The Soroban Abacus

Today we made a Soroban (a Japanese abacus).
And we learned how to use it.

Here's how it works.

First of all, the one we made will go up to 999.  If you need a larger number, into the thousands, then add another column, making four, or however many you'd like.

I decided upon making a temporary, out of a paper box, to start with (if it gets played with often, then I'll commit one of our wooden boxes, or make a frame).  Elsewise we used three bamboo skewers (strong string will also work), fifteen beads, and something sharp or pokey for a piercing tool.

We found 12 natural beads, and three blue beads.  (If you don't have any large beads, why not make some out of paper or clay?)
Using something that will poke through (I used a upholstery needle, a nail will work - just use a slim one so your skewers are snug in the holes), poke holes at one end of your paper box, or if you think you'll use this often, drill holes in a wooden box.

Insert skewers through on end (or you can use string if you like), and in order, add one heavenly and four earthly beads upon each stick.

After drilling or poking the other side of the box, put the other end of the skewer through the hole.

Push the heavenly beads away from you, and the earthly beads toward you, and mark the center point between the two on your skewers or string.  This is where your active beads will be placed. 

I trimmed off the points and excess length of the skewers.

The upper beads are called "heavenly beads".  The lower beads are called "earthly beads".  We made our "heavenlies" blue, and chose natural brown for the "earthlies" (earth and sky seemed logical).
Heavenly beads have a value of 5, earthly beads have the value of 1.

Thus, numbers are represented accordingly:

zero          -          one          -          two          -          three          -          four          -          five

six         -         seven         -         eight         -         nine         -         ten         -         twenty

fifty       -       sixty       -     seventy     -       seventy-five       -       one hundred seventy-five

So.  You see how that works.

Let's take 137,

and add 54.

fifty gets added first

and then two (of the four)

carry over one to the tens column (this adds the third of four)

the ones go back to zero since we've made ten, 

and have added one to the tens column

and add in the last one (the fourth) of the fifty-four.

and we have 191.

Of course I just had to know how to subtract, as well, so did some research on that.

Let's begin again with 137 again, and subtract 54, this time.

We can't automatically subtract fifty from these three (thirty),

so we'll have to take one away from the column to its left,

and add back in five

(because 10-5=5.  If we were subtracting 80, we'd add back in 2.  If we were sutracting 60, we'd add back in 4.)

We can't take away four "ones" (singles) from our last column, so we'll take out the five,

and add one to make four.

 There.  137 - 54 = 83!

See?  That's not so bad!  :)

Some shopkeepers in China and Japan still use an abacus to calculate what their customers owe... they can do it is quickly as they could on an electronic calculator!

I beleive that, for I've already started getting the hang of this machine!
Happy playing.


This was our first project from our book Amazing Math Projects You Can Build Yourself.

Circling In

So this is how Saturday's post began...

Started the day in bed with Trevy laughing uproariously at antics in The Wind in the Willows.  :)
A fine, fine beginning.

An' there was somethin' there this morning about Kipper the dog and lollipops.

Got the book that I'm verrrra excited about... Nomad Press asked me to give them my three top choices of books I'd like to review, and they'd send me one.... my first choice was Amazing Math : Projects You Can Build Yourself and that's the one I received today.  woohoo!!  (It wasn't at my library, so I'm happy to get a free copy!)

Cookies.  (Didn't bake them all last night, as I made a double-batch.  ' Thinkin', see. Eric can't eat a double-batch in one day!)

The Pyramind Game (codename for Totally Tut, you may remember.)

Start supper.  (Crockpot.)

Store run!
Second time to send the babes in alone.  I'm rather gettin' the hang of that.  Funny that Trev came out waving the receipt in one hand and change in the other, and Little Madd was hauling two gallons of milk.  :)

Ratatouille (pc game).

Start those bread bowls for dinner.

Better get on those cinnamon rolls that I've been meaning to make for over a week, now, too.....

Zoo Tycoon....

.  .  .  .  .  .  .  .  .

So there it is, though I didn't finish it. 

Early on in the day, I was looking at my shiny new Amazing Math book.  Amazingly enough, one of the first two projects is making a Sorobon--a Japanese abacus.  That's amazing because I had mentioned to my friend Jessica about a week ago that if she found books or sparkly things to play on an abacus, to please let me know, that I had been thinking about that for years.
The other of the two projects was learning base-five, or counting in different numeral systems.  Which I quickly perused, and wasn't really understanding (I have no memory of learning different number based systems in my life, excepting roman numerals, but that wasn't mathematics), but thought, well, I'll read this again, so I can understand it and not be lost when I read it with Trev....
Then lo and behold, this morning happens.


First thing this morning, while my family still slept I stumbled upon Binary Arithmetic.  Taught Socratically to third graders.  Not only was I able to definitely understand binary arithmetic (I should hope so, as this was for young children, though he did say that it was often a difficult thing for adults to grasp) but I learned that calculators and computers work by firing electricity through circuits via this method, and then they interpret this code back into our numerals and numbers.  Aaaah!  Which is why computer code is a bunch of square zeroes and straight lines that look like " I  "!!  Dang!  How cool is that?!?  I had no idea.  (No software engineers or programmers living in this house, friends.)

Put cinnamon rolls in the oven.

So I was thinking I had this thing in the bag (heh) so I wrote out numbers up to thirty (to make myself a chart), and their binary equivalent.  Multiplication?  Easy.  Addition?  Easy.  Subtraction?  Easy.
Wait.  'Til I got to twenty-eight minus thirteen.  aka, 11100 - 1101.  Uh... wait.  :)  Yeah.  Not so smart after all, is she???
But this is the land of opportunity, this internet we have, and I can just do a search for Binary Subtraction.  And be led here.
And I can feel a little bit better about my taxed brain because presumably (as they're talking math and computer sciences) they're not talking to third graders.  ' Course, it could be that I am embarrassingly wrong, and these things are taught to third or fourth graders.  We did not have computer science classes in 1977 when I was nine, friends!
Okay.  Wait.  What?  I need real problems.  So I go here.  Phew-- It's a college.  Not a preschool.  :)
Aaaaah... of course.  I'm still thinking borrowing means "10" or "9", then got rid of that "9" in my head, but wasn't sure what to do... then remembered/saw that this "10" was "2".  Aha!  Got it.  Maybe....
Let's try 11100 - 1101 again.

Yes!!  I've got it!
Can move on with my life.
Isn't it so awesome the way these little inquiring/learning trails work???

Cinnamon rolls are out of the oven...
and can now get back to Amazing Math with confidence.  :)

On to the living, then!

So... what? : Unschooling

Evidently it's time again for one of those, "So what do you do?" posts again.  I'm not feeling particularly philosophical or intuitive or spiritual about it (read: mushy), and I'm not feeling the need for justification... just maybe an explanation of the ideas and thoughts behind the Play of our everydays.

I was thinking yesterday as Trev was reading and playing Godzilla that his play was just as valuable to me as anything else he could be doing.
Some people might not understand that.  Anything that he's learning isn't obviously valuable or tangible, after all.
He may not even be learning anything at all!  And I have absolutely no problem with that.
He's playing.
He's using his imagination.
He's exploring his knowledge of facts and figures that he's collected inside his head, making up stories (or repeating them in whatever accurate way he may choose, according to his research), creating, expressing, and being comfortable with who he is and his interests.

But would this do for every minute of every day?
And what's my job, then?
My job is to make sure that things stay interesting.
My job is to assess my own personal needs, to present them to the family, and see if they'll come along. And yes, I say Needs, for they are sometimes mad cravings that I get, and it feels imperative to Living.  I need to get into the woods!  I  need a big adventure!  Can we go exploring?, I need to tromp around and do something really, really cool!  Like visit a real-life paleontology site.  Or a ghost town - I get those pretty often.  Or even a favorite museum.
My job is to make sure that everyone else is getting their needs met, as well.  And to help them figure out why and what those needs are.
My job is to pay keen attention to what the babes are up to (over all, not invading their every minute), and to make sure they're thriving.
Thriving is definitely the objective of this way of life.

So.  Does thriving happen on its own?
Not really.  Not consistently and always, without being inspired or prompted.  (I do not mean being forced or coerced, but mean inspiring things like season changes, karate classes, play with friends, going Out, a new game, library visits...)
Can't sitting-at-the-table lessons ensure thriving?  Sure, for whomever that works.  If parents and children feel so happy in their studies that they're ready to spin off the planet, or if in study they find immense satisfaction and great personal purpose. (And I mean sincere personal purpose, here, as in "this feeds my soul", not "this feeds my need to make my children seem superior" or "this feeds my need to have an Honor Role bumper sticker on my car for the sake of my own ego."  Although, even those are among your choices, if you choose to live life that way.)
The way to best see it happening in my own home is to just make sure my children are lively and interested.  Interested in life--curious about the world, and the way it works.  As I've said many times: thinking, discovering, exploring, and creating.

So isn't constant Play (even playing with the Godzilla collection -however impressive and grand :) ) a worry?  Harmful?
Well- that's the thing.  It isn't.  Because thriving is the goal, remember?  And I'm paying attention.  Assessing.  Evaluating.  Asking questions.  Checking in.

But doesn't Play just take over?  Doesn't watching television take over?  Doesn't computer play Take Over?!?
No.  It doesn't.  Because there are lots of other things to do.
Here's the thing-- when life is interesting, we have lots of interesting options.  And we have lots of interests.  True, sometimes a particular theme will run the show for a while.  But not forever.  And not solely, which we'll notice if we keep our eyes wide open to all the other things that are actually going on while The One Thing is happening.

The dreaded and be-damned Screen Time is a huge worry for a lot of people.  But -amazingly!!- some of us don't limit screen time. At all.  AND we still play outside.  AND we take walks in the woods.  AND we play math games and watch math videos (Khan!), and we read The Wind In the Willows and Little House and poetry, and we attend performances at the children's theater on occasion, and we visit museums and we paint and do science experiments and take the dog for a walk and go roller-skating and play at the beach and sculpt with clay and we have conversations about politics, cultures, life and death and God.

I am not saying that people should live their lives as we do.  Hardly.  This family of mine are the only ones that can or should live this life we're living.  (Though some look similar to ours, certainly.)

I'm just laying out plainly a few Things I Know For Sure.

That I'm pretty good at ensuring our minds, bodies, and hearts are in good working order: ie healthful energy flowing into and out of them.
Things like Imaginations make me happy.
Like that I feel quite comfortable in both, equally, the roles of Leading and Following. (And sometimes even stayin' put.  :) )
That seeking Joy, genuinely and authentically, goes a long way toward ensuring that the souls in this family are doing well.
And like that I can be trusted (trusted by my Self) to pay attention to my children, to make sure they thrive.
You know.
Shiny,
happy
people.

So that's what I do--what we do.
We make shiny, happy people.
And we play.

Friday

Maddie's been wanting some Baby time, so I called my dear friend and asked if we could come and play. 
We got some Littles time and got to have lunch at the home of Friends, so that was lovely.

To home, to check in with Trevy and Dad,

then off to get some eggs and the piece of black felt we need to finalize two costumes.  Yay!

Back home to reading (she's getting more serious about it, I guess--though she still has a few letters that she's like, "what does that look like, again?" and really seems to have little real 'knowledge' of letters and sounds consistently.)

There was pretty great Biology play with the Eye-Clops.  (That's a pretty cool toy/tool, we say.)

(Examinations included most of her own body... knee, arms, hand, hair, mouth, nose, ears, shirt... moved onto Annabelle - who got much the same treatment - and finally to some scientific cubed critters in little study blocks.)

Madd was looking for something to do, so "Chemistry?"
"Yeah, chemistry."
"Or magnets, Madd.  We haven't had those out in a while."
"Yeah, Magnets!"
Magnets it is.

Which of course meant discussions of magnetic fields and the center of the earth.

And a robot!  A girl robot, naturally.  (Which I"m totally in love with.)

Mario!!
check.

Kitty ears!
check.
(And her best kittycat face.)

Phew.  Had it soooo easy this year.
I know all you amazing Mama's are probably rolling your eyes or gasping at my offending ineptness, but pieces of felt (that I didn't felt myself!) and a hot glue gun is juuuusst about within my capabilities!!  :)

Repaired Godzilla figures.  whew.  He's a happy boy.

Wild Kratts.

Planning a Halloween Party.
For She and her animal friends.
We're planning decorations.
She's thinking costumes and hats.
Much fun with that tomorrow, methinks!

Dinner.

Chocolate Chip Cookies.

Magic Show.
With a looooooong magic cape.

She wouldn't let me stay.  Clearly this show was not open to the public.

Head stands.

And Kipper.  I love Kipper.  One of the few shows that the sounds don't just drive me mad.  :)

I love this life of ours!

Saturday's Artist

Welcome to Saturday's Artist; a weekly joining and celebration of every kind of creativity.
We hope you'll join us in celebrating this wonderful part of ourselves.
Show us where in the past week you've been shining your artistic, magnificent light!

Something this week that fed your spirit.
An outstanding photograph.
A day of mad painting.
A new yarn discovered that has sparked something fabulous for you.

The only requirement is that it is your favorite artistic Create! of the week!

Linking is open until Tuesday morning.

⊰✿ To link you'll just put in the address of your creative post, and make sure there is a link somewhere on that page back to O.L.M. or Saturday's Artist. That's it! ╰⊰✿

Give-Aways!

Hello, Friends!

Please note that new pretty picture there on your right... I am pleased to welcome a new sponsor, my sweet friend Jean from Heart Rockin' Jewelry!

We'll be having a give-away for one of her bracelets,

and another give-away for a set of books from (those folks I love) Nomad Press, so stay with us!

Thursday

Maddie began with Body stuff.  It was still on the table, after all.
And then stuff that wasn't still on the table was soon brought back in again.  :)

We made cheesy crackers.  Both babes say Aye.

Mama-Mazing to the rescue.  (This was via my mad computer/all things techno skills.  I do love it when I can save the day!)

A search for Get Along Little Dogie.  She just had to know.

Sail away, sail away, sail away.

Play with Dad.

Build cities. Legos.


And then, naturally....

and music, too!

Found the recorder.  woohoo!
Next lessons, then.  :)

Charlie Brown.
And supper.

It's a good life.

From the Hearth

The heater kicked on seventeen minutes ago.
I think the wee hours of this morning may have brought our first frost.
It's dark, still, so I've plugged in the pretty white christmas lights around the window.  (They've been up since last winter.  I like them.)
My beloved three still sleep, and I have some quiet time.

I was just thinking about Home.
There is nothing so nurturing and leaves me sentimental as the latter half of autumn. 
Autumn in the valley... outside my window.  The autumn that wants for pumpkin candles.  The one that turns the grass brown, and leaves frost on the pumpkins.  The one that calls to turn on the oven, and leave it or the stovetop on for most of the day.  Flannel jammie bottoms, cozy socks, and favorite blankets.

Home and Hearth. 


Sometimes we are told we shouldn't like Home so much.  It makes us backward.  We can't deal with society.  It makes us strange... awkward... inept.

[shrug]  But it's hard not to like home. 
It's a place where we can learn how to be ourselves without getting into too much trouble.  How to love others better without embarrassment or impossible-to-bridge chasms.  How to get along without too much fuss.

Home means a place where your wishes are granted.  A place of favorite things.  Favorite stories.  Favorite people.  A place for ideas becoming.  A place for free expression, confidences, and unwavering love.

Home is a place where we have all the time in the world for whatever dream can be dreamed.

In our house, it's a place for exploring freely.   
I think this is my favorite part of Home right now--providing the best nest for my children.
Sometimes that means offering my babes the freedom to learn things when understanding comes simply and easily, instead of spending months or years on them before that is so.  Done by not pressing unnecessary lessons into their heads, but by being comfortable waiting until something can be understood in minutes.  Like learning to tell time.  And like complicated subtraction. 
Some things are learned quietly, slowly, naturally.
Other things in our house are just explored, and learned over time... with paints, the television, cuisenaire rods, and each other.
There is no one at home who raises an eyebrow over anyone finding their way.

Here, in this lovely, warm space, I can be generous of spirit without doubt.
I can shut out the outside world and reflect and smile.
When I am not doing 'good enough', it's often easy to change it.

In this magical place, I can live best by my own (carefully examined) ethics and convictions, and have no doubt but that I am doing the right thing, according to my soul's promptings.

Here we get to do, become, seek, grow, learn, and Be while surrounded by people who welcome us and all that that means.

How could we not love such a place?
How is it possible that it's not considered invaluable?


It seems like a lovely, nurturing place of first, last, and always, to me.

Wednesday

Starting off with calculator play.
At first that looks like "What number is this?", and "fifty-five million, three hundred seven thousand...." and then it looks like making up questions and checking her answers.

Zoombinis!  Logical Journey, actually.
That went on for an hour or two while Mama puttered in the kitchen.

Apples awaiting.

And goo.

Sal Khan, again.

Body, body.

Trev said yesterday he wanted to play, so we brought up a Magic School Bus kit (A Journey Into the Human Body) and the Body game.  Since we didn't get to them yesterday, we'll play today, hmm?
Thar he sits.  And thar he gets dissembled.

 

With narration. 

 

Body books!

And so, an experiment with lung capacity.  (via MSB kit.)

Bill Nye over lunch?... they chose Digestion.
And Body play when lunch was done... still watching Bill.

Jump!!
(and catch-up for the Mama.)

Ready, set, go.

More body books.
(Well--the same books.  Just more perusals!)

And eighty-five (thousand) rounds of Mystery Garden with Honeypot.  :)
It worked.  I was able to edit the day's notes and photos while she and I played.

An' now it looks like we're up for a little MythBusters with our supper.

Life is sweet,
an' that's good enough for me.