Sunday, March 28, 2021

Playful Math Carnival 145

Welcome to the 145th edition of the Playful Math Carnival. Once known as the Math Teachers at Play Carnival, this edition follows the Denise Gaskins' (founder of this here carnival) blowout 144th Anniversary Edition, as night doth follow gentle day, and by that we were blown away.  

Sadly, there's nothing interesting about the pentagonal semiprime 145. Well, besides 145=1!+4!+5!. There are only four numbers for which that's true.  And it's the fourth number that's a sum of squares in two different ways. And it's a Leyland number, because 3^4+4^3=145. (I wonder what the next Leyland numbers before and after are?) And the 145th prime number is 829 and 145829 is prime and the largest prime factor of 145 is 1+4+5+8+2+9 and that 145 is congruent to 1 in mod 8, mod 2, and mod 9. But besides that...  there's practically nothing. (All these are from Pat Bellew's fun number site.) And 145 shows up in Matt Parker's melancoil. 145 degrees (F) makes something medium rare...  maybe that should be the goal for this edition?

Volvo 145. Ove approved.

Hop in the 145 and let's go! 

Books & Essays

Just before this month started I got to participate in a nifty mathzine fest from Becky Warren, Chris Nho and Ayliean. Technically February, it was after Denise's edition so I'm counting it. Several of the results are on the Public Math website, which has more besides. Also see the mathszine hashtag on Twitter.

That was my introduction to Ayliean, who had some thoughts on STEMinism.

Some of those zines inspired Sophia Wood for her first Fractal Kitty zine, on the Cantor Set.

Jim Propp was musing on division by zero. History, what ifs, new possible numbers...

Edmund Harriss has a new children's book out, HELLO NUMBERS! What Can You Do? and has been out supporting the release. Read more at Chalkdust's Math Book of the Year series. Also super curious about Eugenia Cheng's Molly and the Mathematical Mystery.

Speaking of playful math authors, RIP to Norton Juster, author of The Phantom Tollbooth and The Dot and the Line.

Games

Sarah Carter reviewed the mathgame Proof positively.

James Cleveland posted his new linear graphing mathgame. Played it with my games seminar students and I think there's a lot of potential.

Simon Gregg and his learners were making variations on Snakes and Ladders.

Henry Segerman suggests this negatively curved sliding puzzle.

Excellent post at Play and PK on Listening.  Guest appearance from the always welcome Max Ray Riek in that post.

I've been making some GeoGebra for remote learning play. There's a measure division game, a fraction comparison game, a fraction addition/iteration/equivalence game and the classic Shut the Box.

Art

Dana Ernst shared quilts his student Michelle Reagan made on the 5 groups of order 8.

Practically a quilt, Master of the Pattern Blocks, Hana Murray, made this amazing tiling replete with dodecagons. 

Robert Fathauer was interviewed on Math, Art and Tessellations. His new book is a masterwork.

Sophia is also in the middle of a 101 days of coding challenge, and shared her ecliptic ripples.

Paula Beardell Krieg had some practical advice for cutting curves by cutting straight.

I got to work on a fun project with my son studying art education, Yemeni squares


Wait There's More

I found this perusing old NCTM practitioner journals for fraction tasks and it sparked some interesting conversation. Like just how many solutions are there?

And it wasn't the only time 1/3 appeared in this third month, as I saw a nifty Roger Nelson proof with out words of an odd identity.



Iva Sallay is hosting the next Playful Math Carnival, 146. It's sure to be a treat, as she is a prodigious puzzle poster herself (take these Easter season Egg Puzzles, for example), and found several possibilities for this edition!

I enjoy putting these together, even though I am not regularly blogging myself. (Despite my best intentions...) One of the reasons I started blogging was to share and curate some of the cool things I was seeing from the amazing MTBoS, and it's still a good thing. If you're interested in hosting, just let Denise know.

NPR made a comic of this teacher's pandemic teaching story. (Less helpful, probably, McSweeney's suggestions for teacher self-care.) Hope you are taking care of you and yours, and getting vaccinated!

So long 145! Hope it was 5x5.










Sunday, December 13, 2020

Escape Dr. Latham's Laboratory

The final game from the 2020 math capstone GAMES class. Begun by Char Beckmann, I was thrilled to teach this course and will soon have my second group. Here's the final entry, an escape room. Ashly was committed early on to make an escape room and I am impressed at the work as well as the perseverance required to finish while student teaching during the pandemic under the conditions .

GUEST POST by Ashly Latham

Escape Dr Latham’s Laboratory is a game I created for my capstone project for MTH 496. When I first heard that we were creating a game I thought of the escape room me and my friends played before the class where we sat down and started talking about creating our game. This inspired me to create an escape-room inspired math game that allowed students to have fun while also doing math!

This game originally started as a fifth grade game but as I got into an accident and injured my hand, I had to postpone the idea. Finally, when I received enough function to get back to work I was a Teacher Assistant in a third grade class classroom. These third graders inspired me to adjust the game so they could play it. 

The puzzles students will complete in this game will focus mostly on multiplication skills as this is what my students were working on at the time I created this. There are ten different puzzles but some puzzles have two answers which allow students to only play six puzzles each play. 

To create this game I searched the internet for fun multiplication puzzles. This included literal puzzles but also some riddles. After I found enough puzzles for what I wanted, I began to construct the scene cards. These tell a story as students work from puzzle to puzzle. The hardest part was constructing the solution wheel so that it was hard for students to guess answers and each answer had a different code. This took me spending lots of time creating my own symbols.

When I tried it out with my third grade students, they LOVED it. I tested out the first couple puzzles and the students were constantly asking where the rest were. After finishing it, I had those same students try it. It took two 30 minute sessions to complete but they sacrificed their recess time just to finish it! They even want to do it again to find the other solutions! 

In the attachment for the game, all of the topics and standards are explained along with how to begin the game and set everything up. Though it’s in color, you can absolutely print it out in black in white. I hope you give it a try as it’s very fun and rewarding! Though carving out an hours time of your classroom might be hard, you could have students do one puzzle a day for a morning or ending activity for the day. 



Ashly's extensive materials and instructions, including for her supper cool solution wheel are here.

In addition, each capstone student picked a good math game to promote with a video. Ashly picked Michael Pershan's Baldermath.




Thursday, December 3, 2020

Fractions vs Decimals

 From the things you forgot you wrote file...

Fractions vs. Decimals

The Battle of the Century



Ringside Announcer (RA): Welcome ladies and gentlemen to the Battle of the Century:  Fractions vs. Decimals!

Old Man Fractions has been king of the hill for so long he can remember the pharaohs.  But relative new-comer decimals has been rocketing through the ranks past previous contenders like Mixed Numbers and Percents, buoyed by the rise of science and handheld technology.  Tonight they settle the issue once and for all, mano a mano.

Color Commentator (CC):  That’s right, Jim.  And they have both clearly prepared.  Fractions has developed his upper body so much he looks positively improper.  Decimals has emphasized speed work, and is awfully quick to the point.  Hey, looks like they’re ready to start.

>ding<

RA:  They come out swinging!  Fractions looks like his strategy is to corner decimals and work his weaker visual representations.  Oh there’s a pie model and a fraction strip combo!  Decimals finally lands a 100 grid haymaker and gets back out to the center of the ring.

CC:  Looks like that speed work is paying off, Jim.  Decimals is coldly calculating without having to hit any special menu buttons on the calc, if you know what I mean.

RA:  Not really, Howard, but I’m used to it.  Oh!  Decimal made a rounding error and Fractions lands an uppercut.  

CC:  That’s exactly the answer, Kid Decimals!

RA:  The traditionalists are out of their seats, cheering on Fractions.  Even the French are into it!

CC:  He’s certainly got that je ne sais quoi, eh, Jim?

RA:  Huh?  Back to the action, Fractions is pressing his advantage.  But decimals sees an opportunity and – oh! The referee calls time!

CC:  I don’t think it was intentional, but that was definitely below the vinculum.

RA:  The referee gives Decimals a warning and they’re back in.  Fractions still looks a little wobbly, and Decimals presses the advantage, really working over Fraction’s arcane and misunderstood algorithms.  

CC:  Invert and multiply that!  Whew!

RA:  Fractions gives a nice example of unit fraction multiplication and is back in the fight.  Oh, and lands a nice left hand on a complicated long-division problem.

CC:  Decimals looks like he doesn’t know if his point is going left or right, Jim.

RA:  It’s back and forth at this point folks.  Fractions simplifies nicely, and catches Decimals a good one.  Decimals lands a nice easy comparison, but Fractions hits a unit confusion counter-punch.  

CC:  That’s half of something, alright.  

RA:  Then Decimals comes right back with a repeating combination!  Oh, and a non-terminating, non-repeating wallop!  Fractions has no answer for that.

CC:  Right in the Pi hole!  Practically transcendental ring work, Jim.

RA:  They’re really taking a beating out there.  Howard, I think the crowd’s getting confused about what’s important here.

CC:  I think you’re right, Jim, there’s kind of a baffled silence.   Not that unusual at a rational battle like this one, though!

>Ding<

RA:  That’s time.  The fighters move to their corners.  The judges communicate their decision to the ref.  It’s pretty close on my scorecard, Howard.  What do you think?

CC:  Did you double check your answer, Jim?  Nothing would surprise me –

RA:  The ref is ready and brings both fighter’s to the center of the ring.… he pulls up both fighter’s hands!  It’s a draw!

CC:  The judges have called them equivalent!  Oh the equality!  Looks like we’re in for a rematch.




Wednesday, October 28, 2020

Zoom Chat

 I'm teaching fully remote this year and have been struggling with many aspects of it. Like one does.

My courses were scheduled online synchronous, hoping for ways to get these preservice teachers working with kids... which hasn't happened yet. We do an hour of synchronous time, then there's asynchronous time for the remaining, with a set assignment, and then homework for a time, usually with a fair amount of choice. Reading (NCTM journals, teacher blogs, ...) , video, problems, etc.

Today my class was pretty quiet. We do Zoom, using Jamboard for an interactive whiteboard. Often there are problems or discussions that start in breakout groups, randomized every few weeks, then come back for whole group discussion. Today, on our last day of trigonometry, we were tackling identities. I tried something new, which was going old school. We stayed whole group, I did an example, and then asked them to work individually and contribute. 

I usually start out with a Jamboard data prompt, sometimes my question and sometimes theirs. (I share these pretty frequently on Twitter.) Today was their question, and I tried having a parallel chat, where I asked them 'what's the scariest math problem or course?'


Tough call for me. The original Halloween, Hocus Pocus... and if you include monster themes, Young Frankenstein, Abbott and Costello Meet..., Universal monster movies... how do you pick? I will ask people to comment or explain, which hopefully gets some mics on and conversation started.

The chat was an effort to make sure they had that window open and were using it. 

Logs
triple integration using integration by parts
Triple integrals
calc 3 
Integrals with no foreseeable solution
MTH350 [modern algebra]
Calc 2
Calc 2
Scariest math problem/course…
MTH 350
I don't like logarithms. I didn't like Calc 3, but I had a hard time visualizing 3d problems. 
Combing multiple antiderivative rules to solve one problem
calc 2
I loved calc 2, but didn't like calc 3 as much. Maybe it was the teacher I had

Not everybody, but good participation. And, whoa, integration. Would not have called that.

The visual prompt was my favorite trigonometry diagram.


We talked a bit about the history, the mistranslation of sine, and a recurring theme for this unit, the connections between geometry and algebra.

We then looked at just one section together to get at the similar triangles we would be using. 

We started with the triangle in the center. I shared how I learned from a student in the long ago to pull them apart and reorient them. We worked through three questions, where each time I left them more to fill in in the proportion. They had a minute to think by themselves, then we discussed. But only two students were willing to take the mic and share what they're thinking.

So I asked them in the chat publicly to share how comfortable they were with these kind of problems, 0 = don't know how to start, 5 = confident they could solve them. I also asked them to privately message me a word about their participation. We've been using WAIT - Why Am I Talking or Why Aren't I Talking (from Jennifer White's great Desmos norm activity) as a framework for this.

Sorted (public): 

1




3  3  3  3  3  3
3.5
4  4  4  4  4  4
4.5
5  5

Timeline (private):

  • Wishing I was on fall break
  • I think I am confused on the proportions. I'm not seeing where to get those. 
  • I guess I’m not uncomfortable participating in discussion, but I didn’t, and haven’t been lately, because I am really burnt out and need to just focus on listening
  • I am at home and can’t really turn on my mic
  • I'm just confused about why we are talking about sin, cos, and tan as side lengths, and not ratios of the sides.
  • honestly I am fine with talking sometimes I knew my answer was wrong however but after switching the triangles around I really understood it
  • I found these problems kind of confusing. I was listening to the others to see if I could understand it from there and that did help.
  • Trig for me has always been a hard subject, it took me a lot longer to realize how all 3 triangles are related and then create the ratios
  • I feel ok with talking, but there are times where I would say something ang you're talking but I can't raise my hand, I'm not sure how. So I never get to say my thought.
  • I was not completely understanding the triangles
  • I felt like I could follow along well enough, but couldn't really piece it together. I'm still half asleep, I'm not a morning person
  • Very busy week with other classes and I’m trying to keep up with them too
  • I've always had a hard time with trigonometry so I don't have a lot of confidence in answering those types of questions in front of class
  • I could follow what was happening and what was being discussed, but I was struggling to answer the questions and explain the thinking behind them. But after they were explained, they make sense
  • I would have felt comfortable speaking aloud because I understand this material 
  • I don’t like talking in front of the whole group because I’m afraid I’m going to be wrong. This stuff is sort of confusing, and I’m not terribly confident in my answer.
  • I wanted to observe what other students come up with and have others the opportunity to do trig

So much to think about here. I said we'll discuss it on Monday (next class). I want to stress (again again) how we are looking for thinking and questions, not correct answers. About how they need to practice doing what they will want from their students. About their relatively privileged position (successful students, math majors, etc.) and empathy for their future learners. About how hard teaching is, but worthwhile. About how I'm trying to figure out this new teaching medium and that's hard. About how much I appreciate their honesty and honestly want to hear their thinking.

Genuine question: what would you want to discuss about this with novice teachers?

Class then went on to discuss a different diagram in their breakout groups, with mixed success. Here's a group that got more than typical written down about it. I also did a slide as a worked example for them to see afterward.


So that's my story! How are you creating opportunities for engagement or cultivating discussion in remote teaching? In the chat, or message me privately. Wait, is this mic on?

Tuesday, July 14, 2020

Moving Patterns

Anyone familiar with this blog will know I have three main avocations in math and math ed: using tech for visualizing, combining math with art, and doing math through playing games. And things that combine any two of those things, wowee.

But here is one! Malke Rosenfeld has developed a math game that builds off of her depth of experience exploring math through movement, in particular dance. I had the amazing experience of being in her workshop first for my first Twitter Math Camp. My dance partner was the phenomenal Melynee Negelee, who is the moving force behind #elemmathchat. That was where I first got to meet Glenn Waddell and Edmund Harriss in person, too.

Since then, I've brought in Malke to work with my preservice teachers, present at the university, asked her to speak at our local conference Math in Action. I always get more out of each time, and the preservice teachers are very positive. I've tried to incorporate some of what I've learned from her by including embodied mathematics in all levels of courses and even trying a (non-professional dancer) version of the Math in Your Feet work with preservice teachers and kids.

The game is a learning game that develops your understanding of the possible moves and combinations as you play. There's a lot of rich mathematics to recognize and do as you problem solve, recognize and develop patterns, see transformations in three dimensions and look for and create symmetry. She has put so much work and development into the ideas behind the game and the look and play of the cards as well. For myself, knowing a lot of the math already, it still is engaging as you try to get your body to do that, and there was plenty of math to think about. Kids and college learners have deep insights and good connections.

Find out more at Malke's game site: http://movingpatternsgame.com/ or at the kickstarter https://bit.ly/MPKickstarter. And I love how Malke has set it up so that schools get a copy of the game when you get a copy.



Bonus #mathcomic in honor of Moving Patterns.


Everybody dance now!

Wednesday, May 20, 2020

Playful Mathematics Carnival 138

Welcome to the Playful Mathematics Carnival 138, the edition with its choice of theme song? (Techno or punk. I vote for the Misfits, I guess.)  

I was frankly a bit surprised at how interesting 138 is. 138 is a sphenic number(the product of three distinct primes from the Greek for "wedge shaped"), but is special among the sphenics for being the smallest product of 3 primes, such that in base 10, the third prime is a concatenation of the other two: (2)(3)(23). What is the next such special sphenic? (Some of the pictures here were made with some Brent Yorgey inspired GeoGebra or David Mrugala inspired GeoGebra.


138 is the sum of four consecutive primes (29 + 31 + 37 + 41); which is the previous and the next? 138 the sum of 2 successive primes; which? And not only is 138 the average of twin primes, it is a number such that 6 times 138, is the center of twin primes, 827 and 829. Is there another number like that?

I had never heard of Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms in exactly one way. 138 is an Ulam number... what are the two terms which make it? Which is the first counting number not an Ulam number?

Obviously, this month's edition is in the time of social distancing. So it has produced some stand out creative home mathematics. Nikky Case made an interactive explanation how the epidemiological models work. Eva Thanheiser wrote a post about numeracy in the pandemic time. Here's an applet if you're trying to model a gathering... or a classroom?

Denise Gaskins, the initiator of this here carnival here, has a post for those new to it on how to homeschool math and Peter Rowlett at the Aperiodical wrote about playful math at home

Whilst there you might check out the 2020 Lockdown Math-Off, with some really accessible entries this year. And you can submit until they run out of entries or they're allowed outside.


Lily Cole
Math Art
Evelyn Lamb collected some of my favoritest math away from school resources. Cited there, Annie Perkins' #mathartchallenge (Twitter) is maybe my favorite thing ever. Here's the home (blog) for it. Brings together so many amazing projects from so many amazing artists and mathers. Like, Paula Krieg's origami firework on Day 53. Several have compulsed me to try to make things, like the Hitomezahi stitching from Day 14. Annie's going until she hits the magical 100! 

Clarissa Grandi's #Maydala challenge has filled Twitter with lovely images.
Clarissa herself
Janet Annetts

Japleen Kaur











Miss Bowkett


Paula Krieg

More mathy math
Henri Picciotto put together two amazing posts looking at wallpaper symmetries, and a catalog of pattern block Wallpaper symmetries; part I and part II. (Challenging, I think, because the blocks themselves are so symmetric.)

Luca Moroni pointed out Raffaella Mulas' self-illustrated article on Wild Mathematics. Quick mind bending read or just ponder the pictures.

ImagePaula Krieg also pointed out this classic puzzle that Dr Olsen points out can be made from origami.

Karen Campe covers a wide variety of puzzles, from the jigsaw to the Catriona Shearer.

Simon Gregg started this thread about duck tiles, which continue to delight. He also published a sweet book on pattern blocks. If you just want the pdf, let them know and they'll donate the book to a local school.

Pat Bellew (of On This Day in Math) chases a white rabbit, running around My avorite Theorem and the arithmetic triangle. (I'm hoping that catches on over Pascal's someday.)

Justin Time
Not sure how to categorize this, ironically, but Justin Aion's post on alignment charts and teaching is amazing.



Games 
Denise Gaskins, the initiator of this here carnival here, has a War meta-post with variations from preK through HS. I use several of these in a variety of classes. 

Sam Shah collected many activities and games you can do over videochat with a class. Nia (@ihartnia) put together a Google doc of quarantine games: tinyurl.com/quarantinegamez 

Dan Finkel updated his Horseshoe Math game with a theme song!

Ben Orlin shared 6 intriguing pen and paper strategy games.


Carole Fullerton covers a silly game called Penguins. Kind of a computation bingo variant.

Kent Haines' kids are chips off the ol' block, having invented Math Ball.

My retired colleague Char Beckmann developed many math games with our students and they've all been collected here. Materials, instructions, and video demonstrations.

This past semester I got to supervise three preservice elementary teacher/math majors in their senior projects to make math games. Char Beckmann's project! Our emphasis was to make instructional games that you could play with materials on hand or with minimal printing. Sam Bosma made a fun Guess Who variant for multiplication and division, Multiply Who. Maggie Eisenga developed Choose Your Path, a hit the target game with playing cards with some very cool discrete elements. Grace Gay increased the math content in Quixx, a dice game with some subtle strategy, to make Rolie Polie Operation Olie. All are upper elementary-middle school, and have how-to-play videos.

In Memoriam 
Playful math lost two giants recently and I wanted to close with some remembrances.

John Conway was an all time great mathematician. Siobhan Roberts, his biographer, wrote two pieces for the New York Times, a memorial and a personal memoir. (Her book is excellent.) Sunil Singh said if you watch just one bit of Conway talking, watch this. James Propp is an unabashed groupie. Ivars Petersen shared a couple recollections. Pat Bellew remembered his impossible knot and Quanta covered its solution. Matt Baker remembered some of his lesser known results. I can't pick a favorite, but some of the most fun I've had with students is the rational tangle.


Don Steward was an amazingly creative and generous middle school maths teacher in England. Brilliant problem poser and visualizer and entirely low tech. Colleen Young wrote about some of her favorites. Jo Morgan wrote about her collaborations. Steven Cavadino shares an irrational triangle. Many people shared their favorite Don Steward task on Twitter. He did a sweet analysis of a Keith Richardson-Jones drawing that inspired some GeoGebra from me. Don's local paper wrote up a note on his importance to the community, and of course you should check the blog of the man himself, which he made arrangements to keep available and free.

On that somber note, we close the carnival.  Be safe, be kind! 

But on your way out... maybe check last month's Playful Math at Life Through a Mathematician’s Eyes or their recent post, 10 math movie recommendations, and look for next month's at Math Mama Writes, or check her post about Pythagorean Triples for an online math circle.  The carnival's homepage is at the site of Denise Gaskins, the initiator of this here carnival here. Contact her for your chance to host!



Rolie Polie Operation Olie, a Math Game

This past semester I got to teach a senior project class. Four preservice elementary teachers working on understanding math games, game design and making their own. Grace was fascinated by several games, but especially Quixx, a dice game. All the games were tested with kids, and went through multiple revisions and I'm really proud of their work and the games they made.

GUEST POST by Grace Gay

Rolie Polie Operation-Olie is a quick-playing mathematics game played with dice! It is a spin-off of the family dice game Quixx, in which it is a simple game to play but each decision is crucial. There is no downtime in between your turns, so there is a lot of catch-up as you always have a chance to gain from each and every player’s roll. 

If you have kids or students who are working with their basic operations of addition, subtraction, multiplication, and division, then this game is a fun way to test their computations! The object of the game is to score the most points by filling in as many boxes in the three columns as possible while avoiding penalty points. Each player takes a score sheet and something to write with. Before playing, there is one basic rule that is similar to Quixx, which is boxes must be filled out from top to bottom in each of the columns. If you choose to skip any boxes, they cannot be filled out afterward.

Take a quick look at this scoresheet. The score sheet has three columns. One “up” column, in which the values that you will fill in the box will be in increasing order; one “down” column, in which the values that you will fill in the box will be in decreasing order; and one “choice” column, in which you are able to choose whether you want an increasing or decreasing column. In the sixth row of the columns, there is a 12 that is filled in. In order to fill in any boxes past the 12, you must fill in the 12. Lastly, in the last row of the columns, there is a lock symbol. In order to lock a row, you must have filled in at least 6 boxes and rolled either the attached 36 or 0. The “Operation column” is a place for you to write the operation that you computed in order to derive the number in the box.

A how-to-play: the first player to roll a 6 takes on the role of the “active player.” The active player would then roll all four dice. They now have two play options: 

  • The active player announces the first two dice that were rolled. All players may then (but are not required to) use any operation in order to combine the two dice to find a value that they can fill out in one of their columns.
  • The active player (but not the others) may then (but it is not required to) take one of the other dice together with one of the first rolled dice and combine them, using any operation in order to fill in a box with the number corresponding to this found value in one of their columns.

Similarly to Quixx, there are penalty boxes, which must be crossed out if, after the two actions, the active player doesn’t fill out a box of at least one number. Each penalty box is worth -5 points at the end of the game. The non-active players do not take a penalty if they choose not to cross out a number.

Once all players are ready, the player to the left becomes the new active player and re-rolls all four dice. Then the two actions described above are carried out again, one after the other. 

Now, If you wish to cross out the number at the very bottom of a column (up 36, down 0, and choice either 0 or 36), you must have first filled in at least six numbers in that column above, including the 12. If you cross out the number on the bottom, then also cross off the lock symbol directly next to it. This indicates that the column is now locked for all players and numbers of this column cannot be crossed out in the future rounds.

If a column is locked during the first action, it is possible that other players may, at the same time, also cross out the number on the bottom of the column and lock the same column. These players must also have previously filled in at least six numbers in that column. Also, the cross on the lock counts toward the total number of crosses marked in that column when you are scoring.

The game ends immediately as soon as either someone has marked a cross in their fourth penalty box or as soon as someone has locked two columns. Beneath the three columns is a table indicating how many points are awarded for how many crosses within each column (including any locks marked with a cross). Each crossed out penalty is worth five minus points. Enter your points for the three columns and the minus points for any penalties in the appropriate fields at the bottom of the scoresheet. The player with the highest total score is the winner.

I hope you enjoy this fast-paced mathematics game! 



Handouts: gdoc & pdf

John's Postscript: This game is pretty complex on first approach. But the strategy is subtle, and repeated playings
have a good variety. So don't give up with this one! I actually like Grace's over the original. More streamlined, and
the extra operations add interest.

In addition to their own games, the teachers selected an already made math game to promote for classroom use.
Grace selected one of my all time favorites, Fill the Stairs. I have a post on it here, and Joe Schwartz has
an amazing one.