## Monday, April 27, 2009

### Good Problems

Where do you get good problems for your students?

One source is that problem-of-the-day widget at the bottom of the blog. A couple times a week, I'm copying those, put them into a Word document, and then save them for a good opportunity.

But my all time favrite source is from the English (or British?) parallel to the NCTM: Nrich. Problems are sorted by content, tagged, by grade band (stage) and challenge level (number of stars). Some are unsolved, but accessible. Almost all are clever and/or interesting. Soooo nice! Give them a try. Here's an account of a teacher and how they use Nrich.

Here's one that I gave on a math for middle school final this semester:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Take, for example, four consecutive negative numbers, say
−7, −6, −5, −4
Now place + and/or − signs between them. e.g.
−7+−6+−5+−4
−7− −6+−5− −4
There are other possibilities. Try to list all of them. Now work out the solutions to the various calculations. e.g.
−7+−6+−5+−4=−22
−7− −6+−5− −4=−2
Choose a different set of four consecutive negative numbers and repeat the process. Take a look at both sets of solutions. Notice anything? Can you explain any similarities? Can you predict some of the solutions you will get when you start with a different set of four consecutive negative numbers? Test out any conjectures you may have. Try to explain and justify your findings.