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

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.

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.

Look at this amazing construction!

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

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.


Building Bridges–Classy Connections

Earlier this year a student from my room hurt the feelings of a peer by pointing out a physical characteristic that contrasted the child’s appearance with the other kids in the classroom. The rudeness was unintentional (Whitman, n.d.), but painful nonetheless. 

firstThe only reason that I knew about this interaction was the hurt child came over and told me about it. It almost seemed like she wasn’t sure if she should be upset or not. As she told me her story, others, overhearing the tale, chimed in with their two-cents. This additional commentary seemed to spin the story into a negative frenzy, so that I put an end to the retelling in order to address the class.

I talked to my third grade students about the effect that pointing out differences among people can have. I explained that while the observant student may not have done anything overtly wrong, it wasn’t polite to focus on what makes someone different from you. It is great to be proud of what separates you from others; These characteristics make us unique and special, but don’t draw attention to how other people are different from you. Rather, we should celebrate our similarities.

secondWhat the boy did when he pointed out the way a little girl looked different from himself was a natural thing to do. We humans can’t help but categorize things (Vanderbilt, 2016). We have genres for music, books, movies, art, dance; You name it! It’s much easier to find things when they are labeled. When I’m in the mood to read a mystery, it’s much faster and easier to go to that section of the bookstore, rather than sift through every single shelf. But, what about those books that are very funny true stories about a person’s life that happen to also be highly mysterious? Now what? Often times, we simply create a new category.

silly facesTom Vanderbilt (2016) goes a step further, suggesting that the more we like something, the more we want to categorize. A person who enjoys candy will separate a bag of treats into several groups of like sweets. How many times has the book-lover rearranged his or her library, recategorizing titles? I have grouped books that I read close in chronology, only to separate them after reading new texts.  

The problem with doing this to people is that genre-making exaggerates differences (Kaufman, 2012). When we categorize things, we look for what makes them unique. When it comes to relationships, it is wise to seek similarities over identifying differences. Contrasting characteristics can create wedges and rifts between people. Locating, examining, celebrating, and strengthening the things we have in common will pull people closer together. This will build relationships that will be useful, helpful, comfortable, and enduring.

IMG_0463I came up with an activity to help reinforce this concept in my classroom. I call it “Building Bridges”. We have a snack/play time in the afternoons, when we give ourselves a brain break. I instituted a “constructive” play rule, where kids use items that can be connected or built upon in order to make things, rather than just mess around. We have Legos, Lincoln Logs, Tinker Toys, 30+ year-old Robotix toys from my childhood, and we also use the colorful interlocking blocks that came with our math curriculum. Because we have the most of this last medium, I chose to have the whole class use the colorful blocks in a contest. (The competition makes it more exciting.) Groups of kids–I not only let the kids pick their own groups, I didn’t limit the size of groups–arranged and connected blocks to form bridges that spanned distances between desks. I told them that the bridge had to be able to hold and transport a Thymio robot–This is a little robot that students can program to drive. The robot was the trick. Students worked to make their bridges wide enough, thick enough, and strong enough for the robot to use. Rather than drop robots on the floor during trial runs, we measured the weight with a simple scale. The robot was equal in weight to a half-full pencil box.

We discussed the concept of working together right after having experienced it first-hand. The kids loved constructing the creations.

The thing is, the blocks in our bridges were all different colors. Not only that, but they stuck together in varying strengths. Some had tight connections. Some were very loose. But every block had way more in common with the others than it did with the desk it rested on!

In the same way, humans are all different; We look, think, behave, talk, dress, and smell different. But, we have way more in common with each other than our differences would let on. Lets focus on our connectivity, building bridges, rather than tearing each other down.    

Celebrating similarities is classy.


Kaufman, S. (2012, October 13). The Pesky Persistence of Labels. Retrieved November 5, 2018, from

Vanderbilt, T. (2016, May 28). The Psychology of Genre: Why we don’t like what we struggle to categorize. The New York Times. Retrieved November 5, 2018, from

Whitson, S. (n.d.). Is it Rude, Is it Mean or Is it Bullying? Retrieved November 6, 2018, from

It’s #Playtime!

For years I’ve let my students bring in a snack, but I usually have them eat it while working. I tried that this year, but quickly realized that this wasn’t going to work.

These kids missed the classroom #playtime, so they took a brain-break in the hall.

Because of an early lunch, my students and I have a very long afternoon. Our math time is from 11:30 to 12:30. Then I have Language Arts time until 2:25, when Special time begins. So, I have students for about three solid hours!

I never even considered playtime before. I figured, that’s what recess was for. But, a class I am taking from Kutztown U changed my mind. During snack time, I have introduced our classroom makerspace. I am calling it playtime, but the idea is that students will be involved in creative creating or building. 


Learning Social Skills

Mission Statement: 

Students will take a break from formal learning every afternoon post Math time and prior to Language Arts learning (12:30-12:50, approximately), in order to creatively construct things with a variety of toys and tools, while snacking.

Philosophy: Hybrid of “Open Space” (self-driven) and “Workshops” (learning/practice time)

Screen Shot 2018-10-07 at 7.18.01 AMMerriam Webster defines playtime as “a time for play or diversion” (n.d.). The very first time I introduced this idea, I talked all about the concept and went over the parameters or policies prior to math time. Then during math we used connecting blocks to build arrays that  were broken apart, displaying split multiplication problems. When math time was over, I told the students that they could keep using the blocks, but now, they could “Build whatever you want.” They were in heaven. It was like I had taught them the proper way to use the monkey bars, and then told them they could play all over the playground doing anything they wished. Stay within the fence, and follow the general rules, but have a blast and blow off steam. They sure did.

Playtime isn’t relegated to only grade-school pupils; parents and adults can benefit from merriment as well (Chatty Feet Team, 2016). It helps us relax and promotes problem-solving skills. Also, it will help us play with our kids better. Libraries are using playtime to help kids develop literary skills. Parents at a library in Texas get out toy cars, tape, race tracks, and bowls of tiny road signs (Celano, Knapczyk, & Neuman, 2018, p. 68). Playing and building with these road toys helped the kids learn some of the concepts necessary for understanding the read aloud they were about to experience.


This is NOT a “free-for-all”, nor is it even “free-time”. It is playtime, and it is governed by rules.IMG_6875

  1. No fighting or arguing.
  2. Don’t be too loud.
  3. Share/Play nice
  4. Keep clean; Wash hands first/keep snack away from toys.
  5. Don’t be gross. No licking your fingers and then touching the toys. (I’m not even going to mention picking noses.)IMG_6999


I limit the supplies that my students have access to during their playtime. I do this for a variety of reasons. One is that I want this time to be manageable. If there are ten different things out and spread around the room, it will take too long to clean up. Another reason that I limit the supplies is because I want the groups of students to interact. If one group is playing with Legos and another is building with Lincoln Logs, kids will not be as likely to share, collaborate, blend groups, etc. They have to stop playing with Legos in order to work with Lincoln Logs. Eventually, I want to see the class creatively incorporate a variety of building mediums into the same project, but all in good time. I want the kids to have some experience with each one, learning, exploring, and problem-solving with a single medium before branching out and combining.

Here is a list of the mediums that I have so far.

Abe Lincoln may have carved these, himself. They are from my childhood!
  • Connecting blocks
  • Legos
  • Lincoln Logs
  • Tinker Toys
  • Robotix
  • Thimios (robots)

Potential Future Play Mediums: Video and Music

A future direction of this playtime that I foresee is publishing videos. Students will use the things that they have built to produce films with plots and themes. I imagine these to be silly and fun; Remember this is playtime! I can picture students making Monty Python-esque cartoons, old school Gumby claymation-style movies, and motion-stop videos.

Publishing videos on Youtube is scarily public. Students and kids have no idea what that means. They are lured by the fame of notoriety and the glamour of numbers. The idea of something going “viral” is the new “anyone could be president”. Except that there are serious hurdles to achieving most powerful person in the world, while going viral needs nothing more than a video camera, creativity, and luck… mostly, luck. And, every kid in America is banking on luck, these days. What if one of our videos did go viral? It is important that our movies present an accurate picture of our playtime. 

When kids publish to Youtube or another online video platform, they are taking their play on the road… or information highway. What kids want is for their numbers to rise: They want the number of views to go up. The way to do that is to promote the videos, but more importantly produce something that people want to watch. In the same way that playing the games that others enjoy playing will get more people to join your playtime activity, videos that are attractive will get the views. In the incredibly interesting and informative article on this subject, “Raised by Youtube” author Alexis Madrigal (n.d.) writes about a company that I hadn’t even heard of: Chuchu Tv. This company is dwarfing Disney, Sesame Street, and all the rest of American video producers on Youtube. Their BILLIONS of views make these other companies look like online ants. The Indian-based company uses seemingly lotech imagery–two-dimensional characters to tell traditional nursery rhymes. Madrigal (n.d.) went to the headquarters and interviewed its creators and CEOs. The concept began with an audience of one: The creator’s toddler. The entrepreneur with a background in media began making videos for his young son. They almost instantly took off and went viral. He now employs 200 artists. Compared to Disney’s thousands of employees, this number is infantesmal! The mission of Chuchu Tv is to provide wholesome videos for toddlers that share moral messages. Madrigal spoke with a child development expert who reviewed Chuchu’s videos, Colleen Russo Johnson from UCLA’s Center for Scholars & Storytellers. She told him that the videos were so overly-stimulating that the good message is lost on young kids. Chuchu was born on the concept of seeking the most views. Although its mission is admirable, Chuchu plays to what is going to be viewed the most. Johnson sees this as dangerous, because it will develop viewers who want (need, like an addict) more and more stimulation.

I’ll be blogging about this a lot in the near future, but suffice to say, the app Garageband is a virtual playground of music. We had one lesson with Dylan Peters, and I now have to pry the iPads out of student hands!

Screen Shot 2018-10-07 at 7.17.33 AMMy students and I are super excited for this new #playtime initiative. I haven’t told them about making videos, yet. But, our creative building has completely revolutionized our Language Arts time. Kids are more attentive, well-behaved, and cooperative in centers, after having a brain break. I look forward to sharing more about this time, how it is working out, and what my students are producing throughout the year. Please share with me articles that you have read that either support this idea, add to this concept, or even contradict my thinking. Thank you.


Celano, D. C., Knapczyk, J. J., & Neuman, S. B. (2018). Public Libraries Harness the Power of Play. YC: Young Children, 73(3), 68. Retrieved from

Chatty Feet Team. (2016, June 14). Why It’s Important For Adults To Play Too. Retrieved October 7, 2018, from

Madrigal, A. C. (n.d.). Raised by Youtube. Retrieved October 6, 2018, from  [No publishing date, but available in the November 2018 print edition.]

Merriam Webster. (n.d.). Playtime. Retrieved October 7, 2018, from