Place Value & Redwood Trees

This is a lesson I have mentioned on the Column Algorithms / Place Value page on my website but I wanted to give a more complete explanation of it here. We did it on Monday and it went so well!

she was tickled pink to share her family's magnet
of a car driving through a redwood tree!

Waldorf always centers a lesson around a story. For this one, I like Redwoods by Jason Chin.

There are lots of different numbers that you can pull out of this book and make with the Number Cards and Golden Bead Material (Montessori hands-on math manipulatives) but I think the best are 2000, 200, 29, and 2.

Small Wooden Number Cards with Box

Montessori color-codes the digits to show their place value.

units place - green

tens place - blue

hundreds place - red

Note that the thousands place is green again because it is the units place of the Thousands Family. Every set of 3 digits between the commas always follows the predictable pattern of units, tens, and hundreds.

134 , 237 , 984

My earlier post, How I Teach Place Value, goes into this in more detail and also explains the Dice Game, which is wonderful for learning how to read big numbers!

We aren't up to the Dice Game yet. We are just working in this lesson on understanding that the digit 2 can mean different things depending on where it is in the number.

NOTE: I explain Fractions in a similar way. The top number, the numerator, tells "how many." The bottom number, the denominator, tells "what kind." The bottom number in a fraction is which kind of piece you are getting from the Cut-Out Labeled Fraction Circles. In place value, the location of the digit is what kind of piece you are getting from the Golden Bead Material!

100 Golden Unit Beads

45 Golden Bead Bars of 10 with Box

10 Wooden Hundred Squares

9 Wooden Thousand Cubes

So, here is what we did.

First, we read the book Redwoods together.

Then we got out the Golden Bead Material and reviewed which piece is which (units, tens, hundreds, thousands). They hadn't see the thousands pieces before so that was very exciting! (I introduced the Golden Beads after we read The 500 Hats of Bartholomew Cubbins by Dr. Suess. At the end of the book the king gives him 500 pieces of gold for his hat. A perfect transition!!!! We looked at the units, tens, and hundreds pieces of the Golden Bead Material and made some numbers from the story and wrote them in colored pencil.)

Then we got out the Number Cards and I suggested that -- just as we did with The 500 Hats of Bartholomew Cubbins -- we make some different numbers from the story with the Number Cards and then build them with the Golden Beads.

The four numbers I like to use from Redwoods are presented in the story in just this order, so it is absolutely perfect.

2000
"One tree can live for more that 2,000 years, which means that there are trees alive today that first sprouted during the Roman Empire."

200
"Redwoods regularly grow to be more than 200 feet tall."

29
"A redwood trunk can be twenty-nine feet in diameter at its base. That's so wide that a tunnel can be cut in it, big enough for a car to drive through."

2
"With enough light and water a redwood sapling can grow fast -- up to two feet per year."

Notice that in 29, two cards are used. I love the Number Cards because you can unstack them from each other and lay them side by side to see expanded notation (20 plus 9), and then "slide 'em and stack 'em" to see standard notation. This makes it easier for the children to figure out how to build the desired number with the Golden Beads as well.

Once we had built all four quantities, I worked on writing them down in colored pencil and while I was doing that I asked them to look and see, "there's something really interesting here... what is the same about all of these numbers?"

They looked for a bit and then noticed that all of the numbers have 2 in them! How can that be? They are all 2 but some of these numbers are really big amounts and some are really small. And then we were able to talk about how the 2 means something different depending on where it is in the number. I introduced the terms thousands place, hundreds place, tens place, and units place.

We will work more with this idea in the coming days and weeks. But it was such a nice and interesting way to introduce it!

NOTE: In Montessori we use the term "units" instead of "ones." In the Simple Family, it is true that the units are worth one. But the units of a Thousand Family are worth 1000. In the Millions Family, the units are worth a million! So it may seem calling them "ones" is making it more clear for the child but in the long term I think it is actually more confusing.

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