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I'm sharing this lesson in part so that those of you on supply lists can load it onto your MP3 player, throw a set of speakers into your car, and teach kindergarten or grade one music at the drop of a hat. If you find yourself in a classroom with youtube access, you don't even need the MP3 player.

Learning goal: students will associate various elements of music (tempo, timbre, pitch, rhythm in particular) with various animals according to the animal's characteristics. They will move creatively to the music, pretending to be the animals in question.

(You can find expectations to match this in the full day kindergarten curriculum. I suspect you can probably find expectations in any kindergarten program. Bonus points if you can get video of the kids moving, to leave for their regular teacher so she can use the lesson for evaluative purposes.)

Materials: A variety of music tracks or video tracks referencing animals, and the technology to play them.

Set: Who can tell me about hippos? Are they big or little? Are they slow or fast? (This is almost certainly a misconception - hippos are actually very fast. I'd let that go for this lesson.) As you play the song "Mud, Mud, Glorious Mud," ask the students to tell you what it is about the song that reminds them of hippos.

Play the song once. Get a few answers to the question: there are low notes, the music goes fairly slow, lots of talk about mud. Play it again, and this time invite the students to move like hippos. If they're having trouble, get right in there and move ponderously around the carpet.

Then ask the students about bumblebees: how do bumblebees move? Would you imagine high notes or low notes for bumblebees? Quick notes or slow notes? Tell them the next song is about a bumblebee, and when they're done listening, you'd like them to be able to tell you why it sounds like a bumblebee. Then play "Flight of the Bumblebee." (I used a version recorded by Perlman on the violin; this piece has been recorded on everything from a piccolo flute to a tuba, so make sure you choose one to start with that is played on a violin, otherwise you'll confuse the heck out of the kids.) Watch for the kids who move like bumblebees, buzzing and flapping and darting or running in place. It's only a little more than a minute long, so let it go to the end.)

Get answers about why it sounds like a bumblebee. If you're in the regular classroom and have a place for such things, this is a good time to make an anchor chart with pictures and words: a hippo with the words "slow, low", and a bumblebee with the words "high, fast."

Lesson part two, probably during a second class period:

Remind the students of the previous work and the anchor chart. Tell them that this time, they're going to listen to the music without knowing what animal it's about. They get to move to the music and then guess what the animal might be. You can give them some examples: if the music is slow and low, they're going to move one way, and if the music is jumpy, they can jump, and if the music is calm and flowing, they can glide smoothly.

I used several pieces from the Carnival of the Animals, by Camille Saint-Saens. Some of the recordings had a poem about the animal at the beginning, so I set it up ahead of time to skip that part. I played the kangaroo first, and the kids quickly realized it was jumpy music with some calm parts. When asked what they thought it was, I got one kid who said it was a cat, because sometimes cats prowl and sometimes they jump on stuff; that's a level four answer. Another kid guessed a bunny, and another a kangaroo. After that I played the elephant one, which is played on double basses; they got that one quickly, too. Then I played the swan one, and they had more trouble with gliding movements; I got a lot of ballet twirls from the girls for that one, but the answers were about fish and birds, because it sounded like the animal was gliding calmly.

Wrap-up: Students can contribute to the anchor chart about elements of music, and talk about how music can represent movement in different ways. Since the point of the lesson is to explore movement rather than language, it's up to you how much you want them to talk about what they did or learned. It might be valuable to get them to draw their perception of one of the pieces of music, for an art/music connection; perhaps use the Aquarium from Carnival of the Animals for a drawing connection.

It was an awesomely fun lesson to teach and I got a lot of good information out of it.
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The grade five curriculum requires kids to develop a basic understanding of a variable for the first time: as an unknown number and as a series of values dependent on each other.

My kids already have the first definition. So yesterday we started on the second.

I put up on the board ___ + ___ = 17 and asked them to find all the ordered pairs that would fit in the blanks. I showed them how to write an ordered pair (0, 17) and then let them have at it in their groups. Meanwhile, on a piece of chart paper, I drew the upper right portion of a co-ordinate grid (because my kids haven't learned integers yet and I didn't have a lot of room, anyway.) When my kids were acting like they were done, I explained that a co-ordinate grid was a way of using math to draw things; it was just a format that everyone would use in much the same way, like a language, so that anyone who saw it would understand how it worked. I rewrote the equation on the board as x + y = 17, and asked one kid to come up and plot a point on the grid. She took (0, 17) and pointed to seventeen on each axis, saying that they were different points that were written the same way. She drew both points. I told the class that this was a problem; how could the same two numbers indicate two different points? How would that help anyone to figure anything out? I let them stew about it for a minute, and discuss how the points were different, until someone finally said, "But in the equation, x came first." I got that person up to the chart to explain what she meant, and we figured out that (0, 17) was a different point from (17, 0).

After that, we plotted each of their ordered pairs on the grid in turn, and I showed them how to label the points correctly. When we had about half the points up there, I got one of the girls who was complaining she didn't get it to come up. I handed her a metre stick and told her to play connect-the-dots.

I had expected the lesson to end there, but it didn't, because when my students notice something, I run with it. Half a dozen of my kids looked at the resulting triangle and said, "That's a right-angled triangle!" One more said, "It's a half-square triangle like in our quilt blocks!" We discussed the other two angles - both 45 degrees - and I asked the kids, "What do you think you'd have to do to get a triangle that wasn't a half-square triangle on this grid? What would the equation look like for that?"

Well, they tried x + y = 12, though my gifted kid told them right off the bat it was going to just make a smaller version of the same triangle. It did. When it seemed they were stumped, I took the metre stick and drew a line from (7,0) to (0,14). Then I asked them to figure out the relationship between seven and fourteen. They eventually got it, with a bit of help to get the form right: 2x=y, where x=7.

Every kid in the class understood the basics of the co-ordinate grid. Every kid as far as I could determine understood the ordered pairs and how they were graphed. A few kids couldn't wait to pull out the graph paper and try some equations on their own. They were tickled by the idea that I did this math in grade nine and it's currently in the curriculum in grade eight.

Today's lesson: Explain why x + y = a whole number is always going to produce a half-square triangle, no matter what the whole number is.
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The grade five curriculum says that students are only supposed to measure angles up to 90 degrees this year. In grade six it's 180 degrees, and by grade seven it's the whole circle.

Of all the ridiculous and counter-productive divisions of concepts they could have made, this one has to be near the top of the list.

My kids were having difficulty understanding exactly what it was they were measuring with a protractor, and understanding the units was even worse. So I drew a co-ordinate grid on an overhead (no numbers, just the lines.) They told me it was a t-chart, it was an X, it was four triangles - that's when I stopped them. Where are the triangles? So one kid came up and drew the lines that connected the four points of the grid into a square, bisected diagonally twice. We measured the angles in the middle and the angles on the outside and discovered they were ninety degrees and added up to 360 degrees.

Then we talked a bit about the Babylonians, who came up with a number system with a base of sixty. They figured out that they needed a way to divide up a circle into even fractions. Since they did things in base 60, when they divided a circle their first instinct was to divide it into six parts, each of which was 60 degrees, and the 360 degree circle was born. We talked about why you might need to measure angles, and how that was used. I gave them the vocabulary words they needed: bisect, radius, diameter. At this point I'm well into the grade seven geometry curriculum, and they're eating it up.

Then I pointed out that you can draw a triangle in a circle by going through the centre point of the circle, using the radius as sides. We measured the inside angle of that triangle and found it to be 58 degrees. With one more line, I showed them the complementary triangle: the one made with the 122 degree angle.

They spent the rest of the period exploring triangles as fractions of circles and investigating the number of degrees involved. I have three different kids who realized that the sum of the outside angles would be greater than 360 because they were measuring a radius but also a line that went through two points on the circumference. I had a fourth kid who realized that if she drew the X so that the angles weren't all 90 degrees, she could figure out the measure of all the other angles if she knew the measure of any one, by doubling it for the opposite angle, subtracting that number from 360, and then halving the result. (Convoluted but it works just as well as figuring it out using 180 for the straight angle. Efficiency will come later; right now I want comprehension and wonder.)

I'm going to get those four kids to present their findings to the class tomorrow so the rest of the class can be exposed to those ideas and play around with them themselves. So basically, I can give a B to any kid who can measure an angle less than 90 degrees accurately, and an A to those who can explain how angles are related to circles and why triangles add up to 180 degrees.

I love it when lessons become kid-directed explorations of important mathematical ideas.
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But a quick run-down of yesterday's math lesson:

The problem: Your little brother tells you he gave away fourteen pennies to his friend. It turns out they were fourteen loonies, and he took them out of your wallet, so you're out fourteen dollars! How do you explain the difference to your little brother?

Then I put out base-ten blocks on all the tables and watched while the kids figured out how base-ten blocks could be used to answer a question about money. It was fun, and showed that my kids do have a basic grasp of place value. Furthermore, the problem had actually happened, with different numbers of course, to every kid in the class whose family includes a younger sibling. Now that's engagement. :)
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Part of my job involves making sure kids can draw or stack blocks to represent the number 100 000. That's as high as grade fives in Ontario are expected to be able to understand.

Well, here's a much bigger number, represented in stacks of $100 bills.

Probably the most difficult thing about math, either scientific math or advanced economics, is the understanding of quantity that comes with it. One trillion dollars is really hard to visualize. Nobody will ever hold that much cash in their hands, or even in their warehouses. It's 10 to the power of 12, and it's just at the limit of how big something can be and still be relatively simple to represent visually (as this website did.) Once you get past that, it becomes a lot easier to compare it to something else: like, one in ten trillion is one drop of water in an Olympic-size swimming pool, for example. (Note: I don't know if that's true.) I think a big part of the reason most kids have trouble with math in the higher grades is quite simply that nobody takes the time or the energy to draw those comparisons for them in such a way that they understand the concept of "orders of magnitude."

Math gets hard at exactly the rate that it gets abstract. Make it less abstract, and most people can do a lot more of it. The problem with the traditional methods of teaching math has always been that it left math as an abstract concept long, long, long before most people were ready to think, "I can manipulate these numbers in certain ways without thinking about what the numbers actually mean at every point along the way."

Anyhow. An economic visualization and a little plug for concrete methods of teaching mathematics, at the same time.
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Last week sometime, my class somehow managed to get onto the topic of sweat shop labour. It started with a fairly innocuous non-fiction poster about diamonds, which we were studying for its text features. Then we asked one of the questions we've been asking about everything in our current literacy unit: what information about diamonds is missing from this poster? So I explained about the diamond cartels which were artificially lowering supply and increasing demand, resulting in diamonds being far more expensive than they ought to be. (If I'd been really on top of my game, I would have made them look up that information for themselves, but I'm not quite that progressive yet and the computers are as old as the kids themselves.) Then we got onto the topic of why their clothes could be purchased for so little. We discovered very quickly that only two items of clothing in the whole class (at least of the ones whose tags were easily accessible) were made in North America. There were a few from Mexico, a few from Turkey and Pakistan, and the rest from Southeast Asia. Again, I sidestepped the research piece and just told them that their clothes were mostly made by people being paid less than a dollar a day, barely enough to live on, and probably a lot of them were made by children who consequently weren't going to school. There were appalled, and jumped right over the question most adults would have asked next - what does this have to do with us? - and right to, "What can we do about this?"

Fast forward to last night. I was shopping at a local mall and happened into the Body Shop. Remembering that store's original schtick was about being against animal testing, I looked for pamphlets that would reveal their current social conscience. I had no trouble finding them. So I picked up a bunch of pamphlets and took them into my class today.

We started with a brief context lesson, where we discussed three questions. (That means everyone sat at the carpet and discussed these questions in knee-to-knee form, then I took input from several groups until we had a list of point-form answers.) The questions were:

1) Why do stores advertise? What do they want us to do?
2) What reasons might you have for choosing one store or product over another?
3) What techniques do stores typically use to get you to shop in their store?

Once we had a good list of reasons, I pulled out the flyers, along with some cue cards that had questions on them. We talked a bit about the Body Shop; then I divided them into groups and gave each group a couple of pamphlets and a question card. Then I let them have at it to discuss in small groups. The questions on the cards:

1) Who is the target audience for this pamphlet? How do you know?
2) Finish this sentence the way the producer of the pamphlet would finish it: "We think you should shop in our store because. . ."
3) How is this pamphlet the same or different from a Walmart flyer?
4) How does the message of this pamphlet connect to the discussion we had last week about sweat shops?
5) What does the producer of this pamphlet want you to feel when you shop at the Body Shop?*

Along the way, some of the other questions the kids asked, which we then discussed:

1) How do we know that the pamphlets are telling the truth? (To me, this should be one of the questions asked amongst the Great Five.)
2) How much of an effect does it have if a few people buy these products instead of similar ones at Zellers? Are we just spending more money to feel less guilty?
3) What happens when the demand gets too great for the fair trade co-ops in Namibia to produce all of the ingredient the Body Shop buys from them?
4) The pamphlet makes it sound like the women sending their kids to school is the greatest thing ever. Why is that?

The whole lesson took almost the entire literacy block. I finished up with an open response question, to which they had to write a paragraph answer using the Better Answers formula:

Based on the information in these pamplets, would you shop at the Body Shop instead of buying a similar product at Zellers? Why or why not? Give evidence from the pamphlets and your own ideas to support your answer.

It was a fabulous lesson and I'm so proud of it. I've made copies to put in my portfolio, which after some eight years, I'm finally updating.

* BTW, I didn't come up with these randomly; they're based on the five questions that Deborah Meier says form the basis of all critical study: How do we know what we know? Whose point of view is represented here? How is this related/connected to that? Why is this important? And the last one which I left out this time, How might things have been otherwise from how they are presented here? I recommend Alfie Kohn's book "The Schools Our Children Deserve" for a good overview.)
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First, I got all the kids from the grade five class to join my class for half an hour. This lesson is best taught with a large group. (I teach 4/5; I didn't have the grade fours doing something different, because I'm two days back from a maternity leave and didn't have time. Also, they would just have been listening anyway. It won't hurt them to hear this one two years in a row.) I got them sitting on the carpet, and started to teach.

"A long time ago, in the land we now call Iraq, people lived in large family groups under the authority of one patriarch. The word "patriarch" means "rule of the father," and that's exactly what it was. In our patriarchy, the father will be T." (I picked the biggest, baddest of the grade five kids, first to get him out of trouble and second to make him feel important. It worked. He spent most of the class preening.) "Now, in these family groups, bigger was better. The patriarch wanted as many children as he could get, to help him tend his large herds of cattle and sheep. He might have several thousand animals, and they were his wealth. There was no paper money or coins; you were rich if you had a lot of livestock. So the Patriarch had many wives." I paused at this point to let the giggles run their course. "I need seven girls to be wives." I got my seven girls up there, blushing furiously, getting teased a bit by those still sitting. I let that run its course with a few quelling looks, because their turn was coming. "One of the reasons a patriarch would have had many wives was because of the likelihood that some of them would die in childbirth. We are very lucky in Canada, in this century. For the last hundred years or so, it has become more and more rare for women to die in childbirth. Now, most people only have a few children because they're pretty sure all of those children will survive to adulthood. That was not the case for most of history. In a real patriarchy, probably half the women would die in childbirth at some point in their lives. About half the kids would die, too, usually before they were five. If you survived that long, you had a good chance of making it to adulthood."

"The next group of people would be the children of the wives. These were the potential heirs. They were taught how to work from an early age, and they learned how to manage the herds and the servants. The boys might have waited until their late teens or early twenties to marry. The girls were probably married in their early teens.

"I need all the rest of the girls up here now. These girls are servants. Most of them are concubines, who are also going to give birth to children who are the children of the patriarch. These children, though, won't have equal status with the children of the wives. If there is no other male heir, one of them might become the heir. More likely, though, they'll be servants too." I divided up the rest of the kids as children of the servants. Then I got them all sitting down again.

"Now, T is looking for a wife for his eldest son." Snickers in the direction of the eldest son, M, are promptly quelled. "He knows that his youngest wife, A, has a younger sister who would be a perfect wife for his son. But A's family lives a long way away. It takes a lot of land to support herds of the size that T has, so there aren't a lot of other people really nearby. Probably, the nearest other patriarch is a few days' walk away. A's father is further than that. It's going to take a week or two to walk there. The messenger is taking a few head of cattle with him - say, five - as a gift to the bride's family." I pause in my narrative to pick up a piece of modelling clay that I have on my desk, and start working it in my hands.

"The problem is that T doesn't have anyone he really trusts to send this message. There are no phones, no computers, no roads, no cars, no writing, no mail. There's only one way to send a message: have someone go to the other person and repeat it, word for word. None of T's sons are old enough. His servants aren't competent enough. The best person to send is someone T thinks might try to steal from him. So T needs a way to send a message to A's father about how many head of cattle have been sent." I pause a moment to explain that "head of cattle" doesn't, in fact, involve beheading any cows. "He takes some clay, the kind his family makes pots out of, and makes five little pellets out of it. He bakes these so they're hard. Then he makes a hollow ball of clay around them, and bakes that. It's now hard. He gives this to his servant," I have T do all of this, "whose job is to give it to A's father. He in turn will break it open and count the pellets. If the number of pellets matches the number of cattle, then the servant doesn't get killed for stealing from his master." (This catches their slightly-flagging attention again.)

"A's father realizes that there's no need to bake the pellets into a ball. He can just as easily press them into a clay tablet and bake the whole thing. After all, the clay will become just as hard, and T will still know how many are in it. So when he sends his younger daughter back to become M's wife, he also sends six sheep, and a clay tablet with pellets pressed into it," and I demonstrate the technique. T knows then that there are six sheep. No one has cheated him."

Then I come up with another problem: how to tell the difference between cattle and sheep? So you get little clay cows and little clay sheep pressed into tablets. Then someone figures out that all you really have to do is scrape a picture of a sheep or a cow into the tablet, and make marks indicating how many you've got. And so on, and so forth, until you get pictograph writing, ancient Mesopotamian style.

At the end of the lesson, kids get to play work with modelling clay, making a message to send to their father-in-law when they want to trade some of their livestock. They can choose any one of the types of messages. At some point, I point out that this clay tablet serves exactly the same purpose as a cash register receipt in our culture.

And that's my favourite lesson of all time.

June 2017

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