Sunday, March 27, 2011

Roots and Fingertips

(A hodge-podge today.) Two quick notes that I want to jot down for myself.

The first is for our Botany unit. One of the topics we are covering this week is Roots: type and function. I want to introduce it with a wonderful book of poetry that I first found on the shelf at the local library as part of Black History Month. I saved it for this unit.

Roots and Blues: A Celebrationby Arnold Adoff

Roots sustain you. They dig deep into the soil to hold the plant, give strength, give a sense of place.

The other surprising observation I made last week was about the word "digit." We had a visitor some into the classroom and before he talked about binary and hexadecimal number systems (he works on weather satellites), he asked the children about the number system we all usually use every day. It has ten digits, right? And he held up his finger and wiggled them. And I thought, AHA. Digits! Like fingers... I don't know why I had never figured that out before.

I had a world of trouble helping my students understand the math term "digits" until it finally came to me, to tell them that digits make up a number like letters make up a word. Digits are actually more complicated than that, because the place they occupy in the number is what gives the digit its value, but it was an easy way for them to shift to seeing the number as a whole to looking at the digits that make it up. For the first time (after that explanation) I would ask a child, how many digits are in this number, and they could tell me.

Do you know the mathematician who finally persuaded Europeans to ditch the obsolete Roman Numeral system?

His biography (and 14 others) can be found in Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2

Sunday, March 20, 2011


What a great weekend! Saturday we had brunch in the morning with my family and then my boyfriend and I took the girls rock climbing at Carderock, along the C&O Canal. Sunday was a program at the Walters Art Museum in Baltimore. I'd never been to this museum before and I was very pleased. It was quite lovely. We had a tremendous docent, too. Did you know that sarcophagus literally means "flesh-eater"? These marble boxes were crematoriums. Marble gets very hot in hot climates and ancient Romans would place the bodies in these large marble boxes, close the heavy lids, and several months later they would open them up and sweep out the ashes. I was astonished; I never knew that before.

Two great resources that I found while I was there, the first was a book that was out by a bench in the ancient Greek and Rome section: Pandoraby Robert Burleigh. (Happily, the story of Pandora's Box was also part of the Greek Storyteller performance that we saw by Seth Reichgott). It was wonderful... if you can imagine a one-man show/Greek Mythology performance. I have adored everything I've seen by this profoundly talented writer, actor, and storyteller. His link includes a YouTube video. Enjoy!)

The second book I found today that I was very pleased with was a book in the gift shop: Vincent's Colors

Author: Vincent Van Gogh

I quite like it because it has Vincent Van Gogh's actual words that he used to describe his paintings (he wrote extensively to his brother Theo, among other people). You can buy Vincent Van Gogh's collected letters for $650.00 (my cousin got this as a gift from her husband last year, the lucky duck) but this book simplifies things a bit.

Vincent van Gogh: The Letters: The Complete Illustrated and Annotated Edition (Vol. 1-6)

Tuesday, March 15, 2011

Monday, March 14, 2011

Botany Resources

First and foremost, if you want to teach Botany using the Waldorf method of storytelling, Keepers of Life: Discovering Plants through Native American Stories and Earth Activities for Childrenby Michael J. Caduto and Joseph Bruchac is an ESSENTIAL resource. This book weaves in Native American legends to introduce the concepts in the unit, beginning with Biomes. Algae, Fungi and Lichens, Mosses and Ferns, Wetlands and Bogs, Carnivorous Plants, Conifers, the Fibonacci Sequence, Flowering Plants, Pollination, Prairies and Other Grasses, Deserts and Desert Plants, Plants of the Arctic Tundra and Alpine Environments, Temperate and Tropical Rainforests, and Endangered and Threatened Plants are just a few of the topics covered in this wonderful curriculum.

The FABULOUS and comprehensive (covering every continent, including Antarctica) Biomes material by Waseca would be a wonderful tie-in to this book.

As for the artwork portion, we are creating Botany journals with watercolor paper. Sketching first in pencil, then outlining in fine line marker, then using watercolor pencils for the colors.

Drawing from the Book of Nature is an excellent Waldorf resource for Botany.

Chapter 11: The Leaf
Chapter 12: Algae, Fungi, Lichen, Ferns
Chapter 13: Higher Plants
Chapter 14: The Flowering Plants

Charles Kovacs has also written a Waldorf Botany curriculum which I haven't yet had a chance to buy, but which Nancy Parsons recommends highly.

Science Experiment Templates

We are beginning our Botany block -- this would be a grade 5 block in Waldorf -- and so I am going to be posting helpful resources. We began it with a science experiment and so the first thing we needed was a template to record the steps of our experiment and what occurred.

Here are a variety of science experiment templates:

Investigation Planning for Class 1 (pdf)

Investigation Planning for Class 2 (pdf)

Investigation Planning for Class 3/4 (pdf)

"My Experiment" (Word doc)

Sunday, March 6, 2011

Math Adventures - Probability

Here are the directions for the Probability exercises that we did.

Probability I
When you toss a coin, how many possible outcomes are there?
How many outcomes can there be at one time? In other words, can I toss a coin and get both heads and tails?
We say that the probability that something will happen is the number of ways to get that outcome out of the total number of outcomes.
For a coin toss, there is a 1 out of 2 chances that I will get heads. This means 1/2 or half the time. Toss a quarter ten times and keep track of the number of times you get heads.

(For Probability activities II and III, a "sock drawer" was created using a small basket and a number of pairs of baby socks. The socks in the basket were as follows: two blue socks, four pink socks, six white socks.)

Probability II
Remember that the probability of an event is the number of ways to get that outcome over the total number of outcomes.
Look through the sock drawer.
If you close your eyes and pull out a sock at random, what are the chances you will get a pink sock? A white sock?

Probability III
Probability gives us an idea about our chances, but sometimes we really need to be sure! After all, who wants to walk around wearing socks that don't match?
Suppose you wake up and it is dark because the power has gone out. You will have to grab some socks and bring them with you to school -- hopefully you will have a match! You have six white socks, four pink socks, and two blue socks in the drawer.
How many socks will you need to take to guarantee you will have a matching pair of socks (any color)?
How many socks will you need to take to guarantee you have a matching pair of white socks?

(The mathematician pointed out that the skill students are learning here is the value of negation. When they need to determine the number of socks required to guarantee a pair of white socks, this means the need to determine the number of socks that are not white -- as in, worst case scenario, they have grabbed all those first -- plus the two white socks. To be 100% sure you have something you need means you need to have everything you don't need also!)

Math Adventures - Toothpick Games

If you play a strategy game often enough, you start to see the best way to win. Sometimes it is best to go first, other times it is best to go second. Here are the directions for the toothpick games that we played.

Toothpick Game I
Play this game and find the winning strategy:
Take seven toothpicks and put them on the table between you and your partner.
When it is your turn, you must take ONE, TWO, or THREE toothpicks (your choice).
Whoever takes the final toothpick(s) wins.

Toothpick Game II
Let's change the rules a bit and see what happens. Does the strategy stay the same? Play this new version and find the winning strategy:
Again, start with seven toothpicks.
On your turn you must take ONE or TWO toothpicks.
Whoever takes the last turn wins.

Toothpick Game III
So, you figured out the winning strategy for Toothpick Games I and II? Let's change the rules a bit and see what happens. Play this new version and find the winning strategy:
This time, start with eight toothpicks.
On your turn you must take ONE, TWO, or THREE toothpicks.
Whoever takes the last turn wins.

Math Adventures - Voting

My school had a mathematician visit this week and develop a parent-child seminar on math concepts. These are hands on activities for parents and children to do together. They're wonderful and I'm glad to share them! Here are some of the activities that we did at the Elementary level:

The first was an exercise that demonstrated the importance of how district lines are drawn in voting. This has become a big issue in our neighboring state of Virginia, following the most recent Census.

To first demonstrate the "popular vote" she passed out colored index cards with letters on them. Each person got a card. We were voting on chocolate, strawberry, or vanilla ice cream. Ignoring the colors of the index cards, we tallied the votes by letter. More people had a "C" on their card than any other letter so the popular vote was in favor of Chocolate.

Now we organized our voters into districts. The people with yellow cards went to sit at a table together (Yellow Town). Green Town and Violet Town were also quickly formed. Now, within each town, a vote was once again taken. Whatever flavor was the majority choice would be the vote of the entire town. The students were amazed to see that two towns voted "V" for vanilla and only one town voted "C" using this method. Even though Chocolate would win in popular vote, using the district system resulted in a win for Vanilla.

The mathematician shared some classroom (or at home) follow up ideas for this activity: Talk with your students about what it means to have a representative democracy as opposed to a true democracy. Have them explain to you potential benefits and drawbacks of each system. Discuss other ideas for voting. Instead of voting for someone, you could vote against someone. We could rank candidates and give three votes to our top choice, two votes to our second choice, and one vote to our third choice. We could be given three votes to cast and distribute them as we wish (all three to one candidate or split the votes across two or three candidates). Test these ideas... do you always get the same winner? Which one is most "fair"? What does it mean to be "fair"?

To reproduce this activity in your classroom with 12 students, the directions to prepare the cards are as follows:

Cut four cards out of green cardstock. Label three C, one S.
Cut four cards out of yellow carstock. Label two V, one C, one S.
Cut four cards out of violet cardstock. Label two V, one C, one S.