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.
A colleague of mine at work shared this excellent resource with me for interesting and perplexing mathematics problems. The Galileo project looks like it has about 100 interesting mathematics problems for students to do for a variety of different age levels.
Here is an example:
How many parents do you have?
How many grand-parents do you have?
How many great grand-parents do you have?
How many great-great-grand-parents do you have?
How many great-great-great-grand-parents do you have?
Wait a minute! Do you see a problem with this?
Malke Rosenfeld shares another example of her daughter’s mathematical thinking, this time when her daughter finds a protractor and decides to use it to make a map of some angles. Read more about her daughter’s mathematical thinking on her blog.
I have been working with some 4th grade students, and we have been exploring colouring in maps as per this investigation. Here are a couple of examples of their work.
Notice how the students are experimenting with different arrangements of the map. In the last example, the student is trying to find ways to create connections between different “countries” on their map in an effort to force their map to require more colours. Notice also that they have started numbering the colours instead of actually colouring them in. This is a form of abstraction, and something we hope all of our students develop.