Episode 23: Math Lesson with Ms. Stoddard

January 19th, 2024 /
Shauna Sprunger /

Sup with the Sup

00:00 / 26:05

Welcome everyone to the next episode of Provo City School District’s What’s Up With The Sup podcast. I am Superintendent Wendy Dau. This week we have another episode where we crashed a class at Edgemont Elementary School. We visited Jeneal Stoddard’s fourth grade classroom and participated in a math lesson about fractions. Ms. Stoddard’s lesson was outstanding and her students were amazing. But before we listen to that episode, here are our updates.

The next school board meeting will be a study session and business meeting on Tuesday, January 23rd. Study sessions are held in boardroom one at the district office and business meetings take place in the professional development center. Both meetings are open to the public and public comment is welcome at the business meeting. The study session will begin at 5:00 p.m. and the business meeting will begin at 6:30 p.m.
We want to make you aware that we are seeking feedback on the priorities for our strategic plan. An email will be coming out shortly to all families in Provo City School District, asking you to rank and rate what priorities that we need to focus on as we move forward with this three to five year plan. So please check for that survey in your email box. We will also provide links on our social media accounts.
This next update is specific to our families that live in the Dixon neighborhood. We would like to get your feedback on what you would like to see at the Dixon Middle School site, since our school is going to be moving over to Shoreline next fall. We have scheduled two meetings to meet exclusively with our Dixon neighborhood. The first meeting will be held on January 25th at 6:00 p.m. at Timpanogos Elementary, and we will have Spanish language available. We will also host a meeting on January 31st at 6:00 p.m. at Dixon Middle School in the auditorium. We would love to have a discussion and receive feedback about what that neighborhood would like to see prioritized on that site. I hope to see you there.
Parent teacher conferences are coming up in February. Elementary schools will be February 7th through 9th. High schools will be on
February 15th and middle schools will be on February 20th. Please look for more information to come directly from your school.
Independence High School will be hosting a community job fair on Thursday, January 25th from 4 to 6 p.m. This fair is for teens and adults. In collaboration with the Utah Division of Child and Family Services, the fair will include job listings, resume assistance, and interview coaching.
Look for the weekly video cast from me every Friday. In the short video, I provide important information and updates about work happening throughout the district and more specifically about inclement weather protocols.

Today I visited Ms. Stoddard’s fourth grade class for their lesson on benchmark fractions. It’s a math lesson using multiple strategies for students to learn how to compare fractions. They learned as a class, in groups, and then on their own. The lesson involved drawing on whiteboards, playing with toys, looking at visuals, and challenging students with the game, ending with a three or four question worksheet to check for understanding. As you’ll hear, Ms. Stoddard made sure every student could participate by adjusting how they learned and the products they worked on. Throughout the lesson, students had to think about their thinking and articulate their thinking, explain those thought processes so that she could determine what they understood and what they were still confused about.

It was fascinating to hear students share how they personally face problems. I think you’ll see what I mean throughout this episode.

First off, kids read their learning targets for the day, which are specific goals students aim to achieve in their math lessons. In our classroom visit, the kids tackled two math learning targets, writing equivalent fractions for one half and comparing fractions using a benchmark fractions, which also happened to be one half.

Ms. Stoddard used plastic manipulatives to compare equal fractions with different denominators. This approach made the concept more tangible for our young learners. Students then began making observations together as a class. To encourage sharing and deeper understanding, Ms. Stoddard asked each student to pair up with a classmate to share their thoughts and explore fractions together.

They were then encouraged to express their observations. Whether it was noticing even denominators or recognizing the consistent halving of numbers. Ms. Stoddard posed simple questions, encouraging students to find other halves with different denominators. Now let’s listen in.

Ms. Stoddard: Now, I’m going to stop here for a minute. I want you to look at the numbers we’ve got so far. We have 1/2, 2/4, 3/6, and 4/8. Do you see any patterns there? I love the fact that you’re raising your hands. Let’s see. Ramona, go ahead.

Student: It’s all half of the circle. Like, two fourths is half of the circle.

Ms. Stoddard: They are half of the circle. Who wants to add something a little more? Paxton. What do you, what pattern do you notice?

Studnet: On the top you keep adding one, and on the bottom you keep adding two.

Ms. Stoddard: Oh, interesting. We’re counting by one on the top, we’re counting by two on the bottom. Great. What else? Fox.

Student: Um, so it could go two ways. There’s like songs basically, and you could use them for multiplication in some way.

Ms. Stoddard: Oh, you’re noticing, uh, skip counting like you do for multiplication. 2, 4, 6, 8. I like it.

StudentL Doesn’t order, it goes 1 and then 2. Doesn’t go like 1 then 5.

Ms. Stoddard: Oh, interesting. Okay, Emmeline, you wanted to add something?

Student: Um, it also seems like, like 1 plus 1 equals 2, 2 plus 2 equals 4, 3 plus 3 equals 6, 4 plus 4 equals 8.

Ms. Stoddard: Ooh, now that’s interesting. You want to keep going with it, Micah.

Student: So the, the, the bottom number is even, and even numbers you can always split into, you can always cut in half.

Ms. Stoddard: Ooh, that is interesting. So, these are all even numbers. Do you guys remember when we were drawing the fractions and the circles? Which ones were the easiest ones to draw?

Student: The even ones.

Ms. Stoddard: Yeah, because of exactly what you said, you could cut them in half. Okay, I’m going to ask you another question. And you do see the pattern like this. What if I have this number? Boy, we took a big jump from here to 20. What do you notice? Any pattern with the numerator and denominator?

Student: Half. So half of 40 is 20. So that’s basically like saying one half.

Ms. Stoddard: Is that two of these other ones too?

Student: Uh huh.

Ms. Stoddard: Is two half of four?

Student: Yeah, they’re all, they’re all basically saying like a half of it. They’re all saying half of something.

Ms. Stoddard: Oh, is that what you were gonna say? Rider? I noticed you had your hand up.

Studnet: Yes.

Ms. Stoddard: Okay. Good. Hands down for now. Good thinking. Well, you know what, let’s practice something. Get your whiteboards and your markers ready. I’m gonna put one half up here. Now, I’m going to remind you what, it was Stone that said it. He noticed that in all the fractions that were equivalent to 1/2 that had equal value, if you draw them, they would take up the same amount of space. The numerator was half the denominator. If that’s true, how many twelfths would be equivalent to 1/2? Are you ready to tell me why? You know we like to talk about why. Okay, on three. We’re holding them up. Ready? One, two, three. Show me. Oh, I see so many six twelfths. Why is six twelfths equivalent to one half? Allie, what did you put six?

Student: Half of twelve is six.

Wendy: Now that students had practiced recognizing the one half benchmark fraction, it was time to tackle comparisons. Students of various fraction scenarios. Then, to gauge their understanding, the students used a fun thumbs up and thumbs down approach to agree or disagree with answers. These little moments became critical checkpoints to ensure everyone was on the same page.

Ms. Stoddard: Yeah. Ready for a step a little harder? Okay. Of course you are. Thumbs up. Rider, what if one of the fractions I write is not one half? What if neither one of them is one half? Can you still use one half?

Student: Yeah

Ms. Stoddard: Okay. Let’s try it. Now, of course we could draw. That would take us a while, but can you use what you’ve already figured out about one half to do this? Can you compare each one to one half? Alright, if you’re ready, you can hold them up. Okay, all the ones I see held up are like that. Who’s brave enough to tell me why? I see some of you did a little quick draw, which is not a bad thing. That’s good to know. Go ahead, Adrian. I love that you’re, you guys are brave at sharing.

Student: Well, since five, five, well, five is half of ten. Six is more

Ms. Stoddard: So how many tenths would be a half?

Studnet: Uh, wait, five tenths would be

Ms. Stoddard: five tenths would be exactly half. Okay.

Studnet: And six is more than half, but it would take four eighths to have a half of an eighth. So, therefore, six tenths is bigger than three eighths, because it takes, it, well, 6 tenths is more than a half, and 3 eighths is less than a half.

Ms. Stoddard: Okay. Agree or disagree on that, class? Tell me. Is there anybody who thinks you can say that again in a different way? Kind of show me that you understood what he just said. Give it a try, um, Rider. Can you just say that again?

Student: So he was saying how 6 tenths is 1 over the halfway mark. Okay. And 3 eighths is one under it.

Ms. Stoddard: Okay, so if we think, look at the denominator, and if we’re talking about eighths, half of that is four, so four eighths would be our, our um, checkpoint, and with tenths, its five tenths.

Wendy: After revisiting their learning targets, each student took on a real world problem straight from their workbooks on their own.

Ms. Stoddard: Alright, in your math books, there is a problem that’s similar to this. I want you to open to 271. Now, there’s that benchmark. Read it with me. I can- Ready? Go.

Whole Class: I can use benchmarks to compare two fractions and record the comparisons with the symbols greater than or less than. Abbott and Rowan go to the climb-a-thon. They both climb ropes that are the same length. Who climbs higher than halfway up the rope?

Ms. Stoddard: So, we know that this is, I’m just going to put A for Abbott. And let’s put R for Rowan right here. Got it. Let’s look at Rowan’s. Where would four tenths be on this rope? You’re not counting the bottom one. Where would it be, Cadence? Yeah, four. Okay, count with me. One, two, three, four. Everybody just kind of make a bigger dot right on that. So that’s Rowan. Now let’s do Abbott. Five eighths. I’m going to count up how many Cadence

Student: Five.

Ms. Stoddard: You’ve got it. Let’s go. One, two, three, four, five. So, where’s the halfway point in all of these? Three Okay, so this is the halfway mark. Let’s go back to our question. Who climbs higher than halfway up the rope? Is it Abbott or Rowan? On the count of three, you’re going to say it. Ready? One, two, three.

Whole Class: Abbott

Ms. Stoddard: You got it.

Wendy: To wrap up the session, the students engaged in a fun game, taking turns comparing fractions and explaining their reasoning. This game reinforced the lesson content and added an element of excitement by turning it into a paired activity.

Ms. Stoddard: Now, you’re going to play a little game here. Alright, this is called Partner Sort, and we’re going to come try and decide if a fraction is greater than one half, equal to one half, or less than a half. Okay? We’re just going to work together. And let’s look at the first fraction. Five tenths. Where should I put that? Am I going to put it in greater than half, equal to one half, or less than a half? What do you think, Ramona?

Student: Equal to. Ms. Stoddard: Okay, put it in the middle. Good job. Now it’s my turn, but I’m going to need some help from the class. Two eighths. Do I put it on greater than a half, equal to a half, or less than a half? Where would you put it on, Akilah? Class, agree or disagree? Up or down? Yeah. Would you put that in for me? How many understand how to play the game? Alright, it’s, it’s not like a game where somebody wins or loses, but um, you’re just going to practice these. You’re allowed to help your partner, but don’t say an answer first. Let them think, and if you need to, you can give them a hint.

Wendy: Finally, as a concluding assessment, the students independently completed an exit ticket, featuring three to four questions, which allowed them to showcase their newfound knowledge and skills. After they completed the worksheet, I was able to speak with Ms. Stoddard and her students about the lesson.

Wendy: So tell us a little bit about the math lesson that you did today. I noticed it was about fractions. And so how what are the standards that are tied to that? And how does this fit into the whole scheme of what they’re learning about fractions and in math?

Ms. Stoddard: They need to be able to compare fractions and not just a one half, but, um, to, you know, two thirds and four fifths. But they do need to have some strategies. And one of the standards is to use benchmark fractions. Um, the most common being one half, also one whole one fourth. Um, so. After we’ve done the one fourth, then we’ll probably use a different one, like a one fourth. And then use that to build on the next place we’re going is probably, what if it’s an odd number?

Wendy: Yes, that would be an odd number.

Ms. Stoddard: We’ll deal with that tomorrow. Okay. Because this is pretty easy. Once we understand half, then we get that. But I wanted them to have that really solid in their minds before they start doing something a little trickier, like thirds.

Wendy: Yes, that’s going to be a little bit harder. I also noticed you use lots of different ways to teach the concepts. So talk a little bit about that because you had some manipulatives of visuals using your document camera. You had them do a game. How are each of those kind of building and, and helping that process? Like what does that, what does your mind go through as you lesson plan that and figure that out as to what will help the students to the greatest degree?

Ms. Stoddard: Yeah, well, um, drawing is, we usually start with drawing, and that’s something that everybody can easily do, even before they have, um, those benchmarks in their mind. So we, we, on a different day last week, we spent a lot of time just drawing them, comparing by drawing. And then, um, with the little fraction pieces, when we draw them, we typically use rectangles, but with the fraction, uh, the circle, they can see what is a hole, or is a rectangle on.

If I’m using manipulatives, it’s harder to see what a hole is. So that’s why I use the circle. And, um, they can easily see what the half is. And then, plus it gives them lots of chances to just kind of think about it. Um, and grapple with that. And then, um, the whiteboards let me know who’s got it. Who doesn’t immediately. Um, and sometimes I’ll do what’s called a Fist of Four where they rate themselves how well they know it or don’t know it. We didn’t do that this time. And then the game is usually, we do that quite often. I wouldn’t say every lesson, but um, probably at least once a week. It just solidifies it. It’s much more interesting to do sorting, comparing to a half in a game and getting able to talk with someone than if you just have a worksheet.

Wendy: Yes.

Ms. Stoddard: Also, I, our math book has some good things but sometimes, um, they’re not quite ready to jump into that.

Wendy: Right.

Ms. Stoddard: So we scaffold it a little bit first and then they’re ready to do more in their book

Wendy: And do that more independently. So they’re kind of working as partners first,

Ms. Stoddard: Right.

Wendy: To kind of help each other. And when they’re, when they’re going through this process, I noticed you, you did a really good job of asking them to explain their thinking. So tell me what you’re thinking. And then you asked, give me another way to say that. Um, I thought that was really good so that students could see it from lots of different perspectives and how to analyze that. So,

Ms. Stoddard: Yeah, it’s good for them to hear. There’s more than one way to think about this thing. Like, somebody was skip counting.

Wendy: Right, yes.

Ms. Stoddard: And somebody else was trying to compare it to a whole. And, and you can see where they’re misguided too. When they’re, um, so we’re not just going to call on somebody that I’m pretty sure is going to have the right answer because I need to know what misconceptions they have and so I can, we can fix that.

Wendy: Well, and as you’re asking them those questions and you’re checking for that understanding, so then you can go back and correct those misconceptions,

Ms. Stoddard: Right. Exactly.

Wendy: Which is incredible.

Ms. Stoddard: So yeah. And then just the little exit card, just like four problems. So that’s where I can see individually. We’ve done work as a group, we’ve done work with partners and now I need to know who has it more than the whiteboards, ye, gives me an idea, but you know,

Wendy: We can still look at somebody else’s for help or help each other.

Ms. Stoddard: You can help each other. So and then the computer is just I Excel, one more way to practice it so they’ll be working on fractions on their I Excel when they finish and plus I on the back of their exit cards, I love for them to come up with their own problems and then we use them in the morning for daily review.

Wendy: That’s awesome

Ms. Stoddard: When they see their problem up there.

Wendy: Okay, it’s really exciting I bet. Well one of the things I know Just, I have a secondary background and fractions still stump kids when they get into middle school. So this is really important work that you’re doing to help build these skills for our kids.

Ms. Stoddard: Number sense. They have to have it, rather than just memorize a rule.

Wendy: That’s exactly right. So I want to thank you so much for letting us come and crash your class today. This was an awesome lesson and I thoroughly enjoyed it. So thank you.

Ms. Stoddard: Thank you for holding the microphone.

Wendy: You’re welcome.

Ms. Stoddard: I do have a wonderful class.

Wendy: Yeah, they’re awesome. So.

Wendy: So I just want to ask a couple of you some questions. So if you want to volunteer, you’re going to be on a podcast, which means it’s like a radio broadcast and we’re going to have your answers on there. Tell me what helps you the most when you’re trying to learn something like with fractions and math. What are the things that you love that like help you really understand it? And tell us your name first cause I want your name too.

Student: Well, my name is Abraham. What really helps me is like knowing what kind of like fraction it is before I do like the problem like if it’s a half or like a whole or less than or greater greater than and then I can compare the other one with the one that I reviewed.

Wendy: So, like, that benchmark fraction is really helpful as you’re creating those comparisons. That’s awesome. Okay, tell me your name.

Student: Ryder, and one thing about, uh, that helps me doing math problems sometimes are, like, little shortcuts that you can do with them.

Wendy: Yeah, you always want to have those shortcuts, right? So that you can get through it fast. Okay, I’m coming over here. Here we go.

Student: Um, my, my name is Calder. I like to, what helps me is breaking it down. And knowing what’s possible with it and what I can do.

Wendy: So when they take it and break it down into different steps, right? Oh, I love that. Okay, tell us your name.

Student: My name is Laken, and for me, it makes, um, fractions easier when I draw things and figure it out.

Wendy: Good, so you’ve learned some different strategies to help you. Okay, two more people.

Student: Oh, my name is Fox and, uh, one of them is these multiplication songs. One of them goes 6, 12, 18, 24, 30, 36, and 42, 48, and 54, 50, 56, 7, wait.

Wendy: You got it. Yeah.

Student: Another strategy is the standard algorithm. It’s just a little bit more easier to find out math. No, it’s just easier to answer math questions.

Wendy: For two digits, you have a standard algorithm. That was, that’s a lot of words. That’s a big word. That’s impressive. What’s your name?

Student: Um, I’m Emmeline, and I like reading the instructions. And like, Not just a quick read, you have to really, uh, focus on the instructions to make sure you know what to do.

Wendy: So then that helps you so that you’re making sure you’re getting the right answer, right? Does it help you guys when you’re working when you’re able to talk with your partner and kind of work through stuff? Like how does that help you? And tell me your name.

Student: My name is Stone and um, it helps because sometimes your partner can have different ideas so like you can discuss ideas and then he can and then like if you still don’t understand you could probably read it through a couple of times like read the problem and then usually it will come out and you, and you guys will find the right answer.

Wendy: Good, so by helping each other kind of explain it, that super helps.

Student: Uh, so, I think it’s really nice when, it’s kind of harder to find your own mistake in your problem, and a partner can find it much more easily. So, like, if you made a mistake and you don’t think so, the partner can point that out and it’s really helpful when you’re trying to solve complicated math problems.

Wendy: Well, and that’s awesome that you guys feel okay about helping each other. You see that as a help, right? Rather than they’re trying to find your mistake, right? Okay, so I’ve got a couple more comments and then we’re going to let you get back to your lesson today. Okay, tell me your name.

Student: My name is Micah. And, um, my partner, when we do partners, they always help, um, with, uh, telling you how you need to do it and what your mistakes were and what to fix.

Wendy: Good. So they kind of help you with that. This is how I did it. And this is where you kind of went wrong. Sometimes they can see something you can’t. Okay. Calder.

Student: Um, you both can. They can help you with a bunch of stuff, and you can see what their answer is, and you can, and they can see what your answer is, and you can see their answer, and that can help you go through the questions more easy.

Wendy: Awesome. Just thank you so much you guys for letting me come and crash your class today. You guys had an awesome math lesson and you guys are getting so smart at fractions. I’m so impressed.

Thank you for joining me for this episode of What’s Up with the Sup? As always, all episodes will be posted on the district website, YouTube, and anywhere you get your podcasts. If you have any topics or questions you would like us to discuss on the podcast, please email us at podcast @provo.edu.

We hope you enjoyed this episode where we were able to see the real life learning that takes place in our classrooms and how incredible our students and teachers are across our district. Please join us next week for an all new episode of What’s Up with the Sup. Until then, have a great week, everyone.