Leprechaun Traps: Addition Within 100
Teacher: jeannie Wright

Jeanne (in interview): My name is Jeanne Wright. Come with my as my first graders find the mathematical reasoning of Leprechaun traps.

Teacher (in class): So we're gonna go ahead and we're gonna start with math. Now listen up, cause yesterday was the 125th day of school. Well, I guess...

Teacher (in interview): Today's lesson was our typical math routine. The kids come to the carpet. There are a couple of things that we've done since the beginning of the year. They guess my number, mental math, some strategies with ten frames and double ten frames. So it was sort of a review.

Teacher (in class): What's our mystery number today?

Student: 33

Teacher (in class): And what's one more?

Student: 34

Teacher (in class): And what's one less?

Student: 32

Teacher (in class): Man! I was trying to trick him. Cause I asked him in a different order this time. How many until my next friendly number?

Student: 7

Teacher (in class): How did you know that so fast?

Student: 3 and 7 is 10

Teacher (in class): 3 and 7 is 10! Do you? Now wait a second... what's my next friendly number gonna be?

Student: 40

Teacher (in class): How did you know that?

Student: It goes: 3, 4.

Teacher (in class): Ohh. So if you were using that with 10s, it would go 30, and then...

Studen: 40

Teacher (in class): Look at you, lookin at the patterns. Good job!

Teacher (in interview): There are just certain benchmarks: the friendly numbers the decade numbers. They're supposed to be able to get to those cause then they're able to do mental math quicker.

Teacher (in class): All right, well let's see if you can do that one. Austin.

Student: 31

Teacher (in class): 31! How'd you get 31?

Student: Because I took away 5 from the 6 and then I had 30 then I just had 1 left and then I made 31.

Teacher (in class): Ok, so let me get this straight. You told me that you took the 5 from the 6, and what does that do?

Student: It makes 30.

Teacher (in class): It makes 30 cause you've added it to that 25, and then how many do you have left over from that 6 then?

Student: 1

Teacher (in class): And then when you add that 30 and that 1, you get?

Student: 31

Teacher (in class): Excellent.

Teacher (in interview): It is definitely good news when the kids see patterns because they pick up on things that I wouldn't necessarily see.

Student: I heard Demetrius say that's 30 and then 24 plus 1 is 25 and then you add 1 more from the 24 and then that's gonna be one more from the 30.

Teacher (in class): That's right! High five, girl. Let me tell you something, I didn't even notice that. When I made those problems, I didn't even notice that. And here you see these patterns on these numbers. You are amazing.

Teacher (in interview): I had 26 plus 4. But then the kid said 26 plus 5, we had already solved 26 plus 5 and that's 1 more so that's how I saw it. And I thought, "oh my goodness, I didn't even see that!" Because I'm so into to trying to get them to use their strategies - they notice the patterns.

Teacher (in class): How would you solve that one? Ms. Gianna, how did you do it?

Student: I know that 6 and 4 make 10. And if you add 6 more it would make 16.

Teacher (in interview): Oh my goodness. It's very thoughtful. The addition problems I used were a review and they're also looking to where we're going.

Teacher (in class): I am moving to a part-part-whole here. What's my whole thing? Ok. Mr. Pierce, what's my whole thing?

Student: 12

Teacher (in class): 12 is my whole thing. What do you see?

Student: A 6.

Teacher (in class): I see a 6. Now think about that. 6 and what - cause I have my hand on it, I'm covering it up - 6 and what give me that 12?

Student: 6.

Teacher (in class): How did you know that?

Student: Cause 6 plus 6 equals 12.

Teacher (in interview): It's really one of the most difficult things for first graders to understand it the missing add-in. It's algebra.

Teacher (in class): And how do we know that 6 and 6 make 12? Justin?

Student: Because you have to take away 1 from the 5 and then take away another 1 from the 5 and then you have 2.

Teacher (in class): Ok. So, let me get this straight. You're saying take 1 away to make this...

Student: 5

Teacher (in class): 5. And then you're saying add another 5, and that would give you what? 5 and 5 make...

Student: 10

Teacher (in class): And then you're saying add 2 more?

Student: 12

Teacher (in interview): These kids are able to see that you're solving for what's missing. So they'll be the kids that see that 5 and the 1. They'll be the kids who see 2, 2, 2 and then 2 more. It's just how they see the dots.

Teacher (in class): All right, so, I have a situational story for you. I need your help to solve a problem. All right? Can I count on you? All right. Our family Leprechaun projects are due. In first grade, we try to be very creative. The month of March, their family homework project was to come up with a Leprechaun trap. Who doesn't want to catch a Leprechaun and come up with a pot of gold? But I can't shove 'em all into a room, I need them in containers. So, It thought the kids could come up with, "how many containers would I have to go to Target to buy to house the 30 Leprechaun traps? Now each container has to have the same number of traps. So, how many containers should I buy at Target? I want you to find 2 different ways.

Teacher (in interview): This lesson was not about division. This lesson was about addition. What are the different number combinations of 30 that would make them in different groups? So, the kids who see 3 groups of 10, the kids who see 6 groups of 5, everybody could see 30, but everybody saw it a different way.

Teacher (in class): How do you have 3 tens?

Student: You have 10 and 10. It equals 20. If you have 10 and 10 it equals 20. And then 10 more equals 30.

Teacher (in class): Ok. Now think about this: how many containers would that be?

Student: That would be 3 containers.

Teacher (in class): Ok, so if I had 3 containers and you're saying...

Student: 10 in 1, and then 10 in another, and then another 10 in another.

Teacher (in class): Ok, so that's one way. Can we think of another way?

Student: I was thinking of something... you count by twos. 2, 4, 6...

Teacher (in interview): The number 30 was chosen because there are so many different ways to be able to make the number. We didn't make the number with just one solution. I want them to explore. I want them to see that there's more than 1 way.

Student: I counted by twos because at first I was doing them in groups of 6 or something but then I said I don't think we have enough cubes for that so I don't know how it could do 5 but maybe we could try doing twos, so I did 2, 4, 6, 8...

Teacher (in interview): It's definitely all about mathematical reasoning. With Common Core, they just need to be immersed in it. But now they're really using it as a strategy. And I'm hearing what strategies and it's not just, "I'm counting in my head." They can mathematically reason how they get to answers.

Teacher (in class): There's another way. Juliana?

Student: It's like on a dice.

Teacher (in interview): It's like on a dice. So I know that there are 5. So we have 5, 10, 15... when I was a youngster, we used to play games that had dice in them. So, you just knew what 5 looked like. Subatizing. Like, they don't have to count each dot to know that it's 5, they can just know the formation. They know it's 5 so they know the next number would be 6. It's just looking at numbers - the patterns that they see in them.

Teacher (in class): Ok, so she had these like this and then what did she do? She had 6 in one and then 4 in the other.

Teacher (in interview): We ran into a problem where she had broken the 10 into a 6 and a 4. But without any prompting, she could see that the groups then weren't the same and she was able to move them around so that they were.

Teacher (in class): And why do you think she did that? What was so important about this lesson and about doing that? Garbriella?

Student: It had to be the same amount. But she had that one the biggest, but she could have took one off that one...

Teacher (in interview): She discovered that 6 groups of 5 would still use the 30 traps.

Teacher (in class): So, what did you do?

Student: I put 2 threes in the basket so you would only need 5.

Teacher (in class): So, Jeanne-Marie is over there with Alexa and remember I told you she had 10 piles of 3? So what did you just say? You thought that you would take 2 piles of 3...

Student: And put them in one basket.

Teacher (in class): And put them in one basket, so she did 6, look at this...

Teacher (in interview): She was the only one that had groups of 6. So when I asked her about it, she said, "well, I was working with the group and they had groups of 3 and I just put 2 groups of 3 together and I thought, "oh, my goodness! I would have never known that had I not asked her what it was she was doing."

Teacher (in class): You know what? If I'm thinking about which ones I'm gonna buy, am I gonna buy 10 containers? Am I gonna buy 3 containers? Am I gonna buy 15 containers? What do you think my best choice would be? Then you're gonna tell me why.

Student: i think you should buy 3 containers because it's the cheapest way.

Teacher (in interview): She's relating it to money. She's seeing that there is math even beyond our classroom. I just want them to see that there are patterns. And we're gonna take a journey all year long on why do those things work that way.

Student: They're containers and each one must cost the same amount of money. And something plus something plus something makes an even bigger number and I was thinking everyone wants to save money.