This weekend our Girls on the Run team ran the final 5K of the year. I ran as a buddy with one of my current students. Buddy runners are along to encourage and push the girls during the race. Looking back and reflecting on the race I realized that my buddy did great when I set goals she could see and felt she could achieve. Telling her that we would stop and walk when we got to the halfway mark did not do much to motivate her, even if the halfway mark was only a short distance away. She couldn't see anything significant marking that point so she couldn't really tell how much farther it would be. However, if I said we could walk once we got to the bottom of the hill, she kept up a good, steady pace down the hill. At the very end, when we came around the corner and could see the finish line she full out sprinted. It was impressive.
This got me thinking about teaching (of course). Right now we are working on a huge, end of the year, social studies and technology project. I'm really excited about it and as a result, so are the students. I've worked hard in my thinking to be sure I can see the big picture and the final goal. It's important that I can see this. But I don't know that they need to at this point. I think that one of my jobs is to set smaller, achievable goals for them throughout the project. The project, as I see it, is massive. It involves a lot of research, plenty of synthesizing what they learn, some tough decision making about technology tools to use, and serious work with those tools. I've set it up for them in those four parts, and we're currently working on the first and second. However, I'm thinking it needed to be broken down even more, at least for some students. The massive amount of research they are doing intimidates some and they want to give up. They can't see an end in sight so it doesn't feel worth the effort.
Anytime something is new and difficult, one needs to see success fairly regularly. A project of this scale is not something these students have done before. I've got to help them set a pace they can continue, hopefully with a burst of energy at the end.
Showing posts with label planning. Show all posts
Showing posts with label planning. Show all posts
Tuesday, May 20, 2008
Friday, March 07, 2008
Tangram Joy
We've been working on perimeter and area lately and I usually find it to be fairly dull. This year has been a pleasant switch. I gave each student a set of tangrams (punched out from a file folder so that they hold up pretty well). Using the medium sized triangle and the two little triangles they had to create five regular polygons. This step alone made for a pretty good discussion. 
Once they had created various polygons (triangle, square, rectangle, parallelogram, and trapezoid) they were to find the area and perimeter of each of them. I was surprised at how difficult it was for them to realize that all five shapes had the same area. They worked really hard to calculate the area for each one based on their measurements. It was fascinating.
After giving them some time to struggle with this we came back together as a group. We shared the different shapes because some students hadn't been able to figure out all five. Then we moved into looking at all of this algebraically. We compared the sides of each triangle and figured out that there are only 3 different lengths, the base of the larger triangle, the sides of the larger triangle or base of the smaller ones, and the sides of the smaller triangles. Using that knowledge we wrote one shape's perimeter as an algebraic expression. It was a challenge for them to write the rest that way, but they worked through it.
This also helped them see that all five areas are the same. Then we finally had a discussion of the relationship between perimeter and are (the main goal, initially). Most students firmly believed that no shape could have a larger area than perimeter. This activity had shown them that the perimeter and area aren't always the same (shapes with the same perimeter can have different areas and vice versa). As a result, I immediately opened up a grid on our smartboard and had students try some different shapes and calculate the area and perimeter. They quickly found shapes that disproved their theory. Off they went, back to their seats with grid paper to see what else they could discover. They loved exploring this way (both with the tangrams and with the grid paper) and, I think, have a much better understanding of area and perimeter than my students have had in the past.
Once they had created various polygons (triangle, square, rectangle, parallelogram, and trapezoid) they were to find the area and perimeter of each of them. I was surprised at how difficult it was for them to realize that all five shapes had the same area. They worked really hard to calculate the area for each one based on their measurements. It was fascinating.
After giving them some time to struggle with this we came back together as a group. We shared the different shapes because some students hadn't been able to figure out all five. Then we moved into looking at all of this algebraically. We compared the sides of each triangle and figured out that there are only 3 different lengths, the base of the larger triangle, the sides of the larger triangle or base of the smaller ones, and the sides of the smaller triangles. Using that knowledge we wrote one shape's perimeter as an algebraic expression. It was a challenge for them to write the rest that way, but they worked through it.
This also helped them see that all five areas are the same. Then we finally had a discussion of the relationship between perimeter and are (the main goal, initially). Most students firmly believed that no shape could have a larger area than perimeter. This activity had shown them that the perimeter and area aren't always the same (shapes with the same perimeter can have different areas and vice versa). As a result, I immediately opened up a grid on our smartboard and had students try some different shapes and calculate the area and perimeter. They quickly found shapes that disproved their theory. Off they went, back to their seats with grid paper to see what else they could discover. They loved exploring this way (both with the tangrams and with the grid paper) and, I think, have a much better understanding of area and perimeter than my students have had in the past.
Thursday, February 28, 2008
Technology in Math
This lesson didn't begin with technology. Initially the students were working with three triangles from tangrams and creating polygons. Five regular polygons can be made with those triangles. They then had to find the area and perimeter of the shapes. The goal is for them to realize that shapes can have the same area but different perimeters (or the other way around). It was harder for them than I had anticipated, but they enjoyed it.
We ended up writing the perimeters of the shapes as algebraic expressions based on the sides of the triangles. Actually measuring was not working well and this was good practice for them writing expressions. Plus, that pushed some of them to finally realize that the areas of the shapes were all the same. Once they recognized that the sides of the triangles remained the same no matter what shape they created, they were able to realize that the areas of each triangle did so as well.
As we neared the end of the lesson we realized that we needed to look at some of it a bit more deeply. I gave each student some fresh graph paper and asked them to try and create shapes with areas greater than perimeters, perimeters greater than areas, and equal perimeters and areas. (I know we are comparing apples and oranges to an extent here because we are comparing units with units squared, but they had a lot of preconceived notions that needed to be questioned.)
Then I wanted to be able to look at some of what they found together. So I pulled up grid paper on my smartboard.
They drew several different shapes to show how each of the possibilities might look. Some students were just amazed that you could have equal perimeter and area or that the perimeter could ever be a larger number than the area. It was interesting to hear their discussion. Then Mr. B opened up Geometer's Sketchpad with a shape that he could manipulate so they could watch the perimeter and area change. This allowed them to test some theories quickly without having to do a lot of tedious computation (which would have caused them to not test their theories). They were enthralled.
This was the best on-the-fly use of technology I've done all year. I was so glad to have the smartboard and Geometer's Sketchpad at my fingertips. The one depressing piece was that I hadn't originally thought to do these things as a part of the lesson.
We ended up writing the perimeters of the shapes as algebraic expressions based on the sides of the triangles. Actually measuring was not working well and this was good practice for them writing expressions. Plus, that pushed some of them to finally realize that the areas of the shapes were all the same. Once they recognized that the sides of the triangles remained the same no matter what shape they created, they were able to realize that the areas of each triangle did so as well.
As we neared the end of the lesson we realized that we needed to look at some of it a bit more deeply. I gave each student some fresh graph paper and asked them to try and create shapes with areas greater than perimeters, perimeters greater than areas, and equal perimeters and areas. (I know we are comparing apples and oranges to an extent here because we are comparing units with units squared, but they had a lot of preconceived notions that needed to be questioned.)
Then I wanted to be able to look at some of what they found together. So I pulled up grid paper on my smartboard.
They drew several different shapes to show how each of the possibilities might look. Some students were just amazed that you could have equal perimeter and area or that the perimeter could ever be a larger number than the area. It was interesting to hear their discussion. Then Mr. B opened up Geometer's Sketchpad with a shape that he could manipulate so they could watch the perimeter and area change. This allowed them to test some theories quickly without having to do a lot of tedious computation (which would have caused them to not test their theories). They were enthralled.
This was the best on-the-fly use of technology I've done all year. I was so glad to have the smartboard and Geometer's Sketchpad at my fingertips. The one depressing piece was that I hadn't originally thought to do these things as a part of the lesson.
Sunday, August 05, 2007
One Week Down
It's astounding how quickly time passes in an elementary school. We've finished the first week already.
This year I managed to get through the entire first week without teaching any content. It may be the first time I've done that. We organized supplies and got everything set up to facilitate our learning this year. We've read a lot of books together. We've had many discussions about books and organization. We've played math games and talked about strategies. We've had morning meetings in which we shared about ourselves. And we've done lots of teamwork activities together.
Next week we'll get started with some curriculum, but not too much. I firmly believe that I've built a better foundation for our year than I ever did before.
We'll see if that holds true as the year continues.
This year I managed to get through the entire first week without teaching any content. It may be the first time I've done that. We organized supplies and got everything set up to facilitate our learning this year. We've read a lot of books together. We've had many discussions about books and organization. We've played math games and talked about strategies. We've had morning meetings in which we shared about ourselves. And we've done lots of teamwork activities together.
Next week we'll get started with some curriculum, but not too much. I firmly believe that I've built a better foundation for our year than I ever did before.
We'll see if that holds true as the year continues.
Subscribe to:
Posts (Atom)