Pentominoes, Part 1 of 2

5/22/2013

I started this lesson by telling kids they would be working together to create a new game. I asked them if they’d ever played TETRIS. The response was mixed. I don’t know when this game hit its peak, but I remember wasting tons of time on it and practically having a heart attack as pieces didn’t go where I wanted them to and the screen filled up. I wanted to use that sort of hysteria as classroom fuel, so I went over to tetris.com and pulled up some of the interactive tutorials. These are quick, direction-led tutorials that allow you to get a feel for the game. I randomly picked a few students to give these a shot while the class watched.

The first tutorial involves moving a piece from the right wall to the left.

Piece of cake. Then we rotated a piece and cleared a line. But then we had a few pieces coming one after another and had to move rather quickly.

A student came to the front and got started. When she got to this point, the class was screaming at her.

ROTATE! ROTATE! ROTATE!

It was great to see such a need for rotation.

After we discussed the rules and some observations they made about the pieces, I presented them with the new challenge. What if we used five squares, rather than four, to make these game pieces? How would it change the game? How many unique pieces would we need? Students made some conjectures and most agreed that we’d have more pieces than we used in the TETRIS demos.

I gave each student five squares and asked them to build a piece they thought should be included in the game. After about a minute I asked students to get up, leave their pieces on their desks, and do a quick gallery walk around the room to view the other pieces. After they returned to their seats I asked students if they had seen any pieces they would include in the game. I also asked them if there were any they thought should be excluded.

Several students weren’t sure about this one:

But others pointed out that it made sense because of this one:

Then the attention was drawn to this one:

Most students thought this should be excluded. I told them that if they wanted to exclude it, they would have to come up with a new rule to clarify the guidelines for piece production. Here were their first attempts:

“A square can’t be in the middle of two other squares.”
“A square can’t be on a crack.”
“It has to allow others to fit without gaps.”
“It can’t be over half a square.”

With each of these attempts, I tried to show how these statements eliminated viable pieces they had already created. I pressed them regarding how very imprecise their rules were, and encouraged them to think about what each square had to do, rather than what it couldn’t do. From this discussion, we came up with:

Use five identical squares. Put the squares together so that each square shares an edge with at least one of the other squares. Turns or flips are duplicates and should be excluded.

Satisfied with the guidelines, students set off to explore possible pieces.

In the next lesson students will be cutting these out and exploring ways they fit together. Some will most likely find pieces that slipped past the guidelines, like this one:

60 Comments

Stacy Gasteiger

1/24/2015 11:30:47 pm

I really enjoyed this task. First, the buy-in was great, because the students were instantly motivated by video game play. The task of creating all the possible four piece solutions was easily approachable by all students. I liked that students were using both graph paper and squares to come up with their ideas.

The evaluation stage after the gallery walk was great. Students were finding the "suspicious" shapes and discussing them. I loved that they created their own rule about what makes a legal shape. When they were then coming up with the definitive number of shapes, I'm sure it led to a lot of discussions of flips and turns, increasing their understanding of those geometric terms, as well as increasing their spatial awareness-which has been shown to increase success in physics.

Lauren

12/18/2016 01:10:58 pm

I agree that this was highly motivating for students! I am amazed when teachers come up with these great ideas. This task really got kids thinking and discussing. Also, what a great way to teach students to respectfully disagree with one another!

Jackie Balster link

1/3/2017 07:03:56 pm

Great idea to engage students in a math task based on a video game! I liked how you started with the 4-part game pieces and had them play the game virtually before presenting the challenge of creating a game that uses a 5-part game pieces.

The gallery walk was a great way for students to view one another's thinking and promote class discussion. Creating a rule for creating 5- part game pieces proved to be challenging and required students to use precise math language.

This task is a great way to promote spatial awareness, as students need to think about how pieces can be flipped, turned, and/or rotated. While some students may be able to anticipate how pieces will fit together, others definitely benefit from working with manipulatives to simulate the possibilities.

kendra

8/6/2017 04:08:02 pm

I agree that the tie to technology is key here. If students thought they were just drawing and cutting out shapes, buy-in would have been way less. This way, they feel like they are recreating a video game!

Heather Komac

2/14/2015 01:21:37 am

I really like the hook for this task! I too spent many hours of my life perfecting my Tetris techniques, and yet I don't consider them a total waste. I learned about rotations and translations of non-standard shapes, a skill that was not my best. My brain became more adept at fitting pieces together. Students will respond to this so quickly, especially if you have access to labs or laptops where students could play Tetris for a while to get a feel for the game themselves.

I love that students came up with the criteria for including or excluding pieces. There would be students who would never think to put a square across the edges of the two below, and so showing that piece would be a good question for the teacher (if no one comes up with it). I think creating and cutting out the shapes is a logical next step. I might make lots of copies of the shapes for each student, then have them play their Tetris with a partner. Draw a random piece from their bag, and their partner has to place it. Points for every completed row, extra points for completing simultaneous rows.

Colleen Sempek

5/8/2015 03:18:56 am

I like your idea of putting the shapes in a bag and having them pull them out randomly. It will be like a "real-life Tetris" game for the students. What a great ending to an amazing lesson.

Jennifer Gilliland

5/15/2015 02:13:14 am

I also like your idea. So neat!

Arlene

7/7/2015 01:07:07 am

I love the idea of providing shapes in a bag for each student and allow them to play with each other.

Gayle Stiller

9/6/2016 09:50:24 pm

Hmmm...this could be taken further by working against a team and sabotaging their game. Some Tetris shapes would hurt another teams chance. That would take thinking to another level. Definitely for at least middle school students.

Scott Smith

4/5/2015 12:13:34 am

I remember the game, but I have only seen others play it. It kind of reminds me of a game I play on my daughter's IPod called Flow. The hook for this activity is great; what child doesn't like video games. I don't know enough about the game, but it looks like it would be great for teaching rotations(as mentioned in the game above), reflections, and translations. If this isn't part of the game Tetris it could easily be modified to include rotations, reflections, and translations. I see off to the right that you have other math tasks on your site. I will have to check those out.

Jacqueline Moua

8/16/2016 05:36:19 pm

Hello Scott, I would agree with you that this is a great way to do rotation reflection. I remember having a lot of trouble in geometry when we did reflection and rotation. But I have never thought of using Tetris to engage the students learning. This is such a great way to engage the students in learning more and more about rotation.

Joanne link

4/7/2015 06:35:20 am

This is a cool idea as a geometry lesson on tessellations and transformations. I love that the teacher decided to ask the students to write a list of rules to create the shapes for the game. It showed them how difficult and important it is to use specific terms when writing the rules, and they still had an example slip by them.

Jenna Evans

4/11/2015 09:12:12 am

I love Tetris! This task would have been right up my alley in school! What a great way to engage the students quickly. It's interesting to read about their rules for the pieces and how they were primarily focused with what the shapes "couldn't" do. I could see myself getting hung up on the same thing. I also love that they were creating the game pieces using manipulatives first, to give them a more concrete visual.

Gael Ketch link

4/23/2015 01:58:37 pm

I loved this task as it has such a great buy- in for kids by using the video game of Tetris. A great way to motivate the students. The game of Tetris uses skills such as slides and rotations to solve. Students get to learn the game then use their understanding of the game to explore the 5 shapes and how they can be put together. Letting them come up with rules for shapes they could use for the new version of the game is a great way to show them how specific rules need to be. Using the squares along with the graph paper helps students see how the squares can go together and what could work and not work. Cutting out the graph paper shapes and actually playing the game would let students really build that solid understanding of how shapes can go together in different ways. I would love to laminate many copies of their shape choices and have students play the game using those shapes by random picking from a box. Playing a table top version of Tetris using 5 blocks would be fun for the students as well as solidify how shapes can transform to fit different ways.

Tim Lurz

4/30/2015 06:37:34 am

Great task! Very nice way to engage the students in critical thinking. I especially like having the students set guidelines on what an acceptable piece should be. I think it is also a great idea to put the shapes into a box and randomly pull one out to play a tabletop version of Tetris. That activity could also introduce a probability aspect to the task.

5/8/2015 02:14:07 am

What a great introduction into this lesson!! I too remember the stress of playing tetris and trying to get each piece to fit just right!! This is a wonderful way to show students how important rotation can be and the usefulness of it.

5/15/2015 02:06:35 am

I absolutely love this lesson. I love Tetris! I might even try this with some of my advanced kindergarten groups!

Jenny Magistro

5/24/2015 07:00:37 am

What a great way to engage students! I love the hook...Tetris that's genius. I like how students were involved in setting up rules/guidelines. I know with my 4th graders the rules for a game are very important to them...they want everyone to play fair so making them a part creating them would definitely get their attention. I like how you challenged their thinking with what a square could do instead of couldn't do. Walking around and looking at what others came up with is such a great visual. Last I just love that it's fun...you can have fun and learn at the same time.

Dan Imhoff

5/26/2015 03:11:34 am

I really liked this set up for the lesson. I can already picture some of my students really getting into this. Even if they've never played Tetris, the puzzle aspect to this is something that appeals to everyone.

Laura Viehman

5/27/2015 04:48:22 am

I loved the way you introduced this lesson. Using video games will always get students excited. The other thing I really liked was letting the students know that they were going to be creating something. I want to try this with my third graders next year!

Karen

6/4/2015 12:01:01 am

This was a great activity. My students would certainly be engaged and enjoy moving the pieces around.

Debbie Huckleberry

6/14/2015 08:12:21 am

This is a great lesson. The students would get excited about the idea that they are creating a version of a video game. This activity provides opportunity to problem solve and builds persistence. I like the idea Gael had to laminate the pieces to make a table top version of Tetris. I will be trying this lesson in with my class.

DENNIS R ISAACS

6/16/2015 11:34:52 pm

I was and still am a Tetris junkie. I love everything about this game. In college, we would have tournaments. The idea of developing a new/adapted version of the game is a great way to get the kids thinking about irregular shapes in a creative context that will keep them engaged.

Dianne Fife link

6/23/2015 11:21:15 pm

I loved how the lesson was introduced. The Launch, getting them to use the video game, was a great idea. I also liked how you gave students real world experience playing the game, as many of the them may not have known the game (I didn't). The idea of a gallery walk, where the students can look at each other's ideas is a good one. My class would really love this activity, I can see how it can fit into many learning levels.

Brian Thornley

7/2/2015 10:53:42 pm

What a great way to work with spacial reasoning and challenge students to adapt the game in what seems to be such a small way, but makes students solve a problem with buy in. The launch phase was so critical in this activity as it provided students with the interest to attack the new design from many different ways. This is a very open ended task which allows students to critically analyze what is possible or not possible with the new ground rules and shape requirements.

7/7/2015 01:05:20 am

I love this way of motivating the students to take part in something so concrete. I love the idea to get them up and moving to look at how others solved and also brainstorming the rules as to why something does not fit the rules of the other shapes. We do a similar activity in kindergarten with tiles and they too have to come up with their own rules.

Kelly Beck

8/5/2017 08:56:06 am

I do a similar activity with 8th graders. Students use the idea of perimeter and area. The square blocks are used and they are given an area and perimeter and have to find a shape that fits. There are multiple ways to do this so the gallery walk works well here to.

Catherine Gehman

7/26/2015 03:09:49 am

You launched this lesson in a way that would capture most kids' attention. Those who were unfamiliar with the game may gain interest just from the excitement of the other kids. I appreciated the way you kept the lesson fueled with the questions you asked. This is something I can learn from. I recently read a book called Getting it to Got it by Betty Garner. She talks about the need for adults to let kids struggle in a problem so they can develop cognitive structures, thereby developing higher level thinking skills, as a foundation to success in life. Also, you kept their minds involved by keeping their hands busy in the task with graph paper and tiles. And the fact that they had to come up with rules shows the level of engagement that was present in this lesson.

Ryan Kennedy

8/30/2015 05:54:05 am

This was a great task. Who doesn't like TETRIS? The launch was very important. The students really needed to see how the game works before having any good chance with the explore stage. I am sure there was a very interesting conversation about which shapes to keep and which to dismiss. The students were able to learn math and design a game to share and learn from. Great task!

Michelle Doris

9/8/2015 09:30:02 am

First, I agree that it is really a shame that not every student knew about Tetris, but still thought it was a great introduction into this lesson. Giving students the opportunity to do a gallery walk not only let them see what everyone else was thinking, but also got them up and moving around the room for a few minutes. It is something that I do forget to do and is something that is just so important. It was a great idea to have them explain what was permitted instead of what was not permitted before having them create pieces on their own. It was good that you did not tell them the rules or remind them of some rules they may have forgotten. Like shown in the example, they will all be able to see that they have to hone in their rules even more when presented with the last figure.

Dave Johnson

12/13/2015 11:18:23 am

It is important to hook a readers attention in the first paragraph in an essay. Likewise it is important to gain the attention of your students in the beginning of a lesson. The idea of using a simple game to have the students understand the concept of rotation. Even though Tetris is such a simple game the idea of incorporating it in class will reach most students because it is a multi-sensory approach. I liked the idea of you presenting a challenge to the students because it allows them to try to solve something on their own. The students have the ability to use the blocks to create new shapes which allows them to have a hands on experience. This is a great lesson and is really complete because it contains all the aspects of an amazing lesson.

Katie Cole

2/9/2016 11:26:58 am

Getting the students engaged in this task by introducing Tetris is a great idea. I think that if you can engage and hook your students early then their buy in is there and they are more excited to explore and put forth the effort and time in the task. Providing a real life experience, like a video game, is something that many students can relate to. The lesson continues to engage and challenge the students in a deeper way. There are different ways for the students to engage and problem solve.

Lynn Klunder

2/12/2016 09:02:01 am

Video games are a great way for a Middle School math teacher to get the interest of the students. Tetris is a fantastic game that brings Pentinomes into a higher level task. Competitiveness allows for the continuous trials to "win." The use of student engagement through challenges and real-world tasks can provide for success and perseverance of higher level tasks.

Laura Billings

2/16/2016 10:28:09 am

Excellent task! With a fun connection to Tetris, I can guarantee the students would be extra excited and engaged, which can make the learning that much more meaningful. The questioning strategies throughout were brilliantly implemented and effectively built upon one another to help students develop a deeper understanding. Also, having the students establish their own guidelines for the different pieces was an excellent way for students to defend their reasoning and critically evaluate the components of an effective game piece. Fantastic!

Keri Flynn

2/24/2016 06:13:06 pm

I LOVE this task. Tetris was one of my all time favorite games. Using this game for the Math task would definitely grab the students attention and get them excited about learning more.I like how they students use manipulatives at first to create their Tetris shape then transfer their shapes on to graphing paper.

Wong Lee

3/24/2016 02:13:51 pm

Believe it or not, TETRIS is the only game I played. I love how you approach the lesson by connecting to something that teenagers enjoy the most, game. The gallery walk is a very good idea; students get to see what other people are thinking.

cindy walsh

5/1/2016 05:37:21 pm

With our promethean boards accessible in the classroom, it would be interesting to see how kindergarteners reacted to Tetris. There is quite a bit of manipulation required; however, come to think of it, XBox has quite a bit of manipulation as well.
Getting back to subject at hand, how about constructing the pieces out of cardstock and gluing them together in order to simulate the action. I know that would help me.

Mona Sullivan

5/11/2016 01:09:50 pm

This is a GREAT idea for so many lessons for my math students. It is amazing how many hours spent on this game! I can see how the students would be engaged and we could use this during the rotations and translations lesson in my Geometry unit.

Jessica DeLumeau

6/12/2016 08:33:39 am

I always loved Tetris and I think playing the game first is a great way to get the kids engaged. This lesson seems like a great task that would engage all students. I think that a lot of kids that tend to struggle in math would really enjoy this because of the video game connection.

Kate Hogentogler

6/26/2016 02:12:09 pm

If I were a student in this class, I would be immediately hooked as I recall playing Tetris as a kid! I appreciated how you encouraged students to write rules, as they realized the importance of being precise and using correct vocabulary. I liked how you had the students think about what the pieces should be able to do instead of what the pieces could not do. Additionally, I think going from the concrete manipulatives to the representational drawings is important.

Matt

6/27/2016 11:25:18 am

Great activity. There is a definite goal for the mathematical thinking involved, but the method they use to arrive at their goal is almost totally up to them. There are so many ways to go about creating these tile pieces. The discussion piece is essential, though. When students are designing things on their own, they will make mistakes and not know they are making mistakes. Facilitating a discussion gets everyone giving input, and good “rules” are made. The game of Tetris makes it engaging for the students as well.

8/16/2016 05:37:38 pm

Wow! I used to play this game all the time but never realize I made the connection to mathematics. This will be such a rich and engaging math task for students to learn about rotation and reflection. Thank you for sharing

Chris Lucarini

8/24/2016 09:33:50 am

This sounds like an absolutely awesome lesson. I think that in a technology-savvy era, anything that has to do with video games (old or new) will be an instant hit. I also think it's great that you have the kids involved in the rule-making process because it has them take ownership of the activity and they feel as though their voice is important. While the game is really neat and a great tool, I think the discussing of why pieces fit and some of the challenging aspects will be the real payoff. I know that in my class, anything that the kids can hold or play with in their hands is usually a fan favorite.

Lisa D'Amico

11/3/2016 10:01:50 am

This is such a great activity the bring geometry/math together with a game. I love how you had the students think of their own shapes to add to the game. This requires the students to think at an independent level. Once all student thought of their own ideas having them take a "math walk". Allows them to see what students may have come up with. This requires the students to critically think about whether each piece would be beneficial or not. This is a great activity that I hope I can incorporate into my class.

Chrissy M.

11/17/2016 05:22:53 am

I really like how this activity had real world application with the Tetris tie in. Many of my students are interested in video game design as a career path. I loved seeing an activity that had direct correlation to scenarios that they might encounter.

Teresa

1/6/2017 05:38:00 pm

What a terrific activity. I love the way it delivers the message that precisely worded directions are critical to the success of communication. This finding has no age, gender, or subject area limitations.

Victoria Thornton

4/8/2017 04:36:56 am

What a fantastic way to get students motivated to work through this task! I also remember the thrill of playing a tetris game and being very excited but also anxious when the pieces started falling faster and faster. Perhaps it is just as important for the teacher to feel strongly and passionately about a topic before they expect students to get invested in the topic.

Natasha Weaver

4/14/2017 08:22:24 pm

Tetris is such an awesome game to use in the classroom as it pulls the player into the game. I love the idea of having the students create new Tetris pieces, and allowing students to have a gallery walk gave students the opportunity to see the other students' work. Allowing students to create their own rules to creating shapes gave students ownership in this project, and helped them to think deeper into what types of pieces might work. What a great challenge!

Tim Sanchez

4/29/2017 11:07:24 am

A fantastic way to engage students! Kids love video games and tying in a math lesson in with creating a type of video game is an awesome way to link student interest with math.

Gallery walk allows students to gain different perspectives on spatial awareness and determine what shapes they feel would work and which would not work when creating their own video games using 5 squares.

Also, students raised questions through their visual discoveries thereby increasing the opportunity for greater classroom discussion.

Wiliam Forney

5/18/2017 09:36:56 am

There are so many aspects of this activity that are fantastic! Any time a game is involved, the majority of the students will immediately have their interest piqued. I love that you had a student "play" the game in front of the class. This activity is also an excellent use of the gallery walk. I imagine most students were genuinely interested is seeing what their peers had come up with. Allowing students to be part of the rule-making process allowed students to take ownership in the task. Having students draw and ultimately physically create the pieces allowed this activity to appeal to a wider group of learning styles.

Sasha Friedman

5/30/2017 12:09:45 pm

I really like this task, especially the part about pressing the students and helping them realize just how imprecise their rules were and how previous pieces they made violated these rules. I could really see this task making the students think!

Jennifer Acconzo

7/28/2017 09:19:15 pm

This task is so fun! I was cracking up at the visual of students yelling at the one student to "rotate, rotate, rotate!" It really showed they were engaged in the lesson. I personally was slightly addicted to tetris as a kid. It's funny how in a game situation, they can quickly determine what is necessary but if not posed in that way, they are stuck. I really liked how you probed questions that got them to revise their rules for how their pieces could be formed. It forced them to think critically about the mathematical language. I'm already thinking about how I can use this in my geometry classroom in my unit on transformations and tessellations!

8/5/2017 08:59:01 am

I like this concept from the start with the game, incorporating the gallery walk and creating new rules. I think this would be great conceptually with the idea of transformations. Students were yelling rotate and this could easily be used with translate (to get it to move to the side), rotate and reflect (to flip the pieces). Students could also have to say what degree to rotate and what direction to flip.

Kendra

8/6/2017 04:10:35 pm

I am really excited by this task's emphasis on spatial thinking. At the heart of this task is "what IS area???"

Rebecca

8/11/2017 06:16:23 pm

I love this lesson but am completely sadden by the fact you only had a mixed reply of who was familiar with the game of Tetris! I mean, this was the best game around! What a great way to get students thinking about what characteristics have to be present to be a "playable" piece. I really liked the gallery walk so students can showcase their creativity.

Scott link

8/28/2017 02:05:32 pm

What a great idea. I love the discovery part of the lesson (I too cannot believe some of the students weren't familiar with the game). It creates the "buy in" described in the video lesson, and the tie in with the video game these days is sure to connect. I also like that students were finding pieces that slipped passed the guidelines reinforcing a constant need to check work, even when you think you are all done. Just like the readings promote, there are many avenues for the students to choose themselves, and a great presentation opportunity to share/discuss/summarize results. Cool!

Meredith

10/1/2017 06:22:50 am

Love the idea of tying this mathematical concept to a video game...a true motivation for most kids! I like that students made their own pieces, but were also involved in viewing/analyzing/providing feedback on the pieces of their peers. Very cool activity!

Nicholas DiFrancesco

1/26/2018 06:23:42 pm

I really like how this lesson is focused on student engagement. It begins with a video game and the focus is on gameplay, creativity, and strategy throughout the lesson. Also the students are doing so much of the thinking here. They are contributing the shapes, making their own rules, and correcting and helping each other. Very powerful!

Reese Ornellas

2/3/2018 08:59:52 am

I love the way this hooks and engages students because it pulls them into something that most already love, video games. I also love how you extended the activity into a suitable task for this grade level. The task also imbeds so many opportunities for rich discussion. I've found that this is what helps students reach those 'aha' moments because they are discovering together and discussing their ideas along the way, reworking their own misconceptions as they go. It's a very powerful strategy for learning.

Lora

4/3/2018 08:10:50 am

Students love playing video games, so this activity will quickly grab their interest and engage students in problem solving. The "gallery walk" allowed students to view different representations of using 5 squares and provided for meaningful math discussion. When students were asked to create a rule for building a piece using the 5 squares, this gave them ownership in the activity. It also helped them develop communication skills by creating a more precisely worded rule.

Pentominoes, Part 1 of 2

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