Wednesday, March 13, 2013

Waldorf Math: A Story for Learning Place Value and the Value of Stories for Learning

Check out numerous great Waldorf posts at the gracious host


loads of  Creative Learning posts over at  
(a blog chronicling a family using Waldorf and Charlotte Mason)

By Dinah

There's a thing about Waldorf that if you know even a teeny bit about Waldorf, you know Learning Through Story is Big.

I know a teeny bit (and that's about it) about Waldorf -- so I at least know about the importance of Story.

There's a large body of Steiner theory about why Story is important.  I've skimmed about .01% of it.  And I don't plan on reading any more.  Because I don't need to know why Rudolf Steiner thinks Story is important.  Why?  Because I already know it's valuable to our family and that's enough for me.

By Dinah

Stories about people, even fictional people, stick with us.

Sometimes, dependent upon the story, it's like the fictional people are part of our lives.  They weave their way into our minds and hearts and we feel we know them.  They are unforgettable to us.

It's this unforgettable and rooted trait of stories in our lives that makes learning those things that are otherwise hard to remember (or are entirely forgettable) so much easier.

So, let's talk math.

For those without a toe in the Waldorf pool, that was abrupt.  "I thought we were talking stories, not math?" Well, it's the stories about math that I'm here to talk about.

My friend, The Offshore Banking Queen, is a math genius.  I will not forget that she told me once that the concept of "carrying" and "borrowing" in multi-digit arithmetic was absolutely mystifying to her as a child when she was trying to learn it.

Although I have a large inventory of memories of being befuddled by math, this isn't one of them.

So, I wondered what my own children's experiences with multi-digit arithmetic would be.

It has proven to be effortless.  Effort-less!

And it's all because of Mr. Place Value and his housing development.

Mr. Place Value's housing development on "Decimal Lane"

In September, after seeing that both the Oak Meadow and Math U See curricula used a story in an attempt to teach place value, I made up my own.  (I'll note here that there are a lot of "math stories" out there.  Especially with the four processes.  I've been surprised that the rules of the math being taught are not more intimately tied to the plot of the story.  But, that's another story.)  Here it is:

There was once a man who lived in a most beautiful place (insert description of how beautiful the place was).    And in this beautiful place, he lived in a glorious old rambling house.  (insert description of how beautiful house --including the color.  We chose Green).   However, as beautiful as the place was and as comfortable as his old house was, Mr. Place Value wasn't entirely happy.  Because he was so very lonely.

So, one day, he decided that to make the beautiful place he lived in absolutely perfect he was going to find a way to bring people out to where he was.

So, he decided to change his house a bit.  He changed his ballroom into two more bedrooms.  He changed the sitting room into another bedroom.  He thought about making the dining room smaller, but he wanted it to be big enough for everyone to eat in together..  He thought he might make the living room a bit smaller, but, this too, he wanted to be big enough for everyone to gather in together.  He filled it with cozy chairs and a window seat and make it a place where many people could sit and read together in the sun.  So, finally,  Mr. Place Value decided that he could not fit one more bedroom.  So, he took the six bedrooms the glorious old house already had and he added the 3 more he was able to make and figured out that he could fit exactly 9 people in his glorious green house.  Exactly 9 and no more.

Mr. Place Value excitedly called the newspaper.
"I want to place an ad!  This is what I want it to read:

Beautiful Boarding House on Decimal Lane for rent.  1 lonely, friendly person looking for 8 more folks to live in paradise!  Sunny reading room.  Spacious dining room.  Hurry!  It won't last long!”

And in no time at all, he had his first tenant.  She couldn’t get over how beautiful Decimal Lane was and how magnificent the boarding house was.  She and Mr. Place Value were very happy in it together.  Now there were two people living on Decimal Lane.  But they had room for 7 more, so she called all of her friends to tell them what a wonderful place she had found.  Pretty soon, the green house was all full up.  So, when another friend came knocking on the door wanting to live in such a beautiful place, in such a beautiful house, with so many of her wonderful friends -- they didn't know what to do.

The friends went to Mr. Place Value --

“Mr. Place Value, this is our friend and she wants to live in your beautiful boarding house on your beautiful lane.  But, as you know, we’ve already got 9 people here, won't you please please please let her live here too?  We'll squeeze in!  We won't mind!”

Now Mr. Place Value was a very kind man, but he knew that having more than 9 in the boarding house would just not do.

“We’ll all be too crowded and no one will like living in our beautiful boarding house if you try and squeeze another person in here.  I’m sorry, it’s for the best, I promise you.  Nine is as many as can fit.  Anymore than nine just won’t do!”

Mr. Place Value looked at each sad face.  He, too, was sad.  And he looked from sad face to sad face and then, when he got to the 10th face, the saddest of all, he knew he just had to find a way that she could come and live on Decimal Lane with all them, too.    "What ever can I do?”
“I know!” exclaimed Mr. Place Value.  “Decimal Lane is such a long street.  The longest street there ever could be.  In fact, it never ever stops.  So, we can fit as many houses on this street as we want.  Why don’t we build another place, right next door?   We can all move in there, all ten together, and I’ll rent out our beautiful boarding house to another 9 happy folks?”

All ten jumped for joy and ran outside.  “Right here.  Right next door.  We’ll still be on Decimal Lane, but in a bigger house!"  

Now Mr. Place Value was a prudent man and he knew that he shouldn't be rash in building his next house.  Yes, the Little Green Ones Place had been popular.  And, yes, the Tens Place already had one group who wanted to live there, but how big should he make it?  Not too big, but not too small.  Well, 9 had been a good number for his Ones Place boarding house.  But he couldn’t make it 9 again – he needed it to hold at least 10 folks or else he’d have the same problem as he had now!  Well, how about 9 floors in his great big house?  And each floor had to be big enough to fit all 10 friends together.  So, 9 floors with 10 friends on each, well that’s 90 folks who could all live together    Yes, 90 folks in the Tens Place; we'll call it the Tens Apartment Complex.
“Okay, my friends, here are the new rules."  Although Mr. Place Value was a kind and generous man, he did require a couple of rules to be strictly followed, all the time, without exception.

His first rule had been that 9 and only 9 people could live in the, now by comparison, little teeny, green house.

His new rule was that anyone who moved into Decimal Lane must first live in the Little Green House.
That nobody could move into the Tens Apartment Complex unless there was a group of 10 to move into, all at once, as a nice group of ten and fill up a whole floor at once.  And since there would be only 9 floors.  There can never ever ever be more than  90 people living in the Tens Apartment Complex and never ever ever less than 10.

"Agreed?" he asked.

"Agreed!" everyone shouted.

Well, the ten friends moved in to Tens Place and it was just as lovely as Ones Place and they just couldn’t keep the wonderful place all to themselves and, so, they started inviting everyone they knew.

First, the new folks lived in the beautiful boarding house at Ones Place. 
(Move each new person in)

Then, when the 10th friend wanted to move in too, they all had to move to the Tens Place.

And guess what happened??

More people moved in and more and more until finally all nine floors of the Tens Apartment Complex were full and all nine bedrooms of the Little Green House were filled  and then another friend came knocking.

"Oh, Mr. Place Value, all 9 bedrooms in the Little Green House are full and all nine floors of the Tens Apartment Complex are full and now here's a 100th friend and there's no room for her! Can't we just squeeze her in somewhere.  100 is not so much more than 99!"

Now Mr. Place Value was a very kind man, but he knew that having any more than 90 people in the Tens Apartment Complex and 9 in the Ones Little Green House would just not do.

“You’ll all be too crowded and no one will like living in our beautiful houses anymore if you try and squeeze another person in here.  I’m sorry, it’s for the best, I promise you.  Ninety and Nine are as many as can fit.  Any more than ninety-nine just won’t do!”

Mr. Place Value looked at each sad face.     “Oh, I just can’t turn that 100th sad face away.  What ever can I do?” 

“I know!” exclaimed Mr. Place Value.  “Decimal Lane is such a long street.  The longest street there ever could be.  Why don’t we build another place, right next door?   We’ll build a palace, with 9 enormous ball rooms that will fit 100 people each!  And then 900 people can live in the Hundreds Palace and we can all move there together.

 And all the folks yelled for joy.  And it was pretty noisy, since there were now 100 of them.
So, everyone -- the 90 from the full Tens Place and the 9 from the full Ones Place and the one newest friend – everyone, all 100 of them, moved into the first ballroom at the Hundreds Palace.   

Do you think they lived happily ever after ?  Or do you think they had to call Mr. Place Value again because there was just one more person more than 999 that wanted to live on beautiful Decimal Lane?

We’ll have to wait and see.

By Gracie

We've been using this story since October.  A pleasant surprise has been that we can talk the story as we've come to the new concepts, generally called "borrowing" and "carrying."  We've also naturally moved the idea that there are buildings on both sides of Decimal Lane, but now everyone wants to move into together.

+  4

Here's how Dinah or Grace talk it out:

"7 people are living in the little green house and four more want to move in.  They can't because only 9 people can live in the little green house at once.  So 10 have to move over to the tens apartment complex and that leaves 1 in the little green house.

Now we move the new floor of tens over to the Tens Apartment Complex and add it to the floors that are already full -- so there are now 3 floors of the Tens Apartment Complex filled."

Similar conversation surrounds "borrowing" -- where one flood of the Tens Apartment Complex comes over for just a minute to be able to have enough to take away from when people are moving off of Decimal Lane.

And even though we've talked about what we'll call each new column (The Thousands Kingdom, the Ten Thousands Continent, etc.), we've not actually named anymore and it's just become imbedded in their knowing that each can only have 9 and you carry the group of ten over to the next, or borrow the group of ten from next door.

It's been perfect and having effortless math has been such a welcome change round here.

I'm looking forward to the remainder of 3rd grade being connected with some more Waldorf or Waldorf-Friendly math.  But that's an upcoming post.   The effortlessness of Math Story makes Waldorf inspired math a great fit for us right now.


  1. WHAT???? Why didn't you send this to me? Don't you love me??? How come I can't subscribe to your blog so that I don't have to stalk you to get the good stuff. I'm a bad stalker. I forget to stalk. Maybe I need to put it on my calendar. BTW your blog looks beautiful. I am sure if you tried really hard you could figure out how to put a follow me button on top. Just for me??
    Thank you for this story, from the very bottomest of my heart, I will be copy and pasting it so that I can keep it for my very own and benefit from your awesomeness. Your worst stalker ever.

  2. I wish you were more stalkeresque in your stalking because I love your comments (:

    I don't know why, but I've never wanted to add a "follow" thing. But, since you insist, I put one way way way at the bottom where only you will find it (:

    I'm coming out soon with an awesome synthesizing post on math. Good resources abound in it. Now that you'll follow me, you'll see it (:

    How's the new blog coming? ahem....


  3. What a wonderful post. I taught my seven year old son about the 4 properties of math using a Waldorf story. I look forward to telling your story to my sons. Who knows, maybe I might even make some peg people to go along with it :) Thank you for telling your readers about Creative Learning and sharing this post - so many children will benefit :)

    1. Thanks for hosting (: It's a great link up and I'm enjoying reading other's ideas.

      We're just about to embark on a long math block (including the 4 processes with story). I've been working on a "math series" of posts and I hope someone will find them useful (:

      Thanks again!