PSLE Maths question. How to solve?

[1fast1]

hai....all the fancy pedagogy when our kids haven't even master the fundamentals...

 

 

I am old house....means I believe in memory work to build up the fundamentals b4 going to HOTS such as applications...

 

it is like building a house...if the fundamentals are no good, no matter how creative or how well u package the exterior, a real storm will show u its worth....

 

I agree to an extent. I think all this "new-age" pedagogy is detrimental. It's jumping on the bandwagon for its own sake.

 

But I don't believe in too much "memory work" either. Especially in math. I remember all my formulae because I learned their derivation, practised the derivation myself, and for some, even found new ways of my own to derive them. If every student had the commitment to do that, surely, memory work can be almost eliminated in subjects like Math and Physics.

 

Memory work should be reserved for subjects that actually need it - for e.g. History, and even Biology (woefully memory-reliant amongst the Sciences).

 

For math, I want them to go back to rigorous teaching of symbolic logic and manipulation - maybe even start algebra off much earlier.

Edited July 1, 2010 by Turboflat4

[Leslielai]

Being a mother of primary school going children, i am struggling with extremely difficult maths homework they are bringing back everyday.

I scored straight A for maths from primary to uni but i am not able to explain or teach them. They kept saying that my method is very confusing and their teachers wont accept the way i solve.

 

For the question you have posted, I saw this OCTO channel video. Norman Tien explained using model drawing and I heard he is quite well known in teaching maths to PSLE students.

 

video link:

OR you can view from their company's website www.pslemath.com

 

 

Hope this helps :)

 

Vicky

 

This post smells like an advert.

 

Any decent tutor will be able to explain the way that was demonstrated in the video [rolleyes]

[Sabretan]

agree, yet disagree....

 

derivation is the application of first principle...thus to derive a secondary law or formula, you need to have knowledge of first principles first...and that is through memory work...of course if we were to live in Newton's era, it is thro assumption and experimental science that they will have to start with....

 

 

and derivation at Primary school level?? I think that is asking too much of the kids...my preference is for them to build up their fundamentals from P1 to P4....through manipulatives, hands-off, experiential learning and so on and so forth is fine w me...but at the end, they have to memorize what they had learnt....

 

 

when u practise your derivation many times, you are actually unwittingly committing it to memory....that is why practice makes perfect...coz u r prog it to your long term memory n hence u are able to retain and recall it for a longer time and even discover new ways of derivation...

 

On the other hand, I strongly agree w u that upper sec and JC should focus on derivation from 1st principle and application of these techniques to solving real life problem....this is what we are strongly lacking now...everything is so watershed and superficial...

[Joseph22]

I meant that proving that an isoceles right triangle has maximal area for a given hypotenuse requires calculus.

 

Finding the area (like in your question) is a trivial application of Pythagoras' theorem.

 

 

that is what i mean. when we know more thing. Simple things like the sum i refering to. WE will be cracking our head to think of what is the best method of finding the answer.

And normally the most simple method is overlook.

Edited July 1, 2010 by Joseph22

[1fast1]

that is what i mean. when we know more thing. Simple things like the sum i refering to. WE will be cracking our head to think of what is the best method of finding the answer.

And normally the most simple method is overlook.

 

Forget the calculus. That's to answer a different question, something that I just mentioned for interest. It's not required in your question.

 

Yours is simple, and Pythagoras' theorem is the simplest way. If the hypotenuse is x, then each of the equal sides (s) which form the base and height is given by s^2 + s^2 = x^2, so s is equal to x/sqrt(2). Then the area (half times base times height) is (1/2)*s*s, giving (x^2)/4. There's no reason that Poly students should've been scratching their heads because Pythagoras' theorem is taught in Primary school and shouldn't be forgotten since then, because there are ample applications in Math at all subsequent levels and in subjects like Physics and Engineering.

[1fast1]

agree, yet disagree....

 

derivation is the application of first principle...thus to derive a secondary law or formula, you need to have knowledge of first principles first...and that is through memory work...of course if we were to live in Newton's era, it is thro assumption and experimental science that they will have to start with....

 

 

and derivation at Primary school level?? I think that is asking too much of the kids...my preference is for them to build up their fundamentals from P1 to P4....through manipulatives, hands-off, experiential learning and so on and so forth is fine w me...but at the end, they have to memorize what they had learnt....

 

 

when u practise your derivation many times, you are actually unwittingly committing it to memory....that is why practice makes perfect...coz u r prog it to your long term memory n hence u are able to retain and recall it for a longer time and even discover new ways of derivation...

 

On the other hand, I strongly agree w u that upper sec and JC should focus on derivation from 1st principle and application of these techniques to solving real life problem....this is what we are strongly lacking now...everything is so watershed and superficial...

 

It's one or the other - either there's too much memory work involved at Primary level math, or there isn't. If there's too much memory work, it has to pertain to formulae, in which case my point about teaching derivation stands. Students should not be expected to use formulae they haven't been taught (or don't understand fully) how to derive from first principles or simpler results they've already mastered - for e.g. if they are to be taught Pythagoras' theorem, they should be shown one of the simplest derivations (there are several, some elementary, some extremely obscure). If there isn't too much memory work, then there's no problem.

 

Frankly, I don't remember having to remember anything at all in Math at Primary school level. It's really extremely elementary stuff. So there shouldn't really be any memory work involved. In fact, expecting students to solve these "word problems" in a particular stylised, rigid way (that's often non-intuitive, even to us) can actually *cause* more problems and need for memory work since they need to force themselves to learn unnatural methods instead of going with the far more natural algebra.

Edited July 1, 2010 by Turboflat4

[Sabretan]

Agree that formulae should only be memorized when they know what each variables stand for and what is/are the underlying assumptions before the formula can be applied.

 

 

Maybe your primary sch years are too far back in history for you....but if u had been in pri sch in the 80s n early 90s, it shld be mostly rote learning...

 

 

Agree that algebra is the more natural for gen x and y...coz we are taught that way...but for the newer gen, they are very used to model method and had problem adopting to algebra when they are in sec sch....then they ditch model method and adopted the algebra method....why? I have no answer...u got to ask MOE

[1fast1]

Agree that formulae should only be memorized when they know what each variables stand for and what is/are the underlying assumptions before the formula can be applied.

 

 

Maybe your primary sch years are too far back in history for you....but if u had been in pri sch in the 80s n early 90s, it shld be mostly rote learning...

 

 

Agree that algebra is the more natural for gen x and y...coz we are taught that way...but for the newer gen, they are very used to model method and had problem adopting to algebra when they are in sec sch....then they ditch model method and adopted the algebra method....why? I have no answer...u got to ask MOE

 

My Pri school years were 81-86. Don't remember learning much by rote in Math (lots in Science and other subjects). Unless you're counting multiplication table, etc.

 

Consider Euclidean geometry (not that we learned that name in Pri school, hor). Even stuff like angle sum of triangle = 180 degrees (which is often taught as rote) can be built up slowly with concepts that can be immediately "seen" - e.g. angle sum of line = 180 degrees (two right angles) - no need to prove because self-evident (result 1). Then seeing that corresponding angles made by a line intersecting two parallel lines are equal - again no need to prove, because the symmetry is obvious (result 2). Similarly, seeing that opposite angles formed by intersecting lines are equal should be a trivial thing (result 3). Combine results 2 and 3 to see that in a "Z-shape" formed by two parallel lines intersected by another line, the interior angles of the Z are equal (result 4). Then use that and some simple construction on any triangle to prove the angle sum result.

 

I think it's more informative and rewarding to lead even Pri. school children through this sort of process rather than just shoving facts down their throats. At least for Math.

 

I am in complete agreement with you about the uselessness of teaching these dumb "model" methods, then discarding everything at higher levels. Just teach the kids algebra at the right time!! Sheesh...

Edited July 1, 2010 by Turboflat4

[Sabretan]

haha....same era...to be exact...exactly the same....

 

maybe my now defunct pri sch did it differently from yours....my is memorized....then memorized...so went for the gifted selection at P3....but too much zombie memorization...couldn't think properly....but I must admit they gave me a very good fundemantals...as after the P3 selection test.....I started asking why.....why like this...why like tat....until all teachers TBT me....

[Wind30]

I meant that proving that an isoceles right triangle has maximal area for a given hypotenuse requires calculus.

 

Finding the area (like in your question) is a trivial application of Pythagoras' theorem.

 

??????

 

alamak what Pythagoras theorem.....

 

trust me you don't need Pythagoras theorem to solve that.

 

Just Flip the triangle so that the hypothenuse is the base. Then divide the triangle into two by a vertical line in the middle which is the HEIGHT.

 

And a primary school kid should be able to deduce the height is half the base by deducing the two new triangles are isoceles triangles. Then the answer is just base times height / 2.

 

much simpler maths involved. no sqrt. I am not sure but I don't think primary kids have learnt the concept of square root or pythagoras theorem.

 

I think I should open a primary maths tuition center. :)

Edited July 1, 2010 by Wind30

[1fast1]

??????

 

alamak what Pythagoras theorem.....

 

trust me you don't need Pythagoras theorem to solve that.

 

Just Flip the triangle so that the hypothenuse is the base. Then divide the triangle into two by a vertical line in the middle which is the HEIGHT.

 

And a primary school kid should be able to deduce the height is half the base by deducing the two new triangles are isoceles triangles. Then the answer is just base times height / 2.

 

much simpler maths involved. no sqrt. I am not sure but I don't think primary kids have learnt the concept of square root or pythagoras theorem.

 

I think I should open a primary maths tuition center. :)

 

Haha, true.

 

I'll concede - that is the simplest method.

[Mivec9]

Wind30 is correct. You have to apply primary school methods to solve their problem sums, like box methods..not using algebra.

[Joseph22]

Forget the calculus. That's to answer a different question, something that I just mentioned for interest. It's not required in your question.

 

Yours is simple, and Pythagoras' theorem is the simplest way. If the hypotenuse is x, then each of the equal sides (s) which form the base and height is given by s^2 + s^2 = x^2, so s is equal to x/sqrt(2). Then the area (half times base times height) is (1/2)*s*s, giving (x^2)/4. There's no reason that Poly students should've been scratching their heads because Pythagoras' theorem is taught in Primary school and shouldn't be forgotten since then, because there are ample applications in Math at all subsequent levels and in subjects like Physics and Engineering.

 

 

Yes but this show that we human are complicated at times to think of the most simple solution.

[Joseph22]

??????

 

alamak what Pythagoras theorem.....

 

trust me you don't need Pythagoras theorem to solve that.

 

Just Flip the triangle so that the hypothenuse is the base. Then divide the triangle into two by a vertical line in the middle which is the HEIGHT.

 

And a primary school kid should be able to deduce the height is half the base by deducing the two new triangles are isoceles triangles. Then the answer is just base times height / 2.

 

much simpler maths involved. no sqrt. I am not sure but I don't think primary kids have learnt the concept of square root or pythagoras theorem.

 

I think I should open a primary maths tuition center. :)

 

 

Dont think this method will work cause you still cannot measure the height of the newly form Square.

[1fast1]

Dont think this method will work cause you still cannot measure the height of the newly form Square.

 

It works. An even simpler way to see the solution (rather than looking at isoceles triangles) is to envision the right triangle as half a square. Then you can see the height of the right triangle (taking the base as the hypotenuse) is exactly half the diagonal of the square, because of the symmetry of the square. The diagonal of the square is also the hypotenuse of the triangle. The rest quickly follows.

Edited July 2, 2010 by Turboflat4

[Getzsfv]

Need some help for this PSLE math questions, anyone can help:-

 

Joshua has 240 less stickers than zac. zac gives 40% of his stickers to Joshua. Joshue then gives 75% of his stickers back to zac. In the eend, zac has 530 more stickers than Joshua. How many stikers soes Joshua has at first?

 

Thanks hor

[Little_prince]

Need some help for this PSLE math questions, anyone can help:-

 

Joshua has 240 less stickers than zac. zac gives 40% of his stickers to Joshua. Joshue then gives 75% of his stickers back to zac. In the eend, zac has 530 more stickers than Joshua. How many stikers soes Joshua has at first?

 

Thanks hor

Zero.

 

Because.he burnt his manure sticker book after moyes and LVG too over.

 

Haha

[1fast1]

Need some help for this PSLE math questions, anyone can help:-

 

Joshua has 240 less stickers than zac. zac gives 40% of his stickers to Joshua. Joshue then gives 75% of his stickers back to zac. In the eend, zac has 530 more stickers than Joshua. How many stikers soes Joshua has at first?

 

Thanks hor

 

This was bloody maddening because I kept making idiotic careless mistakes in basic arithmetic, but it's very simple.

Start J off with 20 units, Z off with 20 units + 240 stickers.

 

First step: J goes to 28 units plus 96 stickers, Z goes to 12 units plus 144 stickers.

 

Second step: J goes to 7 units + 24 stickers, Z goes to 33 units plus 216 stickers.

 

Finally, do the simple algebra: 33units + 216 stickers - (7 units + 24 stickers) = 530 stickers, giving 1 unit = 13 stickers.

 

So J has 260 stickers at first.

 

EDIT: Rationale for choosing 20 units: it is the lcm of 5 (the denominator of the 40%) and 4 (the denominator of 75%). This way you avoid all the mucking about with fractions, which is what screwed me up in the first place.

Edited September 13, 2014 by Turboflat4