P3 & P4 Parents ’ Seminar Mathematics Sharing 19 Jan 2019 Heuristics Springdale Primary School 1
The Future of Work Springdale Primary School https://teddintersmith.com/innovation-playlist/the-future-of-work/ 2
What is the MOST important factor to be successful? • Go to https://www.menti.com • Enter the code 44018 Springdale Primary School 3
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 Springdale Primary School 4
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Curriculum Framework Springdale Primary School 6
Thinking Skills • 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 Springdale Primary School 7
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: Springdale Primary School 8
Overview of SDPS Heuristic Plan Primary 3 Primary 4 • Act it Out • Systematic Listing • Guess and Check • Make a Supposition • Look for Patterns • Working Backwards Springdale Primary School 9
Look for a Pattern (P3) • 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 Springdale Primary School 10
Look for Patterns (P3) How many dots are there in Pattern 10? 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 Springdale Primary School 11
Look for a Pattern (P3) What are the missing numbers in the 5 th row? (P3 TM p42) Springdale Primary School 12
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? Alternative answer Day No of Times Pattern 1 3 1 × 3 + 0 3 2 7 2 × 3 + 1 3 + 4 3 11 3 × 3 + 2 3 + 4 + 4 … … … … 8 31 8 × 3 + 7 = 31 3 + 4 + 4 + 4 + 4 + 4 + 4 + 4 Springdale Primary School 13
Guess and Check (P3) • 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 Springdale Primary School 14
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? Springdale Primary School 15
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? 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 16
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? Have I solved similar questions before? What skill should I use? Guess & Check? Model drawing? Systematic Listing? Looking for patterns? Springdale Primary School 17
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? Chickens Cows No. Legs No. Legs Total Legs 5 10 5 20 30 3 6 7 28 34 … … … … … 2 4 8 32 36 Springdale Primary School 18
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? Refeed the answer back to the question: 2 chickens and 8 cows 2 x 2 = 4 8 x 4 = 32 32 + 4 = 36 Springdale Primary School 19
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? 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. Extra 4 legs 4 ÷ 2 = 2 10 – 2 = 8 Ans: 8 cows, 2 chicken Springdale Primary School 20
Make a Supposition (P4) 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 Springdale Primary School 21
self-confidence Springdale Primary School 22
Make a Supposition (P4) 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? $7 $13 Springdale Primary School 23
Make a Supposition (P4) 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 Springdale Primary School 24
Make a Supposition (P4) 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? Springdale Primary School 25
Make a Supposition (P4) 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 . Springdale Primary School 26
Make a Supposition (P4) 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 Springdale Primary School 27
Systematic Listing (P4) • It is to list all the possible outcomes for two or more combined events enables you to calculate the probability of any particular event occurring. Springdale Primary School 28
Systematic Listing (P4) I am thinking of a 2-digit number. It is a common multiple of 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 ones place 2 units tens place 1 unit Asked to find? Find the number Springdale Primary School 29
Systematic Listing (P4) I am thinking of a 2-digit number. It is a common multiple of 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? Springdale Primary School 30
Systematic Listing (P4) I am thinking of a 2-digit number. It is a common multiple of 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. Springdale Primary School 31
Systematic Listing (P4) I am thinking of a 2-digit number. It is a common multiple of 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? Springdale Primary School 32
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) Springdale Primary School 33
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