Homework help functions/patterns

[debrawallenger]

Help!

I have this homework problem that is as follows: The first sequence has 1 block, the second sequence has 5 blocks, the third sequence has 13 blocks and I am supposed to come up with an equation to find out how many blocks are in any sequence. I know that the 4th sequence has 25 blocks and the 5th sequence has 41 blocks and that the difference between the sequences is a multiple of 4, but I am stuck! Help!

 

[arildno]

debra:
Just for the record, don't double post.

Note that
$$1=1^{2}+0^{2}$$
$$5=2^{2}+1^{2}$$
So we have;
$$a_{n}=n^{2}+(n-1)^{2}$$

 

[debrawallenger]

Thank you. I guess I need to read the rules! I'm new to the website. Thank you for the post, as well. That seems to work.

 

[arildno]

Now, I'm from Norway, so I don't know what age a "grade" corresponds to.
I think his teacher must have had this formula in his mind; seen this way it is fairly "easy" to spot it (sum of squares and so on..)
I cannot for the life of me think that he requires his pupils to solve general difference equations at their level (that's what you have to do if you should use the "multiples of four"-technique), but of course, he just MIGHT be that mean..

 

[debrawallenger]

Thank you for that reply. You have just confirmed my feelings. Grade 6 is 11 years old here in the States. My son has always been good in math for his grade level. In fact, last year he got the highest score in math on the state test. Because of that he is in an accelerated math class. However, the math department decided to skip the 6th grade curriculum (my son was in 5th grade last year) and jump into a 7th grade text. And my argument is that just because he's bright, doesn't mean you can skip a whole year's worth of work. Many parents are outraged by what is being required of the students. Many parents are complaining. Unfortunately, I do not think things will change fast enough. Fortunately, my husband and I are good in math, but apparently not good enough because we were also stuck on this problem. Part of the reason we could not help is because the teacher skips around the book to boot and we weren't sure what foundation was laid. Neither was my son. This problem is not that hard if you have been studying functions and patterns for awhile, but the kids haven't. Again, thank you for your help. Normally I think it is good to work things out and struggle, but this I felt was much too hard.

 

[arildno]

"Part of the reason we could not help is because the teacher skips around the book to boot and we weren't sure what foundation was laid. "

This seems very difficult for you as parents to deal with. In my opinion, it might well be that the teacher has good reasons to do so, but I think you as parents should be allowed, on request, to know what his plans are, so that you can give optimal home-support for your kids.

I cannot see that the teacher in question should have any valid reasons for declining to reveal his plans concerning the pace&choice of topics; it is, in my opinion a crucial part of parent/school relationship that parents know, or should be allowed to know, what the school/teachers are up to, and doing, during class hours.

 

[shmoe]

Hi, you mentioned "blocks" a few times in the first post. Was this sequence given as pictures then? something like:

*

then

*
**
**

then

**
**
***
***
***

and so on? Note how I've arranged these "blocks" (*'s actually). Each has 2 squares in it, one with sides length n-1 and one with sides length n, so the corresponding number is the area of these two squares n^2+(n-1)^2 (as given by arildno).

If it was given in this sort of picture/geometric looking form, I think it's much more feasible for a 6th grader to come up with a formula. Just given the sequence of numbers 1, 5, 13, 25, 41 without a picture like above I don't think is feasible for most 6th graders to come up with a general formula. They should be able to come up with the next 10 numbers in the sequence, but I'd doubt a general formula.

 

[debrawallenger]

There were pictures, but they did not look like that. I cannot seem to draw the correct picture so I will describe it. The first sequence was one block. The second sequence was 5 blocks arranged 3 horizontally and 3 vertically with the middle block being shared by the vertical and horizontal lines of blocks. In otherwords, the blocks were lined up corner to corner. The next sequence was similar, but larger. They had to construct the 4th and 5th sequence which he could do, then write the equation or expression that could be used to solve for the nth term and explain how they got the answer.

 

[arildno]

From what you've written, debra, it certainly seems that your son's teacher is less than perceptive of the level one should expect for kids around 11.

I hope you will continue to use PF; hopefully, we might be able to provide perspectives on math which you find to be better explanations to give your son than those provided by his teacher.

 

[debrawallenger]

Thank you!

Absolutely! We consider this website a blessing! We will be using this website for the rest of the year.