Primary 6 MATH
-
Hi, I need help for the following problem sums for my daughter's SA1 preparation. Didn't know P6 maths for me is like mental block. Thanks people.
(1)
-
Originally posted by Vendredi:
Hi, I need help for the following problem sums for my daughter's SA1 preparation. Didn't know P6 maths for me is like mental block. Thanks people.
(1)
You will have to edit your 'Questions', I guess.For the benefit of doubt, we will just assume that your com re-booted on you or something along that line.
-
First timer in this forum, i think i pressed enter and it ended up with 2 threads. well, here's the questions. Thanks in advance.
(1) A shopkeeper had 63 red pens and 108 blue pens. He bought more pens and found that the ratio of the total number of red pens to that of blue pens was 2:3. How many red pens did he buy if he bought 15 more blue pens than red pens?
(2) Mr Goh always gives 20% of his salary to his mother. His salary for march was 15% more than that for february. as a result, the amount of money he gave to his mother increased by $90. How much did he earn in february?
(3) Cindy and Damien collected some money. if cindy spent $10 each day and damien spent $20 each day, then cindy would have $480 left when damien had spent all his money. if cindy spent $20 each day and damien spent $10 each day, then she would have $60 left when he had spent all his money. how much money did damien receive?
(4) If Mr Chong sells a laptop at a discount of 20% of the usual price, he will make a profit of $80. If he sells it at a discount of 40% of the usual price, he will make a loss of $340.
(a) what is the usual price of the laptop?
(b) what is the cost price of the laptop?(5) Tammy had 20% fewer marbles than Bella. In school, a teacher confiscated 81 marbles from Tammy. Then bella gave 15 of her bookmarks to tammy and the ratio of the number of tammy's bookmarks to bella's became 2:5. how many marbles did tammy have at first?
-
(1) let the number of red pens bought be x. Hence, the number of blue pens bought is equal to ( x +15 )
From there, we add x to 63 ( original amount of red pens ), and equate it to 2 units.
Then, we add ( x + 15 ) to 108, and equate it to 3 units.
From there, u will work out that 3 ( x + 63 ) = 2 ( x +15 +108 )
3x + 189 = 2x + 246
hence, x = 246 - 189 = 57.
That means he bought 57 red pens in all.
(2) 15% increase in salary = 15% increase in givings = $90 increase in givings
Original amount of givings = 100% = $90 X 100/15
= $600
$600 = 20% of Feb's pay, so total amount earned in Feb = $600 X 5
= $3000
(3) It will be better for this question to be solve using models, but since I cannot do it here, I will show you a method more advanced, and isn't really suited for P6 students.
Logically speaking, damien will take twice as much time to spend all his money when he spend $10 a day as compared to spending $20 a day.
Hence, let the no. of days needed for him to spend all his money when he is spending $20 a day be x. The no. of days needed for him to spend all his money while spending $10 a day will be ( 2x )
We work an equation using the amount of money that Cindy has,
10x + 480 = 20 ( 2x ) + 60
30x = 420
x = 14
Remember that amount cindy spent also depends on amount Damien spent.
Amount of money Damien collected = $20 times x
= $20 X 14
= $280
-
(4) 20% discount = $80 profit
40% dicount = $340 loss
Hence, 20% of usual price = $340 + $80 = $420
Usual price = $420 X 5 = $2100
Cost price of labtop = 80% of usual price - $80
= ( 4/5 X $2100 ) - $80
= $1600
(5) errr.......how did marbles become bookmarks...0_0
original ratio of tammy's marbles to bella's marbles = 4:5
current ratio = 2:5
This question is REALLY hard to solve without simultaneous equations, which is only taught in sec 1, since the total amount of marbles at either time wasn't given.
I will give you the simultaneous equations working till I can think of something better.
let the original ratio be 4x : 5x, and the current ratio be 2y : 5y
In all, Tammy lost 66 marbles after she gained 15 from Bella, and Bella lost 15 marbles.
4x - 66 = 2y and 5x -15 = 5y
Hence, y = 2x - 33 and y = x - 3
Sub this 2 equations together and you will get 2x - 33 = x - 3
x = 30 marbles
the amount of marbles tammy have at first = 4x = 4 ( 30 ) = 120 marbles.
-
Just got another idea for Q5, let the original ratio be 4x : 5x
5 ( 4x - 66 ) = 2 ( 5x -15 )
20x - 330 = 10x - 30
10x = 300
x = 30
4x = 120
Hence, Tammy has 120 marbles at first.
Forget what I said about it being really hard. Just understand that your child will need to be able to find the link between the old ratio and the new ratio.
-
Hi,hope this helps.
-
nope it doesn't
edit: ok... now it does. nice background
-
Originally posted by Forbiddensinner:
(1) let the number of red pens bought be x. Hence, the number of blue pens bought is equal to ( x +15 )
From there, we add x to 63 ( original amount of red pens ), and equate it to 2 units.
Then, we add ( x + 15 ) to 108, and equate it to 3 units.
From there, u will work out that 3 ( x + 63 ) = 2 ( x +15 +108 )
3x + 189 = 2x + 246
hence, x = 246 - 189 = 57.
That means he bought 57 red pens in all.
Primary school do not learn algebra so they would mostly be using the guess and check method to answer such questions i believe since such algebra is sec sch level work.
-
thanks, people. I will go home and learn all the working steps to teach my daughter. however, can i have model form so that she can understand better. haiz, it is so sad case that even with baiyun's working steps, i am still sort of mental block. I will go home and study p6 maths in order to help my daughter.
THANKS PEOPLE!!!!!=)
-
Originally posted by Vendredi:
thanks, people. I will go home and learn all the working steps to teach my daughter. however, can i have model form so that she can understand better. haiz, it is so sad case that even with baiyun's working steps, i am still sort of mental block. I will go home and study p6 maths in order to help my daughter.
THANKS PEOPLE!!!!!=)
get a tutor. it helps.
-
Originally posted by dkcx:
Primary school do not learn algebra so they would mostly be using the guess and check method to answer such questions i believe since such algebra is sec sch level work.
You are right in saying Mainstream Primary schools generally do not teach or teach very little algebra. But you are wrong in saying that students are taught to use the guess and check method.All the questions posted can be solved using model diagrams, but I cannot draw them here, hence I have to resort to using algebra.
If it is for an exam, PSLE included, students will not be faulted for using algebras and even higher level methods of solving, as long as they can show proper workings and steps.
The reason why Primary School students are strongly discouraged from using algebra is because they often use it with no idea about how it works. ( e.g. What does 'x' and 'y' stands for, why are certain numbers and signs equated to others )
-
Originally posted by Forbiddensinner:
You are right in saying Mainstream Primary schools generally do not teach or teach very little algebra. But you are wrong in saying that students are taught to use the guess and check method.It was a P6 boy who tell me they learn that method and can use it. Unless you are a P6 boy yourselfi think they know better what they can and what they cannot use.
Models are too troublesome to draw and personally i won't use models unless the question specifically say its required since being careless and you get the whole question wrong and some people may understand the question wrongly and draw wrong models which confuse them even more.
-
Originally posted by dkcx:
It was a P6 boy who tell me they learn that method and can use it. Unless you are a P6 boy yourselfi think they know better what they can and what they cannot use.
Models are too troublesome to draw and personally i won't use models unless the question specifically say its required since being careless and you get the whole question wrong and some people may understand the question wrongly and draw wrong models which confuse them even more.
I just went for a talk on methods of tackling PSLE Maths by speakers from MOE at Sembawang Primary last Saturday.The current most common method which is being taught to students to use to tackle such questions as mentioned by the TS is by drawing models.
Personally, I NEVER teach my students to try and guess the correct answer for problem sums, but well, maybe you have a very unique way of teaching which you will like to share with all of us here.
-
The method was a valid method used in primary schools during my time and we were even tested on that on questions like mixture of 20 coins consisting $0.20 and $0.50 coins and giving a total amount which u need to guess the number of each coins.
Obviously the questions are tougher nowadays n models do work but how many students have problems with models these days? Last time when i used to teach pri sch tuition, my students always have problems drawing the correct model due to difference in understanding and end up giving up on such questions.
-
Unless a primary school teacher or tutor teaches the PSLE students Secondary School Algebra in advance ie to teach the students to formulate equation (s), expansion, factorise, solve the equation and so on, it is not advisable to teach PSLE students to use Algebra to solve PSLE problem sums. (MOE specialists' views that secondary school Algebra can be used in PSLE are meant for those students in the gifted programme who are capable of mastering the secondary school Algebra in advance)
Primary School Teachers and experienced tutors are very well-versed in model drawing method to solve the PSLE problem sums. PSLE Students who are adequately trained at using model drawing method have no problem to use it to solve problem sums.
Usually, it is the problem of parents and those who are good at Maths who are not familiar with model drawing model that tries to use Secondary School Algebra to teach PSLE students to solve problem sums. However, these PSLE students have not learnt Secondary School Algebra and they are taught in schools by their teachers to use model drawing method to solve problem sums. So, these students will not be able to understand the solutions provided by their parents or those who are good at Maths who use secondary school Algebra to solve PSLE problem sums.
To really help these PSLE students, parents and those who are good at Maths SHOULD learn the model drawing method themselves and then use the model drawing model method to help their children or students to solve the PSLE problem sums.
For parents and those who are not familiar with model drawing model, there are many resources eg Model Diagrams by Maths456.com, Top Challenging Mathematics Problems in Examination by Maths456.com, i-Excel Heuristic and Model Appraoch Levels 1 to 6 by Fan Maths and others by Fabian Ng and Andrew Er and so on to help them to learn the model drawing method.
-
Hi, hope this helps
-
Hi moderator
I tried unsuccessfully to delete this post.Please help.I think I've clicked twice, thus resulting in duplication.
-
Originally posted by dkcx:
The method was a valid method used in primary schools during my time and we were even tested on that on questions like mixture of 20 coins consisting $0.20 and $0.50 coins and giving a total amount which u need to guess the number of each coins.
Obviously the questions are tougher nowadays n models do work but how many students have problems with models these days? Last time when i used to teach pri sch tuition, my students always have problems drawing the correct model due to difference in understanding and end up giving up on such questions.
Indeed during our primary school time, those tikum-tikum methods are still allowed, but nowadays, if my students tikum-tikum for me to see, I will definitely deduct marks off their work.
As I said, Model Drawing is a must in almost all problem sums nowadays, and proper workings must always be shown. Times have changed a lot, and I can assure you year after year I can also feel the pressure mounting on me as syllabus from Sec school level keep getting brought down to Pri School level.
-
Originally posted by Forbiddensinner:
Indeed during our primary school time, those tikum-tikum methods are still allowed, but nowadays, if my students tikum-tikum for me to see, I will definitely deduct marks off their work.
As I said, Model Drawing is a must in almost all problem sums nowadays, and proper workings must always be shown. Times have changed a lot, and I can assure you year after year I can also feel the pressure mounting on me as syllabus from Sec school level keep getting brought down to Pri School level.
Thats the way our education system is becoming. Example matrics used to be a JC topic during my time and now its taught in sec 3 E maths now and there are some topics i've never seen or learnt before appearing in the sec sch syallabus these days and teaching tuition is like teaching myself new things sometimes.
Model drawing requires a very good understanding on the question. I've often seen students who misunderstood the questions or have problems with drawing their models and often they get the whole question wrong due to a wrong model. Somehow the type of models i used to draw in the past are not sufficient to ans the questions these days.
-
Thanks alot for the help.
I have gone through all the working steps. Still, some are so difficult to understand. Now, I am wondering is my understanding that poor? haha.
I have got a Math tutor for my daughter. The tutor always said that I will bring back the questions and teach you on the next lesson. Nothing is done. That tutor always scold her and it is so wasting time for tuition. Worse, I engaged a school Math teacher in the past. Same thing happened! The teacher doesn't know how to teach when I questioned her. ?????
Thus, I went to the bookstore to look for Maths books like what you guys have mentioned. BUT, how come the school's sums are so much difficult? The answer models I can understand from the book.
My daughter has very strong foundation in maths. Just couldn't do some problem sums. I am so stress!!!!
-
Originally posted by Vendredi:
Thanks alot for the help.
I have gone through all the working steps. Still, some are so difficult to understand. Now, I am wondering is my understanding that poor? haha.
I have got a Math tutor for my daughter. The tutor always said that I will bring back the questions and teach you on the next lesson. Nothing is done. That tutor always scold her and it is so wasting time for tuition. Worse, I engaged a school Math teacher in the past. Same thing happened! The teacher doesn't know how to teach when I questioned her. ?????
Thus, I went to the bookstore to look for Maths books like what you guys have mentioned. BUT, how come the school's sums are so much difficult? The answer models I can understand from the book.
My daughter has very strong foundation in maths. Just couldn't do some problem sums. I am so stress!!!!
What your daughter really need is a very experienced primary school PSLE maths teacher or a full time PSLE maths tutor with at least 15 years of experience as the type of problem sums that appear in PSLE Maths questions are of many varieties.
There are the typical type of problem sums that appear in PSLE Maths exams. These types of questions can be found if you have access to the past 10 to 20 years questions of the top 25 school Prelim Papers. Very experienced PSLE Maths teachers and very experienced full time tutors have already compiled and classified these questions according to topics and why how these questions are set on these topics. (However, MOE setters always surprise them every year with one or two new types of questions).
Next, these experienced teachers and full-time tutors set questions of similar types with variations to stretch the students' abilities further and to train their students to identify these questions and how to approach and solve these questions when these questions appear in the school and PSLE maths exams.
Fully prepared PSLE students can easily identify these questions and solve them in minutes.
You should talk to those PSLE students who score A* in PSLE maths especially those with higher PSLE aggregate score and you will realize that their abilities to identify these questions and solve them in minutes are acquired through practices and practices.
The books sold in the bookshops on model drawing method will only help people to learn to use model drawing method to solve problem sums. But to be an expert in using model drawing method to solve problem sums needs a lot of practices.