Ender Hypersonic July 29, 2017 Share July 29, 2017 Thanks. Think I got it. Though I probably will get confused again No wonder I got B for a level maths hahaha It's new to you. I also gone thru many school papers to familiarise with primary school method. I'm sure you can pick up fast when you coach your kid from P3 ownwards. ↡ Advertisement Link to post Share on other sites More sharing options...
Ender Hypersonic July 29, 2017 Share July 29, 2017 Here's a more complicated exercise where the primary school level is to use area mapping to map out what area to add and what area to take away. This is PSLE level fyi, so parents good to know how. Link to post Share on other sites More sharing options...
1fast1 Supersonic July 30, 2017 Share July 30, 2017 Here's a more complicated exercise where the primary school level is to use area mapping to map out what area to add and what area to take away. This is PSLE level fyi, so parents good to know how. 30.8 sq cm It's easier for old fogeys like me to scribble a couple of equations. But one can also think about "double counting" areas and even "negative areas" to conceptualise this sort of problem. Link to post Share on other sites More sharing options...
Ender Hypersonic July 30, 2017 Share July 30, 2017 30.8 sq cm It's easier for old fogeys like me to scribble a couple of equations. But one can also think about "double counting" areas and even "negative areas" to conceptualise this sort of problem. Correct, but I don't know how to do it via equations. Like you said about counting areas, the primary level are taught to "count and remove" the area. So after going thru the count, the student should be able to realise the answer is just, Big Circle + Small Circle - Big triangle. 1 Link to post Share on other sites More sharing options...
1fast1 Supersonic July 30, 2017 Share July 30, 2017 Correct, but I don't know how to do it via equations. Like you said about counting areas, the primary level are taught to "count and remove" the area. So after going thru the count, the student should be able to realise the answer is just, Big Circle + Small Circle - Big triangle. It's easy via equations (at least from my perspective). See attached. There's an obvious line of symmetry bisecting the triangle, so we can deal with just half the figure. Let small 's' be half the shaded area that we're supposed to determine. Keep all unknowns small case and all knowns large case. C(N) refers to circle of radius N, and H(N) (for "hemicircle") is the semicircle of the same radius. I chose "H" for hemicircle to avoid confusion with the letter 's'. Let R be one right triangle formed by bisecting the big isosceles triangle T. We have that: H(4) - x = s - y Rearrange, s = H(4) + (y-x) ----- equation 1 and (R + y) - H(2) = x Rearrange, H(2) - R = (y-x) ------ equation 2 Substitute eqn 2 into eqn 1: s = H(4) + H(2) - R Double to find the required area, 2s = C(4) + C(2) - T = pi*(4^2 + 2^2 ) - (0.5*8*8) = 30.8 sq cm. If one is not comfortable with even this level of algebra, then one has to consider intricate decompositions, double counting areas and "negative areas" as I've mentioned. I don't think that's a straightforward way of looking at the problem either, to be frank. 2 Link to post Share on other sites More sharing options...
Angcheek Hypersonic July 30, 2017 Share July 30, 2017 Time to use your brains guys. Find the difference in area of A and B. Pi is 3.14 IMG_4076.JPG Pardon the erased pencil marks Thats Easy la ...... A bigger than B . THats the difference 5 Link to post Share on other sites More sharing options...
Angcheek Hypersonic July 30, 2017 Share July 30, 2017 Thanks. Think I got it. Though I probably will get confused again No wonder I got B for a level maths hahaha This is the simultaneous equation equivalent of @ender 's solution haha You only can visualise body parts 6 Link to post Share on other sites More sharing options...
Angcheek Hypersonic July 30, 2017 Share July 30, 2017 This how I taught my son when I was preparing him for PSLE two years back. Have him visualise the shape and removing them one by one. Primary level they haven't learnt complicated equation yet. Unless kid understand to substitute Rect with Area of Rect - B in order to get B into the eq . I simple minded , so I just find B first , than find A . 9 Link to post Share on other sites More sharing options...
Atrecord Supersonic July 31, 2017 Share July 31, 2017 A - B = Big quadrant - small quadrant - rectangle Where big quadrant = pi x 24 x 24 / 4 Small quadrant = pi x 12 x 12 /4 Rectangle = 24 x 12 Wah... brilliant... i better ask my son whether he can visualise these better than his father... If he can't, then jialat liao... PSLE is one month plus away... Link to post Share on other sites More sharing options...
Ender Hypersonic July 31, 2017 Share July 31, 2017 Wah... brilliant... i better ask my son whether he can visualise these better than his father... If he can't, then jialat liao... PSLE is one month plus away... MOE has clarified liao, any mathematical methods if workings are shown is accepted. If your son is comfortable with equations, both @turboflat4 and @Stratovarius method are accepted in the PSLE. Link to post Share on other sites More sharing options...
Atrecord Supersonic July 31, 2017 Share July 31, 2017 MOE has clarified liao, any mathematical methods if workings are shown is accepted. If your son is comfortable with equations, both @turboflat4 and @Stratovarius method are accepted in the PSLE. I think p6 still not yet learn algebra right? my wife is the one teaching, and our age is the equation type... but hor... even equation also i dunno how to solve i better hope she knows... Link to post Share on other sites More sharing options...
Enye Hypersonic July 31, 2017 Share July 31, 2017 I think p6 still not yet learn algebra right? my wife is the one teaching, and our age is the equation type... but hor... even equation also i dunno how to solve i better hope she knows... think you better pay more attention to your son's pri school syllabus and go for tuition class Link to post Share on other sites More sharing options...
Atrecord Supersonic July 31, 2017 Share July 31, 2017 think you better pay more attention to your son's pri school syllabus and go for tuition class you're right there... Link to post Share on other sites More sharing options...
Ender Hypersonic July 31, 2017 Share July 31, 2017 They do recycle question. They rotate 90 degree, change the values, renames some variables. And it's a new question for next year paper. Link to post Share on other sites More sharing options...
Stratovarius Turbocharged July 31, 2017 Share July 31, 2017 Here's a more complicated exercise where the primary school level is to use area mapping to map out what area to add and what area to take away. This is PSLE level fyi, so parents good to know how. Wow. This is really not easy for primary school kids. To simplify, see only half the image. Half of total area = a+b+c a = big semi circle -(area of triangle -small semi circle + b +c) a+b+c = big semi circle - area of triangle + small semi circle. Multiply the answer by 2 to get 30.8 This is probably the easiest way to explain to a pri sch kid i guess. Link to post Share on other sites More sharing options...
Ender Hypersonic July 31, 2017 Share July 31, 2017 (edited) This is the area mapping I was talking about. You break them into smaller sections and name them A, B ,C , D. And You will see, The square is A + B+ 2C +D The quadrant is B + C + D The semi circle is just D If add the 2 quads, you have 2 count of B, C and D= >2 quads= 2B + 2C + 2D Then you take away the square 2 Quad - Square = 2B + 2C +2D - (A + B + C +D) = B + D - A B - A = 2 Quad - Square - Semi circle (D) BTW, the answer in the picture is not by me. Pick it out from the onsponge forum here, http://www.onsponge.com/forum/35-thinkingmath/14029-p6-circles-overlapping-method Edited July 31, 2017 by Ender Link to post Share on other sites More sharing options...
Ender Hypersonic July 31, 2017 Share July 31, 2017 (edited) This is the area map out method I taught my son to use. same as above. Once familiar, no need to go thru the same workings. Should arrived at the Big circle + Small Circle - Big Triangle fast. This website saved me two years ago when I was struggling with this question. http://www.mathseason.com/skills/area.html Edited July 31, 2017 by Ender 1 Link to post Share on other sites More sharing options...
Ender Hypersonic July 31, 2017 Share July 31, 2017 I think p6 still not yet learn algebra right? my wife is the one teaching, and our age is the equation type... but hor... even equation also i dunno how to solve i better hope she knows... Not cheem stuff. But they may not know it as algebra, but they have learnt the 'u' and 'p'. Which already the beginning of algebra. ↡ Advertisement Link to post Share on other sites More sharing options...
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