Newspapers and Math??

In reading a newspaper, you notice that 4 pages of a section are missing.  One missing page is pg.13.  The back of this section is pg.40

What are the other 3 missing pages?

My first step was to figure out what a newspaper is and how the pages are organized.  A newspaper is constructed by stacking sheets of paper on top of each other and then folding it in half.  Therefore each sheet  of paper contains 4 pages.  Having a hard time visualizing this? Simply grab a few pieces of paper, stack them on top of each other and then fold it in half.
So in our example this first sheet would contain pages 1,2,39, and 40.

Now that we know how a newspaper actually works lets tackle the problem at hand.

Since 40 pages is a relatively low number we can just work our way through all the sheets until we get to page 13

We already know the first sheet contains pages (1,2,39,40).  So the second sheet will contain (3,4,37,38)
and so on
(5,6,35,36)
(7,8,33,34)
(9,10,31,32)
(11,12,29,30)
(13,14,27,28)

So our answer would be pages 14,27,28!
Easy enough.
But what if we said there was 1000 pages and one missing page was page 217?  So the first sheet would contain pages (1,2,999,1000) and we need to find out (217, ?, ?, ?)

I'm way to lazy to write out each section one by one!

Here's a faster way.  We should be able to see that page 218 will also be included because the starting page of each sheet contains the next page as well. Also based on our previous example, page 5 goes in hand with page 6, page 7 with 8, all the way to page 217 with 218.  So now we have (217,218, ?, ?).  We can figure out the rest easily if we just subract 217 from the last page.  1000-217 = 783.  And then we can figure out the last page because 783 goes in hand with 784.

so we get (217,218,783,784)

We can do this subtraction because we already know how a newspaper is organized.  However many pages we go in from the front must mean we go the same amount of pages from the back.

A few words of teacherly advice:

If a student is having trouble
            - I think most students would have trouble visualizing how the newspaper is organized.  So if that is the case then simply just bring in a physical newspaper and show them!
           

Some ways to extend this problem
            - Increase the page numbers
            - Try removing a page that is past the "halfway" mark