Marsbarn Designs...

Box template method of Algebraic equations

In working with mathematics, I love finding
alternate ways of solving a problem.  If something
doesn't make sense, there should be another way to work it out.

What makes me happy?  Discovering another method.

The girls who I tutor are just entering that new
world of Algebra. It's a land of mystery that either 
inspires adventure through problem solving, or
tears through confusion.  

You have an equation like:

     
 2x  +  4 = 4

        6

Now, the way I solve it, is to work on isolating
my variable, X.  I do this by working my way 
backward through the order of operations;
ie, I multiply to get rid of the divisor 6.

So, multiplying each side by 6, gives me:

2x + 4 = 24  

Then, I get subtract 4 from each side.

2x = 20

Finally, I divide both sides by 2, which gives me:

x = 10

This is the method I was taught, and it works for me,
but there it can be a frustrating method to teach.   

This is the new-to-me method the girls I work with
were shown in school:

You take your equation: 

     
 2x  +  4 = 4
      6

and you use a template to create a sort of map that follows the journey of x.
On the left hand side, you have X.  X is multiplied by 2, then has 4 added to it, and then is divide by 6.

Then, we write the inverse function of each operation along the bottom of the template.

Finally, we work from right to left, following the operations on the bottom of the template, writing the answer of each step in the box.  We are effectively backtracking through the equation.

What I like about this method is that it breaks down
the algebraic process into steps that are easy to follow.
There is less mystery as to where to start.  You start
with your variable, and follow the mathematical actions
that are done to it. For the beginner who is intimidated
by the idea of variables, and who struggles with order of
operations,  it is a confidence builder.  

I am waiting to see if this method can be expanded to 
more complicated equations, but I love how quickly
my students absorbed it.   It is a much better beginning
than I had. 

Let them eat cake

Oh yes, another food photo.
I've been cooking.  I find I can only do one
creative venue at a time.  I can either create with
sewing, or collage, or baking, and while I can
rotate through them, I can only do them one at a time. 

The meals get planned, or the art gets made.
If we are eating well thought out, creative meals,
I am only going through the motions at the sewing
machine.  If I am quilting, or creating new bags,
or making aliens come alive with thread and fabric,
we are eating grilled cheese and eggs.

So, at the moment, let them eat cake, for soon, soon 
it will be packaged cookies and random fridge findings.

Pi Day

Cherry pie for Pi Day, March 14th.  (You know, 3.14)

So, I thought I'd get a post up in time for Pi Day, but
I am late.  Of course, Pi goes on forever, is eternal,
and irrational, so I think being a week late is okay.

Pi.  Pi is magical.  Honestly, it is.  It translates between
dimensions; distance, area, volume.  Pi does it all.
And yet, when I ask the 6th graders I know "What is Pi?"
They tell me, "3.14".  When pushed, they say, "It goes on forever."
I get shrugs when I ask "Where does it come from, what 
does it mean?"  "It's a constant." Is the best answer I get.
I would be lying if I said this didn't hurt my heart just a bit. 

So here is what I want them to know.
Pi is a wonder of the universe.  What does constant mean?
It means that all circles follow a rule.  One rule to govern
them all, and in the darkness bind them. 

Pi is a ratio.  It is the number of times the distance across
a circle (the diameter) can wrap around the outside
of the circle (the circumference).  You could find this 
measurement on your own, with a piece of string.  It's
a physical thing, a real touchable thing.  It is simple,
but profound, because it is true for every circle.

Pi is history.  It is practical and an object of obession.
Ancient Babylonians and Egyptians knew of Pi
through physical experiments (hello string).  
Archimedes (he who could move worlds) worked out
the first mathematical approach to Pi, which began
an endless obsession by mathematicans with the
irrational number.  Is a million numbers in Pi enough?
No, they keep expanding the decimal. 

Pi can catch the imagination, and make mathematics
come alive.  It makes so much possible with
just one piece of information: 3 dimensions of a
circle, with just the radius.  It can make a person fall
in love with problem solving.  

Is Pi Day just a gimmick?  A chance to eat pie?
I think it is what we need to inspire our children.
It is a chance to talk math with your child,
and make them think beyond the numbers, beyond "3.14" .

Done and gone, but tasty none the less

Homemade, from scratch, oh so tasty Monkey Bread. 

This is from last weekend, and is, of course, long gone.

As I try to capture the past two weeks for the blog,
I realize how little I have left in hand to show.
There has been art workshops, collaging, baking,
sewing, dice bags, and all of it is gone.  Poof!
Consumed, given, sent, and taken home with their 
creators.  The fact that I'm noticing this means two things:
1. I need to take a lot more photos.
2. It must be time to start a new project that is mine.

In the ebb and flow of work versus personal art,
I think my time has drifted almost entirely into work.
I love my work.  I love that people pay me to sew,
or to teach, or to make, but there is something
different between work and pure play.  As fun and
fulfilling as making for others and teaching might be,
making for yourself is different. 

So, long story short, it must be time to make a quilt. 

Needle felted basket, version one

This little basket/box/bowl is a project I've been working on.

The body of the basket is fulled wool, that I decorated
with needle felting before sewing the side seams.

I lined the basket with cotton, and then put seam
binding along the edge.

I think the next version will be bigger, and I have
ideas for a handle, too.  I used some of my new
roving for the needle felting.  It was so nice to 
have a chance to use my new colors. 

Mr Fuzzpants: No one appreciates the cuteness

Look into my eyes...

Am I not cute?

We know I am.

From my furry little feet,

to my extravagant eyebrows, I am so cute.

What's that?

You cannot mean it.

You do not want me here?

Pah.

The Tank, slowing down

The Tank gets cold these days.  He spends a lot of time
lap surfing, in between visits to the heat vent when it's
on.  This increased affection as he gets older seems so
bittersweet. 

He's still our big guy, even with his skinny old man
hips.  He makes as much noise as ever as he prowls
around the house, and if Mr Fuzzypants gets out of line,
he reminds him whose house he lives in.  But our boy
is changing.

He limps more often than not, and he'll allow you to
lift him into your lap (a move he disdained even as a
kitten).  He purrs the same rumbling, deep bass, and
he still sleeps behind my knees every night.  We tell
the girls that he's an old cat now, and that our time
with him is getting short, but I think that is as much
to prepare ourselves as to prepare them. (I avoid even
thinking about what Mr Fuzzypants will do when his
friend and Godfather (think mafioso) leaves us.) Perhaps 
our warnings are premature;  he may go on for years
as he is.  But with all of the changes we've seen in 
him during the past 18 months, it is hard to imagine
the landslide of age leveling out into a plateau.