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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Planning a Party, Pirate-Style

IMG_3446Over the weekend I finally experienced “Teach Like a Pirate”. I listened to the recently produced (Jan. 2019) audio book, read by the author, Dave Burgess. There were tons of great take aways, some of which immediately developed in the first math lesson, Monday morning!

First of all, if you haven’t already gathered, I am one of the “freaks” that Dave mentions at the outset of his book: I bubble with passion, naturally and eternally. I live for teaching and love “bringing it” every day in every way. In addition to this, possibly because of this–There is definitely some cause and effect, here–I am quite creative find it easy to come up with new, innovative ideas. I left my accidental slip of type in the last sentence because it reminded me of one of my favorite points from “Teach Like a Pirate”: The six worst words that Dave Burgess has ever heard (loved that chapter!)

Monday morning, I was getting ready for the day and week, when an idea hit me: Have students learn time through using it to plan a party. We have been working on elapsed time for a couple days, and there are lots of ways to use real-life scenarios, but are any of them more fun than planning a party? Definitely not. I’m pretty good at hook-development, but it certainly didn’t hurt me to hear Burgess talk about it in “Teach Like a Pirate”! No more hook was necessary than “Today we will be planning a party.” I didn’t have to count to get kids on the carpet. They came ready to contribute… to their own learning!

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When Math Time = Party Time

Through discussion, I let the hook sink deeper and deeper, so that the students were mesmerized with math. I refused to answer the question, “Are we actually going to do this party?” I upped the ante when a student suggested that rather than include “Set Up/Clean Up” in our 60 minute time window, “We should just set up before the party and clean up when it is all over.” This sounded perfectly reasonable to everyone, but I told the class that “We will be renting a ballroom that costs $250 an hour. We don’t get the room until noon, and if we go over our time, the price doubles. So, we have to squeeze all of our activities within this 60 minute window.” And then I added, “Also, we have to include plenty of time for clean up, because the hotel will charge us extra if we leave it a mess… plus, that wouldn’t be classy.”

Boy, were they hooked. I mean I have never seen a group of students more engaged in discussion and riveted to each utterance! Every hand was shooting up with ideas. Who doesn’t want a party? The first thing I did was facilitate brainstorming of ideas of things to do at our “Math Party”–That’s what I called it; This wasn’t just any ol’ party; It was math-time, and that’s what we are doing; Make no mistake about it; You will learn math by the end of this. Many students were sharing themes. I praised “Pajama Day” and “Electronic Day”, but redirected to coming up with events that actually take up time. “We can make crafts wearing pajamas or with electronics, but it is the building-of-the-craft that takes up time,” I explained. So that the students felt heard, I wrote the theme ideas on the side.

IMG_3458During the brainstorming time I was building rapport. Not between myself and the students–that happened in September, and I had plenty of it–but between my students and the subject matter. Remember, I am teaching them math through all of this! The way I see brainstorming, it is like student ability: Every kid can do the math, some faster, some easier, some needing patience, help, and additional explaining. In my brainstorming sessions, every idea is acceptable. This makes it fun and funny, also. When a kid suggests a water event, I say, “Did you just say No-holds-bar-water-balloon-war!?” The classroom erupted… and the ideas poured in like the water filling those metaphorical balloons. Just as a teacher needs to redirect thought to shape learning, I rephrased student ideas to write a list of potential party events on the whiteboard.

Next, I drew a circle with ticks or lines that made the circle look like a clock. But, I didn’t write any numbers. I pointed out that there were 12 increments. Students mentioned that it resembled a clock. I agreed, but told them that this was a measurement tool, instead. I asked how much each segment was worth, reviewing our fraction sense: one increment was a unit fraction of 1/12. “If the circle represented 60 minutes, how much was each segment worth?”

“Five minutes.”

That being established, we worked together, discussing how long the events might take. Students made suggestions as to which events we would want to have in our party. As students shared ideas, I filled in the pie graph. (I didn’t tell them that this is what the circle was, until afterward.) “Wait a minute, we have a lot of fun things planned, but what about set up/clean up time?” I inquired. “It’ll take some time to fill up enough water balloons to have a 20 minute war! And, we better plan on cleaning up all of the debris.”

As I filled the pie graph I asked questions like, “How much time do we have left?” And, “What fraction of all of our time have we used up?” Here is a tough one: “Of the time that we have planned, what fraction is eating?” This forced them to come up with a new denominator. You better believe we reduced our fractions to their simplest form each time, as well!

When done, I had students analyze our pie chart with questions like “Which two events equal the same amount of time as Water Balloon War?” After several of these, and Turn & Talk partner sharing, I modeled taking the information and turning it into a bar graph. First, I asked, “Why don’t we have to bring the (y axis) all the way up to 60 minutes?” Students knew to only go as high as the greatest amount of the events. After making the graph we did some more analysis: “How much more time will we be soaking each other with water balloons than eating?”

IMG_3459Finally, it was their turn. I showed the class the graphic organizer that I had made for them. They gasped when they saw that it was exactly like what we had just made. Because I presented it screen mirroring my iPad, I could quickly draw all over it. I showed them how they would plan events, fill in the pie graph, and make a bar graph. I told them that they weren’t allowed to use the same exact ideas that we had come up with together. They could have “eating”, but not the same amount of time. In other words, don’t copy, create. They were all cool with that. I stimulated this by writing crazy ideas on the graphic shown on the board: “Picking nose for 5 minutes, followed by washing hands for 20 minutes… because that was gross!” They loved it.

When everyone had their paper the room was abuzz with feaverish creativity. No one, not even my “I can’t think of anything to write” students, was stumped for ideas of things to do at a party, albeit “Math Party.” As students brought me their papers, they continued to ask, “Are we really going to do this?” All I did was raise my piraty eyebrows.

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Proud Work

Google slide with graphic organizer for convenient printing and reproduction. Please pirate this to use as much as you like:)Screen Shot 2019-03-29 at 6.00.50 AM

Burgess, Dave. (2012) Teach like a pirate :increase student engagement, boost your creativity, and transform your life as an educator San Diego, Calif. : Dave Burgess Consulting, Inc.,

Critical Thinking is Classy

Screen Shot 2018-09-22 at 9.26.39 PMTo be able to critique something, one must have background knowledge. Unfortunately, some teachers focus solely on pouring information into their pupils (Watanabe-Crockett, 2015).

What Does Critical Thinking Look Like?

I tried something new this year to get kids to introduce themselves to each other. The class visited the art room outside of their typical art time. Kids were told that they were going to make a self portrait. The catch was that they could only use scrap paper and glue; no drawing utensils, no scissors, only their hands and glue. They had a blast tearing the paper and sticking it together. Making shapes round was tricky. Some students made their art three-dimensional. Some used nonconventional colors.

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Polite Pirates of Room 207 Make Self Portraits

After making the self portraits, students composed “Who Am I” riddle poems. They had to write down a list of sentences telling information about themselves that makes them unique from others in the class. They wrote their names on the back of the papers. I attached them to the self portraits. The kids got to read each other’s poems, guessing who fit the characteristics listed. The portraits were little more than clues, since they were not very realistic.

The project was not only presented several facets of critical thinking, but it also dressed up my room for Meet The Teacher Night! Parents loved trying to figure out which portrait/poem combination was their offspring:)

How to Foster Critical Thinking: Don’t Settle

When I have students figure out a math problem, I tell them to solve it multiple ways. This forces them to rethink the math. They are required to analyze the problem. My students are asked to not only “show their work”, but also explain how they arrived at their answers. When they share the process with a partner the two of them evaluate each other’s work. Having to find other ways to solve a math problem causes students to be creative, looking for novel ways to think about the numbers.

A way to inspire critical thinking during a writing assignment is through allowing students to view their peers’ written responses within Google Forms. When I administer an assessment through giving a quiz from Google classroom, I instruct my students to click on “See Previous Responses” upon submitting their quizzes. They are to read their classmates’ writing, evaluating the responses and comparing them with what they wrote. They may go back and add information to their own writing, then, adapting new ideas to the answer.

One More Thing: Call it what it is.

Watanabe-Crockett (2016) suggests actually using the term critical thinking. “How to Develop A Critical Thinking Mindset in Elementary Students” supplies a graphic aid from Andrew Churches that shows Bloom’s Taxonomy applied to technology. It has long lists of verbs under each thinking skill. It isn’t a bad idea to make a poster of this and put it on the wall.me

In order to critique something, one must create an opinion. With this end in mind, educators can work to teach students how to think critically in order to complete the task.

Sources:

Watanabe-Crockett, L. (2015, July 24). The Importance of Teaching Critical Thinking. Retrieved September 22, 2018, from https://globaldigitalcitizen.org/the-importance-of-teaching-critical-thinking

Watanabe-Crockett, L. (2016, May 28). How to Develop A Critical Thinking Mindset in Elementary Students. Retrieved September 22, 2018, from https://globaldigitalcitizen.org/critical-thinking-mindset-elementary-students