ratio.

Page 44: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the

box was 1:2. When 135 more apples were added into the box, the ratio of the number of

apples to the number of oranges became 9:3. How many apples were in the box at first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question)

Before AfterA : O A : O1 : 2 9 : 3

3 : 6 18 : 6

Step 3:

I will write out the

steps of my solutions

Find the difference between the number of units in apples in both ratios. 18u – 3u = 15u (Unitary Method)

Find 1 unit of apples

1u = 135 ÷ 15 = 9

Find the number of apples at first. 3u = 9 X 3 = 27

Page 45: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Kim had a box of fruits. The ratio of the number of apples to the number of oranges in the

box was 1:2. When 135 more apples were added into the box, the ratio of the number of

apples to the number of oranges became 9:3. How many apples were in the box at first?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Part Concept (PSLE Question) Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Number of apples at first: 27Number of apples in the end : 27 + 135 = 162Number of oranges = 6 x 9 = 54Apples : Oranges = 162 : 54

= 18 : 6= 9 : 3

Check the steps and use the actual number of apples and oranges calculated to express the quantities in the form of ratio as 9 : 3.

Page 46: P5 and P6 Parents’ Workshop 2021

Constant Total Concept

• 2 parts (2 quantities) in a word problem. • There is a redistribution of quantities between the 2 parts while the sum/total of the quantities remains unchanged.

• Make use of the unchanged total (sum of the quantities) to solve the word problem.

• Constant Total concept is related to ‘Internal Transfer’ concept.

Page 47: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,

the ratio of Jane’s money to Mary’s money became 1:2.

what was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question)

Now, Mary has $24 more while Jane has $24 less (same amount of money is redistributed (internal transfer)

Before ratio-- Jane : Mary : Total 3 : 4 : 7

After ratio -- Jane : Mary : Total1 : 2 : 3

No change in total amount of money altogether

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

Page 48: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,

the ratio of Jane’s money to Mary’s money became 1:2.

what was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question)

Make use of this constant total concept to solve the word problem.

Before ratio-- Jane : Mary : Total 3 : 4 : 7

After ratio -- Jane : Mary 1 : 2 : 3

Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

Page 49: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,

the ratio of Jane’s money to Mary’s money became 1:2.

hat was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Make the total number of units in both ratios the sameBefore After

J : M : T J : M : T3 : 4 : 7 1 : 2 : 3

9 : 12 : 21 7 : 14 : 21

X 3 X 7

Note: 21 is the first common multiple of 3 and 7

Page 50: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,

the ratio of Jane’s money to Mary’s money became 1:2,

what was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Before AfterJ : M : T J : M : T3 : 4 : 7 1 : 2 : 3

9 : 12 : 21 7 : 14 : 21

X 3 X 7

Multiply the units of Jane’s and Mary’s money in each ratio by the same number used to multiply the total units in the same ratio.

X 3 X 7X 3 X 7

Note the difference in the amount of units of Jane’s money (or Mary’s money) before and after the transfer. Difference is 2u (9u – 7u or 14u -12u)

Page 51: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first. After Jane gave Mary $24,

the ratio of Jane’s money to Mary’s money became 1:2.

what was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Before AfterJ : M : T J : M : T3 : 4 : 7 1 : 2 : 3

9 : 12 : 21 7 : 14 : 21X 3 X 7X 3 X 7

Find 1 unit of money2u = 24

1u = 24 ÷ 2= 12 (Unitary Method)

Find the total amount of money21u = 12 X 21 = 252

Page 52: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

The ratio of Jane’s money to Mary’s money was 3:4 at first.

After Jane gave Mary $24, the ratio of Jane’s money to Mary’s money became 1:2.

What was the total amount of money they had altogether?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Total Concept (PSLE Question) Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Total = $252$252 ÷7 = 36Jane in the end : ($36 X 3) – 24 = $84Mary in the end : ($36 X 4) + 24 = $168Jane : Mary = 84 : 168

= 1 : 2

Check the steps and use the actual amount of money calculated to express the quantities in the form of ratio as 1 : 2.

Page 53: P5 and P6 Parents’ Workshop 2021

Constant Difference Concept

•Constant Difference means the difference between 2 parts (before and after ratio) remains unchanged.

• Usually this concept applies in questions related to ‘Age’

Page 54: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1. In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question)

The same number of boys and girls joined the chess club

Before ratio-- Boys : Girls : Difference4 : 1 : 3

After ratio -- Boys : Girls : Difference 3 : 1 : 2

No change in the difference between the number of boys and girls

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

Page 55: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question)

Make use of this constant difference concept to solve the word problem.

Before ratio-- Boys : Girls : Difference 4 : 1 3

After ratio -- Boys : Girls : Difference 3 : 1 : 2

Step 2:

What strategy

should I use?

Have I solved

similar problems

before?

Page 56: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1. In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Make the difference in the number of units in both ratios the sameBefore ratio After ratio

B : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2

8 : 2 : 6 9 : 3 : 6

X 2

Now, the difference in both ratios is 6.

X 3

Page 57: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 :2

8 : 2 : 6 9 : 3 : 6

X 3X 2X 2

Multiply the units of Boys and girls in the before ratio by the same number used to multiply the difference in the number of units in the same ratio.

X 2 X 3 X 3

Page 58: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2

8 : 2 : 6 9 : 3 : 6

Note the difference in the amount of units of girls or boys before and after. Difference is 6u (8u – 2u or 9u -3u)

Page 59: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of the number of boys to the number of girls in a chess club was

4 : 1.After 6 boys and 6 girls joined the club, the ratio became 3 : 1 In the end, how many

boys were there in the club?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question) Step 3:

I will write out the

steps of my solutions

Before AfterB : G : Difference B : G : Difference4 : 1 : 3 3 : 1 : 2

8 : 2 : 6 9 : 3 : 6

Find 1 unit

1u = 6

Find number of boys in the end.

9u = 9 X 6 = 54

Page 60: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

At first, the ratio of number of boys to number of girls was 4:1. After

6 boys and 6 girls joined, the ratio of number of boys to number of girls became 3:1.

What was the number of girls in the end?

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Constant Difference Concept (PSLE Question) Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

6 x 3 = 18 (number of girls in the end)18 – 6 = 12 (number of girls at first)

9 x 6 = 54 (number of boys in the end)54 – 6 = 48 (number of boys at first)

Check the steps and use actual number of boys and girls to check against the ratio given.

Before ratioB : G48 : 12 4 : 1 (simplest form)

After ratioB : G54 : 183 : 1 (simplest form)

Page 61: P5 and P6 Parents’ Workshop 2021

Everything Changed Concept

• Every part changes, the difference changes, the total changes….Nothing remains the same...no constant variables basically

• Form equations/use unit-and-part concepts• Form equal parts (or units) in order to solve the word

problems.

Page 62: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)

Before ratio-- Carl : Vijay75 : 1003 : 4 (ratio in its simplest form)

Carl has $200 more & Vijay has $50 less in the endAfter ratio -- Carl : Vijay

2 : 1 (ratio in its simplest form)

Everything changes. No constant variable.

Step 1:

What am I given?

(facts/ information/

data)

What am I asked to

find?

How can I make

sense of the

information given to

me?

What can I infer

from the given data?

Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Page 63: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)

Before ratio-- Carl : Vijay3 : 4

After ratio -- Carl : Vijay 2 : 1

Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 2:

What strategy

should I use?

Have I solved

similar problems

before? Form equations /use unit-and-part concepts to solve the word problem.

Before Change After

Carl 3u +200 2p

Vijay 4u - 50 1p

Note: u stands for units and p stands for parts

Page 64: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

Form equations using units and parts.

Vijay (in the end)1p = 4u – 50

Carl (in the end)2p = 3u + 200

Before Change After

Carl 3u +200 2p

Vijay 4u - 50 1p

Page 65: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

Make the parts of Vijay’s money equal to Carl’s money in the end . 1p = 4u – 50 2p = 8u – 100 (twice of 4u-50) Vijay (in the end)

1p = 4u – 50

Carl (in the end)2p = 3u + 200

Page 66: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

2 Parts

2001U 1U 1U

1U 1U1U1U

50

2 Parts

1U 1U1U1U

50

5U = 200 + 100

Page 67: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

From the model.

5U -> 3001U -> 60

Find how much Carl had at first? 3u = $60 x 3 = $180

Page 68: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

2 Parts

2001U 1U 1U

1U ½

u100

1U 1U1U1U

50 spent

Carl

Vijay

Vijay

Now

At first

From Vijay’s models (now and at

first),

1 u + ½ u + 100 + 50 = 4u

4u - 1½ u = 150

2½ u = 150

5u = 150 x 2 (2 sets of 2½ u = 5u)

= 300

1u = 300÷5 = 60

3u = 60 × 3 = 180

Page 69: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 3:

I will write out the

steps of my solutions

Now,Vijay’s money is ‘equal’ to Carl’s money in the end.

Vijay : Carl 8u – 100 : 3u + 200left equals to right8u -100 = 3u + 2008u – 3u = 200 + 1005u = 300 (unitary method)1u = 60Find how much Carl had at first? 3u = $60 x 3 = $180

Page 70: P5 and P6 Parents’ Workshop 2021

STAR Approach to Problem-Solving

Step 2:Think about your plan and strategy you will use

Step 1: Stop and read the

problem carefullyStep 3: Act: Follow your plan and

solve your problem.

Step 4:

Review your answer

Everything Changed Concept (PSLE Question)

Carl had 75% as much money as Vijay. After Carl received $200 from his uncle

and Vijay spent $50, Carl had twice as much money as Vijay.

How much money had Carl at first?

Step 4:

Have I answered the question?

•Is my answer reasonable /

make sense?

•Have I checked my answers?

•Is there a better alternative?

Carl at first : $180Carl in the end: $180 + $200 = $380Vijay at first: $60 x 4 = $240Vijay in the end: $240 - $50 = $190C : V = 380 : 190

= 2 : 1

Check the steps and use the actual amount of money calculated to express the quantities in the form of ratio as 2 : 1 (in the end).

Page 71: P5 and P6 Parents’ Workshop 2021

Carelessness in calculation

Cultivate the habit of checking by working backwards after

attempting the question.

Transfer information wrongly from question to working.

With numbers transferred wrongly from the question, the

subsequent working and calculation may be affected and thereby

causing marks to be lost.

Common Mistakes

Page 72: P5 and P6 Parents’ Workshop 2021

Transfer final answer wrongly from working to final answer

blank.

Students are recommended to indicate final answer by underlining

in working space.

Common Mistakes

Page 73: P5 and P6 Parents’ Workshop 2021

Common Mistakes

Missing units

Forgetting to include units given in 2-marks or more questions.

Decimal notations for money

Dollars and cents must be expressed in 2 decimal places. Example,

$14.50, not $14.5

Reading the question wrongly- missing out the key words.

Page 74: P5 and P6 Parents’ Workshop 2021

Ensure your child is familiar with the essential functions of

his/her calculator and only use it for Paper 2 questions.

Practise the use of the tools like protractor and set-squares

for measuring and constructing figures (Mathematical

Instrument set).

Tips for PSLE

Discourage your child to rely on correction tape or liquid

paper(though it is allowed).

Encourage your child to use a blue ballpoint pen for written

answers.

Page 75: P5 and P6 Parents’ Workshop 2021

Tips for PSLE

Revisit the rules and formulae.

Have sufficient rest especially the day before the paper!

Discourage your child to attempt solving a question for more

than 10 minutes (Paper 2). Move on to the questions that they

may be able to solve.

Temporary to skip questions that the students have difficulty

to do and to revisit them at the end.

Page 76: P5 and P6 Parents’ Workshop 2021

Questions & Answer

Page 77: P5 and P6 Parents’ Workshop 2021
Page 78: P5 and P6 Parents’ Workshop 2021

Thank you!