Rounding is a challenge to learn, knowing how to teach the concept is more complicated, especially to a variety of learners.
One of my tweeps, Amanda (@MsHaughs) made an excellent reference to building context around the action of rounding. Providing learners the opportunities to understand the ‘why’ supports their understanding. Amanda shares many other great ideas in a tutorial video, I highly recommend seeking out.
The goal for my 30 minute lesson is to have learners comfortably be able to understand the general concept of covering up the digits that are not of interest with respect to the place value you are rounding too. Using a number line find your benchmark numbers, remove the peek-a-boo, and determine to which benchmark number it is closest.
One of the things that sticks with me, is finding a way to make sense of the process doesn’t equate to understanding the conceptual ideas.
The lesson starts out with two animated gifs, one showing place value, the other a silly cat being surprised by a puppet popping out of a can. The students are asked to read the question, “What might we be learning about?” One student then reads it out loud, and I ask for 10 seconds of quiet think time. A teaching tip, I included the silly cat gif because I am anticipating that students would find it both humorous and draw their attention to the screen. After the quiet think time, I ask the learners to share out at their table with their partners, as the conversations are going, I’m listening for key words, which I point out, then ask for a couple of ideas. I am assessing their reasoning, while I’m building their interest in the topic.
Moving into the content, I play a video I made through Explain Everything, and follow up with an animation I made highlighting the same steps with a different example. The first number I used was 45, rounding to the nearest tens. The idea of starting here came from a coworker of mine, she’s an amazing teacher, and now a coach in our district. She suggested that I start with something like this, keep the focus tight, and use similar examples. I used the same numbers just ten times smaller for the two examples we worked through. I also had a “secret ingredient” that allowed students ready, or wanting to challenge themselves at the end. The animations showed the case of rounding the number 78 to the nearest tens, and then students were given the choice of 3 numbers, they choose one, and use the number line to round to the nearest ten. I created a quick worksheet with the numbers, the blank number line, and the directions so they would be able to quickly apply their learning. I should mention, after the animation played twice, I paused each step, asking questions, uncovering their thinking before they began their practice.
Once students were working, I saw a variety of misunderstandings, and a variety of students able to make sense of the process. After a few minutes, I started asking students that had variety of answers to present their work on the board. From that point, I asked students to compare what they have to those examples on the board. I am trying to avoid telling the learner of their mistake, rather setting the stage for them to uncover this idea on their own.
By the second iteration, students were able to move through the process with greater fluidity, recognizing the similarity of the process with the question. We were rounding the same digit sets, for example if the first round was 82, then the second round was ten times smaller 8.2. In the former case we were rounding to the nearest ten, in the latter case we were rounding to the nearest ones. I loved that several students chose the same number, chose the same strategy, and were able to articulate that it is exactly the same, just the numbers have a different value.
Several students assumed we were learning about place value, I didn’t disagree, I only mentioned that it shows up in particular ways. Students showed evidence of this understanding by choosing to do the “same number” in the second round, rounding to ones, as in the rounding to tens because they recognized the structure of our base ten system.
When students were prompted with the “secret ingredient” I was pleasantly surprised to hear a couple of students say, “Oh, I’m taking the hard one…” Understanding that students has three numbers they could choose from, the impact of that statement was relative to what they viewed was challenging. In fact, if one student chose their version of a “hard one,” another student had chosen a different number for that same reason.
By the time the two lessons were over, I felt that the lesson was successful overall, there are a few things I think I would have done differently, like not saying, “round up/down,” I’d rather have been consistent with the idea of which benchmark number the number we were rounding is closest too. Keeping the idea of distance is important and plays out in later roles. In the second lesson, I forgot to give the story context of the importance, and I felt the closure in both cases was a little forced, with no requirement for the students to produce any reflection on the learning. A quick summary of the lesson or a 3-2-1 exit strategy, at the least, would have provided some insights into their understanding and allowed them some processing as to what we just did.