Dataset1/D1Mods
From Jsarmi
< Dataset1
Moderators role.
Contents |
Session I
Presented the basic "task situation" to the team, encourage them to generate questions and explore the ones that interested them. Framing postings included:
Moderator: After each session we can share your ideas with other groups and you can learn from them and compare if you want.
But it's not a contest. Each group will be different. For now we are calling you group #, but at some point,
if you want, you can pick a name for your group.
Moderator: So, to get started with the math, we will describe a situation to you and you will then explore it,
make up questions about it, discuss them as a group and try to answer the ones that you find
the most interesting. o.k.?
Session II
Presented a set of questions on the whiteboard, introduced to the teams with these messages:
ModeratorX: As we said before, after each session we can share your ideas with other groups
and you can learn from them and compare if you want. But it's not a contest. Each group is different.
ModeratorX: So, last Tuesday, all groups generated a number of questions about the world that we had
and we collected some of them for you to consider today. I am going to paste then on the whiteboard
for you to look at
Questions: 1. What is the shortest path along the grid between the two points? 2. How many possible routes are there from point A to point B? 3. What is the maximum distance from point A to B if you can only travel on each POINT once? 4. How many ways are there to get from A to B in rectangle ABCD? 5. Make a right triangle with AB as the hypotenuse. What is the area of the circumscribed circle? 6. Can you go off the edge and come back somewhere else? Questions that your work made the moderators think of: 7. What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)? 8. How many shortest paths are there from A to B and how does this vary with changes in the positioning of A relative to B? 9. Suppose the right and left edges of the grid are connected. How does that change the distances between points?
Session III
Via chat:
Today, we will share some questions and observations from other mathematicians who have been looking at the questions and solutions you have been inventing and pursuing. During the first two sessions of this program the groups have at times explored a math where points only exist at the intersections of a grid (this one is 12 lines by 12 lines), evenly spaced one unit apart as in the image on the whiteboard. There are no "diagonal" lines, at least not in the way we usually think of them. Distance between any two points in this grid world is defined as the length of the shortest path along the grid lines connecting the points. Several groups showed there may be several shortest paths, but the distance is well-defined. This is a system of math that you are inventing, just as the Greeks invented geometry. Did anyone think of any other questions after the last session? ... Here are some questions that come up when looking at your work. You don't need to pay any attention to these if you don't want to. Again, your goal is to identify or invent new math questions that are interesting to you and pursue them.
On the whiteboard:
1. What is a mathematical formula for the distance between any two points on the grid? Call the points “A” at some grid coordinate (x1, y1) and “B” at (x2, y2). 2. How many shortest paths are there along the grid between pairs of points? Is a general formula? 3. Suppose that the left and right edges of the grid are connected, so there is 0 distance between them. For instance, the distance between (0, 5) and (11, 5) = 0. (One could say that those two sets of coordinates are two different names for the same point.) Now what is the distance along the grid between points? How many shortest paths are there? 4. Suppose that all the edges of the grid are connected, so there is 0 distance between them. For instance, the distance between (1, 5) and (7, 10) = 2. (One could say that all the edge coordinates are different names for a single point.) Now what is the distance along the connected grid between points? How many shortest paths are there?
