Part to Whole

Colorful Math: Area, Multiplication and Square Numbers Edition

Two things our house has a lot of: math and color.

 

We eat colorful, mathy breakfasts.  (Isn't this hexagon egg-citing?)

And then we work on our colorful and original attributes matching game.  The attributes include a multitude of choices in the following categories: shape, color and pattern.  We ask: How can I make the pair exactly the same?  How can I make the next pair different?  How are my designs similar to each other?

After a bath and second breakfast, we learn about square units and determine the size and area of each picture.  But why stop there when there are colored pencils around?  I wanted to move on but quickly concede that not only is color is a great addition for highlighting structure within the areas in question, but basic math gets a whole lot more fun to do!

At which point I think: Wow, I've got some graph paper...how about tomorrow we look into square numbers?

And how do I start that lesson?  Pick your seven favorite colors!

We do the first six numbers and the child, unbidden, suddenly looks over her work and says "Wow, they get bigger!  Oh, and there's a pattern!"  We figure out the specifics and then use that observation to predict the seven square.  I know there is lingering confusion about how exactly that number is made but, as you know, tomorrow is another day and I think I have an idea...involving colored pencils, of course.

When the Math Stars Align: Geometric Tiling Edition

I've been experiencing some serious math kismet recently.  I rediscovered a thrifted book on 16th century mosques that I bought to read with my daughter.  We got part way through and I remembered what I was really interested in were Islamic geometric tiling designs, which spurred me to the library where I found an awesome David Macaulay book about the construction of a fictional 16th century mosque.  But still no leads on tiling designs.

A few days passed.  Today in the mail, totally unexpected, was this Christmas gift:

Not Islamic, but still fascinating and exactly the kind of resource I was looking for.  From the book:

"These geometric patterns radiate symmetry and order.  Drawing the patterns is not just a question of mechanically copying the work of someone else square by square, but of understanding the underlying structure.  These patterns are built up from simple elements which seem to 'grow' and develop in an almost organic or living way."  Perfect.

As I looked through it tonight I realized that some of these designs would be great inspiration for the mathematical paper weaving I've been exploring, and other designs would be perfect for the non-quilting paper patterns activity I developed this summer.

And, to top it all off, when I looked the book up I found that there are other books by the same author on the topics of geometric patterns from tile and brickwork, churches and cathedrals, patchwork quilts AND Islamic art and architecture which, it turns out, was heavily influenced by the geometric designs of the ancient Greeks and Romans.  So, really, if you think about it, the very most perfect book appeared at the very most perfect time.

I have so many new ideas I may never sleep again...

Beading Attributes: Pattern, Color, Shape, Size and...Straws!

My house is a laboratory.  My daughter is the lab rat er, cat.  I'm doing a lot of body-based rhythm and dance this summer with multiple groups of kids ages 6-12 (50-100 a week) but want to balance it out with other representations of pattern, shape and design.  I want whatever we do to have as much choice, challenge, beauty, self-expression and mathematical meaning as possible

I'm trying to figure out how to do all that on a budget.

One of my ideas is a beading project that will work well for both boys and girls in the younger and middle age groups.  I'm thinking about starting with both these books. 

I want the bead patterns to be as simple or complex as the kids require or desire.  I want there to be many possible right answers using a diverse inventory of attributes.  So far that means stiff string, pipe cleaners, spherical wooden beads with multiple colors and sizes, and...straws!!

Yes, I am making my own colorful straw beads.  They're the leftover parts of colorful bendy straws I cut to make this cube: 

 

And these.  

 

And this!

The older kids, incidentally, will be making at least the tetrahedron and the cube.  If they want to do more I plan to have enough materials on hand for that to happen.  There's a nice balance, a nice ecology, to this me thinks, what with the whole straw being used in different ways over the 6-12 age range.  Here's what I've done to make it work:

Make your first cut at the bottom of the bendy part.  The long part of the straw is about six inches, and perfect for constructing the Platonic solids using pipe cleaners as connectors.  With the remaining portion of the straw I cut the bendy part off (it's the part that expands -- in this case, I'm leaving it unexpanded, but the ridges make a nice texture.)  The top straight part, which is at the top, I've cut into half.  You could leave it longer, if you want, but I liked the shorter pieces better.  That's just me, though.

I experimented with some beautiful plastic pony beads as well but, in the end, there's only one attribute -- color.  The resulting design was really not interesting at all and I think even the youngest kid deserves more than one design element.  The wooden beads are wonderful with so many different sizes and colors and I'll keep my eye out for more sales so they can be a choice for everyone.  The straws are wonderful too because they're less than a penny per straw, offer a different/unusual bead shape, with multiple color choices AND a choice of texture! 

I'm happy with the options so far but will keep searching and experimenting.  What other kinds of (inexpensive but beautiful and varied) beads could I use?  I'd love your ideas!

Make Your Own Attributes Matching Game!

I have had attributes on the brain for a couple weeks now.  Most of my thinking has been on how the practice of identifying similarities and differences (a closed process) really opens up when put into a design context. 

So, given how much I've been thinking about it, it's no wonder that what I thought would be a ho-hum, pass the afternoon kind of game turned into an incredible brainstorm. 

The kid and I were playing a Blue's Clues matching game.  I was, truth be told, not 100% engaged, but it was a pleasant enough way to pass some time.  At some point I noticed that this particular matching game was really quite tricky.  You'd turn over two cards with green dogs on them but they were different in some very tiny ways. 

Despite some very minor irritation that I might actually have to pay attention, I started to think about what those game designers were doing.  Nothing like a little internal meta-conversation to help put the pieces together....

Click!

Attributes!  On the matching game (brilliant, brilliant, game designers)!  What if we made our own?  Could we make our own?

"Do you wanna make our own matching game?" I asked the kid.  

Needless to say, the answer was yes.  We rushed around the house trying to locate the 3"x5" cards but, of course, they were nowhere to be found.  I rounded up some other paper, the paper cutter, some shapes to trace, and the crayon caddy. 

It was fast and furious, but in the midst of it all we managed to agree on my some parameters:

Geometric shapes only. This is (sneaky) math after all.  We used tangram pieces, pattern blocks, some Cuisenaire rods, and some magnets from the fridge.

Each pair of cards has to be exactly the same.  It's never too early to experience congruence, and what better way to do that then to be personally responsible for it?  This is a key point in my still-developing argument (one that is based on my experience with Math in Your Feet as well as what I've been doing lately) -- it's one thing to observe congruence, it's another to have to be congruent yourself.  I realized as we went along that the 'make a game' energy really motivated my kid to do this part up right. She paid a lot of attention to sameness in her designs.

Each pair of cards have to be different from the other sets in some way.   We have yet to explore this fully, but this means that if you make make more than one set of triangle cards, the sets have to be different from each other in color or design or size.

It's this last point that created the most conversation as we created our cards together.  According to the kid, I was altogether too boring in my designs.  I would say, "But every design you make is colored in!  They have to be different from each other, so I'm going to leave mine uncolored."  This, apparently, motivated her to copy my 'boring' designs and make them 'more interesting' than mine!

So, we had a lot of levels of similar and different going on, including not only what we created but how we were doing it and what our personal design aesthetic was and how these creative choices were different or similar from each other.  My brain hurts just thinking about it!  See what you think:





All told, and in very short order, our prototype set of matching cards totalled fourteen pairs, which made for a very satisfactory game.  I'd love to find a calmer time to for us to work more slowly, carefully, and thoughtfully on another set.  She wants to make sets of matching games to sell at her ever-evolving lemonade-origami-bookmark stand in the spring, which I think might be motivation enough to take a closer look at how to generate similarity and differences. 

If you end up making your own attribute matching game I would SO love to see what you create (please, please, please?!?).

White...Red...Light Green...Purple...Cuisenaire Rods!

I pulled out the cuisenaire rods yesterday.  The set had been sitting on a shelf for almost a year.  If you don't know what they are the best I can say right now is that, essentially, they are unit blocks of specific colors designed to (at least at first) help kids develop number sense as well as strengthen conceptual understanding of addition, subtraction, multiplication and division. 

The girl immediately remembered the long ago time when we played a 'trick' of putting the first four (white, red, light green, purple) behind our backs.  One of us would tell the other which color to bring forward, and every time we'd be right!   I can tell I'm going to do a little more research on how to use these things, but I know from what I've seen so far is that the first thing you do is focus on the attributes of each color in relationship to each other before assigning a unit number.  Here's how things developed today:



Girl: "I'm going to put them biggest to smallest..."  Mama: "Say it with me!  Orange, blue, brown, black...  Okay now, with our eyes closed!  Orange, blue, brown...Yay we did it!  Now smallest to biggest, white, red, light green, purple..."



Mama: "Hey look!  A blue with a white makes an orange.  Oh, and a red with a black makes an orange, too!"  Girl: "Let me do it."

Girl: "It's divided here."  Mama: "Oh, I see it, on the diagonal.  Let's put a block down to show where it is."

Girl: "I want to pull them apart."  Mama: "Look, they're in the same order!"

Girl: "Now I want to make a design."

What she figured out is that to make this design work you had to skip colors: orange + 2, blue, (skip brown), black, (skip green), yellow, etc.

So many more things to do with these -- I can't wait!!