I like to start class with an opening activity that promotes discussion and gets lots of students to participate. Questions in the format of "Which One Doesn't Belong?" allow a lot of student voices to be heard. It also gives a voice to students who think outside the box. There are many different ways to answer these questions. The important part is to provide a logical reason for the item you've selected. I'm consistently impressed with the creativity of students. The WODB question below combines two of my favourite things... math and pencils!
You can find lots of great examples of this type of question on the wodb.ca website, or check out the @WODBMath twitter feed.
A divisibility problem Erick and I worked on together was featured on the website "Open Middle".
What is an Open Middle problem? From their website:
Teachers in our province are implementing a new curriculum this school year and the first topic addressed in grade 7 is divisibility rules. Some teachers were surprised at the emphasis on this topic; the more we reflected on it, the more we realized that divisibility is a topic that builds deep number sense and operational fluency. We need to be careful not to teach "the rules" but rather the conceptual understanding and mathematical connections. This lays the groundwork for future success with a number of topics such as factoring quadratics, sequences, and polynomial long division.
Check out our submission! http://www.openmiddle.com/divisibility/