3 Essential Steps for Teaching Interpreting Remainders Part 2 (EP16)

3 Essential Steps for Teaching Interpreting Remainders Part 2

Hello, everyone, and welcome to another episode of Elementary Math Chat, and Happy Halloween! 

I know this is always a crazy day to be a teacher, as is the day after Halloween, if I remember correctly. Hopefully, your students don’t bring too much candy back. That’s always the problem. So, hopefully, that is not the case for you.

All right. So, this week, we are continuing the conversation on interpreting the remainder. But before we do that, I want to go back and highlight two main ideas from last week’s episode.

The first big idea I talked about last week was to have your students write an answer statement because this will help them make sure that their answers actually make sense. I saw such a difference in their understanding when I had them start writing an answer statement. So that’s a big one.

And then the second big idea from last week was to use a CPA approach. Remember that stands for concrete, pictorial, and abstract, when you are teaching interpreting the remainder. And we actually went through the concrete and pictorial phases last week.

So, let’s pick right up where we left off last week. I mentioned a small group activity that I did to practice solving these problems in the pictorial phase, and so that’s where I’m going to start today.

First, I want to tell you why I created this activity for my students. Year after year, I was noticing that they could do a division problem, and they could identify which number was the divisor and which number was the remainder. 

But they had no idea how it connected to the story, which in turn meant that they really didn’t understand the problem to begin with.

So, I created this activity to help address those gaps in their learning because I knew if we couldn’t get past that, they were really going to struggle on interpreting the remainder.

This activity includes very simple division word problems, and the division is actually the very last thing that they do. So, instead of just jumping right to the division problem and not even thinking about what they’re doing, they go through every single part of the division problem, and they identify exactly what it means in the story.

For example, it has them identify the dividend and then explain what the dividend means in the story. So, maybe it’s the total number of pencils, or it’s the total number of cookies in the story. And the same goes for the divisor. They have to identify the divisor and then write what it represents.

And by the way, these are all fill-in-the-blank questions. So, for example, the dividend. There’s a line right next to it to write the dividend, and then it says the total number of ______, so they fill that in. 

That could be the total number of apples, the total number of people, whatever it is, they fill in the blank there, and they repeat this for the remainder and for the quotient.

So again, this is the first thing that they do. And when they finish this section, they move on to the second part, which is to draw a model just like they learned in that first lesson. So, just a very simple model with circles and dots is all they need for that part.

At this point, they should have a much better understanding of the problem. So, they are ready to finally do the division and interpret the remainder. So, that’s what they do in part three, and I make it really easy because I put all three ways to interpret the remainder in little checkboxes. So, they just check off if they are dropping the remainder, adding one to the quotient, or the remainder is the answer.

And then, of course, the final step is to go back to the answer statements. Those are already written for them, by the way, and they fill in the answer after they’ve interpreted the remainder.

Now, most of this is fill-in-the-blank, like I mentioned, but there is one space at the bottom that is not because it has them explain why they interpreted the remainder the way that they did. And this is going to lead to some incredible conversations in your small group.

In fact, that’s when I knew this activity was working because my kids were able to tell me why we had to add one to the quotient and why we were able to drop a remainder in a certain situation. That certainly would not have happened as easily had we not gone through the division problem and made sure we understood every single component.

So, if you’re interested in this activity, I will have it linked in the show notes for you. And there are four questions included. You can do all four in one day. If you do that, I recommend either splitting it up to where you do two in whole group and two in small group. Or what I did was I did all four in my small groups, but I only saw half of my class one day, and then I saw the other half the next day.

The last thing I’ll share about this activity, and then we’ll move on to the second part of the lesson, is that it’s editable. I know different grade levels have different ways to interpret the remainder. And I also know you may work things a little differently than I do. So, you can make all those necessary adjustments as you need to. And again, I’ll have that linked in the show notes for you.

By the way, I did have someone reach out to me about the show notes. They were a little bit confused when I said show notes like where that is. So, I want to take the time really quickly and just explain that just in case anyone else has that same question.

The easiest place to find them is on your phone. So, just scroll down to the very bottom of the episode, and you’ll see I have an overview of the episode, like a little summary. And underneath that is where I provide all the links. 

So, anytime I mention an activity or a resource, those links will always be in the episode description, which is what we call the show notes. So, that’s one place you can find the show notes.

The second place you can find them is on my website, and that website link is always within the show description. So, you’ll see if you go to the very bottom, it says “To view the show notes with the full transcript head to krejcicreations.com/episode16.” 

They all follow that same pattern, so it’s really easy to find that link. And if you click on that link, it will take you to my website, and you’ll see the same show notes there. But it’ll feel more like a blog post because I’ll include pictures when possible. I have the full transcript on my website. 

You can also listen to the episode on my website. So, there’s just a little bit more that’s included when you visit that link for the show notes rather than just reading it in the show description.

So again, show notes can be found in the episode description on your phone, or they can be found on my website.

Alright, let’s move on to day two where students are solving these problems without modeling. So, they are in the abstract phase of the CPA approach. There were two really good activities I used for this lesson, and the first one is a free online PowerPoint that I found. So, you may know about this, but it is called Leftover Brownies.

This PowerPoint is so effective in helping them realize that you can have the same exact division problem but end up with four different answers because the question changes each time. For example, in one scenario, it wants to know how many brownies are left over. And then in another one, it asks them how many plates they need to hold all of the brownies.

So, even though every single time they’re taking 26 divided by four, they’re gonna end up with a different answer because it all depends on what the question is asking. So, they begin to realize why it is so important to pay attention to the question, and also why the answer statements are so helpful.

So, this is a really good warmup for your day two but it’s not going to be enough for a lesson. So, for my whole group lesson, I again used a PowerPoint, and this is one of my own creations. This is actually, I think, my best seller, and the reason it works so well for your whole group lesson is because there are guided notes that come along with it.

So, that adds a little engagement to this lesson, and it’s a great way for them to take notes and follow right along with the examples that you’re doing.

One of the things I love about this PowerPoint is everything is broken down into four simple steps. Number one, they read the problem. Number two, they do the division. Number three, they interpret the remainder. And number four, they fill in the answer statement.

Now, this is meant to teach on the second day when you’re in your abstract phase. So, the guided notes do not provide a space to model the problem. You can certainly do that separately in their notebook or something like that. But this activity was really training them to just solve it in the abstract way.

The other thing I really like about this PowerPoint is it covers all three ways to interpret the remainder. So, there are two questions for dropping the remainder, two questions for adding one to the quotient, and two where the remainder is the answer.

So, it was the perfect amount for my whole group lesson, and this is part of the same resource that includes the small group activity I talked about at the beginning of the episode. So, this is already linked in the show notes for you.

You’ll notice I’ve also linked an additional practice worksheet. This is free. It’s in my TPT store. I think the more practice they can get with interpreting remainders, the better.

Now I do want to share something with you. When I was preparing for this episode, I was going through my old lesson plans, and I saw these notes that I had written to myself. I did that a lot, so I wasn’t surprised to see that I had written notes.

But I thought it would be helpful to share this with you, and I was not aware that I would be leaving that year. So, I wrote these notes for me to consider for the next year.

I was just kind of thinking like, is this too much too soon? Would it be better to save this for the end of the division unit? You know, get them comfortable with division and with remainders, and then throw in the ways to interpret them.

I mean, for us, it was like the second lesson in the division chapter. So, they were first learning, you know, what is a remainder and how do we model them? And then all of a sudden having to decide how to interpret them. So, I just kind of felt like maybe this would be better to save for the end of the unit. So, it’s just some food for thought, something to consider.

Well, we have certainly covered a lot when it comes to interpreting remainders in these last two episodes. So, I want to do a quick recap of how to use the CPA approach to teach interpreting remainders.

In the concrete stage of the CPA approach, you’re going to use manipulatives to act out and model the problems, and I suggested using dried pinto beans and sticky notes to model the problems.

Then you move to the pictorial phase, and this is where you’re going to draw a picture to represent the problem. This can be just simple circles and dots to represent how many groups you have and how many are in each group.

And then all of that prepares them for the abstract phase where they just simply write an equation to solve, and don’t forget to have them write their answer statement, because that’s going to be a great way for them to check their answer and make sure they interpreted it in the correct way.

Alright, so that’s going to take us to today’s teaching tip of the week.

This one is a really fun tip to encourage your students to get things done in a timely manner. Maybe it’s cutting and gluing something down in their notebook. Or maybe it’s when you need them to count out a certain amount of something that you’re going to use in your lesson. Some students are going to do this quickly, and they’re going to start right away. But then others might need a little motivation to get started. So, that’s where my idea comes in.

What you’re going to do is you’re going to play a song, and this could be like a quick two-minute song, whatever time you need them to complete the task in. Play the song and give them the challenge of finishing before the song is over.

Now, ideally, you’ll want to pick a song that is fast and upbeat because that’s going to naturally make them want to work faster. And if they finish before the song is over, you can give them a little reward. Maybe it’s a PBIS point or a BINGO card that you pull, whatever reward system you use in your classroom will work fine.

Now, if you’re thinking, gosh, I’m not sure what songs are upbeat and school-appropriate. I’ve got you covered because I have the link to my Spotify playlist in the show notes. And these are all the songs that I used for these challenges. Some of them are like 45 seconds, some of them are two to three minutes.

I often did these challenges at the beginning when we were getting materials out or putting things in our notebooks. I also did them at the end when we were cleaning up, and it was kind of a fun way to end the class as well.

Another option instead of a song is you can just put a timer up. I think sometimes that countdown timer is just as motivating as a song. So, you can give them a two-minute challenge or a three-minute challenge. And again, if they finish the task before the time runs out, they get a simple reward.

All right, that is all for today’s episode. Have a great week, and I will see you next Tuesday.