Hands-on Exploration of Capacity

Here is how I introduced Volume.

We began with a work station on Monday morning: a variety of containers set out on a mat, all with the milliliter measurements on the side covered over with masking tape. These were containers such as vanilla extract, facial lotion, vinegar, cooking oil, and so on. The students were asked to order them according to how much liquid each container could hold. Then they were to try to find the two that had the same capacity (they were radically different in shape). I found that students were using a lot of mathematical language in their discussion of which of our mystery containers had the greatest capacity. I saw students getting out rulers, and explaining to one another that you had to measure the container in more than one direction to compare their size.

The can of hair spray, being tall and thin, caused the most discussion. Some children were insistent that it held the most simply because it was tallest. Others kept moving it to another spot, because it wasn’t very wide and, they argued, it didn’t hold much. I gave everyone time to visit this station before we had our Morning Meeting.

During Morning Meeting I went around and asked the children to say what item they would move to another place in the line and WHY. We had a wonderful discussion, and I saved taking off the masking tape for the very end, at which point I revealed the correct order of the containers. During the meeting, when a lot of people were saying, “it doesn’t just matter how tall it is, it is how fat it is that matters,” a student pointed out that there were actually three sides that had to be measured, which led us to then working with the volume cubes, and finally learning the formula for calculating the volume of a rectangular prism. One child even became interested in the challenge of measuring the volume of a sphere, and pulled me aside to explain to me some of his ideas for doing that.

After our hands-on exploration with the milliliter, I explained the units of liter and kiloliter, and we referred to the Wooden Hierarchical material again to understand the scale.

By the way, even with colored masking tape over the mL measurements on the containers, I still needed to scribble with Sharpie over it. But the masking tape pulls off nicely in the end, and the Big Reveal is a fun moment.

My two containers of the same capacity were a 250 mL squat glass bottle of maple syrup and a 250 mL aluminum can of La Tourangelle Toasted Pumpkin Seed Oil






Not a single person guessed correctly.

Worksheets for Volume

Some quick links to worksheets for volume. I'm sorry that I don't have time to write up our volume/capacity lesson from this morning right now... but I will as soon as I can. It was awesome!

I never would have expected my students to spontaneously get out rulers and start arguing among each other -- using mathematical language and reasoning of course -- but since they did I am online looking quickly for resources to help me show them how volume is calculated and some practice pages for those who want more.


Volume Cubes - Easy

Volume Cubes - Harder

Volume Cubes - Hardest


Montessori has a material for building figures and calculating their volume using small wooden cubes, so these sheets will be easy to implement in the classroom.



Small Wooden Cubes for Volume with Box

Or, if you are going to teach the traditional formula, try
Volume of a Rectangular Prism (l x w x h)


And, if you're the type who likes to make your own worksheet, try WorksheetWorks.com - Calculating Volume. This website allows you to customize the problems on the page (simple figures or complex figures, English/Imperial units or metric units or a combination of both, and your desired paper size). Then it creates a free worksheet for you with reproduction rights allowed for a home or classroom for up to fifty students. And they give you an answer key!

Estimation & Measurement in Grams

This year I decided that I was going to focus a good amount of attention on the metric system. When I taught 4th grade in the public school, we did a week or so on the metric system of measurements, which never did anyone any good. Learning a new system of measurement can only be done with a little bit of practice each day, spread over many days. For example, we switched the thermometer in my truck to read in Celsius instead of Fahrenheit and now I know C so well that I have to convert temperatures in my head before I have a good feeling for what other people are talking about. It's just more natural to me to think in C.

My big goal this year was to have my students completely internalize the gram. Once you have a good feeling for the gram, you know whether you should go down a step to mg or up a step to kg for the object you are measuring. (I wasn't looking to get into the math for the conversions, I just wanted them to know which unit would be the most appropriate for any given situation, and to have an understanding of the prefixes.) Daily practice in grams? This is how we did it.

When I first introduced the gram, I got out the Montessori Wooden Hierarchical material -- which is built to scale -- and told my students that the thousand cube would represent a gram. The unit cube was 1/1000 of a gram, called a milligram. The million cube was 1000 grams, called a kilogram. Then I told them that I would set out an object on a special tray each morning for them to feel and weigh in their hands, then write down their guess as to its weight in grams on a slip of paper and place the paper in a basket. At morning meeting I would weigh the object on the Triple Beam Balanceand we would see who was the closest to being correct.



The students all got to choose something from the classroom right then, for me to weigh and announce the weight of, just so they'd have a starting rough idea on which to base later estimates. Each morning for two weeks, I would set something on the tray and place the basket, slips of paper, and pencil alongside. Each day at morning meeting we would order the estimates from largest to smallest (duplicate guesses were placed below each other), talk about the Range and the Mode, and then I would weigh the object with great ceremony. As I moved the weights and eliminated guesses which were too low, we would turn those over. Finally we would look at the number to the left and to the right of the final answer and see which was closest... this is an unexpected benefit to this activity! Students were doing mental math and arguing with each other about who was closer, one child or another. For example, if the object weighs 302.6 grams and one person guesses 250 and another guesses 350, who was closer to being correct? I heard some great mathematical discussions and people explaining their reasoning to each other. The person who was closest was line leader for recess and I wrote a slip of paper with the name of the object and the correct weight in grams and taped it to the door. After a few days, these taped slips became crucial as students used them to fine tune their estimates. I would see students standing with a smooth red rock in one hand and a large beanbag in the other, then weighing the red rock against the tape dispenser. It was wonderful! (Recording and taping up the answers in order from lightest to heaviest was also an unexpected spur-of-the-moment idea, which came about because I saw students going to previous objects for comparison. So we just incorporated it into the activity.)

At the end of the two weeks I gave a test. Yes, a test. I had the students number their paper from 1 to 12. I set out the wooden hierarchical on the floor one more time and labeled the cubes (thousand cube was labeled "gram", unit cube was labeled "1/1000, milligram, mg", million cube was labeled "x 1000, kilogram, kg") and talked about how a student the day before came to me with a single Smartie and told me he had weighed it and it weighed zero. I reminded students that there were units of measurement for objects that wouldn't appropriately be measured in grams because they were way way too light or way way too heavy. (We never once did any estimating in mg or kg.) Then I asked them to tell me by writing g, mg, or kg what they thought would be the most appropriate unit of measurement for the following items. And I stated 12 items. When possible, I held up the item, such as a piece of dental floss, a tissue, or a sunflower seed. For kg I used examples such an elephant, a teacher, a car, and a bowling ball. I reminded students to think about using the triple beam balance. If something is ridiculously too light or ridiculously too heavy for the triple beam balance, then gram may not be the best unit of measurement for it. When I was done I collected and scored the tests and I was extremely happy with the results of our daily estimation practice.




Many thanks to my grandmother, who helped me come up with this activity at the breakfast table over Christmas break!

Cookie Tins Repurposed

We have begun the "Grocery Buddy" process in our house. Each week, in rotation, a child is responsible for looking through the grocery store circular, choosing items that are on a good sale, and making up a menu for the breakfasts, lunches, and dinners. They cut out the sales from the paper and tape them onto the back of the menu. Then when I go shopping, my Grocery Buddy tells me which items we need to buy and what products are at the best prices. In return, whatever savings my receipt shows for sales and coupons goes to the Grocery Buddy for her piggy bank. This requires a largish bank, for bills and change, so we looked through the collection of cookie tins that we amassed over Christmas and each child chose her favorite design. Now the cookie tins are labeled and stacked on top of one of the bookcases.



Something new went into the cookie tins today: Wishlists. The book Skating Shoeshas been a happy fit for this new activity, because it talks so much about making a financial plan, setting a goal and saving up for it. So it seems natural to have conversations with the children about what they'd like to do with their money. I have three girls so several weeks go by before they get another turn to be Grocery Buddy. The first two children each got about $15 so that was fine but this week Leah was so thrifty that she earned an amazing $46.16! At first I was shocked, but I realized that my budget was $150.00 for a week of food and I spent $101.87 thanks to her so, in fact, I can afford the money for her and still be in my budget. She certainly earned it. She worked hard! I am planning on spending the money each week anyway, right? And I don't want to pay them for chores. I think that chores are a fact of life. And I don't want to pay them because they have reached a certain age -- just because -- or because I got rooked in by big blue eyes... so I want them to EARN it and VALUE it. And I want it to be enough that there is a true opportunity for spending and saving. When I was a girl in the 80s I got a dollar a week allowance as a teenager. You can't buy much with $4 a month and so I never learned any money skills... I simply just lusted after everything and when I had my first credit card.... oh boy.

Leah getting such a windfall led to a conversation about saving or spending, and led to everyone making wishlists to help them make more thoughtful choices. At first she wanted ice skates but I pointed out that she would most likely outgrow them very quickly and that it was cheaper to rent. She is determined to save up for something really expensive. Natalie, on the other hand, is ready to burn through hers at the gift shop on our field trip Friday. It will be interesting to watch this aspect of their personalities emerge.

I also really like how invested they are in the meals. Leah helped me make "her" chicken for dinner tonight. When someone opens a new box of breakfast cereal, they turn to the person who chose it and say, thank you, I really like this one. They stay up at night whispering about their chosen menus. And it makes me happy that they are so happy and proud.

Bowie Ice Arena

Today we belatedly celebrated Rebecca's 6th birthday. On the "for-real" day of her birthday I took her out to lunch and gave her one gift (a pair of ice skates from L.L. Bean) and my mother gave her another gift that evening (Skating Shoesby Noel Streatfeild). Today my boyfriend gave Rebecca his portion of the coordinated gift -- we took all the girls skating at Bowie Ice Arena. It's nearby and the prices are reasonable. It was a GREAT experience! Taking three little girls skating when you are only one person, and they are all clinging to you in desperation, is frustrating and not fun for any one. What a difference having another adult makes. We were able to divide and conquer and by the end, even Natalie (who hugged the wall the entire time the last two times we went & screamed and howled if I moved away from her to help another sister) was out on the ice, confidently pulling him along. In fact, although this was Becca's gift, I think Natalie enjoyed it the most and we ended up not only skating during the public skate session from 1 to 3 pm, but staying to watch the first half of the junior ice hockey game immediately following. Natalie was totally absorbed in the game and now wants me to track down whether skating lessons or ice hockey can be an option for her. I gave the girls all lessons in different things as Christmas gifts this year -- ballet/tap for Becca, tap/jazz and gymnastics for Leah, bellydancing and gymnastics for Natalie -- because I'm trying to get them to think more in terms of experiences than possessions. Of course, at this rate, my entire basement will be filled with sports gear!






Cooincidentally, Becca chose Alligators and Others All Year Long : A Book of Monthsby Crescent Dragonwagon as her book from the library this week (on Tuesdays when both sisters are at gymnastics she and I have Special Library Time to cuddle and read) and she was soooo excited to find that the January page was about ice skating! She thought that was just perfect!

We'll invite Cat,
for soup and skating.
It's time to start
the celebrating!
in January

2011 Winner!

I was soooo excited last night when I went online to see when the 2011 Newbery and Caldecott winners were announced and found that it had already happened! That happy event occurred last week, in fact. I am buying the Newbery winner and honor books right now.


2011 Winner:
Moon Over Manifestby Clare Vanderpool




2011 Honor Books:
Turtle in Paradiseby Jennifer L. Holm




Heart of a Samuraiby Margi Preus




Dark Emperor and Other Poems of the Nightby Joyce Sidman




One Crazy Summerby Rita Williams-Garcia

Waldorf Book of Poetry

So, I went skiing last weekend (Gore Mtn. in the Adirondacks) and the weekend before (Canaan Valley in W.Va.) and now I am back into curriculum writing and life in general. I just preordered the Waldorf Book of Poetry, collected and compiled by David Kennedy, with introduction by Eugene Schwartz. So excited to receive this volume! If you want to also be one of the first to receive this new Waldorf book, here's the link:

The Waldorf Book of Poetry

Calligraphy Worksheets

Calligraphy is part of our curriculum, and I'm tying it in with the Fourth Great Lesson (how written language came to be). Here are some links to alphabets and resources online:

calligraphy lesson - Uncial alphabet

Italic lowercase

Italic capitals

Chancery alphabet

Gothic alphabet

Gothic lowercase alphabet for left hand

Carolingian alphabet, page 1

Carolingian alphabet, page 2

Insular alphabet, page 1

Insular alphabet, page 2

Copperplate worksheet grid


Of course, you can buy beautiful calligraphy resources too:

Art Activities for Paul Klee

Our January artist is Paul Klee. Looking online, here are some good links to art projects:

"Oil Pastel Klee Portrait", inspired by Head of a Man

The Adventures of Bear (blog):
Paul Klee Part 1, inspired by The Tree House (prints, sponge painting, geometric shapes)
Paul Klee Part 2, inspired by Cat and Bird (rubbed chalk pastels)
Paul Klee Part 3, inspired by ?, button tree (blown ink and collage)
I think this might have been inspired by Feather Plant circa 1919

"Drawing Lesson Plan: The Tree House"

"Broken Window Drawings"

"Paul Klee Goes to Africa"
also includes alternate lessons "Sinbad the Sailor" and "Illustrated Poem"


In the second part of the month I plan on having us do a large mural project in his style.

Christmas

Hope everyone had a nice Christmas! I went and spent a week with my grandparents who live in Southern Illinois. They were worried about my driving all that way by myself so they insisted that I fly, which I did. Surprisingly, tickets purchased on Christmas Eve were quite cheap. However, all the parking at the airport was already taken. I guess you never win 100% of the time. I had to park in hourly parking at $22.00 per day. But I made it home safe and sound and that's the only thing that really matters in the end. And I got to spend a relaxing week with my darling grandparents. I read a TON of books (nearly 20), including















and more. I read many others but these were my favorites. I was in the middle of reading David Copperfieldby Charles Dickens when I had to leave... so I don't know if it would have made the favorites list or not. I suppose that by looking at the titles you can tell that I never made it past the "D" section of juvenile fiction! I had a good time, though, and read many books to put in my new project. Under the Same Skyby Cynthia deFelice, January 1905by Katherine Boling, and Morning Girlby Michael Dorris were all important books to add to my list, dealing with modern-day illegal immigrants, child labor at the turn of the last century, and Christopher Columbus' discovery of the Americas respectively.









I have quite a liking for historical fiction and I think this project is an important one. I have completed the Stone Age portion and will add it to the website shortly, along with some notes about where in the continuum of Waldorf education it might best be placed.

Lastly, I wanted to send a "shout out" to an Australian weaver by the name of Melinda Hunter. My brother and sister-in-law, who now live in NSW, came back for Christmas and my sister-in-law gave me a lovely purse and said that she had met the person who made it. Here's the website for her small business, Loominous: http://www.loominous.com.au/.