primary 3 and primary 4 s .u.p.e.r an approach to math ......bukit panjang primary school...
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BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Mathematics Sharing SessionPrimary 3 and Primary 4
Your feedback will assist us in future planning.
URL for Feedback Form: https://forms.gle/L1cZoBcPzYWnFafT8
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
https://www.bukitpanjangpri.moe.edu.sg/bulletin/notifications
Where to retrieve the slides after the sharing?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Objectives of this sharing …
1. Provide an overview of BPPSProblem Solving Processes
2. Create an awareness of the various problem solving strategies / heuristics
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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)
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
S .U.P.E.R. Approach To
Problem Solving
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
S Study and
U Understand the problem
P Plan the solution
E Execute the plan
R Review the solution
Problem Solving Processes
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
• 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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
5 Main Problem Solving Approaches
1. Grouping
2. Model Drawing
3. Assumption
4. Find a constant
5. Simultaneous Equations
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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)
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Learning Experience @ BPPS
✓ Expose students to general problem solving skills, thinking skills and heuristics, and how these skills can be applied.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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).
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Learning Experience @ BPPS
✓ 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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Questions
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
1
Practice Question
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Method 1: Guess and Check
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Step 3 : Execute the plan
Number of chicken
pies
Sales from chicken pies
($3 each)
Number of apple
pies
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
X
25 3525 x $3 = $75
35 x $2 = $70
$75 + $70 = $145
X
24 3624 x $3 = $72
36 x $2 = $72
$72 + $72 = $144
✅
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Note:
● 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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Method 2: Assumption/ Supposition
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Step 3 : Execute the plan
Assume all 60 were apple pies ($2 each):
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1st
60th
Minimum amount of sales
60 x $2 = $120
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
Sales not accounted for
$144 - $120 = $24
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Step 3 : Execute the plan
Assume all 60 were apple pies ($2 each):
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1st
60th
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
$2 $2 $2 $2 $2
$1 $1 $1 $1 $1
$1 $1 $1 $1 $1
$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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Step 3 : Execute the plan
Method 3: Assumption/ Supposition
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 1
Step 3 : Execute the plan
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 Department
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):
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
2
Practice Question
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Step 1 : Study and Understand the problem
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?
13
6 10
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Step 1 : Study and Understand the problem
13
6 10+ 2+ 3
+ 4
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
What are the possible heuristics or strategies
that we can use to solve this question?
▪ Make A List
▪ Look For A Pattern
Step 2 : Plan the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Method 1: Make a List and Look for Pattern
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Method 1: Make a List and Look for Pattern
Figure Number
No. of squares
Number of squares in Figure 5 → 15 squares
Step 3 : Execute the plan
1
1
2
1 + 2 = 3
3
3 + 3 = 6
4
6 + 4 = 10
5
10 + 5 = 15
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Method 1: Make a List and Look for Pattern
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
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Method 1: Make a List and Look for Pattern
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
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Method 1: Make a List and Look for Pattern
Figure Number
19 20
No. of squares
171 + 19= 190
190 + 20= 210
Number of squares in Figure 20 → 210 squares
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Step 3 : Execute the plan
Method 2
Figure 1 Figure 2 Figure 3 Figure 4
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Step 3 : Execute the plan
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
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Step 3 : Execute the plan
Method 2
Square tiles in Figure 5
(5 x 6) ÷ 2 = 15
Square tiles in Figure 20
(20 x 21) ÷ 2 = 210
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 2
Review the solution.
Checking my answers:• Does the answer make sense?• Have I answered the problem?• Have I identified the pattern?
Step 4 : Review the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
3
Practice Question
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Step 1 : Study and Understand the problem
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?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Step 1 : Study and Understand the problem
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?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
What are the possible heuristics or strategies
that we can use to solve this question?
▪ Draw a model
▪ Unitary method in
fraction
Step 2 : Plan the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Method 1: Draw a model
Step 2 : Plan the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
?
Step 3 : Execute the plan
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
bag dress $1536
?
Step 3 : Execute the plan
4 units = $15361 unit = $1536 ÷ 4
= $3845 units = 5 x $384
= $1920
Practice Question 3Method 1
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Method 2:
Unitary Method in Fractional Form
Step 2 : Plan the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Step 3 : Execute the plan
Method 2
Fraction of money left
1 -13
-29
= 1 -39
-29
= 49
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics DepartmentStep 3 : Execute the plan
49
of her salary $1536
19
of her salary $1536 ÷ 4
= $38459
of her salary 5 x $384
= $1920
Practice Question 3Method 2
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 3
Review the solution.
Checking my answers:
• Does the answer make sense?
• Have I answered the problem?
Step 4 : Review the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
4
Practice Question
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
Step 1 : Study and Understand the problem
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?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
Step 1 : Study and Understand the problem
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?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
What are the possible heuristics or strategies
that we can use to solve this question?
▪ Draw a model
Step 2 : Plan the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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
of
the number of apples he had left. How many apples did Raymond have at
first?
Oranges
?
Step 3 : Execute the plan
Apples
194
56
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
Oranges
?
Step 3 : Execute the plan
Apples
194
56
3 units = 194 – 56= 138
1 unit = 138 ÷ 3= 46
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
Oranges
?
Step 3 : Execute the plan
Apples
194
56
5 units = 5 x 46= 230
Apples at first230 + 56 = 286
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Practice Question 4
Review the solution.
Checking my answers:
• Does the answer make sense?
• Have I answered the problem?
Step 4 : Review the solution
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Some tips…
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Some tips…https://www.bukitpanjangpri.moe.edu.sg/departments/mathematics/what-tips-can-i-use-to-help-my-child
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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!
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
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.
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Working together
Parents make a difference!
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
https://www.bukitpanjangpri.moe.edu.sg/bulletin/notifications
Where to retrieve the slides after the sharing?
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
BUKIT PANJANG PRIMARY SCHOOLMathematics Department
Thank you.
Your feedbackwill assist us in future planning.