Yellow Band: by Sea, Week 5

Welcome back everyone! A short post this afternoon, just thinking about the great math work we did this week, and thought I’d share a bit.

A few weeks ago, while we were working on the constellation project, we started studying the Babylonian/Sumerian number and counting system. The ancient Babylonians did not use base 10–the system that we use, and is also the foundation of the metric measurement system. Rather, they counted in base 60. But, hit the brakes. We didn’t start there. We started by looking closely at how we use our hands to count. And we started to have some really neat discoveries!

Emilio records in his journal how he would count up to a few different numbers, some big, some small.

When we got everyone’s hands drawn on the board, we noticed some really neat things. Some people started counting on their thumbs, some on their pointers. Some held their hands palm up, others palm down. And, to count to big numbers, like 47, some people counted up by 5 and others by 10.

From there, we learned how the Babylonians counted on their hands. They did a neat thing: they used their right and left hands differently. On their right hand, they used their thumb as a pointer, and counted out each joint on each finger. This allowed them to count up to 12 on one hand. On their left hand, they kept track of the dozens that they counted on their right. In this way, they could count up to 60 on just their two hands. These first few explorations really focused on our hands, our most concrete way to count, most literal connection to the abstract concept of number.

Samira shows how she is practicing counting on her hands like a Babylonian!

Sakira helps Emilio record in his journal how to count up to a few different numbers like a Babylonian.

Then, we started to talk about base 10 and base 60. We watched a couple of videos about mathematical archaeology, which pointed out to us a few fundamentals of our number system, and contrasted them to the Babylonian base 60 system. Both systems work from left to right, and as we move up an order of magnitude, we add a numeral to the left. In our system, we use a 0-9 pattern, and when we get to 9 in a place, we add one to the place value to the left in order move from 9 to 0. Each place value represents the numeral in that place multiplied by a power of 10. For example, for first place is 10^0, or 1. So, a numeral in the ‘ones place’ is equal to that numeral x 10^0. When you want to move from 9 up to the next order of magnitude, you add one to the ‘tens place,’ or 1 x 10^1 = 10, and the 9 in the ones place turns back to a 0. Well, the Babylonians basically did the same thing, except replace all the 10s with 60s. Or, as Emilio so helpfully put it for us, in base 10 your ‘silent alarm’ goes off at 10, but if you’re Babylonian, your ‘silent alarm’ goes off at 60.

All of this with 7 and 8 year olds! And they really stepped up to the plate! We learned the symbols the Babylonians used (really just 2 different symbols), then started working each morning to practice writing numbers in base 60, which got really interesting when we wanted to write big numbers.

Reyahn works on adding symbols to our ‘glossary’ of Babylonian numbers, to help folks work on translating some different numbers.

Reyahn shows how to carefully organize your symbols. The Babylonians didn’t string out their symbols, the never wrote more than three in a row. Instead, they started to stack the symbols.

Solin shares her strategy for writing a particular number in Babylonian. Solin organizes herself into the first two place values in base 60:  x 60     x 1 . This helped her see that, though she wrote the same symbol twice, one is worth 60, and other 1, so the whole number she wrote is 61.

Sakira shows how she figured out how to write 104 in Babylonian. All these numbers with only 2 symbols! You can see in this picture how Solin organizes herself into the first two place values in base 60:  x 60     x 1 . This helped her see that, though she wrote the same symbol twice, one is worth 60, and other 1, so the whole number she wrote is 61.

Once we were comfortable with the system and the symbols, we could really hit the gas. We worked mostly in just the first to places, which you can see in the picture above–which will take you all the way up to 3,599! This exploration has been so rich with number sense and operations–addition, multiplication and division–and our understanding of our own base 10 system has really gelled. By taking this step outside of our comfort zone, and essentially learning a different counting language, we noticed some really important things about our own number system that will inform the way we work with numbers forever. Woah!

Yellow Band: By Sea, Weeks 3 & 4

All hands on deck!

The constellation team rotating the nightbox onto its side so that we can attach the top.

We’ve got a few fantastic field trips under our belts, and we’re starting to get our sea legs. Last Friday evening, the Yellow Band took an after hours field trip up to Chabot Space and Science Center in Oakland for their weekly stargazing. Every Friday and Saturday night, weather permitting, the museum opens up their telescopes for folks to come take a look for free. AND, apparently they also host a telescope making workshop on Friday nights! So, not only did we get to look through their historic telescopes, we got to hangout with some super nice people who are working on making telescopes of their own!

On the right is Katie. She’s been working on grinding her mirror for 15 weeks, and she thinks she has 15 more weeks to go–wow, talk about perseverance!!!

Last week, she was using 220 grit to smooth out the surface of her mirror. As her mirror gets smoother and smoother, she’ll use finer and finer grit.

She even let us try our hands at grinding the mirror. Thank you so much Katie!

Now, all of this was because of building the constellation, which itself is because of studying a bit about celestial navigation. So, last week and this week we worked both on writing numbers like Babylonians and using a simple sextant, called a mariner’s quadrant to both locate our latitude and determine height of a few very tall things around our bandspace.

Working in other bases (besides base 10 that is) really forces you to think about how our number system works. During our work in base 60, Emilio taught us all a great trick: when working in base 10, a ‘silent alarm’ goes off in your head when you get to 10 that tells you to write a zero in the ones place, and add one to the number in the tens place. So, when doing math like Babylonians, we started sounding the alarm at 60!

Of course, the purpose of all of this was to ground our understanding of degrees. So, then we started to do some application, making mariner’s quadrants and beginning to tinker with the readings the quadrants gave us at different distances from an object.

So, when the sun came out on Thursday we were able to go outside and approximate our latitude! *It was almost noon, just a few days after the equinox, and also we were using very rudimentary sextants, so our measurements were in the ballpark.

Meanwhile, the Red Band has been trying to make little submarines–aka crafts with neutral buoyancy, that won’t sink or float, but rather hangout just under the surface. So, on Tuesday we went to the USS Pampanito! And the Aquarium of the Bay after of course! Our day was full of:

Awesome doorways.

Lots of tiny beds.
*Ask Sylvester about the Captain’s Quarters.


Smashed pennies.

Rough things to touch.

Slimy things to touch.


And SOSO much…

to look at!

Have a great break everybody!

Yellow Band: By Sea, First Weeks

The students of the Beehive are ready to hit the high seas!

We dove right into several different explorations around the idea of transportation by Sea, I’ll run through a handful of them. We got started studying the stars, both building a constellation as an afternoon project, and studying how sailors navigated when out on the open seas. We’ve been doing a lot of experiments around buoyancy–weight, density and water displacement–in order to build small crafts that float, and maybe even carry heavy and dense cargo like rolls of coins. We has an awesome all-school field day, focusing on building a kind and inclusive community here at school! Oh, and we started reading Hemingway! Really!

First off, the constellation project and related celestial navigation explorations. What the heck does it even mean to build a constellation anyway?! I don’t know, that’s why I posed it as a project! One thing we often talk about when selecting projects for both the Tinkering School and Brightworks is that a good project is like a keyhole: it may seem narrow in focus at first, but upon further examination opens up to a world of possibilities and expressions. The constellation is just that! It immediately conjures an image and connection to the real world. There are loads of stories to tell around the stars–just ask the Greeks! Plus, none of us have ever built a constellation before, so there will be loads of neat problems to solve and science to learn along the way.

Right off the bat, the constellation group decided that we wanted our constellation to be rooted in real science: show the magnitude of the different stars, convey their different distances from earth, and demonstrate the connection to celestial navigation. We started with reading some from H.A Rey’s book, The Constellations, which combines facts about stars with star maps and the Greek myths that go along with many well known constellations. When we got to the part about light years and the stars different distances from earth, we did some perspective drawing, showing a chair from two different angles. This helped us wrap our heads around the idea that constellations that are very familiar to us, like the Big Dipper, would look totally different if we stood on a different planet.

These astronomers are drawing this chair from two different perspectives. Afterward, we analyzed our drawings, pointing out the features we emphasized in from our first perspective and our second.

Here is Nolan working hard on his second drawing of the chair!

After doing some research, and nailing down our priorities in what we’d like to get across by building a constellation, we were ready to get to work! We decided that we needed a ‘Night Box,’ for the stars to live inside, and that we wanted to build both the Little and Big Dippers, because one includes Polaris–the North Star–and the other points to the North Star. So, If you can find one of those two constellations, than you can figure out where you are! Then, we decided that we wanted the whole thing to be about as tall as the clock on the wall (which turned out to be 7′). Then we got down to the nitty gritty!

Sylvester explains to May and Dash why the chops stop means that we don’t need to have a line drawn on our wood in order to cut.

A regular fixture during morning choice time has been some type of exploration around buoyancy: what types of things float and why? After exploring some different materials like wood, metal and plastic, and defining what we meant by ‘float’ anyway (if you push it down into the water, it doesn’t come back up), then we got started trying to build some type of craft that would carry a roll of nickels.

Wood floats really well! But metal maybe doesn’t, and the empty plastic water bottle floated, but the one filled with water didn’t. Hm.

Balloons became popular flotation devices because we noticed that air really really floats. But, they didn’t end up working that well to build boats because they were really hard to stabilize–the nickels always flopped over to the bottom and sunk!

Nicole had been doing some origami at choice time, so Reyahn decided to try out his paper boat to see how many nickels it would hold. Not quite a whole roll, but it did hold 25 which was the most a craft held that day!

Then we had field day! During our in-service week, we talked a lot about school culture, and wanting to take a moment to emphasize kindness and caring for each other. An all school community Friday field day seemed like a great chance to have some band-specific communication and teamwork focused activities, but also mix up all the bands to emphasize how much we care about each other. Thank you so much to Jay, Nathan, Justine and Evan for organizing and facilitating! And thank you to the Magenta for offering some great activities too!


Ally shows Phoebe and Sakira how to twist up their t-shirts to get them ready to tie-dye.

May and Sakira inside the parachute.

Nathan led the Yellow Band in a communication focused activity similar to river crossing. In this activity, the group has to figure out the order that they can step on the different squares, Nathan knows the sequence, and only tells them ‘Yes,’ or ‘No!’ One person tries at a time, but as the group figures out the path, they can help each other! And, they’ve got to remember those kind ways to offer help and advice!

And then back to work! Another of our choices these first few weeks has been to read and visualize Hemingway’s classic short novel The Old Man and the Sea. This is one of my favorite books, I’ve read it many times, so it was a clear choice for a novel for us to get into because, you know, don’t dumb it down. That being said, sometimes I have to artfully rephrase things a s I’m reading. But anyway, it’s been great! It’s an excellent story of companionship and perseverance, there is a lot for us to unpack as we read. We’ve had excellent conversations about the difference in the relationship between the young boy and the old man, and the young boy and his father, carefully analyzing the descriptions as we go by making drawings to show what we’re hearing. On a given day, we probably only read 2 or 3 pages because there is so much rich detail to sift through.

Khalilah’s illustration of the old man’s bed and his dreams: his bed with newspapers for sheets and rolled up trousers for a pillow, and his dreams full of lions.

And, of course, we’ve kept up with our morning vitamins because MATH. So far, I’m loving the math of the sea–there is so much interesting stuff to do! Our first exploration is connected to our work on the constellation, the idea of celestial navigation. Did you know that much of our calendar, number system, and organization of time is based on an ancient system that wasn’t even in base 10?! True story! The basis for 60 minutes in an hour, 60 seconds in a minute. and 360 degrees in a circle is the Babylonian base 60 number system! So, we’ve been learning how to count like a Babylonian on our hands, and how to record numbers like the ancient Sumerians would too! It’s kinda tricky, but a great way to stretch our brains, thinking flexibly about numbers.

But first, we had to really nail down how we use our hands to count to begin with. And we went into a lot of detail, in order to emphasize metacognition and reflection. Some kiddos start on their thumbs and work out, others start with their pointers and end on their thumbs. And, we all different ways to count up to bigger numbers–some counted by 5s or 10s, some used one hand for 1s, and the other for bigger quantities. Interesting!

And then we started to practice counting like a Babylonian! They used their hands in a really interesting way, counting each joint on their fingers and using their thumb as a pointer. That way they could count up to 12 (aka one dozen!) on one hand, and keep track of dozens on their other hand.

Armed with an understanding of where the degrees on the compass came from, we went up to the field to start doing some of the basics of navigating. Because, if you’re trying to figure out where you are and where you’re going, you’re going to need to know how to use this tool!

Using compasses up at the field!

Oscar and Sakira used a pencil as a pointer, which Emilio then followed with his eyes to check their degree readings for accuracy. We measured from the center of the field the location of the Bay Bridge, Bernal Hill, Sutra Tower–just to name a few!

Nolan and Reyahn kept their compass on the ground and measured from there. I asked the kiddos to first take two measurements on the same thing–one of the goals on the field–first from the south fence, and then from the center of the field. We’ll use these measurements to talk about the relationship between the angle and the distance next week, but I have to figure that out a bit more first!

More more more to come!

Yellow Band: By Land Expo

We made it!

Chowin’ down at our trail lunch! Read on to hear about the menu.

Across the country, that is. Oh, and all the way through the By Land Arc.

Solin and Ronin working hard to finish up some stabilizers on the the wagon hoops.

For lack of better words, HOLY CRAP. We did so much during this arc! We moved really heavy things, moved hundreds of things, studied simple machines and the scientific method, dug deep into 19th Century North American history, and built, built, built along the way. During Expo Week(s), all of these strands come together in such a beautiful way, and By Land has been no exception.

Thank you so much to all the families, the Blue and Magenta Bands for coming to support us during our presentation!

Let’s start with the Trail Picnic. A few weeks ago, I proposed the idea to Nicole and Nathan. Thankfully, they were amenable, and we all agreed that it would be super fun to make food together and then eat it in a little picnic style lunch. On the calendar it went. Along with it, of course, a trip to the grocery store a few days before. With this date on the calendar to look forward to, our work chugged right along. The buzz of approaching expo presentations adds a bit of pep to everyone’s step; the end is in sight, are we going to finish?

We kept on rolling the dice in our Emmigrant Trails board game, and kiddos started to make it to the end! Here, Sakira works on an illustration of the farm she’d like to start upon arriving in upstate New York.

Abir and Oscar work on installing the tongue of our wagon. We had to use a bolt instead of screws so that the tongue would be able to move and ‘steer’ the wagon.

For many of the Yellow Banders (and a few Red Banders as well) our board game really tied all of our strands together this arc. Not only did we make it ourselves, but the element of both chance and choice coupled with the history made the game fun and engaging in a nail-biting, heart pounding kind of way. Even though the Red Banders didn’t make trail journals and play the game with us, they were deeply interested in the process. Working on the wagon in the afternoon was a great chance for us to share the things we learned, weaving us together as the Beehive even more.

Oh no, Emilio pulled the cholera card! It’s a good thing he also picked up some medicine for the disease that killed tens of thousands of emmigrants while at Fr. Bridger! Emilio had been moving slowly through the game, so after leaving Ft. Bridger he also chose to take Donner Pass–yikes! Winter was fast approaching, and he knew he needed to take a shorter route, so he decided to go for it.

Below: phew, Oscar’s cat didn’t get cholera! Also, Oscar, you brought a cat with you?!?!

2017-02-08 18.58.44

Oh, and the wagon! Wow that wagon was huge! But also, it was the real size, which I think was really impactful for the kids. Like I talked about in one of my last few posts, this project really beautifully wove together our bigger picture goals with day to day work and play. Each day, our planning check-in consisted mostly of teamwork reminders: How will we communicate with each other while we’re working? How should we use the tools in our space and around others’ bodies? What should you do if you find yourself without a job? The Red and Yellow Banders knew what would come next in terms of construction, it was their design after all!

Abir developed a beautiful strategy for finding the middle of the front end of the wagon–the spot to attach the wagon tongue. First, he measured a certain number of inches from one side, then he made a mark. Then, he measured the same distance from the other side to see if it met his mark. He continued doing this, adding an inch each time until he met in the middle.

Oscar, Abir and Emilio moving the finished wagon tongue into place.

Oscar proposed that we build the wagon hoops like an upside down letter ‘U,’ out of 3 pieces of wood, instead of other proposals that included as many 5.

After initially installing the hoops, we realized that they were really wobbly! So, we started adding stabilizers, relying heavily on those triangles we know make everything better when building with wood.

Then, all of a sudden, it was Expo week. But actually, when you researched, designed, built, redesigned, planned, and built as a team, getting ready to tell people about what you’ve been working on isn’t really hard! I was so impressed with the detailed and thoughtful questions and answers we brainstormed in order to frame our presentation. The kids were clearly ready to get in front of the community and talk.

While I don’t have many good pictures of our presentation–it was dark, I was presenting–I’d like to share a favorite moment: After we opened up to questions from the audience, a Magenta Band member (Ally I think?) asked a great question, and one we hadn’t practiced an answer to. “How did the teamwork aspect of working on the wagon go?” I asked the Red and Yellow Banders who were presenting to put up a quick ‘thumb-o-meter’ to show from thumbs-up to thumbs-down how they felt about working on a team to build the wagon. Immediately, the audience saw an array of thumbs, some up, some down, some in the middle. So, I asked a few kiddos to share some more about their reaction. “Because it’s hard to take everyone’s different ideas and put them together,” May explained with her thumb in the middle. And Quinn appreciated that, “There’s always someone there to help you with a tool if you need it.”

With our presentation out of the way, our focus turned back to finishing up our projects and explorations. A few kiddos were still a roll or two away from the West or North in Emmigrant Trails; we set the goal of installing two hoops in time for Expo Night. With the youngest students here at Brightworks, I think I like having our presentation several days before Expo Night, because after the presentation, they really get it: people are coming to look at our work, and it’s our job to have something we can show and talk about. The work in those last few days is always so focused, kiddos ask me so often, “How can I help?”

Reyahn works on stabilizing the wagon hoops.

Sakira, Nolan and Khalilah became the go-to pros working on the gondola. Here, Khalilah measures the length of the gondola flat on the table, in order to figure out what modifications the team will need to make so that the gondola can be installed on the steps up to the cork floor in our space.

Oh, and we got to start actually getting ready for our trail picnic! Really, what better way to close out the By Land arc than with a celebration around food?! First, we researched what foods the folks on different journeys would have eaten, and learned some interesting things along the way. Like how folks on trails West stored their eggs in their barrels of flour and cornmeal so they wouldn’t break on the bumpy journey. And how folks on the Underground Railroad foraged for much of their food. Former slaves needed to be able to move quickly from one place to the next, and leave no trace of their presence. So, they didn’t carry a lot of food. Instead, they ate greens, roots and berries that they picked along the way. This made for a pretty great menu at the trail lunch, because the food of the Oregon/California Trail is frankly pretty boring, and doesn’t include a lot of fresh fruits or veggies.

Devlin researching foods we should get at the grocery store.

Sakira researching food we should get at the grocery store. I think this is the moment she inferred that along with blackberries, folks on the Underground Railroad may have gotten to forage for other berries too–bring on the wild strawberries and raspberries and blueberries!

And, for one last field trip of the arc, I thought we should do some foraging of our own of course! Where does a kid who grew up in the suburbs learn about what’s safe to pick and eat here in the big city? Mackenzie of course! The Blue Band collaborator gave me a few great tips of things we’d be able to find in any park in the city, so a foraging trip to Glen Canyon Park to hunt for miner’s lettuce and chickweed went on the calendar.

Oh, and of course we should shake some cream into butter while we’re on the bus! How else are we supposed to make biscuits?!

Nolan stuffs a handful of miner’s lettuce into Sakira’s backpack.

Because her backpack full of lettuce is SO HEAVY.

Finally, Expo and Trail Lunch day arrived! Thank you so much to Lisa and Kerry for helping cook and setup in the morning. We made rice, beans and biscuits in the morning with the Red and Yellow Bands. Then while the kiddos were at the park, we put together some fresh fruit, washed our foraged greens from the day before, and put the biscuits in the oven. So many kids asked, “How can I help?” all morning, and even though it was a bit hectic and we had to be very patient and take lots of turns to do everything, it was such a great morning. When the Bumblebees got pack from the park to see all the food laid out on the front table, what a great moment. And then we got to sit outside in our courtyard with the big kids from the Orchard eyeballing our feast as they walked back to school for lunch! I even heard Khalilah tell a few as they passed, “We made all this ourselves!”

Oscar and Khalilah took turns to cut the butter into the flour for our biscuit dough. Did I mention that we used butter and buttermilk we made ourselves?!

Reyahn, Sakira and Nolan were all very excited to work with Lisa, Nolan’s mom. It made for some tricky turn-taking, but I think it all worked out!

Thank you Kerry for helping serve! And thank you Lindsay for joining us!

Now my friends, like I always tell the kiddos, all good things must come to an end, including the By Land arc. I’ll wrap it all up with a few pictures of your children hanging in the air on the pulley machine (aka block and tackle) they built earlier in the arc. Because learning should be playful, and we certainly played our way across continents the past few months.

Yellow Band: By Land, Weeks 8 & 9

Welcome back! It’s only been 9 days since getting back from winter break, but it feels like we’ve already done so much interesting work. We’ve started our expression phase group projects, and started some Yellow Band specific exploration that connects to one of those big building projects.


As the whole school embarks on expression this time around, the focus is on the details. Throughout the rest of the school, kids are working on declarations, meeting with the admin team, and making plans for the rest of by land. Over in the Beehive, we reminded the Red and Yellow bands that we make declarations for each project that we work on together! On the first day of any project we make designs together and talk through a plan for how we’ll accomplish our goals. And this time around, we explained, we’ll also need to think about any special materials we might need and present our project idea to the administration as well. In other words, we had our work cut out for us! Nathan announced that he’d be working on a gondola, and I announced that I’d be working on a covered wagon, and we got to work.

Reyahn tinkers with gondola mechanics.

Reyahn and Sakira work on initial covered wagon designs.

Sylvester and Ronin work together on making some 10′ long pieces to make the length of the wagon. One of our goals is to make the wagon a historically accurate size!

Oh, and, the Yellow Band is going to hit the trail! Following our study of fractions, I asked the kiddos to make themselves some spinners–one with 50/50 chances, one with 25/25/25/25 chances, and one that’s weighted to guarantee an outcome. Then, I told them that we’d soon be embarking on a cross-country adventure. And they’d get to choose which adventure they’d like to go on! Would they like to prospect for gold in California? Become a lumberjack in Oregon? Claim some cheap land and start a farm near Santa Fe? Or, would they like to escape to freedom in the north on the Underground Railroad? Each Yellow Bander made their choices, then tested out their weighted spinner, to see if it would work in their favor.

Sakira wanted to travel to New York on the Underground Railroad. So, she gave this choice about 1/2 the space on her weighted spinner.

We also bound little booklets to use as travel journals!

The gang, illustrating covers for their trail journals.

Morning choices have been jam-packed with fun activities as well. I started to delve deeper into the book Bridges and Tunnels by Donna Latham. We checked this book out from the library at the very beginning of the arc, and I just took a closer look this week–bad choice! This book is amazing! Not only does it talk about the history of engineering, but it’s packed with fun and simple experiments for us to do together. We read a bit, then chose an experiment to test what we think about the strength of different shapes.

First, we made lots of paper triangles. Then, we stacked National Geographic magazines on top of the triangles. We chose the magazines because each one very close to the same size.

The next day, we tested folded paper squares. Based on our work in the shop, all of the kids expected the triangles to be stronger, but this wasn’t necessarily true of the paper shapes.

And, we recorded all our data in a table. The next shape we’ll test will be a circle–no folds!

Oh my goodness–and this is barely half of everything we did this week! There was work forming letters, reading our book club books, exercising across the our bodies’ midline, and a trip to the community garden for Class Meeting. We’ve got so many good things going.

Yellow Band: By Land, Weeks 5 & 6

“From each according to their ability, to each according to their need.”

Fractions, parts of a whole. Here in the Yellow Band, we are each an important part of the whole. But, we’re not each exactly the same, unlike the equal parts we’ve been dividing shapes and quantities into.

Nolan tries to add pattern blocks to his design, while keeping the proportions of blocks the same. He needs to have 1/2 of the design one color, 1/4 of a second color, and 1/4 of a third color.

Oscar, on the other hand, thought about area when figuring out how to divy up color in his design.

Last week in Class Meeting, we read the book They All Saw a Cat. It’s all about perspective–everyone sees the cat differently, yet each of their perspectives is beautiful in it’s own way. This idea has permeated a lot of our different explorations, from sharing thoughts and problem solving strategies for vitamins at Morning Meeting, to solving problems at Class Meeting, to writing based on our book club books.

Reyahn works on writing a postcard home, taking on the perspective of Elmer Elevator from his book club selection, My Father’s Dragon.

“Hey, Jenny here!” Sakira’s two postcards home so far as Jenny, from School for Cats. Her voice really shines through in these short notes, and she’s tried to incorporate both Jenny’s hardships, and excitement to be at her new school.

What’s more, our study of the Pony Express led us to an exploration of native peoples of North America. It was important to me to bring the kids’ attention to the ‘discovery myth,’ the idea that the west was discovered by the European settlers as they moved across the continent. A lot of the texts we read about both the emigrants and the Pony Express included this type of language. So, we’ve been spending some time trying to learn about the plains tribes, especially the Sioux, and using resources from the indigenous perspective whenever possible. Oh, and it also informed some of our math-art connections and vitamin work–of course!

Abir carefully folded his paper, then painted in the shapes he had created. Folding first helped us make symmetric designs composed of geometric shapes, inspired by the parfleche paintings on buffalo hides many plains tribes made.

Oh, AND, we started new projects! Nicole is working on a 3D map, and Nathan is working on a fence styled after a fence the Bees fell in love with in Mendocino.

Solin and Dash work on assembling a section of the fence. The group’s goal is to make the fence both collapsible, and walkable–like a balance beam!

Nicole helps Abir, Sylvester and Quinn trace California from the projector, the first step in making a 3D map of California.

This past week, we started giving the kiddos in the Beehive more choice in the morning activities. So, we now have Hive-wide choices 3 mornings and 3 afternoons each week. Our goal is to take cues from the kids, notice the skills and areas each child feels confident, so that we can build from there with each Red and Yellow Bander. Expect to see more pictures and captions about students from both bands, as I’ll get to work with the Red Banders a lot more moving forward!

Yellow Band: By Land, Week 4

Things are really coming together over here in the Beehive. And also coming apart a bit.

Solin, Sakira and Rebecca working CLOSELY on their morning vitamin.

Solin, Sakira and Rebecca working CLOSELY on their morning vitamin.

At the end of last school year, as the faculty and staff brainstormed arc topics for the coming year, we were sure about one thing: we intended to spend the 2016-17 schoolyear working hard to weave math skill building work into our explorations. Plus, a few weeks before school started, the lower school team (Mackenzie, Melissa, Nicole, Lisa and myself) spent a week at a workshop at UCDS in Seattle learning about how this progressive, project-based school integrates math in theme-driven provocations. In these first few weeks of By Land, it feels like these intentions are becoming reality over in the Yellow Band.

Devlin models an equation with cuisenaire rods. These blocks are an excellent math manipulative, with blocks representing different numerical values in different lengths. Students can line up the blocks to show sums, differences and arrays (for multiplication and division).

Devlin models an equation with cuisenaire rods. These blocks are an excellent math manipulative, with blocks representing different numerical values in different lengths. Students can line up the blocks to show sums, differences and arrays (for multiplication and division).

A few of the important take-aways from this workshop included techniques for incorporating manipulatives into a math practice, ways to encourage skill-sharing and cross-pollination among budding mathematicians, and seeing mathematical reasoning in a wide range of activities–not just computation and arithmetic. So, in the reading I’ve been doing about the history of the Pony Express, I’ve also been taking notes on details that would make great morning vitamins. AKA, Pony Express Math.

Oscar models an equation with cuisenaire rods, then builds a proof for his solution.

Oscar models an equation with cuisenaire rods, then builds a proof for his solution.

We start with a story: “You were riding across the prairie, your mochila loaded up with 20 pounds of mail, when a strong gust of wind blew open the pockets holding all of the letters! Some mail flew out, and scattered in the tall grasses. You had to stop, and discovered that you only had 13 pounds of mail left in your mochila. How much mail was lost?” Each student models the problem with an equation (or number sentence) in their journal, then uses a manipulative to solve the problem. And don’t forget, you’re not done until you’ve shown your work in order to prove to me that your answer is true! In other words, you must BUILD, DRAW, RECORD.

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Rebecca and Sakira BUILT the problems on the simple machines worksheet in order to figure out how the lever and pulley would change the direction of force. And they got to use materials from our very own shop!

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Emilio DREW the story from the morning message, to show his understanding of the Pony Express rider heading from one relay station to the next.

Reyahn and Sakira record their work as they go, practicing adding strings of numbers and using the cuisenaire rods to prove their answers.

Reyahn and Sakira RECORD their work as they go, practicing adding strings of numbers and using the cuisenaire rods to prove their answers.

So far, I’m liking the rhythm of this practice. We start one morning with a story and one problem to practice a targeted skill. The next day, the kiddos practice the skill more, often on a worksheet I make with several similar problems. Each day, we wrap up our exploration by sharing our strategies and insights at Morning Meeting. This is a part of the practice that is really important to me, and that our schedule allows us to prioritize. Not only do these nascent scientists need a chance to verbalize and explain their own thinking, but they need to hear the different and divergent opinions of their peers. Because there are many different ways to solve one problem, and by listening deeply to these varied approaches, we enrich our own understanding.

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Nolan shares his strategy for solving one of the pulley problems with Emilio and Oscar.

Finally, this blog post wouldn’t be complete without sharing one bit of bittersweet news: a member of our Yellow family is moving on to a different school. Our friend Rebecca will still be an important part of the Brightworks community, we just won’t get to see her every day like we’re used to. We got to send her off today with a sweet letter that the rest of us wrote together, and we’re looking forward to seeing her at community Friday clubs and Expo Nights.

Not goodbye, just see you soon.

Not goodbye, just see you soon.

Rebecca made sure to give each of her bandmates a hug this morning!

Rebecca made sure to give each of her bandmates a hug this morning!

Oh, and families, there’s a surprise in the mail for you! Literally!