P3-4 PARENTS FRIDAY, 12 APRIL 2019 - - PowerPoint PPT Presentation

MATH WORKSHOP FOR P3-4 PARENTS FRIDAY, 12 APRIL 2019

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

Enables students to encounter math in a meaningful way and translate mathematical concept from the concrete to the abstract.

approach…

• Model Drawing (Before

and After Model)

• Looking for Patterns
• Guess and Check

Heuristics for Problem Solving

WHY Model Drawing?

• Helps students to understand the word

problem in visual form

• Empowers students to think systematically

and master challenging problems by making multi-step and multi-concept problems easy to work on.

Model approach

• Types of model

–Before and After

Before and After Model

When to use ‘Before and After’ model?

• This method is used in questions where there is a

change resulting in a 'before' situation and an 'after' situation.

• You will need to compare the two situations in order to

understand the question fully and find a way to solve it.

• Look out for keywords that show a change:

Eg: ‘At first’, ‘In the end’, ‘After giving 50 marbles’

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 do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense

• f the information?

∙ Is there a Math concept I can identify with?

Gaby had 5 times as much money as Tom. After Gaby had spent $30, she had twice as much money as Tom. How much money did Gaby have at first?

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 do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense

• f the information?

∙ Is there a Math concept I can identify with?

Gaby had 5 times as much money as Tom. After Gaby had spent $30, she had twice as much money as Tom. How much money did Gaby have at first?

Gaby  5 units Tom  1 unit Gaby spent $30 , Gaby  2 units Tom  1 unit Before After

Gaby had 5 times as much money as Tom. Use the manipulatives to help you construct the Before model for the word problem.

BEFORE

After Gaby had spent $30, she had twice as much money as Tom. How much money did Gaby have at first?

AFTER

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

3 units  $30 1 unit  $30 ÷3 = $10 5 units  $10 x 5 = $50 Gaby had $50 at first.

Step 3: Act

• n the plan
• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

Gaby had 5 times as much money as Tom. After Gaby had spent $30, she had twice as much money as Tom. How much money did Gaby have at first?

Bene nefits its of usi sing ng ma mani nipulat latives/model ives/model draw awin ing

• Students have a visual to associate with numbers that

can be abstract.

• Students learn to translate the information into math

concepts

• Students start to see the relationship behind numerical

values.

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 do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense

• f the information?

∙ Is there a Math concept I can identify with?

Ali and his brother shared a sum of money equally. After Ali gave $50 to his brother, his brother had twice as much money as him. How much money did each of them receive at first?

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

Ali Brother Give $50 to brother, Bro  2 units Ali  1 unit Before Same (?)

Ali and his brother shared a sum of money

• equally. After Ali gave $50 to his brother, his

brother had twice as much money as him. How much money did each of them receive at first?

After

Step 1: Study the problem  What do I know about the problem? What am I asked to find? How can I make sense of the information? Is there a Math concept I can identify with?

S T A R Chongfu Star Approach to Problem-Solving

After

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 2:

Think of a

plan  Have I solved similar problems before?  Have I considered all the conditions given in the problem?

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money each had at first.

Ali and his brother shared a sum of money

• equally. After Ali gave $50 to his brother, his

brother had twice as much money as him. How much money did each of them receive at first?

S T A R Chongfu Star Approach to Problem-Solving

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money each had at first.

After

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 3: Act

• n the plan
• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

Before A B ?

$50

? 1 Unit 1 Unit

$50

B

$50

A After

Ali and his brother shared a sum of money

• equally. After Ali gave $50 to his brother, his

brother had twice as much money as him. How much money did each of them receive at first?

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

1 unit  $50 + $50 = $100 $100 + $50 = $150 Each of them received $150 at first.

?

$50

B

$50

A After

Ali and his brother shared a sum of money

• equally. After Ali gave $50 to his brother, his

brother had twice as much money as him. How much money did each of them receive at first?

Step 3: Act

• n the plan
• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

1 Unit 1 Unit

S T A R Chongfu Star Approach to Problem-Solving

After

?

$50

Before

A B

$50

A B

1 Unit

?

1 Unit

$50

1 unit  $50 + $50 = $100 $100 + $50 = $150 Each of them received $150 at first.

After

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money each had at first.

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 4:

Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a

better solution to the problem?

Check:

Ali and his brother shared a sum of money

• equally. After Ali gave $50 to his brother, his

brother had twice as much money as him. How much money did each of them receive at first?

Before After Ali $150 $100 Brother $150 $200

• $50

+$50

x2

S T A R Chongfu Star Approach to Problem-Solving

After

?

$50

Before

A B

$50

A B

1 Unit

?

1 Unit

$50

1 unit  $50 + $50 = $100 $100 + $50 = $150 Each of them received $150 at first.

Check: After

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money each had at first.

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

Lily and James had $200 altogether. After giving Lily $20, James had as much money as her. How much did Lily have at first?

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense

• f the information?

∙ Is there a Math concept I can identify with?

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

• Lily + James → $200
• Who has more? James
• James -$20 = Lily + $20
• Lily at first →?
• Total unchanged (Before and After)

Lily and James had $200 altogether. After giving Lily $20, James had as much money as her. How much did Lily have at first?

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense

• f the information?

∙ Is there a Math concept I can identify with?

S T A R Chongfu Star Approach to Problem-Solving

Lily + James → $200 James -$20 = Lily + $20 Lily at first →?

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

Lily and James had $200

• altogether. After giving Lily $20,

James had as much money as her. How much did Lily have at first? ‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money Lily had at first.

Step 2: Think of a plan ∙ Have I solved similar problems before? ∙ Have I considered all the conditions given in the problem?

S T A R Chongfu Star Approach to Problem-Solving

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money Lily had at first.

Lily + James → $200 James -$20 = Lily + $20 Lily at first →?

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

200 ÷ 2 = 100 100 – 20 = 80 Lily had $80 at first.

J L

Before After

J L ? 20

Lily and James had $200 altogether. After giving Lily $20, James had as much money as her. How much did Lily have at first?

20 $200

Step 3: Act on the plan

• I will write out ALL the

steps.

• I will do my calculations

accurately.

• I will check that each step is

correct.

$200

S T A R Chongfu Star Approach to Problem-Solving

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money Lily had at first.

Lily + James → $200 James -$20 = Lily + $20 Lily at first →?

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

Check:

Before After James $120 $100 Lily $80 $100

• $20

+$20

equal Lily and James had $200 altogether. After giving Lily $20, James had as much money as her. How much did Lily have at first?

Step 4: Reflect

• Have I solved the

problem?

• Is my answer

reasonable?

• How do I know that

my answer is correct?

• Is there a better

solution to the problem?

S T A R Chongfu Star Approach to Problem-Solving

‘At first’ and ‘after’ are hints for us to use before and after model to find the amount of money Lily had at first.

Lily + James → $200 James -$20 = Lily + $20 Lily at first →?

S T A R Chongfu Star Approach to Problem-Solving Lilian had 160 more greeting cards than Joanne. After Lilian had used up 240 greeting cards, Joanne had 3 times as many greeting cards as Lilian. How many greeting cards did Joanne have now?

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

Lilian had 160 more greeting cards than

• Joanne. After Lilian had used up 240

greeting cards, Joanne had three times as many greeting cards as Lilian. How many greeting cards did Joanne have now?

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?

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

Lilian → Joanne + 160 After, Give Lilian used 240, Joanne → 3 units Lilian → 1 unit Before

Lilian had 160 more greeting cards than Joanne. After Lilian had used up 240 greeting cards, Joanne had three times as many greeting cards as

• Lilian. How many greeting cards did Joanne have

now?

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?

Joanne remains unchanged

S T A R Chongfu Star Approach to Problem-Solving

Lilian → Joanne + 160 After, Give Lilian used 240, Joanne → 3 units Lilian → 1 unit Before

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

Lilian had 160 more greeting cards than

• Joanne. After Lilian had used up 240

greeting cards, Joanne had three times as many greeting cards as Lilian. How many greeting cards did Joanne have now?

‘After’ is a hint for us to use before and after model to find the number of cards Joanne has.

Step 2: Think

• f a plan

∙ Have I solved similar problems before? ∙ Have I considered all the conditions given in the problem?

S T A R Chongfu Star Approach to Problem-Solving

Lilian → Joanne + 160 After, Give Lilian used 240, Joanne → 3 units Lilian → 1 unit Before

‘After’ is a hint for us to use before and after model to find the number

• f cards Joanne has

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

Before L J

160

240

1 Unit 1 Unit

J L After

Lilian had 160 more greeting cards than Joanne. After Lilian had used up 240 greeting cards, Joanne had three times as many greeting cards as Lilian. How many greeting cards did Joanne have?

160

1 Unit

Step 3: Act

• n the plan
• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

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

Lilian had 160 more greeting cards than Joanne. After Lilian had used up 240 greeting cards, Joanne had three times as many greeting cards as

• Lilian. How many greeting cards did Joanne have?

240 – 160 = 80 (2 units) 2 units  80 1 unit  80 ÷ 2 = 40 3 units  40 x 3 = 120 Joanne had 120 greetings cards.

240

1 Unit 1 Unit

J L After

160

1 Unit

Step 3: Act

• n the plan
• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

S T A R Chongfu Star Approach to Problem-Solving

Lilian  Joanne + 160 After, Give Lilian used 240, Joanne  3 units Lilian  1 unit Before

‘After’ is a hint for us to use before and after model to find the number of cards Joanne has

Joanne had 120 greetings cards.

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

Check: Lilian had 160 more greeting cards than

• Joanne. After Lilian had used up 240

greeting cards, Joanne had three times as many greeting cards as Lilian. How many greeting cards did Joanne have?

Before After Joanne 120 120 Lilian

120 + 160 =

280 40

• 240

3 times

Step 4:

Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a

better solution to the problem?

S T A R Chongfu Star Approach to Problem-Solving

Lilian  Joanne + 160 After, Give Lilian used 240, Joanne  3 units Lilian  1 unit Before

‘After’ is a hint for us to use before and after model to find the number of cards Joanne has

Joanne had 120 greetings cards.

Look for Pattern(s)

• Systematic way of solving

mathematical problems

• Examine the available data for

patterns or relationships.

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

(a) If the pattern above continues in this manner, how many dots will there be in Pattern 10? (b) Which pattern number has 103 dots?

8

13 18

Pattern 1 Pattern 2 Pattern 3

Study the pattern below.

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3

8

13 18

S T R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3

8

13 18

We need to find (a)the number of dots for Pattern 10 (b) which pattern has 103 dots Present the data in a table and identify the pattern/relationship.

Pattern Number of dots

1 8 2 8 + 5 = 13 3 8 + 5 + 5 = 18 4 8 + 5 + 5 + 5 = 23 5 8 + 5 + 5 + 5 + 5 = 28 6 8 + 5 + 5 + 5 + 5 + 5= 33 7 8 + 5 + 5 + 5 + 5 + 5 + 5 = 38 8 8 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 43 9 8 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 48 10 8 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 53

A

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

Do you find a pattern?

Pattern No. Number of dots 1 8 2 13 3 18 4 23

+5 +5 +5

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

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

Do you find a pattern?

Pattern No. Number of dots Relationship 1 8 +5 1x5+3 2 13 +5 2x5+3 3 18 +5 3x5+3 4 23 4x5+3

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

Repeated addition of 5 = Multiplication tables of 5

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

Pattern Rule: No.of dots = (Pattern Number x 5) + 3 (a) (10 x 5) + 3 = 53 There will be 53 dots in Pattern 10. (b) 103 – 3 = 100 100 ÷ 5 = 20 Pattern 20 has 103 dots

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3

8

13 18

We need to find (a)the number of dots for Pattern 10 (b) which pattern has 103 dots Present the data in a table and identify the pattern/relationship.

Pattern No. Number of dots Relationship 1 8 1x5+3 2 13 2x5+3 3 18 3x5+3 4 23 4x5+3

(a) (10 x 5) + 3 = 53 (Pattern 10) (b) 103 – 3 = 100 100 ÷ 5 = 20

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

Check pattern using 2 sets of data: Pattern 3 → (3 x 5) + 3 = 18 √ Pattern 4 → (4 x 5) + 3 = 23 √

Step 4: Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a better

solution to the problem?

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3

8

13 18

We need to find (a)the number of dots for Pattern 10 (b) which pattern has 103 dots Present the data in a table and identify the pattern/relationship.

Pattern No. Number of dots Relationship 1 8 1x5+3 2 13 2x5+3 3 18 3x5+3 4 23 4x5+3

(a) (10 x 5) + 3 = 53 (Pattern 10) (b) 103 – 3 = 100 100 ÷ 5 = 20

Check pattern using 2 sets of data: Pattern 3 → (3 x 5) + 3 = 18 √ Pattern 4 → (4 x 5) + 3 = 23 √

Pattern 1 Pattern 2

Study the pattern below.

Pattern 3 Question: Andy builds some patterns using square tiles as shown above. (a) If the pattern above continues, how many square tiles will there be in the 10th pattern? (b) Which pattern number has 169 square tiles? 1 9 4

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

Pattern 1 Pattern 2 Pattern 3 We need to find (a)the number of square tiles for Pattern 10 and (b)which Pattern has 169 square tiles. Present the data in a table and identify the pattern/relationship.

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

Do you find a pattern?

Pattern Number Number of square tiles 1 1 2 4 3 9 10 ?

+ 3 + 5 + 7

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

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

Do you find a pattern?

Pattern Number Number of square tiles Relationship 1 1 1x1 2 4 2x2 3 9 3x3 …… …… ……. 10 ? ?

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

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

a) 10 x 10 =100 There are 100 square tiles in Pattern 10. b) 13 x 13 = 169 Pattern 13 has 169 square tiles

Step 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

Pattern Rule: No.of tiles = (Pattern Number) x (Pattern Number)

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

We need to find (a)the number of square tiles for Pattern 10 and (b)which pattern has 169 square tiles Present the data in a table and identify the pattern/relationship. Pattern 1 Pattern 2 Pattern 3 b) 13 x 13 = 169 Pattern 13 has 169 square tiles

Pattern Number of square tiles Relationship 1 1 1x1 2 4 2x2 3 9 3x3 …… …… ……. 10 100 a)10x10 = 100

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

Check pattern using 2 sets of data: Figure 4 → 4 x 4 = 16 OR 9 + 7 = 16 √ Figure 5 → 5 x 5 = 25 OR 16 + 9 = 25 √

Step 4: Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a better

solution to the problem?

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

We need to find (a)the number of square tiles in Pattern 10 and (b)which pattern has 169 square tiles. Present the data in a table and identify the pattern/relationship.

Check pattern using 2 sets of data: Figure 4 → 4 x 4 = 16 OR 9 + 7 = 16 √ Figure 5 → 5 x 5 = 25 OR 16 + 9 = 25 √

Pattern Number of square tiles Relationship 1 1 1x1 2 4 2x2 3 9 3x3 …… …… ……. 10 100 10x10

b) 13 x 13 = 169 Pattern 13 has 169 square tiles

Study the pattern below.

Sam uses triangles to construct structures as shown above. If he continues in this manner, (a) How many triangles will he need for Figure 37? (b) Which figure will need 105 triangles?

Step 1: Study the problem ∙ What do I know about the problem? ∙ What am I asked to find? ∙ How can I make sense of the information? ∙ Is there a Math concept I can identify with?

• Figure. 1 Figure. 2 Figure. 3 Figure. 4

3 5 7 9

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

We need to find the number of triangles needed for Figure 37. We also need to find which Figure has 105 triangles, Present the data in a table and identify the pattern/relationship.

• Figure. 1 Figure. 2 Figure. 3 Figure. 4

3 5 7 9

Figure Number of triangles

+ 2 + 2 + 2 1 2 3 4 3 5 7 9 3 5 7 9

• Figure. 1 Figure. 2 Figure. 3 Figure. 4

Figure Number of triangles Relationship 1 3 1x2+1 2 5 2x2+1 3 7 3x2+1 37 ? (a) 37x2+1=75

+ 2 + 2 + 2 There will be 105 triangles in Figure 52. (b) 105-1 =104 104÷ 2 =52

Pattern Rule: No.of triangles = (Figure Number) x 2 + 1

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

We need to find the number of triangles needed for Figure 37. We also need to find which Figure has 105 triangles. Present the data in a table and identify the pattern/relationship.

Figure Number of triangles Relationship 1 3 1x2+1 2 5 2x2+1 3 7 3x2+1 37 ? (a) 37x2+1=75

(b) 105-1 =104

104÷ 2 =52 There will be 105 triangles in Figure 52.

• Figure. 1 Figure. 2 Figure. 3 Figure. 4

3 5 7 9

S T A R Chongfu Star Approach to Problem-Solving

Observe the pattern

We need to find the number of triangles needed for Figure 37. We also need to find which Figure has 105 triangles. Present the data in a table and identify the pattern/relationship.

Figure Number of triangles Relationship 1 3 1x2+1 2 5 2x2+1 3 7 3x2+1 37 ? (a) 37x2+1=75

(b) 105-1 =104

104÷ 2 =52 There will be 105 triangles in Figure 52.

Check pattern using 2 sets of data: Pattern 2 → 2 x 2 + 1 = 5 √ Pattern 3 → 3 x 2 + 1 = 7 √

• Figure. 1 Figure. 2 Figure. 3 Figure. 4

3 5 7 9

• Make an educated guess and

check its accuracy and revise guess if necessary

Guess and Check

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 do I know

about the problem?

∙What am I asked

to find?

∙How can I make

sense of the information?

∙Is there a Math

concept I can identify with?

There are a total of 19 butterflies and spiders in a

• garden. Given that the total number of spider legs

is 54 more than the total number of butterfly legs, how many butterflies are there?

19

? butterflies ? spiders

Spider legs Butterfly legs

54 more legs

S T A R Chongfu Star Approach to Problem-Solving

19

? butterflies ? spiders Spider legs (8 legs) Butterfly legs (6 legs)

54 more legs

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 2: Think

• f a plan

∙ Have I solved similar problems before? ∙ Have I considered all the conditions given in the problem?

There are a total of 19 butterflies and spiders in a garden. Given that the total number of spider legs is 54 more than the total number of butterfly legs, how many butterflies are there?

There are 2 given conditions

1) 19 butterflies and spiders 2) Number of spider legs is 54 more than number of butterfly legs

There are 2 unknowns – number of butterflies and spiders

Guess and check method Guess the number of butterflies and spiders and check if they match the given conditions.

S T A R Chongfu Star Approach to Problem-Solving

Guess and Check

19

? butterflies ? spiders Spider legs (8 legs) Butterfly legs (6 legs)

54 more legs

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 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

1) Add in the heading into each column

• No. of

butterflies

• No. of

spiders

Difference Check

• No. of

spiders’ legs

8 legs

• No. of

butterflies’ legs

6 legs

2) 2 conditions must be met

19 butterflies and spiders 54

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 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

• No. of

butterflies

• No. of

spiders

Difference Check

• No. of

spiders’ legs

8 legs

• No. of

butterflies’ legs

6 legs

19 butterflies and spiders 54

Start with an educated and calculated guess

11 8

11 x 8 = 88 8 x 6 = 48 88 – 48 = 40

12 7

12 x 8 = 96 7 x 6 = 42 96 – 42 = 54

X / 10 9

10 x 8 = 80 9 x 6 = 54 80 – 54 = 26

X

increase increase

Check guess against the information given in the question

• ensure all conditions are

met

• No. of

butterflies

• No. of

spiders Difference

Check

• No. of

spiders’ legs

8 legs

• No. of

butterflies’ legs

6 legs

11 8

11 x 8 = 88 8 x 6 = 48 88 – 48 = 40

12 7

12 x 8 = 96 7 x 6 = 42 96 – 42 = 54

X / 10 9

10 x 8 = 80 9 x 6 = 54 80 – 54 = 26

X

How many butterflies are there?

There are 7 butterflies.

S T A R Chongfu Star Approach to Problem-Solving

Guess and Check

19

? butterflies ? spiders Spider legs (8 legs) Butterfly legs (6 legs)

54 more legs

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 4: Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a better

solution to the problem?

The two given conditions: 1)19 butterflies and spiders (12 + 7 = 19) 2) 54 more spiders legs than butterflies legs (96-42=54)

S T A R Chongfu Star Approach to Problem-Solving

Guess and Check

The two given conditions: 1) 19 butterflies and spiders (12 + 7 = 19) 2) 54 more spiders legs than butterflies legs (96-42=54)

19

? butterflies ? spiders Spider legs (8 legs) Butterfly legs (6 legs)

54 more legs

Joy counted the number of cows and ducks in a farm. There were a total of 42 heads and 104 legs in all. How many cows were there?

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 do I know

about the problem?

∙What am I asked

to find?

∙How can I make

sense of the information?

∙Is there a Math

concept I can identify with?

Joy counted the number of cows and ducks in a farm. There were a total of 42 heads and 104 legs in all. How many cows were there?

42 heads 104 legs cow → 4 legs duck → 2 legs ? cows

Total

S T A R Chongfu Star Approach to Problem-Solving

42 heads 104 legs cows → 4 legs ducks → 2 legs ? cows

Total

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 2: Think

• f a plan

∙ Have I solved similar problems before? ∙ Have I considered all the conditions given in the problem?

There are 2 unknowns – number of cows and number of ducks. There are 2 given conditions 1) Total number of heads - 42 2) Total number of legs – 104. Guess the number of cows and ducks and check if they match the given conditions. Joy counted the number of cows and ducks in a farm. There were a total of 42 heads and 104 legs in all. How many cows were there?

S T A R Chongfu Star Approach to Problem-Solving

42 heads 104 legs cows → 4 legs ducks → 2 legs ? cows

Total

Guess and Check

Total no. of legs (104) 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 3: Act on the plan

• I will write out

ALL the steps.

• I will do my

calculations accurately.

• I will check

that each step is correct.

There were 10 cows.

21 21 42

21 x 2 = 42 21 x 4 = 84 42 + 84 = 126

× 27 15 42

27 x 2 = 54 15 x 4 = 60 54 + 60 = 114

× 32 10 42

32 x 2 = 64 10 x 4 = 40 64 + 40 = 104

✓

Joy counted the number of cows and ducks in a farm. There were a total of 42 heads and 104 legs in all. How many cows were there?

• No. of ducks
• No. of cows

Total no.

• f heads (42)

Check

S T A R Chongfu Star Approach to Problem-Solving

42 heads 104 legs c → 4 legs d → 2 legs ? cows Guess and Check

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 4: Reflect

• Have I solved

the problem?

• Is my answer

reasonable?

• How do I know

that my answer is correct?

• Is there a better

solution to the problem?

Check the 2 conditions: Total heads 10 + 32 =42 10 x 4 = 40 (number of legs for cows) 32 x 2 = 64 (number of legs for ducks) Total number of legs = 40 + 64 = 104

S T A R Chongfu Star Approach to Problem-Solving

42 heads 104 legs c → 4 legs d → 2 legs ? cows Guess and Check

Check the 2 conditions: Total heads 10 + 32 =42 √ 10 x 4 = 40 (number of legs for cows) 32 x 2 = 64 (number of legs for ducks) Total number of legs = 40 + 64 = 104√

THE END

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