math workshop for p1 parents friday, 10 april 2015
TRANSCRIPT
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MATH WORKSHOPFOR
P1 PARENTSFRIDAY, 10 APRIL 2015
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http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf
Mathematics Framework
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Chongfu’s Curriculum Focus: Heuristics and Thinking Skills
• Development of mathematical problem solving ability through the use of heuristics and thinking skills
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CHONGFU SCHOOL MATHEMATICS
SKILLS ACQUIRED AT THE END OF EACH LEVEL
P1 P2 P3 P4 P5 P6 P5F P6F
Heuristics/Thinking Skills
Part-whole model √ √ √ √ √ √ √ √
Comparison model √ √ √ √ √ √ √ √
Multiplication and Division model
√ √ √ √ √ √ √
Guess and Check √ √ √ √ √ √ √ √
Listing √ √ √ √ √ √ √ √
Looking for Pattern √ √ √ √ √ √ √ √
Before and After model √ √ √ √ √ √
Working backwards √ √ √ √ √
Make suppositions √ √
Use equations √ √
Simplify the problem √ √ √ √ √ √
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Heuristics for Problem Solving (P1 & P2)
• Model Drawing• Guess and Check• Looking for Pattern• Listing
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Model approach
• Systematic way of solving mathematical problems
• Types of model– Part-whole– Comparison
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Examples
6 4
?
Part-whole Model
Comparison Model
6
4
?
Anna
Ben
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9
WHY Model Drawing?
• Visual representation of details and actions which assists pupils with problem solving
• Helps pupils think logically using visuals to determine their computations
• Empowers pupils to think systematically and master more challenging problems
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether?
Step 1: Study the problem
· 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?
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Peter 6 toy cars
John 12 toy cars
What is the total?S T
AR
Chongfu Star Approach to Problem-Solving
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether?
Step 2: Think of a plan
·What strategy should I use?·Have I solved similar problems before?
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Peter 6 toy cars
John 12 toy cars
What is the total?S T
AR
I must find the total number of toy cars.
I can use a part-whole model to represent the number of toy cars.
Chongfu Star Approach to Problem-Solving
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether?
Step 3: Act on the plan
•I will write out the steps of my solutions
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Peter 6 toy cars
John 12 toy cars
What is the total?S T
AR
I must find the total number of toy cars.
I can use a part-whole model to represent the number of toy cars.
6 12
Peter John
? 6 + 12 = 18
They have 18 toy cars altogether.
Chongfu Star Approach to Problem-Solving
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Peter has 6 toy cars. John has 12 toy cars. How many toy cars do they have altogether?
Step 4: Reflect
•Have I answered the question?•Is my answer reasonable?•Have I checked my answers? •Is there a better alternative?
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Peter 6 toy cars
John 12 toy cars
What is the total?S T
AR
I must find the total number of toy cars.
I can use a part-whole model to represent the number of toy cars.
6 12
Peter John
? 6 + 12 = 18
They have 18 toy cars altogether.
The answer must be greater than the number that each person has. (reasonableness)
Check by working backwards:
18 – 6 = 12 (John) (√)
18 – 12 = 6 (Peter) (√)
Chongfu Star Approach to Problem-Solving
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
Kelvin has 25 storybooks. 10 of them are English storybooks.The rest of them are Chinese storybooks.How many Chinese storybooks are there?
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?10
English Chinese
2525 10 = 15
There are 15 Chinese storybooks.
S T
AR
Total No. of storybooks 25
English 10
How many Chinese storybooks?
I must find the number of Chinese storybooks.
I can use a part-whole model to represent the number of storybooks.
The answer must be less than 25. (reasonableness)
Check by working backwards:
10 + 15 = 25 (√)
Chongfu Star Approach to Problem-Solving
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
Ali has 5 ice-cream sticks. Jane has 18 ice-cream sticks. How many more ice-creams sticks does Jane have than Ali?
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S T
AR
Ali 5 ice-cream sticks
Jane 18 ice-cream sticks
How many more?
I must compare the number of ice-cream sticks Ali and Jane have.
I can use a comparison model to find the difference.
18 – 5 = 13Jane has 13 more ice-cream sticks than Ali.
The answer must be smaller than 18. (reasonableness)
Check by working backwards:
5 + 13 = 18 (√)
Or 13 + 5 = 18 (√)
Chongfu Star Approach to Problem-Solving
5
18
Ali
Jane
?
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
Steven collected 376 Australia stamps.He collected 142 fewer Australia stamps than China stamps. How many China stamps did he collect?
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376 + 142 = 518
He collected 518 China stamps.
S T
AR
Australia 376
China Australia + 142
How many China stamps?
I must find the number of China stamps.
I can use a comparison model to find the number of China stamps.
The answer must be more than 376. (reasonableness)
Check by working backwards:
518 - 142 = 376 (√)
Chongfu Star Approach to Problem-Solving
142
376Australia
376China
?
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•Make an educated guess •Check its accuracy and revise guess if necessary
Guess and Check
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
10 motorcycles and cars are parked at a carpark.There are a total of 34 wheels.How many motorcycles and cars are there? (motorcycle: 2 wheels and car: 4 wheels )
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S T
AR
I should make a table and use guess and check
Check the 2 given conditions:1. 3 + 7 = 10 (vehicles)2. 6 + 28 = 34 (wheels)
Chongfu Star Approach to Problem-Solving
Motorcycles and cars 10Number of wheels 34M 2 wheelsC 4 wheelsFind the number of motorcycles and cars.
Find the 2 numbers that fit the 2 conditions:- Motorcycles + cars = 10- Total number of wheels = 34
M C Motorcyclewheels
Carwheels
Total No. of
wheels
Check
There are 3 motorcycles and 7 cars.
10 34
5 5 5x2 = 10 5x4 = 20 10+20 = 30 x
3 7 3x2 = 6 7x4 = 28 6+28 = 34
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
Mr Lim has a total of 15 birds and cats in his pet shop.All the birds and cats have a total of 48 legs.How many birds and cats are there in Mr Lim pet shop? (bird: 2 legs and cat: 4 legs )
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S T
AR
I should make a table and use guess and check
Check the 2 given conditions:1. 6 + 9 = 15 (animals)2. 12 + 36 = 48 (legs)
Chongfu Star Approach to Problem-Solving
Birds and cats 15Number of legs 48B 2 legsC 4 legsFind the number of birds and cats.
Find the 2 numbers that fit the 2 conditions:- Birds + cats = 15- Total number of legs = 48
B C Birdlegs
Catlegs
Total No. of legs
Check
There are 6 birds and 9 cats.
15 48
10 5 10x2 = 20 5x4 = 20 20+20= 40 x
8 7 8x2 = 16 7x4 = 28 16+28= 44x
6 9 6x2 = 12 9x4 = 36 12+36= 48
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Looking for Pattern
• Systematic way of solving mathematical problems
• Examine the available data for patterns or relationships.
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Study the pattern of the figures. Find the number of tiles in figure 5. Step 1: Study
the problem
·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?
Figure 1 Figure 2 Figure 3
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S T
AR
Chongfu Star Approach to Problem-Solving
Observe the pattern
There are 16 tiles in the 5th figure.
• Check pattern4, 7, 10, 13, 16…… (+3 repeatedly)
• Use given data to check the relationship e.g. Figure 3: 4 + 3 + 3 = 10 e.g. Figure 4: 4 + 3 + 3 + 3 = 13
We need to find the number of tiles for the 5th figure.Present the data in a table and try to identify a pattern/relationship.
Figure Tiles
1 4
2 7
3 10
Fig No. of tiles
1 4
2 7
3 10
4 13
5 16
Figure 1 Figure 2 Figure 3
+ 3+ 3+ 3+ 3
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Study the pattern of the figures. Find the number of shaded triangles in Figure 10.
Figure 1 Figure 2 Figure 3 Figure 10 …………..
?
Step 1: Study the problem
·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?
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S T
AR
Chongfu Star Approach to Problem-Solving
Observe the patternFigure 1 2 3
No. ofShadedtriangle
1 3 5
Figure Number of shaded
triangles
1 1
2 2+1=3
3 3+2=5
4 4+3=7
10 10+9=19
There are 19 shaded triangles in the 10th figure.
• Check pattern1, 3, 5, 7, 9, 11, 13, 15, 17, 19 (+2 repeatedly) • Use data to check the
relationshipe.g. Figure 2: 2 +1 = 3e.g. Figure 4: 4 + 3 =7
We need to find the number of shaded triangles for the 10th figure.Present the data in a table and try to identify a pattern/relationship.
Figure Triangle
1 1
2 3
3 5
+ 2+ 2+ 2
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Listing
• Systematic way of solving mathematical problems
• Organise, present or generate the available data in a systematic way
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Chongfu Star Approach to Problem-Solving
Step 2: Think of a Plan
Step 1: Study the Problem
Step 3: Act on the Plan
Step 4: Reflect
Step 1: Study the problem
·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?
Meiling has a blue blouse, a white blouse, a skirt and a pair of jeans.How many different ways can Meiling wear her outfit?
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S T
ARCheck:
-Are all combinations made up of
1 top and 1 bottom?
-Are there any repeated combination?
Chongfu Star Approach to Problem-Solving
Blue blouse, white blouse, skirt and jeans.Outfit -> 1 top and 1 bottom
Since there are many combinations of the different outfit, we need to make a list systematically.
Top Bottom
Blue Blouse SkirtWhite Blouse Skirt
Blue Blouse Jeans
White Blouse Jeans
There are 4 ways.
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Mary puts a teddy bear, a toy car and a doll in a
row on a shelf.
How many ways can she arrange the toys on
the shelf?
Make a Systematic ListChongfu Star Approach to Problem-Solving
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S T
AR
- Teddy bear, toy car and doll- Arranged in a row
Since there are many combinations, we need to make a list systematically.
There are 6 ways to arrange the toys.
Chongfu Star Approach to Problem-Solving
Starting with bear
Starting with car
Starting with doll
Check:
-Are all combinations made up of
three toys?
Are there any repeated combination?
B, C, D
B, D, C
C, B, D
C, D, B
D, C, B
D, B, C
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39
Identify the Heuristics to solve the problems
Let’s Practise
Heuristics Model drawingGuess and check Looking for pattern Listing
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The figures below are made of sticks of equal length.Find the number of sticks required to form Figure 10.
………………….. Figure 10
?
Heuristics Model drawingGuess and check Looking for pattern Listing
Figure 1 Figure 2 Figure 3
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Figure 1 2 3
No. of
sticks3 5 7
S T
AR
Chongfu Star Approach to Problem-Solving
Observe the pattern
Figure No. of sticks
1 3
2 3+2 = 5
3 3+2+2 = 7
4 3+2+2+2 = 9
10 3+(9x2) = 21
There are 21 sticks in the 10th figure.
We need to find the number of sticks for figure 10 .Present the data in a table and try to identify a pattern/relationship.
Figure Sticks
1 3
2 5
3 7
• Check the pattern 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 (+2 repeatedly) • Use given data to check the relationship Figure 1 3 sticksFigure 2 3+2 = 5 sticks Figure 3 3+2+2 =7 sticksFigure 10 3+(9x2) = 21 sticks
+ 2+2+2
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Jenny had 315 stickers. Her sister gave her 45 stickers. How many stickers did she have altogether?
Heuristics Model drawingGuess and check Looking for pattern Listing
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S T
AR
Jenny 315 stickers
Sister gave 45 stickers
How many stickers altogether?
I must find the total number of stickers.
I can use a part-whole model to represent the number of stickers.
45 315
Sister Jenny
?315 + 45 = 360
She had 360 stickers altogether.
The answer must be greater than 315 (reasonableness)
Check by working backwards:
360 – 315 = 45 (√)
Or 360 – 45 = 315 (√)
Chongfu Star Approach to Problem-Solving
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There are a total of 16 bicycles and tricycles in a park.There are 36 wheels altogether.How many bicycles and tricycles are there?
Heuristics Model drawingGuess and check Looking for pattern Listing
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S T
AR
There are 12 bicycles and 4 tricycles.
Chongfu Star Approach to Problem-Solving
Bicycles and tricycles 16
Number of wheels 36Find number of bicycles and tricycles
Find number of bicycles andtricycles I should make a table and use guess and check
B T No. of bicycle wheels
No. of tricycle wheels
Total no. of wheels
Check
10 6 10x2=20 6x3=18 38 ×
11 5 11x2=22 5x3=15 37 ×
12 4 12x2=24 4x3=12 36 √
Check 2 conditions are met:1. 12 + 4 = 16 (√)2. 24 + 12 = 36 (√)
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Lyn’s height is 120cm. Jenny is 10cm taller than Lyn.
Carol is 15 cm taller than Jenny. How much taller is
Carol than Lyn ?
Heuristics Model drawingGuess and check Looking for pattern Listing
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S TAR
Lyn 120 cmJenny Lyn + 10 cm Carol Jenny + 15 cmHow much taller is Carol than Lyn?
I must find how much taller is Carol than LynI can use a comparison model to represent all their height.
Carol must be taller than Lyn (reasonableness)
120 cm + 10 cm + 15 cm =
145 cm (Carol )
145 cm – 120 cm = 25 cm
Chongfu Star Approach to Problem-Solving
10 cm + 15 cm = 25 cm
Carol is 25 cm taller than Lyn.
120 cm
10
Carol
Jenny
Lyn
1510
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Heuristics Model drawingGuess and check Looking for pattern Listing
How many 2-digit numbers can you form
using the following 4 digits?
You can only use a digit once in each number.
2 4 53
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S T
AR
- 2-digit numbers- Use all 4 digits- Use a digit once in each number
Since there are many combinations, we need to make a list systematically.
I can form 12 2-digit numbers.
Chongfu Star Approach to Problem-Solving
2 3 4 5
23 32 42 52
24 34 43 53
25 35 45 54
Check:
- Are all numbers made up of different digits? E.g. 33 (×)
- Are there any repeated numbers?
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Q and A
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THE END