Here’s a question from my 10 year old’s homework:
Yep. Grade 5…
Well… perhaps you could clarify where your confusion is. I assume you know how to do part a) [multiplication], and the start of part b) [subtraction], so your confusion is just on the second half of part b), but just checking in case…
Also, while I can see some connection to Fibonacci numbers, I’m going to assume the problem sheet actually gave some more context/description of such a connection (particularly given that this is the third problem), so it may be useful to see what that was.
Is this in a textbook or on a worksheet? If a worksheet, do you know whereabouts there is supposed to be relevant material in the textbook?
What are the relevant chapter and section headings? What are some of the other problems around this problem? This might help me get a handle on exactly what the problem in question is asking for.
-FrL-
If that’s it, that’s a pretty lame problem. Unless this is a unique triplet in that respect somehow. But even then, it’s hard to see how this would be the right kind of problem to have in a fifth grade math class. I’m all for exposing kids to neat-o number theory magic, but there’s much neat-o-er stuff to show them.
-FrL-
Sounds about right for 5th grade math to my recollection …
Its not just true of that triplet, its true in general that the difference of the squares of two Fibinocci numbers two “steps” apart in the sequence yield a third number in the sequence.
Might be hard to prove to a fifth grade class, but maybe there’s a simple proof of it that I’m not aware of that the teacher walked them through.
Ah, that’s fairly interesting IMO!
I take back what I said.
The problem should have said “interesting” instead of “special” though. “Special” makes me think there’s something unique about the triplet.
-Kris
OK. Good point. Here we go:
Ok, It’s vague in the textbook, but this MAY be an introduction:
-
a) Find the 13th fibonacci number.
b) What is the sum of the first 13 Fibonacci numbers? -
a) Write the firts Fibonacci numbers.
b) Choose 3 consecutive Fibonacci numbers.
Find the product of the least and the greatest numbers.
Multiply by the middle number by itself.
What do you notice about the products?
c) Repeat part b for 3 different consecutive Fibonacci numbers. What do you notice?
I have no idea how to help my daughter with this! 
She’s looking over my shoulder now and is looking for help!
The Fibonacci sequence is defined by the following set of equations:
f[sub]1[/sub] = 1
f[sub]2[/sub] = 1
f[sub]n + 2[/sub] = f[sub]n + 1[/sub] + f[sub]n[/sub]
So to find the 13th Fibonacci number, you just need to find the 12th and 11th Fibonacci numbers and add them together. Does that help?
Question “b” is neat! I didn’t know that.
Try writing out the first few values (the first 8 you quoted are fine) and then follow the instructions… (e.g. if the 3 are a b c, then compare a * c to b * b).
(Do you need help with Problems 1 and 2 as well, or are you OK with those and just posting them to serve as background for Problem 3?)
For problem 1:
Start with the sequence they gave you:
1, 1, 2, 3, 5, 8, 13,…
those are the first Fibonacci numbers. To get the next one, you just add the last two. So 8 plus 13 is 21. Then to get the next one, add the last two again–21 plus 13 is 34. And so on.
For problem 2:
Take 2, 3, 5. Five times two is 10. Three times three is nine. Ten is one more than nine.
Now try 3, 5, 8:
Eight times three is 24. Five times five is 25. 25 is one more than 24.
I’d bet this works out no matter what triplet you pick.
For problem three, I’m betting the poster above got it right–The squares of two consecutive-but-one fibonacci numbers is itself going to be a fibonacci number.
-Kris
Hi. Its Leaffan’s daughter!
The question that my dad gave you was the wrong question I need help with.
The question I need help with is:
3a) Find each product:
2x2 5x5
b) Find the difference of the products in part a.
What is special about 2,5 and your awnser to part a?
4) repeat question 3 using the numbers 3 and 8.
What do you notice?
Do you think this is always true? Explain.
Fibonacci numbers are fertile ground for finding number patterns. Typically you perform some simple arithmatic on a set of F numbers and get a result that is also a F number. Such as the one you first described-- square two fibonacci numbers that are two terms apart in the sequence. Subtract. You should then find another fibonacci number.
That is
5^2 - 2^2 = 21
5, 2 and 21 are all fibonacci numbers.
Compare
8^2-3^2 = 55
8, 3 and 55 are all fibonacci numbers.
For grade five these are good arithmatic exercises in themselves, and encourage skills such as pattern recognition. In higher maths they lead to simple induction proofs and formulation of formulas and generalised rules – all good maths.
The bottom line is, you need to follow the instructions carefully. Making a table of results is a good idea. (Being systematic is another mathematical skill appropriate to grade 5) You should spot the number patterns easily. It is definitely not something to fget stressed over, but a little confusion is understandable if the instructions are not given clearly.
It does – but I had to read your post twice to make sure it agreed with what I’d seen. (Not a maths whiz, but I’d suggest for consistency):
Take 2, 3, 5: 2 times 5 is 10. 3 times 3 is 9. 10 is one more than 9.
Now try 3, 5, 8: 3 times 8 is 24. 5 times 5 is 25. 24 is one less than 25.
Thanx!
~ Leaffan’s daughter
Ah, I hadn’t actually noticed the order switching there.
So it’s always either one more or one less? Is there a rule for determining when it will be one more and when it will be one less?
-FrL-
Yes, it alternates. Sit down and think about it for a little while and the proof should come readily.
I tried working out the 5x5 - 2x2 = Fib# proof but I can’t get it. Help?