This blog serves as another avenue for me to share my knowledge of Math for free with our future generation. I hope this will be of any help to the parents who are dedicated and committed to the education of their children and also to those self-motivated Primary school students. Keep it up my friends!
Basically I have categorised primary school maths into these few topics, Whole number, F-R-P (Fraction, Ratio, Percentage), Rate & Speed, Measurements and Geometry.
For now I will just focus on Whole number concepts and F-R-P. There is a reason why I grouped fraction, ratio and percentage under one, I will elaborate more on this next time.
Whole number is a huge topic, it consists of transfer/sharing questions – (concept of differences), Guess and check, excess & shortage (Common multiples), accounting for events – (every action has a consequence), more than/less than let’s make them equal, etc.
So for today, I will probably talk on transfers since it is relatively “hot topic” in exams.
The reason why I call it sharing because exams question are usually between two person or two items. Basically A/B pass to B/A resulted in something, then A/B pass to B/A something happened again. So again every action has a consequence, the question is truly what actually happened?
First of all there are two things you need to take note in primary math – Total (altogether) and Difference (more than/ less than).
There are also two things you need to take note for transfers/sharing,
1)
Total remains the same
If u observe carefully, the exchanges are only between the two person, there is no third party involved. So if you consider the two person as an entity, there is a no flow into or out of the entity. There is only flow within the entity itself. Therefore there is no change to the total itself.
2)
Difference Changes
Let say that A has more than B at first. If A pass some to B, A might not have more than B in the end, it depends on how much A pass to B.
Questions that requires the use of the idea that total is unchanged is not so common in exams. However the total remains the same concept is required in ratio questions – equating the total.
Example :
Tiffany and Sally had a total of 1386 candies. When Tiffany gave Sally 224 candies, Sally had 5 times as many candies as Tiffany. How many candies did Sally have at first?
Jayden has some $2, $5 and $10 notes. The number of $2 notes is 1/4 of the total number of notes. The ratio of the $5 notes to the total number of $2 and $10 notes is 2 :5. Given that there are 18 more $10 notes than $2 notes, how much money does Jayden have in all?
The ratio of the number of beads John had to the number of beads Sally had was 3 : 7 at first. After Sally had given some beads to John, Sally had 76 beads less than John. The ratio of John's number of beads to Sally's number of beads became 3 : 2. How many beads did Sally give to John?
Most of the transfer questions, either you just have to work out the “New Difference” and u can use it to solve the question or the question just revolves around the changes in the difference.
So let’s talk about how the difference changes. There are different scenarios which lead to different results, different "differences".
So let’s talk about how the difference changes. There are different scenarios which lead to different results, different "differences".
For example, if A has more than B, I say A has something “extra” compared to B. You can illustrate this clearly to your kid with aid of a comparison model. In my opinion, simple model drawings are best to illustrate all the different scenarios clearly for the kids. But let me remind you model drawing are never about the end product, it is always about the process. If you show your kids the end product of your model, especially those in the answer keys, few will understand. However if you draw it out step by step for your kid while explaining to them, you will be amazed at how fast they can grasp the concepts. Model drawing is able to portray a child’s chain of thoughts while they are attempting to solve the problem. Therefore you can also tell whether your kid truly understands the problem or not, what went wrong along the way, through model drawings.
These are some of the concepts that your kids should have with them.
Case 1
If A has more than B, A gives half of the extra to B, they become equal.
Case 2
If A has more than B, A gives less than half of extra to B, A will still have more than B.
Case 3
If A has more than B, A gives more than half of the extra to B, A will have less than B.
Case 4
If A has more than B, B gives to A, A will even more than B in the end.
Note: Case 1 and Case 4 are more common in exams.
It very hard to explain everything in words there are actually a lot more that meets the eye when it comes to transfers but I will just keep it to 4 cases first.
So let’s talk about Case 1 first.
For example, If A has 40 more than B how much must A give to B so that they have equal amount? Ans: 20
Now look at in another manner, which is more commonly used in exam questions, if A gives to B 50, they become equal. They are just trying to tell you that A has, 50 x 2, 100 more than B. (The difference between A and B is 100)
You should instil this in your kid, whenever they see this kind of sentence structure “if A gives B x amount then they become equal”, they should just register in their heads that A has more than B, 2x more. This concept will come in handy from time to time as you often find these sentences in many different questions even if it is not typical transfer questions.
Examples of a typical transfer question:
Jack and Ben have some money. If Jack gives Ben $25, they will have the same amount of money. If Ben gives Jack $68, Jack will have 4 times as much money as Ben. How much money does each boy have?
(Combination of Case 1 & Case 4)
If Ben gives 84 erasers to Abel, both of them will have an equal number of erasers. After Abel gave 54 erasers to Ben, Abel has 5/11 as many erasers as Ben. How many erasers does Abel have at first?
(Combination of Case 1 & Case 4)
Examples of other questions which involve transfer concepts:
Jay and Ken have a total of 548 buttons. If Jay gives Ken 166 buttons, they will have the same number of buttons. How many buttons does Jay have at first? (Case 1 + more than less than, lets make them equal first)
2/3 of Peter’s money is equal to 4/5 of Ted’s money. If Peter gives $240 to Ted, they will each have the same amount of money.
(Case 1 + Fraction comparison)
(a) How much money does Peter have?
(b) How much money do both Peter and Ted have?
2/5 of Zach’s pencils is equal to 3/4 of Amin’s pencils. If they have a total of 1104 pencils, how many pencils must Zach give to Amin so that both of them will have and equal numbers of pencils? (Case 1 + Fraction Comparison)
These questions are set in such a manner that it aims to test whether your kids are able to determine the “New Difference” or “Original Difference”, and equate that to the difference in terms of units, find the value of 1 unit and use it to answer the question.
There are a lot of other concepts that we need to excel in primary maths.
So keep coming back to this blog to learn about these concepts remember its free for all!
I will post step by step solutions to the questions in the this post in the next one.
Also, I would truly appreciate any suggestions on how I can improve and assist you in helping your child in their math. For all the Singapore kids out there if you ever encounter any problem in your math, feel free to drop me a mail -
helpingsgkidswithmath@gmail.com
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