P5 and P6 Sharing 2019 S.U.P.E.R An approach to …...BUKIT PANJANG PRIMARY SCHOOL Mathematics...

BUKIT PANJANG PRIMARY SCHOOLMathematics Department



P5 and P6 Sharing 2019S.U.P.E.R

An approach to Math Problem-Solving



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Where to retrieve the slides after the sharing?



Objectives of this sharing …

1. Provide an overview of BPPS

Problem Solving Processes

2. Create an awareness of the

various problem solving

strategies / heuristics



•Comprehending the language in word problems

• Identifying operations needed for word problems

• Identifying the problem types and seeing the

relations among the types

•Have limited problem solving strategies

•Lack of confidence and willingness to persist

(Kroll and Miller, 1993)

Difficulties faced in Problem Solving


S.U.P.E.R.

Approach To

Problem Solving



Background information

The Singapore Mathematics Curriculum has

adopted George Polya’s four step problem-

solving processes in problem solving :

1.Understand the problem

2.Devising a plan (Choosing a heuristic)

3.Carrying out the plan

4.Reflecting (Checking reasonableness)



Problem Solving Processes

SU

Study and

Understand the problem

P Plan the solution

E Execute the plan

R Review the solution


• What is the problem asking you to do?

• What are we trying to find out?

• Can we restate the problem

in our own words?

• What do we know?

• What do we need to do to solve the problem?

• Do we need more information?

• Is there a hidden question?

• What strategies are useful?

• Carry out the plan.

• Apply mathematical skills,

concepts and strategies.

• R - Reason

E - Equation

F - Final answer

• Compare with the original question.

• Does it make sense?

• Should we revise our plan to

meet all the conditions?

Problem Solving Process: .U.P.E.R


Guess & Check and Make A Supposition

Draw A Diagram / Model, Work Backwards

Look For Pattern, Make A List / Table, Act It Out, Restate The Problem, Draw A Diagram / Picture / Model, Solve Part of the Problem

Draw A Diagram / Model, Work Backwards

Draw A Diagram / Model, Elimination


Guess & Check and Make A Supposition

Repeated Identity, Constant Total, Constant Difference, Equal Stage, External Transfer (Changed / Unchanged)

Look For Pattern, Make A List / Table, Equal Distance, Factors & Multiples, Number of units x Value

Part-Whole / Comparison, Work Backwards, More / Less Than, Before & After

Elimination, External Transfer (Units and Parts)


Practice Questions




Practice Question 1

Mr Tan packed 508 tarts into large and small boxes

to sell. He filled each large box with 20 tarts and

each small box with 12 tarts. All boxes were full and

there were no tarts left over.

What was the least number of boxes used by Mr Tan?(2018 PSLE Paper 2 Question 9)

Step 1 : Study and Understand the problem




Mr Tan packed 508 tarts into large and small boxes to

sell. He filled each large box with 20 tarts and each

small box with 12 tarts. All boxes were full and there

were no tarts left over. What was the least number of

boxes used by Mr Tan?

Possible heuristics/strategies to use :

Grouping - Make A List / Table

Assumption - Guess And Check

Step 2 : Plan the solution

Practice Question 1





Mr Tan packed 508 tarts into large and small boxes to sell.

He filled each large box with 20 tarts and each small box with

12 tarts. All boxes were full and there were no tart left over.

What was the least number of boxes used by Mr Tan?

To find the least number of boxes used, Mr

Tan should fill up the large boxes first.

Step 3 : Execute the plan

Making a List

Logical Reasoning

Practice Question 1




Number of large boxes Number of tarts in small boxes Number of small boxes used


508 ÷ 20 = 25.4 / 25 r 8

25 508 – (25 x 20) = 8 Need 4 more tarts

24 508 – (24 x 20) = 28 28 ÷ 12 = 2R4

23 508 – (23 x 20) = 48 48 ÷ 12 = 4

Practice Question 1Estimated number of large boxes to fill in all tarts




Least number of boxes used

23 + 4 = 27


Number of large boxes Number of tarts in small boxes Number of small boxes used

23 508 – (23 x 20) = 48 48 ÷ 12 = 4

Practice Question 1




Mr Tan packed 508 tarts into large and small boxes to sell.

He filled each large box with 20 tarts and each small box with

12 tarts. All boxes were full and there were no tart left over.

What was the least number of boxes used by Mr Tan?

Total number of tarts

(23 x 20) + (4 x 12) = 460 + 48

= 508

Step 4 : Review the solution

Practice Question 1


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 1 : Study and Understand the problem

A group of girls shared some sweets among

themselves. They tried taking 11 sweets

each, they were short of 5 sweets. When

each girl took 8 sweets, they had 25 sweets

left. How many sweets were there altogether?(Modified from PSLE Question)

Practice Question 2


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 2 : Plan the solution

Possible heuristics/strategies to use :

Assumption - Guess And Check

Grouping - Make A List / Table

Grouping - Factors and Multiples

Draw A Model

A group of girls shared some sweets among

themselves. They tried taking 11 sweets each, they were

short of 5 sweets. When each girl took 8 sweets, they had

25 sweets left. How many sweets were there altogether?

Practice Question 2




Grouping: Factors & Multiples and Make a List / Table

Number of sweets:

(a) A multiple of 11 – 5

(b) A multiple of 8 + 25

A group of girls shared some sweets among themselves.

They tried taking 11 sweets each, they were short of 5 sweets.

When each girl took 8 sweets, they had 25 sweets left. How many

sweets were there altogether?

Practice Question 2



Number

of girls

Multiple of

11 – 5

Multiple of

8 + 25

1

8 + 25

= 33

2

22 – 5

= 17

16 + 25

= 41

3

33 – 5

= 28

24 + 25

= 49

4

44 – 5

= 39

32 + 25

= 57

5

55 - 5

= 50

40 + 25

= 65


(Grouping: Factors & Multiples and Make a List / Table)

Number of sweets can be :

(a) A multiple of 11 – 5 (b) A multiple of 8 + 25

Practice Question 2

11- 5

= 6



Number of girls

Multiple of

11 – 5

Multiple of

8 + 25

7

77 – 5

= 72

56 + 25

= 81

8

88 – 5

= 83

64 + 25

= 89

9

99 – 5

= 94

72 + 25

= 97

10

110 – 5

= 105

80 + 25

= 105

6

66 – 5

= 61

48 + 25

= 73

Number of sweets 105


Number of sweets can be :

(a) A multiple of 11 – 5 (b) A multiple of 8 + 25

Practice Question 2


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan (Method 2 – Draw A Model)

11 11 … 6

8 8 … 8 255




sweets were there altogether? (Modified from PSLE Question)

Practice Question 2



8 8 … 8 25

11 11 … 6

5

Total number of sweets needed to redistribute

25 + 5 = 30

Number of girls

30 ÷ 3 = 10

Practice Question 2



Practice Question 2

Total actual number of sweets

10 x 8 + 25 = 105

Total number of sweets needed to redistribute

25 + 5 = 30

Number of girls

30 ÷ 3 = 10


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan (Method 3 – Logical Reasoning)





Logical Reasoning

Practice Question 2



Difference in number of sweets

11 – 8 = 3

Number of sweets needed to redistribute

25 + 5 = 30





Practice Question 2



Number of girls

30 ÷ 3 = 10

Number of sweets

10 x 8 + 25 = 105





Practice Question 2




For a recycling project, Ali collected 17 bottles, Bala collected

2m bottles and Carl collected 2 + m bottles.

Each of the statements below is either true, false or not possible to

tell from the information given. For each statement, put a tick () to

indicate your answer. (2018 PSLE Paper 2 Question 3)

Statement True False Not possible to tell

Ali collected the most number of bottles.

Bala collected more bottles than Carl.

The 3 boys collected 3m + 19 bottles altogether.


Practice Question 3





2m bottles and Carl collected 2 + m bottles. (2018 PSLE Paper 2 Question 3)


Ali collected the most number of bottles.

As the value of m was not provided in the question,

we cannot conclude whether Ali has collected the most number of bottles.

If m = 5, Bala collected 2 x 5 = 10 bottles and Carl collected 2 + 5 = 7 bottles.


Step 3 : Execute the plan (Assumption – Guess and Check)

Practice Question 3







Bala collected more bottles than Carl.



Step 3 : Execute the plan (Assumption – Guess and Check)

As the value of m was not provided in the question,

we cannot conclude whether Bala has collected more bottles than Carl.

Practice Question 3







The 3 boys collected 3m + 19 bottles altogether.

Total number of bottles17 + 2m + 2 + m = 3m + 19

Step 3 : Execute the plan (Grouping – Letters and Numbers)

Practice Question 3




Jack spent15

of his money on food.

He gave $36 to his Mum and had12

of his money left.

Each of the statements below is either true, false or not possible to

tell from the information given. For each statement, put a tick () to

indicate your answer. (2019 BPPS P5 SA1 Paper 2 Question 4)


110

of Jack’s money is $36.

Jack had $60 left.


Practice Question 4


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan (Draw a model)

Food

15

of his money on food = 210

of his money on food

12

of his money left = 510

of his money left

Mum 510

-210

= 310

Practice Question 4

left$36




Jack spent15

of his money on food.

He gave $36 to his Mum and had12

of his money left.


110

of Jack’s money is $36.

Step 3 : Execute the plan (Draw a model)

Practice Question 4


BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan (Draw a model)

Practice Question 4

Food

left$36


Jack had $60 left.

3 units = $36

1 unit = $36 ÷ 3 = $12

5 units = $12 x 5 = $60




In a shop, candles are sold only in boxes.

A box of 7 short candles costs $2.50

and a box of 5 long candles costs $3.20.

(a) Dan wants 19 short candles and 3 long candles for his lanterns.

What is the least amount of money Dan will need to spend on the candles?

(b) Eva bought 21 more long candles than short candles from the shop.

The total number of candles she bought was fewer than 50.

How much did Eva spend on the candles altogether?

(2018 PSLE Paper 2 Question 17)

Practice Question 5





(a) Dan wants 19 short candles and 3 long candles for his lanterns.

What is the least amount of money Dan will need to spend on the candles?

19 short candles ? box(es) of short candles3 long candles ? box(es) of long candles

31

Least amount of money

($2.50 x 3) + ($3.20 x 1) = $7.50 + $3.20

= $10.70

Practice Question 5




(b) Eva bought 21 more long candles than short candles from the shop.

The total number of candles she bought was fewer than 50.

How much did Eva spend on the candles altogether?

Number of short candles Eva can buy

7, 14, 21, 28, 35, 42, 49, …

Number of long candles Eva can buy

5, 10, 15, 20, 25, 30, 35, 40, 45, …

Practice Question 5



Practice Question 5

Long candles Short candles Difference Total Check

45 7 45 – 7 = 38 45 + 7 = 52 x

40 14 40 – 14 = 26 40 + 14 = 54 x

35 14 35 – 14 = 21 35 + 14 = 49

Number of short candles Eva can buy

7, 14, 21, 28, 35, 42, 49, …

Number of long candles Eva can buy

5, 10, 15, 20, 25, 30, 35, 40, 45, …




In a shop, candles are sold only in boxes. A box of 7 short candles costs

$2.50 and a box of 5 long candles costs $3.20.

Amount of money spent altogether

($2.50 x 2) + ($3.20 x 7) = $5.00 + $22.40

= $27.40

14 short candles ? boxes of short candles35 long candles ? boxes of long candles

27

Practice Question 5


PSLEExamination Format

and Topics



Paper Booklet Item Type Number of

questions

Number of marks

per question

Total marks Duration

1A

MCQ10 1 10

1 h

MCQ5 2 10

B

Short-Answer5 1 5

Short-Answer10 2 20

2Short-Answer

5 2 101 h 30 min

Structured /

Long-Answer 12 3, 4, 5 45

Total 47 --- 1002 h 30 min

PSLE Mathematics



Paper Booklet Item Type Number of

questions

Number of marks

per question

Total marks Duration

1A

MCQ10 1 10

1 h

MCQ10 2 20

BShort-Answer

10 2 20

2Short-Answer

10 2 201 h

Structured6 3, 4 20

Total 46 --- 902 h

PSLE Foundation Mathematics



Mathematics Foundation Mathematics

Numbers Numbers

Measurement Measurement

Geometry Geometry

Statistics Statistics

Ratio and Percentage Percentage

Rate and Speed Rate

Algebra

Topics tested at PSLE



Learning Experience @ BPPS(throughout the whole six years)

Bukit Panjang Primary SchoolMathematics Sharing Session

✓ Expose students to general problem solving skills, thinking skills and heuristics, and how these skills can be applied.



Learning Experience @ BPPS✓ Encourage them to think aloud the strategies and methods

they use to solve particular problems.

✓ Provide them with problems that require planning (before solving) and evaluation (after solving).




Learning Experience @ BPPS✓ Encourage the students to seek alternative ways

of solving the same problem and to check the appropriateness and reasonableness of the answer.

✓ Allow them to discuss how to solve a particular problem and to explain the different methods that they use for solving the problem




PRESENTATION OF SOLUTIONS AND ANSWERS


Example

Number of eggs packed

45 x 6 = 270

Number of eggs given away

476 – 270 – 120 = 86

Format to be used:

R Reason

E Equation

F Final answer


Learning Model

1) Class

Remind your child to pay attention in school.

2) Short Term Memory

Get your child to revise the marked worksheets

or workbooks which our teachers have returned.

3) Revision

Get your child to complete his or her daily homework

and other simple tasks which you have set.

Reward your child your way.

Be as encouraging as possible.


4) Feedback LoopGo through the errors made.

Strengthen certain skills and concepts by giving similar

type of questions or reading materials.

Remember to motivate your child.

5) Long Term MemoryRecap and link a few topics.

Make use of the worksheets which your child has filed.

6) Long Term Memory RetrievalRecap and link more topics from different levels. Application!


7) Assessment

Totally aware when are the examinations dates,

reporting time and venue.

Be familiar with the format of all the subject papers

like the number of items that will be tested.

Know the exact duration for each subject papers.

Bring along the necessary stationery each day.




Be Mentally & Physically Ready




We value your feedback





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P5 and P6 Sharing 2019 S.U.P.E.R An approach to …...BUKIT PANJANG PRIMARY SCHOOL Mathematics...

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