April 27, 2017
Oh my gosh, working with second grade students is so rich.
They have skills, they are enthusiastic and uninhibited, and tapping into their learning curve is delightful.
I’m working with three sections with about 22 students per class, so I’m getting to see about 66 different ways that students are making sense of the 100 cents project that I described in my last post. (oh, there’s an unintended pun in that last sentence, did you get it?
Short recap: students were given images of coins, which added up to $3.00, from which they chose $1.00, or 100 cents, worth of coins to create a design.
These students hadn’t started studying money yet, which was fine. Most students seemed to understand how much coins were worth, though certainly a few students had no idea about the value of coins.
It was fun, when adding up the value of nickels, to say, Now you know why it comes in handy to count by fives.
Making the wallet-book to house the 100 cent images, then making the images was what we got done on the first day. Separating out 100 cents was certainly the most challenging part of the project. The designs flowed freely.
Day 2 was a bit more challenging, but I think that the toughest part was just communicating to them what I was looking for, which was for the students to make matching arrays of the coins that they used in their designs, then providing the equation which showed that the value of the coins equal 100.
Turns out that this array-making uncovered a few mistakes. For instance the airplane pictures above was five cents short, so he added a nickel on to the bottom and all was well.
There was a wide range of simplicity to complication of images.
If students didn’t have enough coins of a certain value left from their original 300 cent to making the matching array, they would exchange change with another student, at least that was the plan, which worked fairly well. I did bring lots of extra coins, for moments when it seemed better just to hand students what they needed.
Still, everyone should have had 100 cents left over. These coins got glued on to a pocket of their wallet book, along with a statement of the value of these coins. That little black folder that contains the 100 cent image now has an enlarged section of a colorful buck glued on to the front. After all that figuring and adding, it was great to end yesterday’s class with some playful coloring in.
Okay, one more day with these students. The next piece that goes into the wallet-book has to do with combining shapes to make other shapes, much in the same way that we combined values of coins to make other values.
The most joyful moments during these days is having this opportunity to be a part of these early moments of learning about addition. When students say that they can’t get their numbers to add up to 100, though they know that they do, I can sit with them and help them sort out what’s going on. It’s so illuminating for me hear them tell me what they’ve done, and then to help them see another way of interacting with the numbers.
Addendum: as soon as this post went up the generous and brilliant connector-of-all -things-math offered me this link to some other coin projects http://mathhombre.blogspot.com/2009/08/money-games.html
April 23, 2017
Tomorrow I will be starting a new project with second graders. Counting money is part of their curriculum, so both the math specialist and teachers liked the idea of addressing money in our book making project. This is a first for me. I’ve never even thought about folding money concepts into bookmaking.
I let my thinking about this be inspired by the idea of the Hundred-Face challenge that Simon Gregg and Malke Rosenfeld have written about, in which students use Cuisenaire Rods to make silly fun faces that have the added value of adding up to 100 (depending on its length, each rod has a value 1 – 10). Okay, great! We can make designs that out of images of quarters, dimes, nickles and pennies!
I created sheets of coins, being mindful that the coins were the actual size of their reality counterparts.
The idea will be to count out one dollar worth of coins, then take that mess,
and make something, anything. Could be a pleasing abstract arrangement, could be a face, a person, a rocket ship, letters, but it must add up to one dollar. Then make arrays with coins to make them easy to count. Since we’re dealing with money, my thought was to make a….
…Wallet Book! Put an ID card on the front, a closure, a little bling…
… and pockets on the inside. There are two folders in the pockets here, the one I’ve written about, and another one that is about shapes, which I will write about at another time.
Something else about this 100 cent folder: its cover is a blow up of a dollar bill. This will be a nice lead-in to talking about a bit of history of printing, that before things were printed in color, making black engravings then coloring them in by hand was all the rage. Here’s a hand-colored hummingbird from Getty Images of a hand painted engravings:
Now here’s my hand-colored dollar, which the second graders, as they color their own, will get to know closely.
Why not? I mean, when else will they be able to color in a dollar? Or course it’s an enlarged copy of just a portion of a dollar bill, so there’s no temptation to try to use it as lunch money.
There’s been many pieces to get together for this project. I haven’t made PDFs of the coin sheets yet, but if anybody requests them so that they can do this project themselves, I will happily post the PDF’s here. They are black and white files, which I printed on colored paper.
Now here’s the video that I made of this part of the project, which I hope to show to the classes tomorrow. My thought is that if it’s possible for them to view this on the Smart Boards in the classroom that it will be easier for the students to see. We’ll see how that goes. I’m looking forward to seeing the designs that kids come up with, and wondering how hard this will be for them.
April 13, 2017
They did it! This group of fifth grades did this hand-lettering kaleidocycle class project! I described the details of this project a few posts back so check out that post for more details. Here’s the general gist: After introducing the project, which is a 3D paper construction with rotating faces that will be graced with references to the Bill of Rights, students were given pages of letter fonts to choose from.
Using the windows of the library as light boxes, students traced out letters to created one phrase each that described one of the first ten constitutional amendments, aka The Bill of Rights.
Every single student was highly engaged. Really.
Within two class sessions the students produced something that I could take home and scan into my computer . I won’t lie..scanning and cleaning up their work took time. Above you can compare what they gave me, on the left, to what I ended up with on the right. Some pages required much more work than others. The middle example above was so easy to work with that next time I will encourage students to just give me outlines. The most time-consuming letters to work with were those that were colored in and touching other letters. I moved things around a bit, like in the top example you can see I centered the word “OF.”
Students made score lines so that the paper would fold easily and accurately. Scoring is generally done with bone folders but we used glitter pens to score the lines. They worked great, and kids were excited to be using the gel pens.
Then came the folding and gluing. I didn’t take many pictures of this process as I was, like, really really occupied helping move this process along.
This project turned out so well. Not everyone had a chance to finish up and decorate, but the wonderful school librarian will be able to help with the few than still need finishing.
Students enjoyed individualizing their own kaleidocycles.
I tried to get them to use completely different color schemes on each face, so that the differences between the four rotation of faces were dramatic. Students didn’t much listen to my suggestions.
Here’s one of their kaleidocycles in action:
I consider this project a great success. I got to talk to the students about design, about hand lettering, and they got to work with some cool geometry. I’d even go so far as to say that they are also much more familiar with the Bill of Rights , as they were constantly asking each other, which one do you have, which one is yours, and talking about their own. I have to say that at first the students were confused about what I was asking them to do, after which the librarian told me that doing a group project was pretty much out of their experience, so the concept was hard to grasp at first.
One thing that made this possible was that this was a small class, just 12 students. I often work with 60 to 70 students in a grade level: I wouldn’t do this project with a big group. OH, but it was so delightful doing this with a small group.
Do I get to pick a favorite project of my teaching season? Yes? This is it.
April 6, 2017
I don’t understand why certain of my projects with kids get more attention than others. My original post about Sight Word Pockets Book for Kindergarteners from 2011 still gets viewed every day. My teaching season doesn’t go by without requests for this project. By now I have taught literally thousands of young students how to make origami pockets, but it’s never easy. I’m always looking for a better way to explain this folding method.
I’ve come into this teaching season thinking differently about folding paper.
For so many years I have been telling students what to do. This year I have prioritized trying to draw their attention towards what to see.
They all recognize a square, but when I tilt it, students say its a diamond, a rhombus, or a kite. Last week I suggested to students that this shape was still a square, then I was relieved when a classroom teacher chimed in and emphasized that tilt or no tilt, the shape was still a square. The main thing, though, is that this simple rotation and the conversation riveted students’ attention to the shape.
I’ve been asking students what happens to the square if I fold it corner to corner. They all seem to be able to predict that folding a square point-to-point can make a triangle. This makes them happy. They seem to like triangles. Then I tell them that with just one fold more I can make many more triangles. What magic can this be? I have their full attention. They are watching to see if this can possibly be true.
Folding just one layer of paper, I fold the tip of the triangle down to the base. The children are delighted. We count the triangles. Are there four triangles? Are there five?
The next step is the tricky step but now students are attached to the shapes that the folds make and have a heightened awareness of triangles. When I talk about tucking the edge of one of the triangles under the flap, they see what I mean. Here, look at this video. It absolutely blows me aware that this five-year-old just learned this folding sequence about a half-hour before I filmed her doing it. Notice how sure her hands are as they move through the steps.
This change in my teaching, prioritizing seeing & predicting over telling & doing feels really good. It’s happening because I’ve begun to be able to answer a question I’ve been carrying around in my mind for years: I’ve really looked hard at origami , trying to figure out what about it compels some people say that origami is somehow like math.
Now I’m coming to understand that it isn’t origami that I needed to see differently, it’s been my understanding of math that I needed to adjust before I could make the connection. Now that I am seeing math less as addition and subtraction, and more as relationships and transformations, the boundary between origami and math vaporizes.
More and more I am trying to be attuned to childrens’ seemingly intuitive connection to ideas that are aligned to a broader understanding math, and I am able to tap into this with great results. I help them see what is already familiar to them, and what happens next is that they better understanding what’s going on, and can figure out what to do next. Yes, even five-year-olds can do this.