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.
Inspiration has a strange way of showing up, a welcome companion when wrought of extreme desperation, which describes a recent situation I was in.
I invited myself to do a lesson in Kindergarten, my first of this school year, and I was excited. The lesson I was thinking of doing was one I had had the opportunity to practice a couple of times, so I felt confident it would go well…then I realized, this lesson is appropriate for the end of the year, but not after a month of school…then panic struck me.
Looking my manipulative chest, a plan emerged and two hours later, I had a lesson I was excited to present to 27 K and TK learners.
For the lesson, I wanted learners to have the opportunity to count, to associate numbers in various representations, to have discussions, and opportunities to ponder. Of course, with any demo lesson, a lot of the engagement will come in the presentation, so I also made sure to bring in high energy and silliness (of which, I have ample supply of).
The lesson starts with a “Which One Does Belong” slide, asking the students to choose one that didn’t belong, I asked the students to share in a Round Robin at their tables, then the students “whispered” their answers to me. Without missing a beat, the students chose the singleton unit as the one that didn’t belong, since the other three dice have a five in some representation. Interestingly, that tells me the students are numerically literate in counting and representing the number 1 and 5, this bodes well for our plans and we move on.
Not knowing what levels the learners are at this point, I wanted to build a little context with counting to five. Using a song from Sesame Street, the 3 minute video has five young adults harmonizing as they count to 5. The video went well with the learners, a pin could be heard as they watched the video. Capitalizing on this attention, I asked the students to share what the video was about, as I ready their unifix cubes.
The next slide asks students to Notice and Wonder, each student takes a little time (cued by a song) to think, then the utilize a Round Robin to share what they noticed and what they wonder. As students noticed the cubes, and I had ready the unifix cubes, the learners knew we were going to be using them.
Each student receives a strip of ten unifix cubes, and a sheet of paper. I model the first case, where I “build” the number with the unifix cube, draw it, then write the number. Practicing this, I verify each student is ready, so we begin with two, then three, and so on. Finishing with the number six, we are ready to go into the next phase, which is determining if there are five in the number six. Interestingly, when I ask the class, several students say no, that there is not five in six.
Using ten frames and red/yellow counters, I asked students to construct the same as the picture I am projecting on the screen. I was interested in how many different representations I saw, including some learners who place anywhere from seven to ten counters on the ten frame, when I asked if that was the same as the representation shown, they agreed it was. When we counted on the screen and the representation they had built, they agreed the numbers were different, but agreed that the representations were equivalent.
One student didn’t stack his as a double, like I had constructed, but made five and one more. When I asked if that was the same, he agreed, I asked him to explain, he proved it to me, by counting. Then he said, “It’s five and one” indicating his construction, and that’s 3 and 3, holding up his little fingers in two three, indicating that I should know that the two forms were equivalent. I apologized for not seeing that and thanked him for showing me.
The final part, due to time, had each student show me how five is in six, students were asked to turn over one to show me. Each student was abel to show me, and that ended the lesson.
Throughout the lesson, as we constructed the various numbers, I would ask if two or three representations were the same. For example, if the number was five, I would ask is three and two five or four and one, and we would count whole class using the unifix cubes. Doing this for each number, gave the opportunity to show the different ways to make the number, an important feature that will be exploited in number talks.
As I reflected with the teacher, I was very excited about the lesson. I felt like I reached my objective in a variety of formats. Students were being asked to draw, build, and write the various numbers. Students were asked various ways to build, we counted out loud multiple times, and students were able to talk about math as they noticed and wondered and shared which one doesn’t belong.
The pace was pretty quick, especially for young learners, but it was slow enough that almost every learner was with me. The teacher provided some very valuable feedback and had some great suggestions on extensions and moving forward. I will be very excited to head back in to continue the extensions in a short time.
A various selection of student work is shown below, the various representations and abilities speak volumes as to where the learners' accessed the content of lesson.
This is my introduction to this resource site and its purpose. The goal of this site is to provide a resource for teachers and students who are actively seeking mathematical knowledge. In time this site will become a detailed respository of mathematics materials.
Lessons I have attempted and student work will show the results of those efforts. Lesson reflections on how the lesson went and what was covered will also make it onto my blog here.
Well this is my first test of the system as I learn along the way. We wish you the best in your endeavors and we hope to see you here frequently.