Arts in Education · Math and Book Arts · Math and Paper Folding · Math with Art Supplies

Peek-a-Boo Skip Counting for First-Graders

Peek-a-boo skip counting
What number is under the heart?

For weeks I’ve been burning through piles of papers and ideas trying to work out an engaging skip-counting project to make as part of a math-activities folder for first graders. Having just done a math activities folder with kindergarteners, which went really well, I’ve been wanting to do something similar for first graders. As I’ve also been doing math-with-art-supplies bookmaking projects with second graders, I’ve been keen to design something for the next grade up.

What I’ve  needed to get me going on this is a school to want me to create a project for them. A couple of weeks ago, late in the season, a school called me, asked if I had any time for them, and we struck a deal. We’re doing the project that I’ve been wanting to create.

There will be four hands-on projects in a folder that the students will be making. This post is about just one of the projects, one that supports skip counting, reasoning, and attention to numerical patterns.

Show me what under the butterfly, Oh, it's a 14.
Show me what’s under the butterfly, Oh, it’s a 14. Still not sure what’s under the heart.

Skip counting is a big deal in first grade. Not only does it set the stage to understand multiplication, it also is helps with learning to count money.

My work with second graders has piqued my intereste in skip counting. The projects we’ve been doing, which is making designs with “coins” that add up to $1.00, has been interesting in that I’ve noticed that even though a student can count by fives, you know, 5, 10, 15, 20, 25, 30, 35, 40….,, they have a really hard time doing this same counting by 5’s when you ask them to start at any number other than zero. So, if they have 25 cents plus two nickels they are at a loss as to how to proceed.

Show me what's under the flower. Oh, it a 6, Now can you tell me what's under the heart?
Show me what’s under the flower. Oh, it a 6, Now can you tell me what’s under the heart?

 

Maybe by now you’ve guess what is under the heart in the photo above. Maybe not. If you need more hints, I can reveal that there is an 8 under the star. This will likely finally be enough for you know know that there’s a 10 under the heart.

We’re not just counting by twos here. I’ve made a paper that slides under the windows that helps with counting by 2’s, 5’s, and 10’s.

I consider this to be an elegant design. One piece of folded paper for the holder, with a one piece of paper for four different number series. The little designs on the peek-a-boo doors are cut with paper punches, which I’ve collected over the years. The rhombus shaped window are made by folding the paper and cutting triangles on the fold.

One of my thoughts with this project is that  it can support students in practicing with going both forward and backwards with their skip counting. For instance, if they see two numbers, say 80 and 85, can they tell me the number that is before the 80 and after the 85? This takes some practice, some thinking, and reasoning, but if they can figure out what number is behind the hidden door, I anticipate the pleasure at solving this puzzle will delight them when the peek-a-boo door reveals the answer.

I do plan to share the template for this after I try it out with some real live first graders. To be continued.

Art and Math · Math and Book Arts

Kindergarten Folder for Making Math

Making Symmetry
Making Symmetry

There are some kindergarten teachers I’ve been working with for years. This year I’ve worked with them to create a math-centered book project for their young students. I launched this with a small class earlier this season then repeated it with about 4 groups, total of about 70 kindergarteners, this past week. It went well.

Actually I’m so delighted with how it went that it’s almost embarrassing.

Making the folder
Making the folder

We made a folder out of a long strip of paper, 35″ x  7.5.”

Folder with four compartments
Folder with four compartments

 

I put some score lines in to help these 6 years olds get started but they made most of the folds themselves. I make a big deal about how to fold paper.

The folder is basically a four page accordion, with pockets for a different math activity in each of the pockets.

The first pocket has a paper with peek-a-boo flaps to help kids visualize the composition of groups of numbers. This was an  unusual folded structure, but they caught on really quickly, as you can see in the video clip below.

After the folding comes the cutting

 

Cutting the peek-a-boo flaps
Cutting the peek-a-boo flaps

Then the coloring…

Compositions of the number 4
Compositions of the number 4

…finally they used these images to become more familiar with number compositions. We made these cards for the numbers 2, 3, 4 and 5.

Here’s how it looked watch kids use these to learn their number facts:

Okay, so that was for one pocket.

In another pocket there were squares that the students cut out. I used these to talk about symmetry.

Symmetry with cards
Symmetry with cards

Where one student placed a card on their side of the midline (pencil)  another student mirrored the placement. Seeing symmetry is important in math as students as it is a non-numerical way for them to experience the balance that an equation like 2 +3 = 5 expresses.

 

I extended this symmetry activity beyond the cards in their pockets. We used items around the classroom to create symmetrical designs, something my twitter community liked and retweeted generously.

We also did a project using beads, reminiscent of an abacus, to make groups of 10.

Separating10 beads into groups
Separating 10 beads into groups

The idea here is to give kids another way to interact with ways to make groupings of 10, contributing to their fluency and grasp of combinations of numbers.

Bead counting book
Bead counting cards

 

Finally, we did a fortune-teller, aka chatterbox, which many of us made when we were children.

Fortune Teller, Chatterbox
Fortune Teller, Chatterbox

 

Of course the insides were math themed, using their sight words, too.

Fortune Teller template
Fortune Teller template

Here’s a little clip of the kids playing with these. They absolutely loved this toy.

At first I had a hard time trying to teach this structure to kindergarteners. Once I realized that if I taught it after I worked with them on the symmetry part of this project, the folding would then make more sense to them. It turned out to not be nearly as hard to show them as it originally seemed to be.

The final touch was putting hands on the covers. Literally.

Front and back covers
Front and back covers

Since the kindergarten math curriculum emphasizes using fingers for counting, it seemed highly appropriate to decorate the covers this way.

Whew! What a week!

I was able to meet with each class for a little over an hour three times each.

Looking forward to repeating this project with other groups.

Also, now I want to create something like this for first graders! That’s what I will be working on this week.

 

 

Art and Math · design · Geometric Drawings

Copy, Rotate, Reflect and add eggs

In the middle of my arts-in-ed season I’ve kept trying to find time to mess around, trying to make beautiful images.

Today I started a wonderful, week-long math activity folder project with four classes of kindergarten students, am barely able to stay awake right now, but I’ve been wanting to at least throw these  images into my blog here.

I started doing this some time before Easter. Just wanted to make something. Started with a graph that I was able to reduce to just these few lines:

https://www.desmos.com/calculator/gqt97ui6ha

Then I copied, rotated and reflected these lines and came up with a nice tiled surface.

I honestly just loved this image. Parts of it I expected, other parts came as a surprise.

https://twitter.com/PaulaKrieg/status/1117260203421052928

Spent lots of time coloring it in. Mostly used watercolor brushes, SAI Japanese Traditional Colors, but also used some colored pencils.

When it was done, I didn’t much care for the finished result.

It was okay, but didn’t make me as happy as I would have liked.

But then I started playing with it. Put it into Photoshop, isolated squares….

 

…then did some copying, rotating and reflecting…

I kept coming up with all sorts of stuff that surprised me.

 

I kept trying out different combinations…

… and then because Easter was on my mind I started wondering if I could map these on to eggs in Illustrator.

Turns out the answer was yes.

 

These were so fun to do.

I liked how the watercolor translated so well in to the digital environment.

Was very surprised that I ended up with these eggs. But very happy.

OK, that’s it for now. Gotta get ready for tomorrow with kindergarten!

 

Uncategorized

About Halfway There

Equivalent Fractions
Equivalent Fractions

I’ve been interested in creating fractions projects for kids exactly as long as I’ve been working with children in schools (decades). This year, after enjoying,messing around with a hexagon/golden ratio project I wondered if I could modify the idea of using scaled hexagons to help fourth graders make better sense of fractions. My first attempt at this didn’t work out so well.

Making 1, or 100%
Making 1, or 100% out of two halves

I gave students hexagons that were scaled to 1, one-half, a third, a fourth, a fifth, a sixth, an eighth, a tenth, and twelfths. The task was to pair and arrange them so they would span the length of a whole, aka 100% across.

1/3 + 1/6 + 1/6 + 1/3 = 1
1/3 + 1/6 + 1/6 + 1/3 = 1

The project went okay, but it just didn’t snap for me.

I’ve been thinking about how to improve this project. Today I had a chance to work with a small group of kids. I tried a new approach that worked so much better. What was especially great was that it included making a simple book. Yay!

Fractions for a Book
Fractions for a Book

I started kids off with a hexagon that was labeled 1/2. I explained about how the lengths we would be looking at would be the horizontal or vertical length of the hexagon (I didn’t use these words, rather gestured what I meant). Then we layered the hexagon with equivalencies. Here you can see two 1/12ths equals 1/6, three 1/6ths equals 1/2, and 1/6th and two 1/12ths equals 1/3.

Equivalent Fractions
Equivalent Fractions

Nice, right? Snap!

The books we made were just two sheets of paper folded in half, bound with yarn using a modified pamphlet stitch. 

Equivalent Fractions Book
Equivalent Fractions Book

What’s great about using hexagons for this project is that you can still see the labels of the lower layers as the equivalencies are built up. The adults in the room had a bit of trouble with accepting that the hexagons were scaled (similar) versions of each other, but the kids had no problem with it. This reinforces my notion that children have a better intuitive understanding of scale than do adults.

This is the way I explain the scaling to adults: We all know what half a candy bar looks like. That’s one way of thinking of one-half. But when we say a child is half the size of the parent, we don’t envision the child to be half a parent, like they were half a candy bar. Instead, we envision them smaller than the parent in their height as well as width.  This explanation seems to work.

The bullseye view of fractions
The bullseye view of fractions

After doing a bunch of equivalencies, this child decided to nest her fractions.

Okay then. Here, what’s obvious is the hierarchy of the hexagons that are scaled by fractions. Nice!

This project can use a bit more refinement, but this is as far as I’m going with it right now.

I’m including PDF of the hexagons. The labeling includes the colors of the paper I use for printing.  Yeah, it’s lots of files. Welcome to my life.

hexagon-10ths-yellow

hexagon halves blue

hexagon sixths halve grape

hexagon 3rds 12ths chartreusegreen

hexagon 4ths orange

hexagon 5ths 8ths pink

hexagon 6ths halves grape

zhexagon 12ths full page chartreuse

2 pieces to make 12 inch hexagon

12 inch hexagon

Notes about hexagons