Types of Heuristics
1) To give a representation e.g. draw a diagram/model, make a list, make a table, use equations
Draw a diagram
Q1 Some flower pots are placed along a street at equal distances.
The distance between the 1st and the 4th flower pot is 18 m.
The distance between the 1st and the last flower pot is 54 m.
How many flower pots are there altogether?
Draw a model
Q1 Mary's age is 1/3 of John's age. Sean's age is thrice that of John's. If Sean is 32 years older than Mary,
how old is John?
Make a list
Q1 Two dice are thrown.
How many combinations will result in the sum of their faces being even?
Q2 A teacher assigns Taylor, Amy and Vanessa each duty to clean the classroom every day. These duties
are cleaning the table, mopping the floor and emptying the waste paper basket. In how many different
ways can she assign the duties to the three students?
Make a table
Q1 Mr Chen has a square plot of land for planting apples and a smaller plot for planting carrots.
The total area of both plots of land is 58m2.
What is the perimeter of each plot of land?
Use equations
Q1 A steel cuboid measuring 35 cm by 7 cm by 7 cm is melted and cast into 5 identical cubes.
What is the length of the side of each cube?
2) To make a calculated guess e.g. guess and check, look for patterns, make suppositions/assumptions
Guess and Check/ Make suppositions/assumptions
Q1 Sammy has 30 pieces of 5-cent and 10-cent coins.
The total value of the coins is $2.40.
Find the number of 5-cent coins that Sammy has.
Look for patterns
Q1 Jane saved $1 in the 1st week and $4 in the 2nd week.
Each week, she saved $3 more than the week before.
a) How much money did she save in the 5th week?
b) In which week did she save $22?
3) To go through the process e.g. act it out, work backwards, before-after
Act it out
Q1 Arrange 9 coins to form a triangle such that there are 4 coins on each side.
Work backwards
Q1 There were some marbles in Box A and B.
25 marbles were transferred from Box A to Box B.
40 marbles were then transferred from Box B to Box A.
In the end, there were 150 marbles in Box A, which was twice the number of marbles in Box B.
Before/After
Q1 There were 352 members in a social club.
75% of them were female and the rest were male.
Later in the year, some female members resigned and the number of female members was 3/7 that of the
total number of members in the club.
How many female members resigned?
Q2 Christina is 4 years old and her mother is 36 years old.
In how many years' time will Christina's mother be thrice as old as her?
4) To change the problem e.g. restate the problem, simplify the problem, solve part of the problem
Restate the problem - to express the given information in another way such that the solution to the
problem is more direct. Letters are used as symbols to represent unknown values or items.
Q1 A dictionary and a magazine cost $30.
The same dictionary and 3 such magazines cost $48.
How much money did each magazine cost?
Simplify the problem
Q1 If 3 chefs can peel 3 potatoes in 3 minutes, how many potatoes can 30 chefs peel in half an hour?
Solve part of the problem
Q1 Mr Ali made a long distance call to India that cost $8.49. The call cost $4.35 for the first 3 minutes and
46 cents for each additional minute. How much time did he spend on the phone?
1) To give a representation e.g. draw a diagram/model, make a list, make a table, use equations
Draw a diagram
Q1 Some flower pots are placed along a street at equal distances.
The distance between the 1st and the 4th flower pot is 18 m.
The distance between the 1st and the last flower pot is 54 m.
How many flower pots are there altogether?
Draw a model
Q1 Mary's age is 1/3 of John's age. Sean's age is thrice that of John's. If Sean is 32 years older than Mary,
how old is John?
Make a list
Q1 Two dice are thrown.
How many combinations will result in the sum of their faces being even?
Q2 A teacher assigns Taylor, Amy and Vanessa each duty to clean the classroom every day. These duties
are cleaning the table, mopping the floor and emptying the waste paper basket. In how many different
ways can she assign the duties to the three students?
Make a table
Q1 Mr Chen has a square plot of land for planting apples and a smaller plot for planting carrots.
The total area of both plots of land is 58m2.
What is the perimeter of each plot of land?
Use equations
Q1 A steel cuboid measuring 35 cm by 7 cm by 7 cm is melted and cast into 5 identical cubes.
What is the length of the side of each cube?
2) To make a calculated guess e.g. guess and check, look for patterns, make suppositions/assumptions
Guess and Check/ Make suppositions/assumptions
Q1 Sammy has 30 pieces of 5-cent and 10-cent coins.
The total value of the coins is $2.40.
Find the number of 5-cent coins that Sammy has.
Look for patterns
Q1 Jane saved $1 in the 1st week and $4 in the 2nd week.
Each week, she saved $3 more than the week before.
a) How much money did she save in the 5th week?
b) In which week did she save $22?
3) To go through the process e.g. act it out, work backwards, before-after
Act it out
Q1 Arrange 9 coins to form a triangle such that there are 4 coins on each side.
Work backwards
Q1 There were some marbles in Box A and B.
25 marbles were transferred from Box A to Box B.
40 marbles were then transferred from Box B to Box A.
In the end, there were 150 marbles in Box A, which was twice the number of marbles in Box B.
Before/After
Q1 There were 352 members in a social club.
75% of them were female and the rest were male.
Later in the year, some female members resigned and the number of female members was 3/7 that of the
total number of members in the club.
How many female members resigned?
Q2 Christina is 4 years old and her mother is 36 years old.
In how many years' time will Christina's mother be thrice as old as her?
4) To change the problem e.g. restate the problem, simplify the problem, solve part of the problem
Restate the problem - to express the given information in another way such that the solution to the
problem is more direct. Letters are used as symbols to represent unknown values or items.
Q1 A dictionary and a magazine cost $30.
The same dictionary and 3 such magazines cost $48.
How much money did each magazine cost?
Simplify the problem
Q1 If 3 chefs can peel 3 potatoes in 3 minutes, how many potatoes can 30 chefs peel in half an hour?
Solve part of the problem
Q1 Mr Ali made a long distance call to India that cost $8.49. The call cost $4.35 for the first 3 minutes and
46 cents for each additional minute. How much time did he spend on the phone?
Terminology of strategies taught in tuition centres in problem solving are:
1) Change families
- Total unchanged
- Difference unchanged
- External Unchanged or Unchanged Quantity
- External Changed or 'Units & Parts' for Everything changed
2) Gap & Difference/Excess & Shortage
3) Advanced Model Drawing
4) Equal Fractions ("Make the numerator to be the same")
5) Repeated Identity
6) Number (Quantity) x Value
7) Branching
1) Change families
- Total unchanged
- Difference unchanged
- External Unchanged or Unchanged Quantity
- External Changed or 'Units & Parts' for Everything changed
2) Gap & Difference/Excess & Shortage
3) Advanced Model Drawing
4) Equal Fractions ("Make the numerator to be the same")
5) Repeated Identity
6) Number (Quantity) x Value
7) Branching
MATHS USEFUL VIDEOS
Fractions
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Let's listen on how Freddy teach 'Fractions'...LOL
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divide_fractions_by_whole_numbers_using_models.mp4 | |
File Size: | 5843 kb |
File Type: | mp4 |
learn_fractions_-_which_fraction_is_bigger.mp4 | |
File Size: | 9851 kb |
File Type: | mp4 |
For more videos guide on P3 to P6 maths topics, please click the link below (Note: Some working presentations may not be in line with what was taught in local schools or within the syllabus hence please keep an open mind when viewing the videos. Do exit the videos if you feel that the videos are not in line):
http://psle.tv/
http://psle.tv/
Learning videos will be updated periodicallly.
Model Drawing Approach
How to use Model drawing
http://www.koobits.com/2012/11/06/techniques-for-learning-the-singapore-math-model-method
How to use Model drawing
http://www.koobits.com/2012/11/06/techniques-for-learning-the-singapore-math-model-method
How to solve questions using model drawing
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Strategies
Step by step guide by mathsclinix
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- 3 approaches used to solve 'Branching' (i.e. "Of the remaining") question
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- 2 approaches on how to solve an advanced 'Quantity x Value' question
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- Common mistakes in Percentages (Part A)
Do you know that Percentage and the rest of the topics like Fraction, Decimal and Ratio are inter-related?! (see pic attached) They are actually one big family!! The unique thing about Percentage is ....it is a fraction OUT OF 100 (and not other numbers) and its symbol is '%'. That is why in P5, the students will be taught on how to convert % into fraction and decimal! :)
The CONFUSION or common mistake
Mistake 1
When comes to problem sums, most students will just add or subtract the % because they see the percentage symbol (%) just like how they see the symbol for the units of measurement, i.e. '$', 'cm', 'kg', etc. Hence, they will just add and subtract the percentages, which is WRONG;p This is because % is NOT a unit of measurement but a symbol to represent "out of 100".
Mistake 2
The whole for percentage is the same, i.e. 100% hence students thought they are the same hence proceed to add or subtract the percentages :<
THING YOU NEED TO KNOW ABOUT %
Once the 100% which we called the "percentage base" is referring to different wholes or different part of the whole and there is no clue given in the question that the different wholes have the same value, then it CANNOT be added or subtracted!
E.g. 1.
"In a dance club, 30% of the members are men, 25% of the members are women and the rest are children. If there are 45 more children than men, how many members are there in the club?"
30% 25%
30%-> Men 25%-> Women
100%-> Total members 100%-> Total members
The percentage base (100%) for both of the percentages are referring to the same whole, i.e. Total members hence they CAN be subtracted or added!:)
E.g. 2
"In a dance club, 30% of the members are men, 25% of the REMAINING members are women and the rest are children. If there are 32 more children than men, how many members are there in the club?"
30% 25%
30%-> Men 25%-> Women
100%-> Total members 100%-> Remaining members
The percentage base (100%) for both of the percentages are referring to the DIFFERENT part of whole hence they CANNOT be subtracted or added.
DO YOU KNOW ...
Percentage problem sums need not solved by using %? It can be solved by the way on how you solve when doing Fractions questions!:)
HOW IT WORKS?
Once the % is converted into Fraction, the question will just look like the usual fraction question! See example below.
E.g. 3
Jolin has some money. She used 60% (60/100 = 3/5) of her money to buy a handbag. She used 25% (25/100 = 1/4) of her remaining money to buy a blouse. She paid $25 more on the handbag than the blouse. How much money did she have at first?
KEY POINT to reiterate
When the denominators are referring to different wholes (or different part of the whole) and there is no clue given in the question that the different wholes have the same value, then the fractions (or Percentages) CANNOT be added or subtracted.
In this question,the denominators are referring to 2 different PART of the whole hence CANNOT be added or subtracted.
Denominator '5' (or 100%) refers to the total money
Denominator '4' (or 100%) refers to the REMAINING money
HOW TO SOLVE?
It can be solved by either:
1) Model ("Pull down" models) or
2) Branching (see sharing on 'Branching' above)
Hope the above sharing has deepen your understanding on 'Percentage' !!:)
The CONFUSION or common mistake
Mistake 1
When comes to problem sums, most students will just add or subtract the % because they see the percentage symbol (%) just like how they see the symbol for the units of measurement, i.e. '$', 'cm', 'kg', etc. Hence, they will just add and subtract the percentages, which is WRONG;p This is because % is NOT a unit of measurement but a symbol to represent "out of 100".
Mistake 2
The whole for percentage is the same, i.e. 100% hence students thought they are the same hence proceed to add or subtract the percentages :<
THING YOU NEED TO KNOW ABOUT %
Once the 100% which we called the "percentage base" is referring to different wholes or different part of the whole and there is no clue given in the question that the different wholes have the same value, then it CANNOT be added or subtracted!
E.g. 1.
"In a dance club, 30% of the members are men, 25% of the members are women and the rest are children. If there are 45 more children than men, how many members are there in the club?"
30% 25%
30%-> Men 25%-> Women
100%-> Total members 100%-> Total members
The percentage base (100%) for both of the percentages are referring to the same whole, i.e. Total members hence they CAN be subtracted or added!:)
E.g. 2
"In a dance club, 30% of the members are men, 25% of the REMAINING members are women and the rest are children. If there are 32 more children than men, how many members are there in the club?"
30% 25%
30%-> Men 25%-> Women
100%-> Total members 100%-> Remaining members
The percentage base (100%) for both of the percentages are referring to the DIFFERENT part of whole hence they CANNOT be subtracted or added.
DO YOU KNOW ...
Percentage problem sums need not solved by using %? It can be solved by the way on how you solve when doing Fractions questions!:)
HOW IT WORKS?
Once the % is converted into Fraction, the question will just look like the usual fraction question! See example below.
E.g. 3
Jolin has some money. She used 60% (60/100 = 3/5) of her money to buy a handbag. She used 25% (25/100 = 1/4) of her remaining money to buy a blouse. She paid $25 more on the handbag than the blouse. How much money did she have at first?
KEY POINT to reiterate
When the denominators are referring to different wholes (or different part of the whole) and there is no clue given in the question that the different wholes have the same value, then the fractions (or Percentages) CANNOT be added or subtracted.
In this question,the denominators are referring to 2 different PART of the whole hence CANNOT be added or subtracted.
Denominator '5' (or 100%) refers to the total money
Denominator '4' (or 100%) refers to the REMAINING money
HOW TO SOLVE?
It can be solved by either:
1) Model ("Pull down" models) or
2) Branching (see sharing on 'Branching' above)
Hope the above sharing has deepen your understanding on 'Percentage' !!:)
- Common mistakes in Percentages (Part B)
Do you make the same mistake as shown in Solution A in the picutre attached? If yes, please take EXTRA note now!!:)
Sharings by other tutors
I would like to thank Ms Vanessa Wong, a Maths tutor who is a regular member in the PSLE parents facebook groups, for granting the permission to share her math videos in my website! :) Her clear explanations on the solutions and graphics used will enhance your understanding on the concept that was applied in the questions.
For more maths videos produced by Ms Wong, you may visit the link below :)
https://www.youtube.com/channel/UCjKi2dchvdBVV9bOMx7n6EQ
For more maths videos produced by Ms Wong, you may visit the link below :)
https://www.youtube.com/channel/UCjKi2dchvdBVV9bOMx7n6EQ
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Average with unknown quantity (video on the left)
A visual illustration using the concept of 'Area' to show the equal distribution to find the unknown quantity. |
Online resources recommended by MOE - CHECK IT OUT below!
http://parents-in-education.moe.gov.sg/primary-education/learning-resources-pri/mathematics-learning-resources/online-resources-for-parents
http://parents-in-education.moe.gov.sg/primary-education/learning-resources-pri/mathematics-learning-resources/online-resources-for-parents
Interactive maths games
To recap or strengthen the understanding of certain basic concepts of a topic, why not practice it through some maths games! :)
Types of Test-taking errors
Are you good in your visualization skill?
Do the origami activity below to test out your skill ! Ask your family members to join you and treat it as a family bonding activity ! :)
Tips: No origami papers? No problem, you can use papers from magazines! ;p
Tips: No origami papers? No problem, you can use papers from magazines! ;p
Try out the pictorial instructions first. If you are stuck at any points, then you can refer to the video instructions :)
For more challenges, you can do a search in the internet for any items that you want to make :)
Enjoy and have fun!
For more challenges, you can do a search in the internet for any items that you want to make :)
Enjoy and have fun!
interested to play some traditional games (non-IT)!
Check out this link on those tradition childhool games which bring back fond memories!!:)
Childhood games -> http://happysharing818.ipub.one/n/12279happysharing818.ipub.one/n/12279
This is where real bondings & communication are built up!! This is also where children can pick up their EQ skills & motor skill!s:)
Childhood games -> http://happysharing818.ipub.one/n/12279happysharing818.ipub.one/n/12279
This is where real bondings & communication are built up!! This is also where children can pick up their EQ skills & motor skill!s:)
How to make one of these traditional games!
P.S.: Want to try out some of the titbits and sweets sold in the 1970s ...visit this website (http://www.biscuitking.com.sg/index.php) to purchase! :)
learning points - soft skills
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Dear pupils,
What have you learnt from the video? Do a reflection after watching the videos and keep that reflection note/letter with you at ALL TIMES to remind yourself in your growing up years what you have learnt today! The things learnt, not only will it apply to your schooling days, it will also apply when you are working at the society :) |
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With teamwork, you can achieve more and with unexpected results!!
T.E.A.M. represents Together Everyone Achieves More Do you know? Ants and Bees are the 2 insects which demonstrate excellent teamwork! |
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Dear pupils,
For anything you do, eventhough the chances are slim but as long as you did not give up and believe in yourself, you still can eventually reach your goal ! :) |
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Learning point:
Never be mean to others and you never know when you need help from others. Be forgiving and the world will be a better place to live in :) |
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One of my favorites!!
Everyone needs a motivation in order to excel. A jar of cookies is the pig's motivation, what's yours? GO and find your motivation NOW! :) |
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Learning point:
Don't judge oneself by its cover or action.. Make your conclusion after seeing the full story :) |
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Dear pupils,
1st learning points: When parents are not around, take care of yourself by first believing in yourself:) 2nd learning point: Don't take your parents for granted. They are the only ones who care protect you when you are in need. Be good and filial to your parents. |
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Learning point:
ACTION speaks LOUDER than words. Don't complain, don't doubt yourself....if you have an idea.......just go and do it! No one can guarantee success. Learn from the mistakes you made. But if you never try....you will never know. What is life? Life is all about success, failure and learning. As someone did say it before "I have tried my best and I have no regrets!" |
Motivational and inspiration real-life stories
Do you hate Maths to the extend that you want to give up and drop the subject? Well, hope that the following video stories will inspire & motivate you to hold on to your faith and beliefs:) If they did not give up, you shouldn't be too as you are much much more fortunate than them! Be grateful and treasure what you have...no matter how small the achievement is....celebrate it!! as it is AN ACHIEVEMENT made by YOU!!! :)
Believe in yourself and do the best you can!! As long as you did not give up, you will see success!!:)
Nick Vujicic (Man with no arms and legs) - Learn his optimistism
https://youtu.be/wBCfxhyEDB0
Colonel Harland Sanders (K.F.C founder) - Learn his fighting spirit!!
https://youtu.be/DoI7RqmjmY0
Be a SPARTAN!!(Be a fighter!! Learn the athlete's determination & drive in this video!!
https://youtu.be/OjQq8buotp0
Rowan Atkinson (Mr Bean) - Be true to Yourself!! Believe that you are the unique one!!
https://youtu.be/crhvEZypCOo
Jessicia Cox (woman with no arms) - World's FIrst Armless Pilot.
I like her favorite words "Think outside the shoes!"
https://youtu.be/aQGI45I5TSQ
Other great men's stories!
Walt Disney was fired by a newspaper editor for lack of ideas. Walt Disney also went banrupt before he build Disneyland.
Thomon Edison's (the inventor of electric light bulb) teachers said he was too stuipid to learn anything.
Albert Einstein (one of the greatest mathematicians and physicists) did not speak until he was four years old and didn't read until he was seven. His teacher describes him as "mentally slow, unsociable and adrift forever in his foolish dreams" He was expelled and was refused admittance to the Zurich Polytechnic School. I like his quote on INSANTIY: Doing the same thing over and over again and expecting different results. For maths, you can't be using the same method and still expect to be able to solve ALL questions!:)
William Churchill failed sixth grade. He did not become Prime MInister of England until he was 66, and then only after a lifetime of defeats and setbacks. His greatest contributions came when he was a "senior citizen." So, never give up until your last breathe.
Beethoven handled the violin awkwardly and preferred playing his own compositions instead of improving his technique. His teacher called him hopeless as a composer!
Our greatest Prime Minister, Mr Lee Kuan Yew
He was diagnosed with mildly dyslexic but that did not stop him from learning. Mr. Lee was fluent in many languages – English, Malay, Chinese and Japanese.
As an adult, he learnt Japanese during the Japanese Occupation, and worked as a Japanese translator.
At the age of 32, Mr. Lee relearnt Chinese – a language he had to master once more due to the lack of use. He published a book thereafter, Keeping My Mandarin Alive: Lee Kuan Yew Language Learning Experience, about his journey in re-mastering Chinese, to encourage younger Singaporeans to learn and speak their mother tongue.
He was a great role model for us to follow! His quote on lifelong learning: "I have never ceased to be a student. I have never ceased to learn."