Big Questions about Big Numbers

Last month, my eighth graders worked on the Big Numbers project. This project is the opening part of my unit on exponential functions. The goal is get students to be more comfortable with the notion of million, billion, and trillion, making sense of the magnitude of large numbers. We start by reading David M. Schwartz's How Much is a Million?. Then I give them their assignment: to make a 2-page spread in the sequel to that book. They need to think of a huge amount of something and make sense of it. One page is an illustration page that shows how they made sense of their quantity, and the other page shows all the math they did to reach their conclusion.

I love doing this project with 8th graders because they come up with the most creative questions! There is such a wonderful balance between intellectual "rigor" and childlike creativity at their age.

Below are some of the questions that my students came up with (including the followup question which is how they made sense of their number (my definition of "making sense" was that their answer needed to be something within their direct experience, eg. something they could directly could see or experienced (such as the distance to fly between 2 cities). Here is the book they made.

• How Big is the Earth's Circumference? How long would it take a horse to canter around once?
• How much snow has fallen in Boston over the past 5 years? If you packed the snow into Empire State Buildings, how many would you need and what amount of space would they cover on the ground?
• If the moon were really made out of cheese, how long would it take the entire Earth's population to eat it?
• How many Roxys (my dog) does it take to get to the moon? How many times would those dogs cover MA? 
• How many Chipotle burritos will stretch across the US? How long would it take everyone in the school to eat them?
• If you made a giant burger out of all the cows in the world, how big would it be? How long would it take Earth's population to eat it?
• How many M&M's are made each year? How many US Pentagon buildings would they fill?

First Blog Post!

Woohoo - my first blog post (as a math blogger)! I have been intending to start this blog for years, with the idea that it would be a place to record all of the aha moments from my teaching. This year, my school has focused on WONDER, and it has been making me think a lot about how questions are greater than answers, yet so often are not the focus of a math class. But when students wonder, they come up with some truly amazing questions. This year I have been focusing on truly listening to them, without an agenda of steering their thinking toward my desire end goal. True, we sometimes get derailed and end up talking about infinity when we "should" be talking about fractions, solving equations when we "should" be adding polynomials, or the meaning of e when we "should" be simplifying expressions with exponents. But I often find that when I follow the students' train of thought, we end up accomplishing more because of their buy in and understanding! (By the way, these are all examples of things that came up in the last week!)

So here's to this blog - may I actually update and maintain it!