Zooming In on Math Puzzles with Dr. Nicki Newton and Ann Elise Record
How to reach Ann Elise:
How to reach Dr. Nicki:
Resources Mentioned in the Episode:
More Magic Triangles
Diamond Addition and Subtraction Puzzles
Transcript:
Melissa Milner 0:09
Welcome to The Teacher As... podcast. I'm your host Melissa Milner, a teacher who is painfully curious and very easily inspired. This podcast is ever changing. And I hope with each season, you find episodes that speak to you in your work as an educator. This is the fifth season of The Teacher As, and it's exciting to see the growth in how many educators are listening. Episodes are released every other week. If you enjoy The Teacher As... please rate it on Apple podcasts and leave a review. It helps the podcast reach more educators. Thanks for listening.
Welcome to The Teacher As... podcast again. And I hope this goes on for years to come. Dr. Nicki Newton and Ann Elise Record, they're back again, they're going to be talking about math puzzles. So welcome.
Ann Elise Record 0:56
Thank you so much for having us again. Thrilled to be here.
Dr. Nicki Newton 0:59
Thank you.
Melissa Milner 1:00
So the benefit of math puzzles, and I'm going to start off with Dr. Nicki, why are math puzzles so important? And I know you have a book coming out. So talk to us about that as well.
Yes, I have been doing a lot of work on math puzzles lately. I think math puzzles are really important. I'm gonna give you a handout. So you can give to people in terms of why they're important. They develop critical thinking. They help kids who work on their math skills, they grow persistence and patience, they build confidence because you get small wins. Just think of the excitement when you finally figure out, Oh, that was that piece. Now I know something. And they have engagement and motivation. Because kids want to play puzzles. They're...You don't have to convince them like this will be fun they want to and they like to do it together. It's teamwork and collaboration. And when you're looking at different kinds of puzzles, and math puzzles, and the logic puzzles, there's creativity involved, because oftentimes in the math puzzles, it's more than one way. It's not just one answer. So there's lots of reasons people should use puzzles. I would say the biggest one is that all of these skill sets prepare kids to live in a future that we don't even know what it looks like that kids are going to have so many jobs before the 35 and jobs that exist today.
Amazing. So you're gonna be listing you and Ann Elise, I think you said the top 11.
Ann Elise Record 2:34
You know, we'll come up with at the moment we have 11. But there could even be some more.
Melissa Milner 2:41
All right, so Anne Elise, I think you said you wanted to start.
Ann Elise Record 2:44
Yeah, so I want to begin with one of my favorite kind of puzzles is called Magic Squares. And so in the magic square, these can go from like four boxes all the way up to many, many boxes. But the vertical and the horizontal and diagonals will add up to the same number. So there's a sum of the numbers in the Magic Square and you got to figure out where the missing numbers are. So they give you some numbers, and then you're figuring out the missing ones. In fact, my good friend, Susan Looney wrote a book called Yang and the Magic Turtle. She wrote like a fairy tale, based on this magic turtle that the turtle that has this design on its back, and Yang has to solve the mystery of it. But I love them, they go from just like single digit math facts, up to algebraic stuff like it is incredibly much they can go up to. So it's a really fabulous way of exploring that flexibility that we're trying to build with the students are thinking you're adding numbers. But of course, it's embedding all within that that like Fact Fluency practice as you're trying to build.
So after students have built the understandings of number of relationships, so let's say fluency within 20, that we can be using doubles to help us if we don't know it yet, or I get a bridging a 10, to make a 10. We want to then be able to help work on the automaticity piece to help them you know, get into their long term memory what these facts are, so they can retrieve it from their memory by playing it and it's fun and engaging ways that are making them think and gain that purposeful practice all the time is really a phenomenal way of doing it. So I do I love the the Magic squares.
Melissa Milner 4:26
Yeah. Would you have this as a center? Or would it be everybody's doing it all at once? In the whole class? What do you recommend?
Ann Elise Record 4:33
Well, I think there's whatever is working best for the teacher, right? So certainly having a station in the classroom that is puzzles, or it can be an option in the fluency center. So you have a workstation, that is fluency. We want to find options and choices for the kids to help build their agency that they're the ones making some choices for themselves. So you might have some of these puzzles along with other choices. That when they're getting that fluency practice they choose what they want to do, usually you can have like nine, nine squares or three by three. And then you then you can give them what the total is for each row and column. And you have like one row that has two out of the three numbers filled in, so they can begin there. And then they can be using that to then be fill it figuring out all the rest of the ones that are there. So once you can do that, and you feel comfortable, the kids understand what the process is for these, then it can become differentiated to the kids as well in terms of how many squares are within the square that you're doing, what numbers are they they can become multi digit numbers, I mean, they can be there's no limit it can be fractions, decimals. Want it to be, but the the format of it is that every row and column and diagonal will have the same sum.
Melissa Milner 5:46
So either with each puzzle or at the end, will you tell us where we can get these types of puzzles and the resources?
Ann Elise Record 5:53
Yes, and I'll be I'll send you an email that has links to examples of what these are.
Melissa Milner 5:57
Perfect.
Ann Elise Record 5:58
It's hard to visualize these persons. So we're going to try to describe them as best as we can. But certainly, we'll send you links to the images of what it looks like so people can get an idea.
Dr. Nicki Newton 6:08
And with Magic Squares, one of the things, you start with the whole boxes filled in all the boxes, and you just tell the kids, what's the sum. Then you go to where there's missing boxes.
Melissa Milner 6:22
Okay.
Dr. Nicki Newton 6:23
You tell the kids Oh, the sum is... and then they have to figure out what's missing.
Melissa Milner 6:29
That makes sense.
Dr. Nicki Newton 6:30
You know, when you get to second and third grade, you do the multi digit numbers. When you get to fourth grade, you do fractions with like denominators, and say the sum is three or four or whatever. But they're fractions with like denominators, then you might do fractions with unlike denominators in fifth, and then you start working with integers in seventh. So there's, you know, there's some really, I love Magic Squares as well and I love Susan loonies book I wrote some for it, I've either the forward or the back. And there's also a book called Benjamin Franklin and the Magic Squares, which is like a kid reader. And it's a math myth about Benjamin Franklin and how he came up with Magic Squares. There's also a Magic Square Maker. So you can it's called Magic Square Generator. So you can go on and then you put in the dimensions, I want a four by four or five by five, I want integers I want, you know, whatever you want, and then it'll generate the puzzle.
Melissa Milner 7:33
Oh, that's amazing.
Dr. Nicki Newton 7:34
And but it will, you know, the theory behind Magic Squares. And what we're going to talk about next, which is Magic Triangles. It's all mathematical. So you can teach kids to make Magic Squares.
Ann Elise Record 7:46
That's what I love. Dr. Nikki always says, We want students not to just be consumers, but to be producers, right, so that they're not just doing a puzzle and consuming that, but that they can produce their own once they understand the patterns and how they work. Right. So another opportunity for them in a workstation is like, I want you to make us a Magic Square. And then you can be putting that up in the hallway, what a great way of increasing the climate of
Oh, I love that. So we're moving on to the Magic Triangles.
Dr. Nicki Newton 8:25
Magic Triangles and Magic Triangles. It's similar in that the base one is, it's a triangle. And then there's three circles. There's one at the top, there's one in the middle, and there's like on the sides. There's one at the top, there's one in the middle, there's one at the bottom, and then at the bottom, going across, there's one on the left, there's one on the right, and there's one in the middle, and then on the right side, there's one at the bottom, one in the middle and one at the top. And you give the kids a number 9, 10, 11, 12 and then you say okay, using the numbers one to six, make a sum of nine on all sides. So it's like a twister. It makes them think and it makes them play with the numbers and they don't get it right necessarily. You have to that's the beauty of the puzzle is that you persevere and you it is it is an understanding between the game and the player that I'm not gonna get you, right. Not gonna give up. Right? That's, that is not stated, but it is an understanding. When you enter into blank puzzles.
I always say that puzzles are a portal for perseverance, because kids will persevere when they're doing puzzles. You just start in your thinking like what could make this nine and every everything that you only have six numbers and every position counts and you can't repeat any.
Melissa Milner 9:56
Oh my gosh.
Dr. Nicki Newton 9:57
They're not as hard as they seem.
Melissa Milner 9:59
Okay.
Dr. Nicki Newton 10:00
I'm gonna talk about the electronic version. Because these things are, you know, as ubiquitous as they are. They're almost hidden in plain sight, because they're out there. Like if I say, oh, have you tried Magic Triangle, you can pull up a Magic Triangle. But most people are like, No, I've never heard of a Magic Triangle. So it's like, ubiquitous, but it's hidden in plain sight, right? The same with the Magic Squares.
Ann Elise Record 10:27
Yeah, so the Math Playground hosts a whole bunch of Magic Triangles on their website for free. I love Math Playground. Particularly, I love the Thinking Blocks for story problem solving and modeling the structure. But they have these phenomenal games as well, like these triangle puzzles that are on there that is just naturally engaging, and they get more and more difficult. And, of course, it's always increasing the thinking and reasoning as well, because the circles are in the corners are used both in one direction and another.
Melissa Milner 10:58
Yeah.
Ann Elise Record 10:59
About like, what value needs to be there from using it in this direction. And that direction, like it is such great thinking and reasoning. And I was all day today presenting together with Dr. Nicki in a district today, and she was talking about perseverance. And I loved how she said that perseverance can't be taught. It has to be nurtured and supported in tasks that require the perseverance to do it. I love that mindset. Right, like, build discipline, perseverance, and the kids and puzzles just a great way to do that. Because Exactly, exactly right. You can't go into it expecting to get it right in the first try. You gotta keep trying try different things. And I love Peter Liljedahl's work, Building Thinking Classrooms. He talks about kids being in productive struggle, they're more willing to engage in productive struggle on the heels of success. So if we give them a puzzle, that's, that's too difficult for right, right, that requires productive struggle out of the gate for every kid, they're less likely to want to persevere at it. But if we give them a couple of Magic triangles, let's say that our, I love how he calls tasks mild, medium, and spicy as opposed to like, easy and medium and hard, right? Because it's what you want to be engaging in. But you know, you give one that has most access for most of the kids. And then another one slightly harder, right? And then you can get to one that is that one is going to build a perseverance, but they're more willing to engage in that productive struggle, because they've already been successful.
Melissa Milner 12:30
I just found that with logic puzzles, we've been doing the logic puzzles, where you've got the boxes, and you put X's and you put zeros. You put O's when you find a match, and those literal like grid ones.
Ann Elise Record 12:42
Yeah.
Melissa Milner 12:43
Yeah. And I could not believe the perseverance. And I'm like, I gotta remind them of this, when they're just struggling with regular math work. You know, if this was a puzzle, what would you be thinking right now, you know, they don't think of that work as a puzzle. But have them apply that to just regular math work?
Ann Elise Record 13:02
Exactly.
Dr. Nicki Newton 13:03
Absolutely.
Ann Elise Record 13:04
Next, we like to mention about Solve Me puzzles, Solve Me mobiles. So it's a website that has a balance hanging, and it will give you the total value of that balance. And it has shapes hanging, some on the left, some on the right, and there are different shapes, and then some of them are multiple of the same shape, which means they have the same value, so you got to figure out what must the values be of the shapes that are hanging from the mobile, in order for it to balance, but also have the total sum that's at the top. So again, they begin really easy with low numbers, and then they become bigger numbers, and then multiple shapes on either side. And sometimes they give you like the value of one of the shapes. So if a circle equals a two, you might see there are four circles on the left hand side, and the right hand side, maybe there's one shape like a triangle, as you're going to think about what what must that triangle be worth if each circle is worth two, those kinds of right, giving you a value of one of the shapes, which of course is building algebraic reasoning. We have these unknowns, but they're as shapes right now. They're not like a variable yet.
Melissa Milner 14:19
And also understanding that equal what that even means.
Ann Elise Record 14:22
That's it, right? That the equal sign relational symbol, it does not mean an action, I must do some math symbol, the value on the left is the same as the value on the right. Too often our kids have not seen answers being on the left hand side of the equal signs, right? You can't do that. They don't think you can do that. So let's say five plus five equals something plus two. They want to put a 10 in that something place because they're seeing five plus five equals Oh, do some math 10 and not attending to that plus two that's there also, right right. visual image of the balance is really a powerful image for their brain as well.
Dr. Nicki Newton 15:04
And the balance tilts. So if you get it correct, it stays balanced.
Melissa Milner 15:09
Yeah.
Dr. Nicki Newton 15:10
If you get it wrong it tilts. So it gives the kids instant feedback. And there's a website that talks in depth about that. But also on solving the puzzles, kids can build their own.
By the way, just so you know, the build your own, I guess I had that subliminally from you. Because I have kids now, creating their own logic puzzles, which is not an easy thing to do.
Ann Elise Record 15:34
No, that's not that's awesome.
Melissa Milner 15:35
They're coming up... Because they've done so many of them. They're like, Okay, we're gonna put this clue down here. No, we're gonna put this clue up here, so that people skip it, and then they might forget to go back. And that makes it hard. You know, they're like, coming up with all these ideas. We used to do the balance stuff a lot when I was teaching third grade, it really is amazing how that helps them understand just that equal sign.
Dr. Nicki Newton 16:01
There's a game that I just thought of, as we were thinking about solving puzzles. It's called Algebraic Reasoning at the Sweet Shop. And it's also Math Playground. And so what they do is you go, there's all these different shelves, and shelves one through four. And if you go into, you go in, and you pick some candy off one of the shelves, so say, and then it'll show you like, oh, there are four hearts on one side, and it says, these arts are worth 16 cents. And then on the other side, there's some hearts. And there's also some blue and red swirlies. And then it'll and they say and these are worth 46 cents. It's really a systems of equations problem. But I always teach it in fourth and fifth grade, the kids love it. Because it what I love about this puzzle is it teaches kids to think logically, if i Where are we going to start, we are going to start on the side with 16. Because we know that they're 16 hearts, that there's four hearts, and there were 16 cents, okay, knowing that, what are we going to do next. And so then, so it teaches kids how to solve like multi step word problems, because you know this, you're going to use that to solve this, then when you figure that out, and they end up doing all kinds of stuff, adding, subtracting, multiplying, dividing, and the shelves get harder.
So like, by the time you get to shell four, it's really, really, there's like three different cases of candy, and you got to figure, none of them are like all the same candy. And it's really, really good. And kids love this game. And it gets goes back to the idea in the research. They talk about small wins, that kids need small wins. And that's what Peter is talking about, as well, this idea that if kids get a small win, then they will go on, they are more motivated. I talk a lot about that in terms of acceleration. And trying to get kids to work on grade level standards. If you give them things that they can do, and they get success, then you can bridge into the grade level standard through small wins. Because people ask all the time, how do you teach kids on grade level when they're this and when they're that and when they're this one there that you teach kids on grade level by giving them small wins? And before you know it, you're in the grade level standard.
Melissa Milner 18:36
I love that. That's great.
Dr. Nicki Newton 18:38
So that's called Math Playground, Algebraic Reasoning. And it's called the Sweet Shop.
Melissa Milner 18:43
I wish people listening could see this visual. It's, it's really awesome. It's colorful, it's the 1, 2, 3, 4. Those are the different levels>
Dr. Nicki Newton 18:53
Yes. So I can go to two. And now you see a level one, all the hearts were the same. Right? So kids can figure but now I'm at level two and the hearts aren't the same.
Melissa Milner 19:07
Yeah.
Dr. Nicki Newton 19:08
So I've got to figure out like, what if I know the value of this is 26? I have to substitute that in here, see what's left over? And what the different right? So it's really it really I was talking with my friend who teaches sixth, seventh and eighth grade. And we were talking about systems of equations. And she was like, Oh, like this is it? This is systems of equations. I was like, Yeah, I teach it exactly. Like you know, just what do we know? And then how are we going to use what we know I do it with fourth and fifth grade all the time.
Melissa Milner 19:43
That's amazing. Is there on this? I'm assuming it's for the teacher to do but on this Math Playground. Is there like a video for the kids to watch how to do it... like examples?
Dr. Nicki Newton 19:54
I think so. I'm not sure about this one but um most of the games there's like at least instructions and sometimes a video that will work.
Melissa Milner 20:01
This is incredible.
Ann Elise Record 20:01
Another kind of puzzle that I found are super fun. There are two different sites that have things like this one's called Mash Up math. And another one is called Solve Emoji. So it's got emojis, but it's algebraic, where it's pictures of things. So it might show a picture of an apple. And so it's apple plus apple plus Apple equals nine. And so you got to figure out what must that Apple be worth if three of the apples make a nine, but they will even combine different lines of the puzzle that you're building on what you've already figured out to get to the next line. Now, you know, an apple is worth a three. And so then, if you have an apple and an orange, and that equals 15, what is the what is the orange worth all grade levels? So they start from primary grade levels up to middle school.
Melissa Milner 20:02
And this is free?
Ann Elise Record 20:43
They're all free.
Melissa Milner 20:56
I wish again, that you guys could see the visual.
Ann Elise Record 20:58
Yeah, they're really beautiful, very colorful. And yeah, and again, they go from easy levels up to with using multiplication and division and, and harder levels. So again, just that, that puzzle of I didn't figure this out that element of doing it. But embedded within that thinking is all this thinking and reasoning in in many cases, like basic facts, which is so much that our kids need to be able to, to get that practice once they understand strategies that help them efficiently get to an answer. But yeah, so that's the Mashup Math and Solve Emoji both offer those picture type puzzles.
Melissa Milner 21:36
Solveemoji.com That's the one you're on now that it's just amazing. It's just so cool.
Dr. Nicki Newton 21:42
That is so cool. And that there's a concept that I want to talk about, in a second called enclosentropy, Marzano talks about it and enclozentropy is the idea that the human mind wants to figure out what's missing. He writes about this idea of enclosentropy and the the need of the human mind to find the thing that's missing. And I can't remember who the main theorist of enclosentropy is, we will put the quotation in the...
Melissa Milner 21:53
Yeah, give me everything for the for the episode page.
Ann Elise Record 22:21
So Diamond Puzzles are another kind of puzzle where you have four numbers, kind of like the north, south east, west, the the left and the right numbers are the have the sum of those two numbers on the top, and the product of those two numbers on the bottom. And in the puzzles, any of those four spots can be unknown. So you begin with having the two numbers and what's the product? What is the sum, but then it might be they give you the product, and only one of the factors is there, what must the other factor one be, but it leads in so beautifully. For the algebra when we're doing, let's say polynomial multiplication, which is way down the road for of course, for our elementary kids, but when you're thinking about factoring, you think of what two numbers do I multiply and get this and add in and get this right? Like it just, I love how the mathematics that we do is a connected journey through all the grades. And so what I can do in one grades, it's a foundation for what then comes in the future. And so these kinds of puzzles, which are fun and engaging, have such an important mathematical role in the math journey. So those are just called Diamond puzzles.
Dr. Nicki Newton 23:27
They're really fun. And there's a Diamond Puzzle Maker. So you can go in, put all these different parameters into that. And so that's something to use and see and do as well. It's that calculator soup, and you put in whatever you want, and you put in the criteria that you want, and then it'll give you all kinds of diamond puzzles.
Melissa Milner 23:49
That's so cool. Wow.
Dr. Nicki Newton 23:51
Next, I think we're going to talk about crossword puzzles, and just the adventure that they are in and of themselves. Kids love crossword puzzles, you know, there's so many kinds. So you can make crossword puzzles, where they have to solve just for addition and subtraction or for multiplication and division or for all the operations. So crossword puzzles are fun crossword puzzle math books.
Melissa Milner 24:20
So sometimes you might have just expressions and the answers and the equation. But sometimes you'll have it more in words, and they have to do it, right.
Dr. Nicki Newton 24:31
Yeah. And which was the puzzles with numbers?
Melissa Milner 24:34
Yeah.
Dr. Nicki Newton 24:35
Then there's crossword puzzles with like, you know, just math vocabulary, right? It'd be like a crossword puzzle. Right? And so the kids have to make the equations true.
Melissa Milner 24:44
I know, for our listeners, it's hard because they're not seeing what we're seeing. But I'm wondering if there's a way I can take screen screenshots?
Dr. Nicki Newton 24:52
Absolutely. We can do screenshots.
Melissa Milner 24:55
Okay.
Dr. Nicki Newton 24:56
Of all the different puzzles.
Melissa Milner 24:58
I think that would be helpful to have on the episode page. Excellent.
Dr. Nicki Newton 25:01
So, I think that, because like what this kind of step does is it's like doing push ups, right? It just builds muscle. And it's fun. And so kids will do it, you know. And though it's it's really when you're working at the retrieval letter level, and you're trying to get kids that and you're trying to build that automaticity muscle, this is after kids, no strategies after they're really efficient after they can talk about what they're doing. And they're just working on that recall stuff like this is just fun, because that's what they're doing is retrieval, quick retrieval.
Melissa Milner 25:01
Yes.
Dr. Nicki Newton 25:01
So although I wouldn't start kids with crossword puzzles, I would definitely put it in the rotation of practice opportunities when they're at that level.
Melissa Milner 25:43
Yes. So let me just describe the top row of the crossword puzzle. There's a box that has a two, and then there's a box that has a plus one. And then there's a box that has a three, and then there's a blank box, and then a seven. So they have to figure out from three to seven, what did we do? And then there's from the seven, it says plus two, and they just need to find the answer to that. And then there's the down from the three and the seven, it goes down. And so it's basically a crossword puzzle. But yeah, that's very cool.
Dr. Nicki Newton 26:15
And it's like self checking, given you put seven plus one is nine and minus three, it's not five.
Melissa Milner 26:21
Right. Good point. self checking is always good.
Dr. Nicki Newton 26:24
Yes. And then that we have these all these puzzles. They're really fun. What they do is they're like mazes? So for little kids, it's like killing what comes next. But as the kids grow older, they're like, Oh, this is a plus three. So you have to work your way from the turtle to the starfish. But you can only add three, so I can go one to four to seven. And then I have to figure out what's plus three. So it's not a word. It's not nine, it's not 11. It's not 13. It's 10. And then I have to figure out what's plus three, from 10. To 13. Is three more.
Melissa Milner 27:00
Yeah.
Dr. Nicki Newton 27:00
Yeah. So, it's just the puzzle. You know what I mean? It's a little tricky. And it's great for kids.
Melissa Milner 27:06
I mean, you could say it's good for skip counting, but your skip count. It's not the same as like multiplication, skip counting. Do you have some that start at three and skip by three?
Dr. Nicki Newton 27:16
Well, you know what we don't, but we have like that. This is really different. I never really, really thought of it like this. But it's good for skip counting off of the multiple, which is something that kids are supposed to be able to do, but they can't. So if you tell a second grader, I want you to skip counting by twos but start at seven. What's exactly, so it's good for that?
Melissa Milner 27:38
Yeah. So I just want to describe so Ann Elise and Dr. Nicki are sharing this like massive slideshow with a gazillion slides in it. It's pretty impressive.
Dr. Nicki Newton 27:50
So what this is all part of I've been really thinking about this for a couple of years now and forcing Ann Elise and Alison to talk with willingly and unwillingly. Oh, that the idea is, I really believe in the gamification of practice.
Melissa Milner 28:15
Yes.
Dr. Nicki Newton 28:16
I mean, and I think that's the bigger idea like, right, how do we get kids to practice in that and what are we competing with? Right, right, because we live in 2024. We are the Jetsons. They grew up watching what we have now become, and we are competing with that for our kids attention.
Melissa Milner 28:39
Yes.
Dr. Nicki Newton 28:40
So how do you get kids not that it even worked with us, but it's definitely not going to work with them. You cannot get kids of this generation to learn their math facts. Like we learn their math facts.
I know.
Like Ann Elise How did you when your dad was added you and your mother? I learned my math back because they gave me flashcards. And they said learn your math facts.
Melissa Milner 29:02
Rote memory.
Ann Elise Record 29:04
Absolutely.
Melissa Milner 29:05
We weren't even, we were, I wasn't taught the concept behind it.
Ann Elise Record 29:08
Never.
Dr. Nicki Newton 29:09
I didn't. I didn't have any choice. Now I couldn't be like through this. I'm gonna go play on my iPad. Be like, Okay, here's my flashcards. And so today kids have we are competing with so much and how do we get kids to practice in school? You know what I mean? When you pull them to the workstation, what does homework look like in ways that engage them?
Melissa Milner 29:39
Yeah.
Dr. Nicki Newton 29:39
And get them to think? And so I really think like puzzles. I always say this puzzles are a portal into kind of persevering because that's why I like a puzzle because it teaches kids to keep trying because when you when you decide we're going to do This and this is a puzzle. The expectations change suddenly, yes. Because kids understand, Oh, it's a puzzle, they will think I'm gonna sit down and I've got to get everything right. They think, oh, it's a puzzle. You have to mess with the pieces. You're not gonna get it right. You have to keep trying. And I don't play video games with everybody I hear always gives me the analogy of this. It's like Tetris, you go in, no, you're gonna lose.
Melissa Milner 30:25
Exactly.
Dr. Nicki Newton 30:26
But you don't not go in, you know what I mean? You're like, Oh, I'm gonna learn some stuff and do better the next time. So with a puzzle, I think that's what kids feel. Even. I mean, I grew up on puzzles, too, right? And so I grew up where you just put the puzzle out there. My grandmother loved puzzles. And we would like be trying to put the puzzle together and kids to this day, when we do family nights, and Annalise does a lot of family night math nights. I always have a puzzle table, just loving them even happy math puzzles. Because what puzzles do is they get kids to think logically, they get them to slow down. They get them to look, to communicate.
Melissa Milner 31:05
To sort.
Dr. Nicki Newton 31:07
Yes.
Melissa Milner 31:07
Sorting, if it's actually a jigsaw puzzle, the sorting.
Dr. Nicki Newton 31:09
Yes, absolutely. Say that doesn't look like it goes there. Right? Where could that possibly go? Oh, I see. Oh, now I got it. If that's that, then this is this. Puzzles have a way of doing all of that. So when I say to kids, I go into classrooms. I do puzzles all the time with kids. I'll be like, Oh, we're gonna do a puzzle kids like, yes, we want to do. And then as we're going through the puzzle, if they don't get something, right, they're not devastated. They're like, Oh, it's a puzzle. Oh, did you try this way? Did you try it that...
Melissa Milner 31:41
So true. The growth mindset goes way up? Yes.
Dr. Nicki Newton 31:45
Yes. I think that there is something more to just saying, Oh, we're gonna do puzzles with kid now puzzles. There's something so, so rich and organic about the way that we want kids to engage as learners. That's embedded in the puzzle.
Melissa Milner 32:03
Yeah.
Dr. Nicki Newton 32:04
When kids are doing puzzles, it's not like you have to externally say, stick with it, keep trying, they inherently stick with it and keep trying, because that's the
Melissa Milner 32:14
Most of them do.
Dr. Nicki Newton 32:17
Yeah. That is the nature of what we are doing. Yeah. So that's, that's why I love puzzles. Right. And I think they have a lot to teach kids. A lot of, you know, if you think about executive functioning skills.
Melissa Milner 32:31
Yeah.
Dr. Nicki Newton 32:31
Puzzles, teach, help to teach kids executive functioning skills to to slow down to think, to be organized. And one of the things that our research says is that executive functioning skills are taught, the kids don't just come with them. They are taught it is a taught set of skills. And so I think that all for all of those reasons. You know, I really think we should be doing more puzzles with kids in their classroom.
Melissa Milner 33:02
Preaching to the choir. I love it. I love it. That was a beautiful way to end. But I don't know if you had more games to share?
Dr. Nicki Newton 33:11
Well, yeah, we had, we had some more. Ann Elise is going to talk about the number line puzzles.
Ann Elise Record 33:15
So in the research number, Lions have their own suggested recommendation, because there's such an important model and representation, because we can put all sets of numbers on it. And so we begin in K in one using number pads, which if not, if you've not heard that before, it's like a rectangle with the number put inside. So it's kind of looking at like a linking of like one inch cubes or something or one inch squares. Because we don't want students to introduce too quickly to a number line with a distance measurement. We want them to see it as like a linear measurement. Before we go to that, you know that hopping on a number line. So in K and 1, we do number paths. But once introducing that number line, we can capitalize and having puzzle holes on the number line where you can be even just estimating the value of a number. So for example, if I have a, the one we're looking at at the moment has like a 38 on a number line. And then two numbers are down below in empty boxes have like what two numbers could these be, if that's where 38 is on this number line and be able to have kids think and reason with the place values with the numbers of what makes the most sense to go in those boxes.
So we're capitalizing on that getting them familiar with a number line which is a huge representation and model they should be using for everything they're doing all the operations as well as getting the place value understanding of the quantities of those numbers. So really powerful, powerful work doing that. And for any sets of numbers right because the number lines you can put anything on there we can put in a numbers within 100 But that could we can be doing numbers with 1000. We can do fractions, decimals, integers, it graduates and follows on along with it and be able to connect you know that The concrete and pictorial and abstract together so we can be kind of solving a problem, you know in a with 10 frames, and then record that also on the number line and then record that with an equation. So we're able to capitalize on connecting through different representations, making that connection and know for myself personally, the one of the biggest things that I see in my work is the algorithm for adding and subtracting being done way too early in the kids journey. I'm seeing it happening in grade one and two, and I just, it's a fourth grade standard, right? Because it's a way I can solve problems. Sure. But there's so many other wonderful ways I can solve.
And it makes the kids think only in basic math facts, we tell them that they must start in the ones place. But if I gave them $100 bills, and $10 bills and a $1 bill, you can start with the ones. But yet we tell kids, when you add numbers together, you must start in the ones. But that's true only if you're doing like the algorithm, right. So we need to give the kids the experience of those years of manipulating and playing with the numbers with their place values attached. So when we make that thinking visible for others, I find it open number line is one of the best representations for that. So we can show that flexibility, if I want to go over a certain amount and come back, or if I want to bridge a 10 like I can make it visual for everyone on that number line. So we can't do enough work on that. And continuing certainly through with the fractions and decimals that their numbers that exist on number line. So the more we can put puzzles together with the number lines, it's kind of like a win win of that engagement, but also on that really important representation.
Dr. Nicki Newton 36:41
One of the other really, I think great puzzles is pyramid puzzles where kids have to, you build so you start, and then you build up. And they haven't for addition, and they have them for multiplication. And they have there's a lot of digital sites that do really great pyramid puzzles, too.
Melissa Milner 37:04
So there's a pyramid here, the top of the pyramid is 78. And then there's two that are blank. And then there's three, that there's a blank and then an 18. And then a 19.
Dr. Nicki Newton 37:17
Yeah.
Melissa Milner 37:17
And then the fourth one is is a blank a 12 and a blank blank.
Dr. Nicki Newton 37:21
Yeah. And so it's all about composing and decomposing numbers. So high, like if this is 18, then this was 12 and six, if this was six, this was 19 and 13. If this was 18 and 19. This was 37.
Melissa Milner 37:33
Right.
Dr. Nicki Newton 37:33
This was 78. So I have to figure out what he was here. Trying to scaffold. I love that puzzle pieces. And so again, you're working on missing number which kids have trouble with all the time, and you're just kind of kind of playing. You don't I mean, like climbing the pyramid.
Melissa Milner 37:52
I love these. Oh my gosh, yeah, these are great.
Ann Elise Record 37:57
I only had one more kind on my list, which was the two types of algebra ones.
Dr. Nicki Newton 38:03
Oh, yeah.
Ann Elise Record 38:03
Some have substituting values and some you don't.
Dr. Nicki Newton 38:07
So these are the ones like they have all this one has four dogs. Each dog has a different value. And then they make like the Bulldog, the oval and the Chihuahua. Bulldog is seven and the poodle is five and the joy that the takeaway the Chihuahua with just four. So it's teaching kids how to substitute values.
Melissa Milner 38:29
Yes.
Dr. Nicki Newton 38:29
And so that's, you know, really good. That's one kind. But then there's this kind where the values aren't given.
Melissa Milner 38:38
Yeah.
Dr. Nicki Newton 38:39
Right, which is another level,
Melissa Milner 38:41
Right. So there's like a planet plus a planet plus a planet equals 36. And you have to figure out what one of those planets is worth. So 36 divided by the three.
Dr. Nicki Newton 38:51
So those are those are really fun, as well.
Melissa Milner 38:55
Because then the next one is Earth, plus another planet plus Earth equals 74. So you know, once you figured out the planet, then you know how much is leftover, then you have to divide by two because there's two Earths. Oh, I love this stuff.
Ann Elise Record 39:13
And how much more fun is that?
Melissa Milner 39:15
Oh yeah.
Ann Elise Record 39:16
Than if we just gave kids these naked number problems to do what's 36 divided by three, right? Like just it's so I want to do these like this. It's fun.
Melissa Milner 39:25
Amazing.
Dr. Nicki Newton 39:26
Well, I also really about the flower puzzles. So the premise of a flower puzzle is that it's always going to be the same sum, no matter which direction you go in.
Melissa Milner 39:38
Okay.
Dr. Nicki Newton 39:39
So you're given a certain set of numbers, and then you've got to make it so that it's the same set.
Melissa Milner 39:45
Gotcha.
Dr. Nicki Newton 39:46
So they're given the numbers one to five. So if you arrange it this way, you're going to have a sum of seven. If you arrange it this way, you're going to have a sum of nine. Hmm. You arrange it this way. You're going to have a sum Have 10.
Melissa Milner 40:01
Oh my gosh, my kids love, love that stuff.
Dr. Nicki Newton 40:03
It's all about algebraic thinking, because it's always going to equal 10.
Melissa Milner 40:08
Right.
Dr. Nicki Newton 40:08
But it's different ways of saying it.
Melissa Milner 40:11
Fantastic.
Dr. Nicki Newton 40:12
I just call them Starburst, but they're known as flower puzzles. Yeah.
Melissa Milner 40:15
So I also on Mashup?
Dr. Nicki Newton 40:18
No flower puzzles, you have to google flower puzzles. They're not. They're not as ubiquitous as some of the other puzzles. Mathlove does some work on flower puzzles. And then there is a school that did a parent night. Actually, Ann Elise would love this. There's a school, they did a parent night. And they did this whole if you look up flower puzzles, I mean, you have to put in flower puzzles math. Otherwise, you'll get just like...
Melissa Milner 40:43
Puzzles of flowers. Yeah.
Dr. Nicki Newton 40:45
But Mathlove has it. But there's a district that has like a whole math Parent Night app of flower puzzle stuff. Oh, here it is. JRMF. And it's Julia Robinson. Oh, it's a math festival. Actually, they have a whole section. Julia Robinson, Mathematics Festival. And they have a whole section on flower puzzles. And it's I want to say in Yep, it's in English and Spanish. And they have that does all kinds of stuff.
Melissa Milner 41:15
So many amazing resources. Like it's kind of blowing my mind right now. So I definitely think I need to up my game on the episode page for this one. I'm really gonna have to, you know, share as much of this stuff as we can.
Ann Elise Record 41:31
I'll go through and send you some links and some of the things we mentioned as well.
Melissa Milner 41:35
That would be great.
Ann Elise Record 41:36
Yeah.
Melissa Milner 41:37
Thank you so much. As always, I mean, this was crazy. We had to cancel because Dr. Nicki wasn't doing so great. And then we had to cancel with a hotel evacuation. And...
Ann Elise Record 41:52
We climbed down eight flights of stairs that day.
Dr. Nicki Newton 41:55
You know, I was sore. Like five weeks. Five weeks. That's an exaggeration. I was sore. Like a week later. I can hardly walk. My legs hurt so bad.
Melissa Milner 42:05
That's so crazy. I mean, did you ever find out why you were evacuated?
Dr. Nicki Newton 42:09
No, some person touched the fire drill. Not serious.
Ann Elise Record 42:14
Thankfully, it was a false alarm. That was cold outside. We're in Philadelphia. And so we were on the outside for like five minutes, then we had to go back in but that was an ordeal.
Melissa Milner 42:25
Alright, thank you again for joining me and, again, always amazing, multitudes of resources. Thank you.
Ann Elise Record 42:33
Such a privilege to be here. Thanks, Melissa.
Dr. Nicki Newton 42:34
Thank you. Thank you, Melissa.
Melissa Milner 42:37
For my blog, transcripts of this episode, and links to any resources mentioned, visit my website at www.theteacheras.com. You can reach me on Twitter and Instagram @melissabmilner. And I hope you check out The Teacher As Facebook page for episode updates. Thanks for listening. And that's a wrap