The beginning of my work with this idea came to light from an article I read from NCTM, this lesson was a handout. My lesson materials is found here, which includes the PPT and handouts I used for this 5th grade lesson.
What I liked….
The first thing that spoke to me about this lesson is the low barrier to entry, specifically, the task has students follow a pattern of crossing out numbers in a distinguishable pattern. With very little in depth thinking, once students see that pattern, the process of finding numbers is relatively easy. Connecting the students’ understanding of prime numbers to composite numbers, this process introduces “hidden” language, like factors in a natural setting as we explore this process. Specifically, the link of why content has developed a language as a necessary way to describe the things that we are interacting with. Finally, the cross curricular idea stands out as a natural progression of this lesson, from the history component of learning a little about Eratosthenes to the connection between mathematics and music.
What I wonder….
This section has less to do with the lesson, and more to do with my implementation of the lesson. Originally, I thought this lesson would take a few days, realistically though, this lesson is more like a unit, and probably would take a full week of instruction for students to really make connections. My implementation of the lesson required me to create a full sequence that spoke to “my style” of teaching, realizing that I would most likely leave behind the idea of the connection to music.
The teacher kind enough to let me use her classroom, also pointed out a really great point, that in showing videos, it would be beneficial to have questions next to video, so students would be able to refer to them, as they were not reading the questions on the handouts I created to accompany the lessons.
What the students got….
So all of the above to say, that the students got a very nice introduction to who Eratosthenes is, what he did, and some insight on how to say his name. Almost all students were able to get the process of how the sieve works, and the students were excited to go ahead with both examples. These pieces of the lesson went well, combined with the fun and many student interactions made for a success in those ways.
On the other hand, I felt I didn’t facilitate the flow of the lesson on the two days very well. The combinations of interacting with individual students, not explicitly detailing what interactions would look like, and being purposeful in the questioning, providing examples, or explicitly modeling left many students without the proper understanding.
My learning objective was to have students be able to recognize how composite and prime numbers are similar and how they are different. This was my target baseline, and I did not make that mark, though many students developed a deeper understanding, and a few were really trying to answer the questions.
My biggest learning is that when you set the stage property, the students will do amazing things, this was amazing thing to do; however, I did not set the stage properly for them to be able to reach out, explore, and do those amazing things. As I write this, I am realizing what it was that was missing, I failed to set the stage properly for the students to be successful. So now I am thinking, what that might look like in a week, or so, as I will be going into another 5th grade classroom. I will modify the lesson to provide a better stage.