This really is one of the best picture books I have ever read related to math and critical thinking. It is the story of Eratosthenes, who was the Head Librarian of the great library of Alexandria. He was also an incredibly curious, and multi-talented scholar who did a bit of everything. However, his work that he is best known for is measuring the circumference of the Earth. He did this over 2000 years ago, and his calculation was within 200 miles. How did he do it?
That is where a great inquiry math lesson pops up, because the book doesn't give you the answer quickly, it builds it up, step by step, stone by stone. And what I love about this book is how you can take your students along for the ride with Eratosthenes.
It also covers a broad range of other subject disciplines and can be stretched out and kneaded into so many different shapes. History, language, science, social inequalities, law, government (it has a bit of everything).
How I use it (and how I describe it below) is as a Math Mystery Investigation, and a good chance to reflect on some Meta-Cognition strategies. Eratosthenes was a very reflective, curious, talented and mentally organized person, and how can we shape our own thinking to be more like his?
NOTE: This was done with grade 5/6, and is geared towards the Elementary and JHS level.
Read the first couple sections of the book. It basically sets up his early life and makes particular note of his curiosity and his ability to generate and create questions. There are a lot of little nuggets of gold in here, but the book itself is quite lengthy, so in the interest of time I will leave all those threads loose, and you can pick them up with your students. The story brings his life up the point where he now Head Librarian, and he finally has the time (and the financial means) to investigate questions that are interesting to him.
The tale starts to get interesting on page 30, when Eratosthenes asks himself an interesting question; is it possible to stand in one spot and figure out the circumference of the earth?
Have your kids try and answer it. I had them in groups brainstorming possible ways to do it on a large sheet of paper. They had some novel ideas (nothing that was even remotely possible!) and they flexed their creative brains (which is the point of this part of the lesson. If we are going to solve a problem like Eratosthenes, we are going to have to go way outside the box!
Finally, on page 35, a clue! There is a wonderful diagram of a grapefruit on one side, and the earth on the other. But don't read the text. Just show the diagram and see if they can make the connection between why a grapefruit is like the Earth. Brainstorm ideas on their piece of paper.
Back to the story, Eratosthenes figures out that is he can measure the circumference if he can find out what one slice of the pie is. All he needs is the inside angle of one of the sections; then he divides that angle by 360 degrees, and presto, he knows how many pieces of the pie there are in the whole.
I gave them a pie shape and some math tools and asked them to use this method to figure out how many pieces of pie would make a circle. Once they had that, I asked them how to figure out the circumference of the whole circle. Some of them were able it together and measure the top part of the circle and then multiply it by the number of pieces of pie. Others struggled, but during the ensuing conversations, we were able to determine that this way does work, and he had some great math talk.
So, what did Erasthonese do? Before I went back to the book, I asked them to brainstorm ways that he could possibly do it, keeping in mind he doesn't have the technology we do, and he is trying to measure a big piece of pie! Again, they came up with some interesting ideas, and a couple of them were even thinking about light (they missed the shadows). We recorded our ideas on our piece of paper (which is getting pretty full at this point!)
Back to the story, Eratosthenes uses the light from the sun shining into a well in Syene (the sun is directly over the well leaving no shadows on the wall, this is our straight line that goes to the point of the pie) and the sets up a big stick in Alexandria and measures the angle of the shadow that the sun leaves (this is the other line that is giving us our angle).
Give the students the measurements; 7.2 degrees, and let them figure out how many pieces of pie the Earth is made up of. Like Erasothenes, they should get 50 (360/7.2). Have them draw the picture of the Earth cut into 50 pieces.
So, all he needs to do now is measure the top part of the circle, and multiply it by 50. Simple right? Ahhh, how do you measure a large distance (put it into perspective, maybe from Sendai City to Iwate-ken worked for us) with no technology, or vehicles? This was 2000 years ago!
Let them brainstorm more ideas on their sheet of paper.
One of my kids said that he should walk it step by step and measure the steps. The rest of the class laughed. However, that is exactly what Eratosthenes did. Not him personally, but profession walker-measurers called bematists. They determined that the distance was 5000 stades (a Greek stadium). One stade was roughly 157 meters (or 515 feet if you like that weird way of measuring things).
Note: If you look online you can find several different interpretations of the numbers and conversions (and many arguments to go with them). To me, that is not the point of this exercise, and the exact number is unimportant. The point is the thinking that goes into it.
I asked them what they can do with these numbers? And how can we use that number to find the total circumference of the Earth? Again, on their sheet of paper they converted the stades into meters, and then meters into KM (those guys walked 785 km!) and they easily found the circumference of the Earth.
The story concludes with the answer and by saying that Eratosthenes lived a long and happy life. It also says that he never stopped asking questions, and he was continuously learning something new. This is a great kick off into the last part of the project, which had to do with analyzing his mind, and our our minds.
First, I gave them a picture or Eratosthenes and had them write the big ideas from the story around the picture. We have defined the term Meta-Learning in my class, so these terms are part of collective language. See one example below;
After that, in our math journals, we made mind maps of the skills and traits that Eratosthenes has, and how he used them in the story (Resilience, Curiosity, Resourcefulness, etc.). Next, we tried to think of times where we used those skills and did a bit of reflective writing. Finally, we set a goal for the month, based on the skills we that Eratosthenes has illuminated for us.
I can see a lot of this book becoming part of the classes collective intelligence and culture. After this activity, it is something that will be able to refer back to as a point of inquiry and thinking for the rest of the year.