The Collaborative Mathematics project, created by Jason Ermer, looks like another excellent source of rich mathematical tasks for students. I recommend following the Problem a Day blog. Jason encourages the problems to be done collaboratively, hence the name of the project.

Here is a sample:

Notice how Jason takes a closed form question (What are the four digit numbers that can be flipped when multiplied by four?) and converts it into a much more open-ended investigation simply by making the restraints less restrictive. This is a useful general strategy you can use to make closed-form problems more open-ended.

Thanks to the Math Munch for sharing this project.

When multiplying by 4, I need to find a pair of numbers that ended with matching digits. For example “2” when by 4 gives us an 8. And “8”, when multiplied by 4 gives us 32 which ends in a “2”. My number must start with a 2 and end in 8. The middle two numbers must be less than 25 since we need to avoid a carry over thus changing our beginning or ending number (as we want the new number to begging with 8, not 9)
The number I found was 2178. 2178×4 = 8712. I also needed a flipped number that was 3 off of a multiple of 4 since 4×8 is 32. 17 and 71 fit that bill Are there more possibilities? Going back to my original thought of needing numbers like 2 and 8 4 and 6 might fit that bill. Of to check

When multiplying by 4, I need to find a pair of numbers that ended with matching digits. For example “2” when by 4 gives us an 8. And “8”, when multiplied by 4 gives us 32 which ends in a “2”. My number must start with a 2 and end in 8. The middle two numbers must be less than 25 since we need to avoid a carry over thus changing our beginning or ending number (as we want the new number to begging with 8, not 9)

The number I found was 2178. 2178×4 = 8712. I also needed a flipped number that was 3 off of a multiple of 4 since 4×8 is 32. 17 and 71 fit that bill Are there more possibilities? Going back to my original thought of needing numbers like 2 and 8 4 and 6 might fit that bill. Of to check

Nope doesn’t work with 4 and 6. These numbers create a 5 digit number.