MATH WORKSHOP FOR P1 PARENTS FRIDAY, 10 APRIL 2015.

MATH WORKSHOPFOR

P1 PARENTSFRIDAY, 10 APRIL 2015

http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf

Mathematics Framework

Chongfu’s Curriculum Focus: Heuristics and Thinking Skills

• Development of mathematical problem solving ability through the use of heuristics and thinking skills

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 √ √ √ √ √ √

Heuristics for Problem Solving (P1 & P2)

• Model Drawing• Guess and Check• Looking for Pattern• Listing

Model approach

• Systematic way of solving mathematical problems

• Types of model– Part-whole– Comparison

Examples

6 4

?

Part-whole Model

Comparison Model

6

4

?

Anna

Ben

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

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?

Peter 6 toy cars

John 12 toy cars

What is the total?S T

AR






Step 4: Reflect


Step 2: Think of a plan

·What strategy should I use?·Have I solved similar problems before?

Peter 6 toy cars

John 12 toy cars


AR

I must find the total number of toy cars.

I can use a part-whole model to represent the number of toy cars.






Step 4: Reflect


Step 3: Act on the plan

•I will write out the steps of my solutions

Peter 6 toy cars

John 12 toy cars


AR



6 12

Peter John

? 6 + 12 = 18

They have 18 toy cars altogether.






Step 4: Reflect


Step 4: Reflect

•Have I answered the question?•Is my answer reasonable?•Have I checked my answers? •Is there a better alternative?

Peter 6 toy cars

John 12 toy cars


AR



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) (√)






Step 4: Reflect


·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?

?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)


10 + 15 = 25 (√)






Step 4: Reflect




Ali has 5 ice-cream sticks. Jane has 18 ice-cream sticks. How many more ice-creams sticks does Jane have than Ali?

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)


5 + 13 = 18 (√)

Or 13 + 5 = 18 (√)


5

18

Ali

Jane

?





Step 4: Reflect




Steven collected 376 Australia stamps.He collected 142 fewer Australia stamps than China stamps. How many China stamps did he collect?

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)


518 - 142 = 376 (√)


142

376Australia

376China

?

•Make an educated guess •Check its accuracy and revise guess if necessary

Guess and Check





Step 4: Reflect




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 )

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)


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





Step 4: Reflect




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 )

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)


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

Looking for Pattern


• Examine the available data for patterns or relationships.





Step 4: Reflect

Study the pattern of the figures. Find the number of tiles in figure 5. Step 1: Study

the problem



Figure 1 Figure 2 Figure 3

S T

AR


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


+ 3+ 3+ 3+ 3





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 …………..

?




S T

AR


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

Listing


• Organise, present or generate the available data in a systematic way





Step 4: Reflect




Meiling has a blue blouse, a white blouse, a skirt and a pair of jeans.How many different ways can Meiling wear her outfit?

S T

ARCheck:

-Are all combinations made up of

1 top and 1 bottom?

-Are there any repeated combination?


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.

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

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.


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

39

Identify the Heuristics to solve the problems

Let’s Practise

Heuristics Model drawingGuess and check Looking for pattern Listing

The figures below are made of sticks of equal length.Find the number of sticks required to form Figure 10.

………………….. Figure 10

?



Figure 1 2 3

No. of

sticks3 5 7

S T

AR


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

Jenny had 315 stickers. Her sister gave her 45 stickers. How many stickers did she have altogether?


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)


360 – 315 = 45 (√)

Or 360 – 45 = 315 (√)


There are a total of 16 bicycles and tricycles in a park.There are 36 wheels altogether.How many bicycles and tricycles are there?


S T

AR

There are 12 bicycles and 4 tricycles.


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 (√)

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 ?


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


10 cm + 15 cm = 25 cm

Carol is 25 cm taller than Lyn.

120 cm

10

Carol

Jenny

Lyn

1510


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

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.


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?

Q and A

THE END

MATH WORKSHOP FOR P1 PARENTS FRIDAY, 10 APRIL 2015.

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