Primary 3 and Primary 4 S .U.P.E.R An approach to Math ......BUKIT PANJANG PRIMARY SCHOOL...

BUKIT PANJANG PRIMARY SCHOOLMathematics Department

Mathematics Sharing SessionPrimary 3 and Primary 4

S .U.P.E.R – An approach

to Math Problem-Solving

5 April 2019

Your feedback will assist us in future planning.

URL for Feedback Form: https://forms.gle/L1cZoBcPzYWnFafT8

Mathematics Sharing SessionPrimary 3 and Primary 4

Your feedback will assist us in future planning.

URL for Feedback Form: https://forms.gle/L1cZoBcPzYWnFafT8

https://www.bukitpanjangpri.moe.edu.sg/bulletin/notifications

Where to retrieve the slides after the sharing?

Objectives of this sharing …

1. Provide an overview of BPPSProblem Solving Processes

2. Create an awareness of the various problem solving strategies / heuristics

Background informationThe Singapore Mathematics Curriculum has adoptedGeorge Polya’s four step problem-solving processes inproblem solving :

1.Understand the problem

2.Devising a plan (Choosing a heuristic)

3.Carrying out the plan

4.Reflecting (Checking reasonableness)

S .U.P.E.R. Approach To

Problem Solving

S Study and

U Understand the problem

P Plan the solution

E Execute the plan

R Review the solution

Problem Solving Processes

Comparing…Polya’s Problem Solving

Processes

S.U.P.E.R. Approach to

Problem Solving

Understand the problemStudy and

Understand the problem

Devising a plan

(Choosing a heuristic)Plan the solution

Carrying out the plan Execute the plan

Reflecting

(Checking reasonableness)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

5 Main Problem Solving Approaches

1. Grouping

2. Model Drawing

3. Assumption

4. Find a constant

5. Simultaneous Equations

Problem Solving Approaches

Concepts

Assumption

Find a constant

Grouping

Model drawing

Simultaneous equation

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)

Learning Experience @ BPPS

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

✓ 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).

✓ Encourage students to seek alternative ways ofsolving the same problem and to check theappropriateness and reasonableness of theanswer.

✓ Allow them to discuss how to solve a particularproblem and to explain the different methodsthat they use to solve the problem.

Practice Questions

Practice Question

Practice Question 1

Judy sold a total of 60 chicken pies and

apple pies and collected a sum of

$144. A chicken pie was sold for $3

and an apple pie was sold for $2. Howmany apple pies did Judy sell?

Step 1 : Study and Understand the problem

Practice Question 1

Judy sold a total of 60 chicken pies

and apple pies and collected a sum of

$144. A chicken pie was sold for $3

and an apple pie was sold for $2. Howmany apple pies did Judy sell?

Practice Question 1

Step 2 : Plan the solution

What are the possible heuristics or strategies

that we can use to solve this question?

▪ Guess and Check

▪ Assumption / Supposition

Practice Question 1

Method 1: Guess and Check

Step 3 : Execute the plan

Practice Question 1

Number of chicken

Sales from chicken pies

($3 each)

Number of apple

Sales from apple pies($2 each)

Total salesCheck($144)

Number of apple pies → 36

30 3030 x $3 = $90

30 x $2 = $60

$90 + $60 = $150

25 3525 x $3 = $75

35 x $2 = $70

$75 + $70 = $145

24 3624 x $3 = $72

36 x $2 = $72

$72 + $72 = $144

Practice Question 1

● Include headings for the table

● Start with a number somewhere in the middle of a given total.

● Equations must be written clearly in the table.

● Decide whether to increase/decrease the numbers for the next guess gradually.

● Check (✔) the row with the correct guess.

Practice Question 1

Method 2: Assumption/ Supposition

Practice Question 1

Assume all 60 were apple pies ($2 each):

Minimum amount of sales

60 x $2 = $120

$2 $2 $2 $2 $2

Sales not accounted for

$144 - $120 = $24

$1 $1 $1 $1 $1

Practice Question 1

Assume all 60 were apple pies ($2 each):

$2 $2 $2 $2 $2

$1 $1 $1 $1 $1

Difference in cost

$3 - $2 = $1

Number of chicken pies

$24 ÷ $1 = 24

Number of apple pies

60 – 24 = 36

Practice Question 1

Method 3: Assumption/ Supposition

Practice Question 1

Maximum amount of sales

60 x $3 = $180

Extra sales

$180 - $144 = $36

Assume all 60 were chicken pies ($3 each):

BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan

Difference in cost

$3 - $2 = $1

Number of apple pies

$36 ÷ $1 = 36

Practice Question 1Assume all 60 were chicken pies ($3 each):

Practice Question 1: Review my Solution

Sales from 36 apple pies36 x $2 = $72

Sales from 24 chicken pies24 x $3 = $72

Total amount of sales$72 + $72 = $144

Step 4 : Review the solution

Practice Question

Practice Question 2

The pattern below is formed using square tiles.

(a)How many square tiles are needed to form figure 5?

(b)How many square tiles are needed to form figure 20?

Practice Question 2

6 10+ 2+ 3

Practice Question 2

▪ Make A List

▪ Look For A Pattern

Practice Question 2

Method 1: Make a List and Look for Pattern

Practice Question 2

Figure Number

No. of squares

Number of squares in Figure 5 → 15 squares

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10

10 + 5 = 15

Practice Question 2

Figure Number

6 7 8 9 10 11 12

No. of squares

15 + 6= 21

21 + 7= 28

28 + 8 = 36

36 + 9 = 45

45 + 10 = 55

55 + 11 = 66

66 + 12 = 78

Practice Question 2

Figure Number

13 14 15 16 17 18

No. of squares

78 + 13= 91

91 + 14= 105

105 + 15 = 120

120 + 16 = 136

136 + 17 = 153

153 + 18 = 171

Practice Question 2

Figure Number

No. of squares

171 + 19= 190

190 + 20= 210

Number of squares in Figure 20 → 210 squares

Practice Question 2

Method 2

Figure 1 Figure 2 Figure 3 Figure 4

Practice Question 2

Method 2

Figure 1 Figure 2 Figure 3 Figure 4

(1 x 2) ÷ 2(2 x 3) ÷ 2

(3 x 4) ÷ 2(4 x 5) ÷ 2

Number of tiles= Figure No. x (Figure No. + 1) ÷ 2

Practice Question 2

Method 2

Square tiles in Figure 5

(5 x 6) ÷ 2 = 15

Square tiles in Figure 20

(20 x 21) ÷ 2 = 210

Practice Question 2

Review the solution.

Checking my answers:• Does the answer make sense?• Have I answered the problem?• Have I identified the pattern?

Practice Question

Practice Question 3

Sandy spent 13

of her salary on a bag and

another 29

of her salary on a dress. She had

$1536 left. How much did she spend on the

bag and dress?

Practice Question 3

Sandy spent 13

of her salary on a bag and

another 29

of her salary on a dress. She had

$1536 left. How much did she spend on the

bag and dress?

Practice Question 3

▪ Draw a model

▪ Unitary method in

fraction

Practice Question 3

Method 1: Draw a model

Practice Question 3

Sandy spent 13

of her salary on a bag and another 29

of her

salary on a dress. She had $1536 left. How much did

she spend on the bag and dress?

bag dress $1536

4 units = $15361 unit = $1536 ÷ 4

= $3845 units = 5 x $384

= $1920

Practice Question 3Method 1

Practice Question 3

Method 2:

Unitary Method in Fractional Form

Practice Question 3

Method 2

Fraction of money left

= 1 -39

BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan

of her salary $1536

of her salary $1536 ÷ 4

= $38459

of her salary 5 x $384

= $1920

Practice Question 3Method 2

Practice Question 3

Checking my answers:

• Does the answer make sense?

• Have I answered the problem?

Practice Question

Practice Question 4

Raymond had an equal number of apples and

oranges at first. After he sold 56 apples and

194 oranges, the number of oranges he had

left was 25

of the number of apples he had left.

How many apples did Raymond have at first?

Practice Question 4

Raymond had an equal number of apples and

oranges at first. After he sold 56 apples and

194 oranges, the number of oranges he had

left was 25

of the number of apples he had

left. How many apples did Raymond have at

first?

Practice Question 4

▪ Draw a model

Practice Question 4Raymond had an equal number of apples and oranges at first. After he sold

56 apples and 194 oranges, the number of oranges he had left was25

the number of apples he had left. How many apples did Raymond have at

first?

Oranges

Apples

Practice Question 4

Oranges

Apples

3 units = 194 – 56= 138

1 unit = 138 ÷ 3= 46

Practice Question 4

Oranges

Apples

5 units = 5 x 46= 230

Apples at first230 + 56 = 286

Practice Question 4

Checking my answers:

• Does the answer make sense?

• Have I answered the problem?

Some tips…

Some tips…https://www.bukitpanjangpri.moe.edu.sg/departments/mathematics/what-tips-can-i-use-to-help-my-child

How can I (as a parent) help?

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.

How can I (as a parent) help?

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.

How can I (as a parent) help? 4) Feedback Loop

• Go through the errors made.

• Strengthen certain skills and concepts

by giving similar type of questions or

reading materials.

• Remember to motivate your child.

How can I (as a parent) help? 5) Long Term Memory

• Recap and link a few topics.

• Make use of the worksheets which your child

has filed.

6) Long Term Memory Retrieval

• Recap and link more topics from different levels.

Application! Real life examples!

Some tips for parents

✓Talk positively about Math so your child also values it.✓Play games with your child, which involve adding dice or numbers,

to show them that Math matters.✓Ask your child how they work out Math problems; it helps build

their knowledge and boosts their confidence. Ask "What is thequestion asking you to solve?”

✓Reinforce to your child that there can be more than one way toget the right answer.

✓Point out Math in everyday life with your child whenever you can.

Working together

Parents make a difference!

https://www.bukitpanjangpri.moe.edu.sg/bulletin/notifications

Where to retrieve the slides after the sharing?

Thank you.

Your feedbackwill assist us in future planning.

Primary 3 and Primary 4 S .U.P.E.R An approach to Math ......BUKIT PANJANG PRIMARY SCHOOL...

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