math ideas about themselves. I've found that these covers become a fabulous jumping-off point for PROBLEM SOLVING.
After students finish their covers, have them generate several problems on 3x5" notecards that use the information they created. For example, on my cover, I posted the following:
I went ahead and wrote my problem on the cover itself, but would have students write on cards. My question, "How many hours do I sleep each night? Each week?" could then be posed to other students. In the classroom, I could put my cover under the document camera and ask students to answer the question posed on my card(s). They could then share a variety of strategies for solving the problem. In a homeschool setting, children could write problems for siblings or parents to solve. Problems could be written at a wide variety of levels, making them grade and age appropriate.
At the Northwest Math Conference I went to a workshop entitled, "Taking the Numb Out of Numbers" by Don Fraser (Ontario, Canada). He began by telling the group of 30 of us, "Did you know that in a group of 23 or 24 there is a 50% chance that at least two people in the group will have the same birthday?" He then gave us a graph showing us the probability of sharing the same birthday in groups of varying sizes. In a group our size--30 people--the likelihood was 70%. We graphed the days/months for birthdays in the room. Interestingly enough, none of us shared the same birthday...we were in the 30%. After looking at the data, Don asked us to come up with problem solving questions--real life questions--based on the information we'd collected. It was amazing to see how many questions we could generate, at all different levels of mathematical knowledge and proficiency.
Don encouraged us to begin each day by reading a "story" and having kids make up a question/word problem. Going back to the math notebook covers, imagine the possibilities if you put ONE child's notebook cover up each day and asked kids to generate questions from the "stories" found there. The problem solving possibilities are endless!