Primary 2 Maths Question

[Wizardofzzz]

Just seeing this.

 

Correct answer: 14 eggs. (7 symbols).

 

One of the standard tools to figure out sequences (other than staring at it) is to compute the difference between successive terms.

 

Just working on number of symbols:

 

Mon: 1 -> call that T(1) (for term 1)

 

Tue: 2 -> T(2)

 

Wed: 4 -> T(3)

 

Thurs: ? -> T(4)

 

Fri: 11 -> T(5)

 

Take differences:

 

T(2) - T(1) = 1

 

T(3) - T(2) = 2

 

T(4) - T(3) = ?

 

T(5) - T(4) = ?

 

There are two "common" patterns that start with 1,2...

 

viz. the natural numbers: 1,2,3... and the geometric progression 1,2,4,8...

 

A bit of trial and error here.

 

If you try the latter, you get a value for T(4) [Thursday] of 4+4 = 8 and T(5) [Friday] of 8+16 = 24 which clearly can't be right because you know T(5) is supposed to be 11.

 

So the differences are represented by the natural numbers (the first choice), giving T(4) = 4+3 = 7 and T(5) = 7+4 = 11, which is what we want.

 

(Actually, the Fibonacci series which starts 1,1,2,3,5... from the second term onward is also a contender for the successive differences, but I would expect this to be beyond the scope of a Primary school question. In any case, it doesn't fit either).

 

So T(4) = 7 symbols, or 14 eggs.

 

For the math geeks, this is a simple linear recurrence: T(n) - T(n-1) = n-1, with T(1) = 1

 

Solving it for a closed form will yield T(n) = (n^2 - n + 2)/2 symbols, or (n^2 - n + 2) eggs. From that you can find the answer for Thursday, which is (4^2 - 4 + 2) = (16 - 4 + 2) = 14 eggs.

 

But the last bit of cheeminology is just for fun. And rigour.

 

 

LoL..really chim

 

[Wasted]

wah bro you can quote Fibonacci sequence .... you are deep ...

 

the only shapes i can teach my monsters are Spade, Heart, Club n Diamond ....

 

the only math i can teach my monsters are 6+7+8 = 21

[The_Bear]

Sunny side up. Nom nom.

[JackRabbit]

Just seeing this.

 

Correct answer: 14 eggs. (7 symbols).

 

One of the standard tools to figure out sequences (other than staring at it) is to compute the difference between successive terms.

 

Just working on number of symbols:

 

Mon: 1 -> call that T(1) (for term 1)

 

Tue: 2 -> T(2)

 

Wed: 4 -> T(3)

 

Thurs: ? -> T(4)

 

Fri: 11 -> T(5)

 

Take differences:

 

T(2) - T(1) = 1

 

T(3) - T(2) = 2

 

T(4) - T(3) = ?

 

T(5) - T(4) = ?

 

There are two "common" patterns that start with 1,2...

 

viz. the natural numbers: 1,2,3... and the geometric progression 1,2,4,8...

 

A bit of trial and error here.

 

If you try the latter, you get a value for T(4) [Thursday] of 4+4 = 8 and T(5) [Friday] of 8+16 = 24 which clearly can't be right because you know T(5) is supposed to be 11.

 

So the differences are represented by the natural numbers (the first choice), giving T(4) = 4+3 = 7 and T(5) = 7+4 = 11, which is what we want.

 

(Actually, the Fibonacci series which starts 1,1,2,3,5... from the second term onward is also a contender for the successive differences, but I would expect this to be beyond the scope of a Primary school question. In any case, it doesn't fit either).

 

So T(4) = 7 symbols, or 14 eggs.

 

For the math geeks, this is a simple linear recurrence: T(n) - T(n-1) = n-1, with T(1) = 1

 

Solving it for a closed form will yield T(n) = (n^2 - n + 2)/2 symbols, or (n^2 - n + 2) eggs. From that you can find the answer for Thursday, which is (4^2 - 4 + 2) = (16 - 4 + 2) = 14 eggs.

 

But the last bit of cheeminology is just for fun. And rigour.

 

 

 

wah piang... my kid primary 2 only leh....

[1fast1]

wah piang... my kid primary 2 only leh....

 

Sorry, bro, I was actually trying to help you and your kid, but I guess my point got lost in all my math.

 

OK, bottom line time. When they give you a sequence (number pattern) at Pri level, it's usually a simple one.

 

The very simple "standard" ones are the arithmetic progression and the geometric progression. The former will give the same number (common difference) when you take one term minus the one before. The latter will give you the same number (common ratio) when you divide one term by the one before. These are easy to spot immediately.

 

This sequence is neither of those. But it's sort of the "next level" of difficulty. The difference between two terms is going up by one every time.

 

So if your kid needs to try and figure out a pattern just teach this hint - try taking the difference between one term and the next (in this case Tues minus Monday, Wed minus Tuesday, etc.) Your kid will be able to see 1,2,?,? then guess the next numbers are 3,4 - then test them out and see that they fit the pattern. Simple enough?

Edited October 26, 2011 by Turboflat4

[Sosaria]

Actually to solve primary school maths at the lower level, only the 4 basic math operations needed: plus, minus, multiply and divide. Anything more is using "excessive force"

 

To be honest, it goes to show that even testing 4 basic operations, the questions can go quite deep and provoke quite a lot of thinking. I think the Maths teaching is going in the right direction in this aspect, although this style of questioning and teaching may "turn off" weaker pupils who'll just give up without sufficient encouragement.

 

And to be honest also, even with A-Level F.Maths and many engin maths modules behind me (even optional, higher level ones also take!) in undergrad days, always scoring the best grade (that's why I always go for the maths modules)... this kind of question threw me off a bit and I took like 10 minutes of concentration and trying before managing to get the answer.

 

Hope this does not scare off potential parents from having kids!!!

 

One thing I don't like about this P2 graph topic and questions is that they just LOVE to use a symbol which is identical to the word, e.g. drawing an egg to represent 2 eggs, or a glass to represent 5 glasses... all this serves to confuse kids, and I think it's not part of testing their maths.

 

They should use some other symbol like a star represents 2 eggs, etc.

[Sosaria]

Sorry, bro, I was actually trying to help you and your kid, but I guess my point got lost in all my math.

 

OK, bottom line time. When they give you a sequence (number pattern) at Pri level, it's usually a simple one.

 

The very simple "standard" ones are the arithmetic progression and the geometric progression. The former will give the same number (common difference) when you take one term minus the one before. The latter will give you the same number (common ratio) when you divide one term by the one before. These are easy to spot immediately.

 

This sequence is neither of those. But it's sort of the "next level" of difficulty. The difference between two terms is going up by one every time.

 

So if your kid needs to try and figure out a pattern just teach this hint - try taking the difference between one term and the next (in this case Tues minus Monday, Wed minus Tuesday, etc.) Your kid will be able to see 1,2,?,? then guess the next numbers are 3,4 - then test them out and see that they fit the pattern. Simple enough?

 

That's right. A series hidden in another series. What I tell my kid is that if the series presented seems to have no order, it's time to write out the difference between terms or the ratio between terms, and then see if these numbers make an orderly series. At lower primary level, there is no non-linear stuff like squaring etc. involved, and usually need to concentrate on only one term before and one term after.

 

Although these questions appear to be different and difficult - it is possible for kids to prepare for them by noting all the various variations and tricks that are applied.

[JackRabbit]

Thanks for the hints, Turboflat and Sosaria... that simplification of figuring it out that way makes it understandable even to me. I'll teach my kid this way.

 

I have to admit the egg symbol threw me off that it represents 2 actual eggs. I wonder if at Primary 2 these kind of twists of logic are readily understood. Looking at my kid, I don't see how he would have realised the correct answer (14 instead of 7), even if he figured out the correct pattern (1,2,3,4). I guess he was destined to get this question wrong!

[1fast1]

Thanks for the hints, Turboflat and Sosaria... that simplification of figuring it out that way makes it understandable even to me. I'll teach my kid this way.

 

I have to admit the egg symbol threw me off that it represents 2 actual eggs. I wonder if at Primary 2 these kind of twists of logic are readily understood. Looking at my kid, I don't see how he would have realised the correct answer (14 instead of 7), even if he figured out the correct pattern (1,2,3,4). I guess he was destined to get this question wrong!

 

Just to pique your son's interest, this sequence (of number of symbols) is actually the Lazy Caterer's sequence (and is related to cake cutting): http://en.wikipedia.org/wiki/Lazy_caterer's_sequence, except that the sequence starts with n = 0. So to get Monday, you put n = 0, Tuesday, n = 1, etc.

Edited October 27, 2011 by Turboflat4

[Porker]

I heard kids are pretending to be parents and asking people on the internet

 

for answers to their homework. That way that get their homework done for them free.

 

 

:D

[Notsogoodman]

The question asks how many eggs did she see on the graph being spilled by the milk ?can be interpreted both ways ba . to be precise, shoud be 14

 

Read again, the question was asked very clearly. It asked how many eggs did Bernice see on Thursday, not what she saw on the graph. BTW, Bernice drew that graph

[Notsogoodman]

Allow me to try to explain in simple terms with the assumption that all eggs survived from Monday to Friday. Note the question asked how many eggs. One symbol represents 2 eggs

 

Monday, she saw 2 eggs

Tuesday, she saw 4 eggs (addition of 2 new eggs)

Wednesday, she saw 8 eggs (addition of 4 new eggs)

Thursday, ?????

Friday, she saw 22 eggs (an increase of 14 new eggs since Wednesday, If the increase follows a pattern, it's logical to assume that we looking at an addition of 2, 4, 6, 8.... Taking the increase of Thursday & Friday of 6 + 8 = 14

 

Let's test it, on Thursday, she saw 14 eggs (8 on Wednesday plus 6 new one)

So on Friday, she saw 22 eggs (14 on Thursday plus 8 new one)

[Requiemdk]

Triangular Numbers.

 

Throw some kiampah sequences at your kids and see whether they can guess the next number or not, like: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ___? or 1, 2, 3, 5, 4, 4, ___?

 

[Scb11980]

Just seeing this.

 

Correct answer: 14 eggs. (7 symbols).

 

One of the standard tools to figure out sequences (other than staring at it) is to compute the difference between successive terms.

 

Just working on number of symbols:

 

Mon: 1 -> call that T(1) (for term 1)

 

Tue: 2 -> T(2)

 

Wed: 4 -> T(3)

 

Thurs: ? -> T(4)

 

Fri: 11 -> T(5)

 

Take differences:

 

T(2) - T(1) = 1

 

T(3) - T(2) = 2

 

T(4) - T(3) = ?

 

T(5) - T(4) = ?

 

There are two "common" patterns that start with 1,2...

 

viz. the natural numbers: 1,2,3... and the geometric progression 1,2,4,8...

 

A bit of trial and error here.

 

If you try the latter, you get a value for T(4) [Thursday] of 4+4 = 8 and T(5) [Friday] of 8+16 = 24 which clearly can't be right because you know T(5) is supposed to be 11.

 

So the differences are represented by the natural numbers (the first choice), giving T(4) = 4+3 = 7 and T(5) = 7+4 = 11, which is what we want.

 

(Actually, the Fibonacci series which starts 1,1,2,3,5... from the second term onward is also a contender for the successive differences, but I would expect this to be beyond the scope of a Primary school question. In any case, it doesn't fit either).

 

So T(4) = 7 symbols, or 14 eggs.

 

For the math geeks, this is a simple linear recurrence: T(n) - T(n-1) = n-1, with T(1) = 1

 

Solving it for a closed form will yield T(n) = (n^2 - n + 2)/2 symbols, or (n^2 - n + 2) eggs. From that you can find the answer for Thursday, which is (4^2 - 4 + 2) = (16 - 4 + 2) = 14 eggs.

 

But the last bit of cheeminology is just for fun. And rigour.

 

 

 

excellent explanation

thank you

[1fast1]

Throw some kiampah sequences at your kids and see whether they can guess the next number or not, like: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ___? or 1, 2, 3, 5, 4, 4, ___?

 

You do know with the Online Encyclopedia of Integer Sequences (OEIS): http://oeis.org/Seis.html, that these are easily defeated? Anyway, are you testing for mathematical ability or effective bilingualism?

 

I love that resource. I have contributed a few sequences to it many years ago when it used to be known as the Sloane's Encyclopedia of Integer Sequences (hence the SEIS in the URL). Stuff I uploaded included two pertaining to the Riemann zeta function and one pertaining to a maximal bound on interior right angles in a planar n-gon. Some dumb word ones like yours, too.

Edited October 28, 2011 by Turboflat4

[Sotong_kia]

Fun sequence... 1, 2, 3, 4, _ , 126... fill in the blank.

 

[Requiemdk]

You do know with the Online Encyclopedia of Integer Sequences (OEIS): http://oeis.org/Seis.html, that these are easily defeated? Anyway, are you testing for mathematical ability or effective bilingualism?

 

I love that resource. I have contributed a few sequences to it many years ago when it used to be known as the Sloane's Encyclopedia of Integer Sequences (hence the SEIS in the URL). Stuff I uploaded included two pertaining to the Riemann zeta function and one pertaining to a maximal bound on interior right angles in a planar n-gon. Some dumb word ones like yours, too.

 

Shhh don't spoil the fun for people who haven't seen these things

 

The OEIS is a fun repository to trawl through in the course of research sometimes. Used it a couple of times myself, but never thought to upload stuff though

[Sk65]

dun say wrong lah... can say half correct!

 

this is math

7 = 14 meh?

 

 

 

but i also got it wrong..

 

omg, damn tricky qn.