Share a favorite book and an extension lesson.
As a math teacher, I was worried about this Day 1 challenge. I then realized I was approaching it wrong. Every year after we talk about similarity, surface area, and volume in 7th grade I read the class a book. "Jim and the Beanstalk" by Raymond Briggs.
I got this idea from a Marilyn Burns book titled Math and Literature Grades 6-8. (here) However I have added some parts to the problem to take it further.
The story is about a giant and a boy who meets and helps the Giant. The giant is of course a typical giant and allows me to get very theatrical as I read the book. I really get to have fun as I walk around the room reading this book. I get into it and do the different voices and really try to act it out.
At one point the giant says something about eating 3 boys on a slice of bread. The math begins when I ask them to get into groups of 3-4, give them a piece of bread, and tell them to scale the bread up to be big enough for their group.
The students have to use ideas of similarity (it must look like a piece of bread), surface area and volume (calculated for the original piece of bread and the giant piece of bread) to answer the questions "how many times bigger is the piece of bread?"
The students must produce a taped out area on the ground to represent the dimensions of the piece of bread. When students are confident of their answer and tape, the students lay down to prove they fit on the piece of bread. They must also calculate out the height (or thickness) of the piece of bread.
Each group is given a worksheet and a piece of bread. Even after all the students in the group and handled and measured the bread, usually someone in the group eats it. I find this gross, but the students are kids and kids will eat just about anything. My son, who is currently 8, once ate gum of the bottom of a bench in church when he was 5. (not the grossest story involving my son either, but that is for another day)
I wish I had some student work to post along with this, (maybe in the spring), it is a really fun day or two in class.