Active Math

IMG_5826I was going to title this blog “The Building Blocks of Math Construction” because I liked the play on building/constructing learning from material things. Really, though, I think the most important thing about this lesson was plain old ACTION. Yes, it was creative and fun, but rather than teachers reproducing the exact lesson, I want to share the philosophy behind it. It is a difference between building a beautiful, popular burger joint that everyone in a region admires and franchising the concept all over the world.

IMG_4095This is what I did. In thinking about teaching money, I was imagining setting up some kind of store in the classroom. In stead, I brought my daughter’s old school, wooden building blocks into the classroom. I thought I would have the students compete to construct the tallest structure while using the least amount of supply: They would stack blocks of value to create vertical towers and add up what it cost them.

I told the students of my plan. They were ecstatic. I assigned value to the blocks, dividing them into four categories: Many of the blocks were around 14cm. Those would cost 80¢. Any block that was less than 13cm would cost 40¢. (I did less than 13cm, because the 14cm blocks were a tiny bit under 14cm.) Now, the fun part. Many of the blocks had round edges that would make it

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Students took pics with iPads and identified styles/cost of blocks. This is an image from a student iPad.

difficult to construct with; Those were on sale. They were half off. Here the kids would be using their recently acquired fraction skills. Lastly, there were two gigantic 28cm blocks in the box. Those were $2 each. Why? Because that’s the number that popped into my head. Also, these are super valuable because they are so solid and long. The kids can evaluate the price of these versus the others.

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After going over costs, I set students loose!

After talking cost, I started centers and left my top kids to figure out constructing cost-effective building on their own, while I conducted guided reading. The buzz from the back corner was electric. Everyone in the class was dying for their chance to add up the cost of blocks!

Halfway through the first center, I stepped away from my guided reading group to check on my little architects. How were they doing?

Rather than constructing a tall tower, this group of three boys and three girls were designing the most beautiful condominium complex you ever saw. They were finding a way to use every single block they could! At first, I was like, “That wasn’t the objective.” But, I caught myself.

I forgot to mention: I had introduced the whole idea through telling the class that they were going to be designing high rises in an urban area. We would have Lego people rent space in our sky scrapers.

This group was not making a cost-effective creation. Was that wrong? No. No, it wasn’t. “Okay,” I managed to say. “This is going to be pricey,” I told them. “You’ve built a Five-Star resort, here,” I joked. “Let’s add up how much it will cost to construct.” They jumped on taking it apart, putting the blocks into piles, categorizing by the characteristics I had assigned, earlier. I told them that they could reconstruct their building after figuring out the price tag for it. Amazingly, there wasn’t a breath of complaint. I’m pleased to report 100% success, albeit after quite some time.

IMG_8975After this experience I realized that the rest of the groups would probably need some guidance with this project. I decided to use math time to teach how to evaluate constructions. While students did some online work, I brought groups over to the construction corner of the room. I went over the prices of each of the four styles of block. We analyzed similar blocks and categorized them according to cost. Then I built a simple structure with one of each price. Students used dry erase boards to add up the cost. I also had manipulatives (plastic coins) there to help. It took a few tries, and as students showed success, I let them build a four block building. They had to add up the cost before moving on. With each success, they were able to build more.

I grouped students with like abilities to work together. There was a group that did so well so quickly that I let them work in teams with more than four blocks. None of my builders cared too much about making their towers tall, even though the example that I gave them was straight up, as tall as could be with one of each style of block. I did not emphasize this, either.

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Look at this amazing construction!

Students had a blast building their block structures. One group built a road. Why not?

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We double-checked the cost of each creation.

One thing I would change, and I was tempted to change this halfway through the lesson, is the pricing. I didn’t like that half the price of the 80¢ block was the same cost as the smaller one. The smaller blocks should have been 50¢. Then there would have been more variation in the numbers and coins. Kids would be counting with quarters.

This was solved the next day. We revisited our building blocks motif, but this time with the vertical challenge. I explained that they were constructing in the inner city. I had actually looked up the price of the average urban block. “A city block in Manhattan is worth ONE BILLION DOLLARS!”

“What?!” Screamed the class with gasps of horror.

I had them use my vinyl chess mats as city plans. Each block or square would cost them 75¢. The trick is that for every inch of vertical they could collect 25¢. I formed a bunch of groups and spread students out all over the room, dividing up the blocks. In seconds the room was a buzz with builders. It wasn’t about how tall their building was, so much as how much money they could make.

My students were on fire. They had no idea they were even doing math! I am planning on putting together an elaborate assessment involving an urban plan where city block prices vary, depending on proximity to highway exits. I’ll redo the price of blocks. I’m even thinking about including fractions or weight! We love a challenge.

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3 Classy Things Dolittle Does

IMG_9875 copyAlthough I read “The Story of Mankind” first, I haven’t finished composing my blog for it. The book covers all of history, from the beginning of time to the “Great War.” (World War II hadn’t happened at the time of its publication–1921, so “World War I” was not numerated yet.) It is going to take me a couple of days to whittle my thoughts down to a handful of classy things. For this reason, I am providing my thoughts about the second ever Newbery Award winner, “The Voyages of Dr. Dolittle” (1923) first.

Hugh Lofting’s creation of a medical doctor turned veterinarian after discovering he can communicate with animals was so successful that it spawned 13 books in all. “The Voyages of Dr. Dolittle” is the second of the series. I was hesitant to jump into a sequel, having never read “The Story of Dr. Dolittle”, but was pleasantly surprised to find it very independent… and immensely entertaining, not to mention very valuable. Here are three classy takeaways.

  1.  A Unique Attitude Concerning Wealth: Dr. Dolittle cares little for monetary wealth. He needs money to go on his voyage and buy provisions, but his true wealth is the knowledge that he gains with new discoveries. The doctor never frets over where his funding will come from. He even seems to avoid the matter. When he is making a wager with Don Enrique during “The Doctor’s Wager” (Chapter 34), I was sure that Dolittle was going to ask for money. I was completely surprised by what the author put together! It was some of the most interesting reading I have experienced. Discussion Point: What is the most valuable thing you can think of? (Discuss the word “value” first.)
  2. Respect: In addition to speaking with the animals, the doctor treats them with respect. Throughout the entire book every animal is given the same level of dignity as humans. Discussion Point: The “Irony” of Dr. Dolittle cooking bacon for breakfast within sentences of a heavenly pig entering the animal-loving home. 2nd Discussion Point: I would talk to my students about the assumption of intelligence. The author, through the character of Dr. Dolittle, assumes every animal not only communicates within its species, but is smart enough to speak with any other, as long as the language specific to the species is understood. This is a fallacy that, in my opinion, ought to be mentioned, so that young listeners’ minds do not develop misconceptions.2369136756_0e0290fb16_b

Respect is given to enemies. In the beginning of chapter 48, “War!” news of a “thievish” and “envious” group of people preparing to ransack the provisions of a more studious tribe is communicated to the Dr. and his party. His response sums up the classiness of the doctor’s character: “Yet let us not judge harshly. Perhaps it is that they are desperate for food, having their own crops frost-killed before harvest” (p. 183). And, I won’t spoil it for you, but you will be as surprised as the Bag-jagderags when you read the end of “The Peace of the Parrots” to find out how the doctor treats these warmongering thieves. Discussion Point: What might someone else have come up with for “terms” of peace? Look up the terms of peace from other great wars.

Warning: With heavy heart I mention that this, like many old texts, contains traces of racism. I read the original 1921 version of the story that is now in the public domain. I thought that I would merely be mentioning the fact that the n word is used two or three times early on in the book as vernacular of England countrymen. But, upon further reflection, I want to mention a bigger idea. There is a character in the text, Bumpo, who is an African prince. This person studies at Oxford, which is prestigious, and one might, at first glance, think that this is doing Africans a service. When reflecting on the tale as a whole, however, I realized something disturbing that cannot be fixed by simple bowderization (Dominus, 2006). Bumpo, the Oxford student, is relegated to carrying things and cooking for the crew of the curlew (ship), while Tommy, an English boy of ten or eleven, is the doctor’s right-hand man. I’m not sure what kind of “discussion point” to make here, other than the fact that people have traditionally favored humans that look, act, and speak like themselves. This royal, presumably rich (Bumpo traveled to and paid for an education in Oxford.), intelligent (Bumpo was halfway through his studies.) man from Africa is portrayed as less of a person than Tommy. Think about it logically. Bumpo and the doctor have way more in common than do Dolittle and a boy. Tommy doesn’t even come from an educated, wealthy family! I must stop.

3. Science: Although purely and fantastically fictional, this fun novel paints scientific study in a perfectly delightful, exciting, and adventurous light. When other books have kids seeking treasure with buccaneers, Stubbins (the boy’s last name) joins an unlikely captain on the most exhilarating voyage any boy could hope to experience. This tale brings science to the plane of pirates, making knowledge and study as exciting and valuable as gold dublins!

Here is a bonus classy point. I loved the emphasis on thinking in this book. It seemed to me ironic that someone who does so much would be named “Do-little”. I was pleased to see his name changed, albeit temporarily, late in the book, to “Thinkalot”. It was rewarding to see this quality pointed out, rewarded, and admired in a children’s book. And with that I leave you. This was a very classy classic that I plan to read to my class this year. I look forward to the thought-provoking discussions my class and I will enjoy.

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Lofting, H. (2012). The Voyages of Doctor Dolittle. New York: Sterling Children’s Books. [Bowdlerized version, omitting or changing several racially inappropriate phrases]

Dominus, M. (2006, January 23). The Bowdlerization of Dr. Dolittle. Retrieved July 8, 2018, from https://blog.plover.com/book/Dolittle.html