Jump to content

Maths problem


Sosaria
 Share

Recommended Posts

Hypersonic

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

Hypersonic

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.

 

post-23584-0-23810800-1501336966.jpg

Link to post
Share on other sites

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

Hypersonic

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.

  • Praise 1
Link to post
Share on other sites

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.

 

post-52704-0-82453000-1501387160.jpg

 

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.

  • Praise 2
Link to post
Share on other sites

Time to use your brains guys.

 

Find the difference in area of A and B. Pi is 3.14

 

attachicon.gifIMG_4076.JPG

Pardon the erased pencil marks

 

Thats  Easy la ...... A bigger than B . THats the difference  :D

  • Praise 5
Link to post
Share on other sites

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  :XD:

  • Praise 6
Link to post
Share on other sites

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 .    [grin]

  • Praise 9
Link to post
Share on other sites

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...  [sweatdrop]

Link to post
Share on other sites

Hypersonic

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... [sweatdrop]

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

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  [bigcry]

 

i better hope she knows...

Link to post
Share on other sites

Hypersonic

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  [bigcry]

 

i better hope she knows...

 

think you better pay more attention to your son's pri school syllabus

 

and go for tuition class

 

:D

Link to post
Share on other sites

think you better pay more attention to your son's pri school syllabus

 

and go for tuition class

 

:D

 

you're right there...

Link to post
Share on other sites

Hypersonic

They do recycle question. They rotate 90 degree, change the values, renames some variables. And it's a new question for next year paper. [laugh]  [laugh]

 

post-23584-0-72906000-1501493327.jpg

Link to post
Share on other sites

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

Hypersonic
(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

 

 

 

post-23584-0-86994700-1501495019.jpg

Edited by Ender
Link to post
Share on other sites

Hypersonic
(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

 

 

post-23584-0-06691300-1501495522_thumb.jpg

post-23584-0-62047300-1501495527_thumb.jpg

Edited by Ender
  • Praise 1
Link to post
Share on other sites

Hypersonic

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 [bigcry]

 

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

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...