Heuristics Springdale Primary School 1 The Future of Work - - PowerPoint PPT Presentation

Springdale Primary School

P3 & P4 Parents’ Seminar Mathematics Sharing

19 Jan 2019

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Heuristics

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The Future of Work

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What is the MOST important factor to be successful?

• Go to https://www.menti.com
• Enter the code 44018

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Objectives

At the end of this session, parents will be able to:

• understand the rationale of using different

heuristics in solving problem sums

• know what SDPS Smart Framework is and how

students use it to solve problem sums

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Curriculum Framework

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Thinking Skills

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• Thinking skills are skills that can be used in a

thinking process, such as – classifying – comparing – analysing parts and whole – identifying patterns and relationships – induction – deduction – generalising – spatial visualisation

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Heuristics

• Heuristics refers to the different strategies

that we can adopt to solve unfamiliar or non- routine Maths problems

• There are different types of heuristics and

they can be grouped into four categories, based on how they are being used:

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Overview of SDPS Heuristic Plan

Primary 3

• Act it Out
• Guess and

Check

• Look for

Patterns Primary 4

• Systematic

Listing

• Make a

Supposition

• Working

Backwards

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Look for a Pattern (P3)

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• Mathematics is often referred to the science of

patterns

• Once a pattern is established, it can be

analysed, extended and re-created

• The following skills are needful

– Creating and continuing a pattern – Spatial patterns (highlighters) – Finding a pattern in a table – Always link it to the pattern number if possible

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Look for Patterns (P3)

How many dots are there in Pattern 10?

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Pattern 1 Pattern 2 Pattern 3 Pattern 4 Pattern Total no. of dots No of Dots No of Dots 1 1 1 × 1 1 2 4 2 × 2 1 + 3 3 9 3 × 3 1 + 3 + 5 4 16 4 × 4 1 + 3 + 5 + 7 … … … 10 100 10 × 10 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

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Look for a Pattern (P3)

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What are the missing numbers in the 5th row? (P3 TM p42)

Springdale Primary School

Look for a Pattern (P3)

Mrs Lim is on a fitness programme. On the first day, she cycled around her estate 3 times. On the second day, she cycled around it 7 times and on the third day, 11 times. How many days must she exercise before reaching her goal of cycling her estate 31 times?

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Day No of Times Pattern 1 3 1 × 3 + 0 2 7 2 × 3 + 1 3 11 3 × 3 + 2 … … … 8 31 8 × 3 + 7 = 31

Alternative answer

3 3 + 4 3 + 4 + 4 … 3 + 4 + 4 + 4 + 4 + 4 + 4 + 4

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Guess and Check (P3)

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• Start with an educated and calculated guess
• Check guess against the information given in

the question

• Ensure all conditions are met
• Can be rather tedious and there is room for

careless mistakes to be made

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Guess and Check (P3)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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Guess and Check (P3)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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What do I know?  10 animals  Chicken has 2 legs  Cow has 4 legs  36 legs in total Asked to find?  Number of chickens  Number of ducks

Springdale Primary School

Guess and Check (P3)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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Have I solved similar questions before? What skill should I use?  Guess & Check?  Model drawing?  Systematic Listing?  Looking for patterns?

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Guess and Check (P3)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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Chickens Cows No. Legs No. Legs Total Legs 5 10 5 20 30 3 6 7 28 34 … … … … … 2 4 8 32 36

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Guess and Check (P3)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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Refeed the answer back to the question: 2 chickens and 8 cows 2 x 2 = 4 8 x 4 = 32 32 + 4 = 36 

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Make a Supposition (P4)

There are 10 animals in a farm. Some of them are chickens and the rest are cows. There are 36 legs altogether. How many chickens and cows are there?

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Assuming all animals are cows, there are 10 cows. Hence, there are 40 legs 4 x 10 = 40 40 – 36 = 4 There are 4 legs extra. (Too many in my assumption) Every time I exchange a cow for a chicken, I can get rid of 2 legs. 4 ÷ 2 = 2  10 – 2 = 8  Ans: 8 cows, 2 chicken

Extra 4 legs

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Make a Supposition (P4)

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Now it is your turn. :)

Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy? $13

$7

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self-confidence

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Springdale Primary School

Make a Supposition (P4)

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Now it is your turn. :)

Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy? $13

$7

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Make a Supposition (P4)

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Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy?

What do I know?  Paid $408 for 42 dinner plates  $13 for large plate  $7 for small plate Asked to find?  Number of large plate

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Make a Supposition (P4)

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Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy?

Have I solved similar questions before? What skill should I use?  Guess & Check?  Make a supposition?  Systematic Listing?  Looking for patterns?

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Make a Supposition (P4)

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Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy?

Assuming all are small plates 42 x $7 = $294 $408 – $294 = $114 There is a shortage of $114. $13 – $7 = $6 The large plate costs $6 more than the small plate. $114 ÷ $6 = 19 She bought 19 large plates.

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Make a Supposition (P4)

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Mdm Chow paid $408 for 42 dinner plates. She spent $13 on each large plate and $7 on each small plate. How many large plates did she buy? Refeed the answer back to the question: 42 – 19 = 23 23 x 7 = 161 (small plates) 19 x 13 = 247 (large plates) 247 + 161 = 408 

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Systematic Listing (P4)

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• It is to list all the possible outcomes for two or

more combined events enables you to calculate the probability of any particular event

• ccurring.

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Systematic Listing (P4)

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I am thinking of a 2-digit number. It is a common multiple

• f 6 and 8. It is between 30 to 50. The digit in the ones

place is twice of the digit in the tens place. What is the number that I am thinking of?

What do I know?  2-digit number  common multiple of 6 and 8  between 30 to 50 

• nes place  2 units

 tens place  1 unit Asked to find?  Find the number

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Systematic Listing (P4)

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I am thinking of a 2-digit number. It is a common multiple

• f 6 and 8. It is between 30 to 50. The digit in the ones

place is twice of the digit in the tens place. What is the number that I am thinking of?

Have I solved similar questions before? What skill should I use?  Guess & Check?  Make a supposition?  Systematic Listing?  Looking for patterns?

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Systematic Listing (P4)

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I am thinking of a 2-digit number. It is a common multiple

• f 6 and 8. It is between 30 to 50. The digit in the ones

place is twice of the digit in the tens place. What is the number that I am thinking of?

Method A Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54… Multiples of 8 are: 8, 16, 24, 32, 40, 48, 56… Method B 6 x 8 = 48 I am thinking of 48.

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Systematic Listing (P4)

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I am thinking of a 2-digit number. It is a common multiple

• f 6 and 8. It is between 30 to 50. The digit in the ones

place is twice of the digit in the tens place. What is the number that I am thinking of? Ans: 48 Refeed the answer back to the question:  Is 48 a 2-digit number?  Is 48 a common multiple of 6 and 8?  Is 48 between 30 to 50?  Is the digit 8 in the ones place twice of the digit 4 in the tens place?

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Systematic Listing (P4)

Use the numbers below to form 4-digit numbers that can be divided by 2 exactly (without remainder). The 4 digits are : 3, 2, 0 and 5 If none of the digits are repeated, how many different 4-digit numbers can be formed? (P4 TM p38)

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Systematic Listing (P4) I am thinking of a 2-digit number. It has 4 as a factor and is divisible by 10. It is smaller than 30. What can the number be?

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Now it is your turn. :)

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Attitude

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Systematic Listing (P4) I am thinking of a 2-digit number. It has 4 as a factor and is divisible by 10. It is smaller than 30. What can the number be?

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Now it is your turn. :)

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Systematic Listing (P4)

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I am thinking of a 2-digit number. It has 4 as factor and is divisible by 10. It is smaller than 30. What can the number be?

What do I know?  2-digit number  It has 4 as a factor means it is divisible by 4.  It is also divisible by 10  smaller than 30 Asked to find?  Find the number

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Systematic Listing (P4)

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Have I solved similar questions before? What skill should I use?  Guess & Check?  Make a supposition?  Systematic Listing?  Looking for patterns?

I am thinking of a 2-digit number. It has 4 as factor and is divisible by 10. It is smaller than 30. What can the number be?

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Systematic Listing (P4)

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• 1. Firstly, list the multiples of the

bigger number, 10. Think: why didn’t we try multiples

• f 4 first?
• 2. Test if the possible answers can

be divided by 4.

I am thinking of a 2-digit number. It has 4 as factor and is divisible by 10. It is smaller than 30. What can the number be?

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Systematic Listing (P4)

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Multiples of 10: 10, 20 20 ÷ 4 = 5 20 ÷ 10 = 5 The number is 20.

I am thinking of a 2-digit number. It has 4 as factor and is divisible by 10. It is smaller than 30. What can the number be?

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Systematic Listing (P4)

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Ans: 20 Refeed the answer back to the question: Is 20 a 2-digit number? Is 20 smaller than 30 ? Is 20 divisible by 4 and 10?

I am thinking of a 2-digit number. It has 4 as factor and is divisible by 10. It is smaller than 30. What can the number be?

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Systematic Listing (P4)

What do I know?  gives 3 sweets  excess of 8  gives 5 sweets  no shortage  number of friends is unknown Asked to find?  Find the number of sweets

Rachel wants to give some sweets to her friends. If she gives each friend 3 sweets, she will have 8 sweets left. If she gives each friend 5 sweets, she will have none

• left. How many sweets does she have?

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Systematic Listing (P4)

Have I solved similar questions before? What skill should I use?  Guess & Check?  Make a supposition?  Systematic Listing?  Looking for patterns?

Rachel wants to give some sweets to her friends. If she gives each friend 3 sweets, she will have 8 sweets left. If she gives each friend 5 sweets, she will have none

• left. How many sweets does she have?

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Systematic Listing (P4)

Multiples

• f 3:

3 6 9 12 15 Extra 8 sweets (+8): 11 14 17 20 23 Multiples

• f 5:

5 10 15 20 25

Rachel has 20 sweets.

Rachel wants to give some sweets to her friends. If she gives each friend 3 sweets, she will have 8 sweets left. If she gives each friend 5 sweets, she will have none

• left. How many sweets does she have?

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Systematic Listing (P4)

Ans: 20 Refeed the answer back to the question: 20 ÷ 5 = 4 4 x 3 = 12 20 – 12 = 8 Ans: 8 sweets left Rachel wants to give some sweets to her friends. If she gives each friend 3 sweets, she will have 8 sweets left. If she gives each friend 5 sweets, she will have none

• left. How many sweets does she have?

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Systematic Listing (P4)

Mr Teng buys some sweets for his pupils. If he gives each pupil 3 sweets, he will have just enough sweets. If he gives each pupil 4 sweets, he will be short of 8 sweets. (a) How many sweets are there? (b) How many pupils are there?

Now it is your turn. :)

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Interest

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Systematic Listing (P4)

Mr Teng buys some sweets for his pupils. If he gives each pupil 3 sweets, he will have just enough sweets. If he gives each pupil 4 sweets, he will be short of 8 sweets. (a) How many sweets are there? (b) How many pupils are there?

Now it is your turn. :)

Springdale Primary School

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Systematic Listing (P4)

What do I know?  gives 3 sweets  no shortage  gives 4 sweets  shortage of 8 Asked to find?  Find the number of sweets and pupils Mr Teng buys some sweets for his pupils. If he gives each pupil 3 sweets, he will have just enough sweets. If he gives each pupil 4 sweets, he will be short of 8 sweets. (a) How many sweets are there? (b) How many pupils are there?

Now it is your turn. :)

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Systematic Listing (P4)

Multiples

• f 3:

3 6 9 12 15 18 21 24 Multiples

• f 4:

4 8 12 16 20 24 28 32 shortage

• f 8

sweets (-8): X 4 8 12 16 20 24

(a) There are 24 sweets. (b) 24 ÷ 3 = 8 Mr Teng buys some sweets for his pupils. If he gives each pupil 3 sweets, he will have just enough sweets. If he gives each pupil 4 sweets, he will be short of 8 sweets. (a) How many sweets are there? (b) How many pupils are there?

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Systematic Listing (P4)

Ans: 24 sweets 8 pupils Refeed the answer back to the question: 24 ÷ 3 = 8 8 x 4 = 32 32 – 24 = 8

Mr Teng buys some sweets for his pupils. If he gives each pupil 3 sweets, he will have just enough sweets. If he gives each pupil 4 sweets, he will be short of 8 sweets. (a) How many sweets are there? (b) How many pupils are there?

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The Way Forward

What makes problem-solving difficult?

• Knowledge Factors

– Conceptual knowledge – Linguistic knowledge – Algorithmic knowledge – Schematic knowledge

http://repository.nie.edu.sg/jspui/bitstream/10497/132/1/ME-2-1- 93.pdf

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The Way Forward

What makes problem-solving easier?

• Affective Factors

– Interest – Motivation – Confidence – Perseverance

http://repository.nie.edu.sg/jspui/bitstream/10497/132/1/ME-2-1- 93.pdf

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Final Words

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Please help us with some feedback

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https://tinyurl.com/sdps2019feedback

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Thank You

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