If you've found some of these tasks, then as a math teacher you have conquered half the battle. To get all the way there, it really depends on how effectively you use these tasks. This can be difficult because you must have a classroom culture where discussion and inquiry are the norm. The culture must also include students who are not afraid to falter (because they will falter). Transforming your classroom into this type of environment won't happen overnight. It takes days and weeks of modeling and discussion. I wrote a blog post for NCTM's MTMS Blogarithm on how to transform your classroom that can be found here (part one) and here (part two).
Implementation of these tasks differs slightly depending on the teacher...but the goal is the same. Here is @ddmeyer's approach...and I took a lot of cues from this because I use a lot of his tasks and believe in his philosophy. Here is what I do...adapt as you see fit.
1. Students walk into my room and everything is ready to start. There is a timer set to know when class starts (we don't use bells), but the students always start before timer because they want to get started...they enjoy seeing what the task will be for the week. This particular week it happened to be about cookies...and who doesn't like cookies?
2. I have a big television in my room. All of the information for the students is front and center on the television so as soon as the students walk in, they know what is happening. The info would look like this minus the person who made the task and the standard numbers. My students all have their own laptops, and since my Google Doc they see on the television is already shared with them, they can go to their computers and have access to all the links and a closer look if they cannot see. I house all of these pages on my classroom website towards the bottom. If your students do not have computers or tablets, you would just show this information to the whole class (like the informational video), but I like it this way because the students can go back at their own pace and view.
3. Some student like to be grouped together, some students like to stay by themselves, but either way I don't select the groups or who is by themselves. Some of these arrangements change from task to task and some stay the same. The students who are by themselves still talk with the other groups and me so they still have a large amount of communication happening.
4. I basically work the room for the whole period...walk around and listen to conversations, trying to help out without helping too much. I am good at walking away from students when my intention is to make sure they think about the situation for awhile. Middle school students are great at throwing out responses that have not been analyzed...and this helps. My 6th graders thought I was just rude at the beginning of the year but they figured it out. Students are going to struggle, but that is part of the process. When you first implement these tasks, students will struggle A LOT...especially if they have only been exposed to the traditional math class where discussion and collaboration can be lacking. Most of the discussion happens between groups or with me, but we will stop as a whole group if someone has discovered something noteworthy or if I can see everyone is struggling on the same idea and we need a classroom discussion.
5. Once a group or individual has finished a task, I will look it over. I may have also heard enough from the group that I just have them turn it in and I will look it over that night. What I am looking for from each student is a unique explanation so it is clear to me that they aren't just writing what a group member has, but that they actually understand. I will often hand back work and ask more clarifying questions to be able to gauge further if everything was understood. Ultimately I give the students an hour in class and then a week to finish the task before it is due. This fits nicely with my self-paced philosophy because some of these students need more think time than the hour.
I have included a link to a video of my 7th grade students participating in a task. The link will take you to a Google Doc with some information setting the stage, and the video is broken into four sections. Hopefully this post along with the video will give you ideas on how you can implement these tasks into your classroom.
Problem-Solving Task Video
Other Posts with Tasks Containing Student Work