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Thursday, July 23, 2015

Paradox of Choice

Every time I attend a gaming workshop, I am reminded to limit the choices that my players will have.  "It will paralyze them."  They say.  "There are too many options and the players freeze."  They say.  Yeah, yeah...I hear them.  I get it and I limit player choice.

And then it happened to me.





Today I had nothing to do, nothing pressing anyway.  The possibilities were endless and it was just me and my two sons.  Should we go to the park?  Maybe a bike ride?  Or a hike might be nice?  Maybe we should try out a new playground?  But sometimes playing in your own backyard is fun too?  I do need to go to Walmart and get a few things?  What about some board games at the dining room table?  I really should clean out my closet?  I could make some meals and freeze them for the school year?  What about the game I'm working on, that needs tweaking?  I didn't finish my library book and that's due back soon, should I relax on the porch and read that?  Teach the dog a new trick?

So as I'm considering all these options, I'm overwhelmed and we did NOTHING for the entire morning.  I wasted an entire morning because I had too many options.  After lunch I got my act together and took the boys to the playground, but for crying out loud.  This paradox is real.


Then I did some searching and I found an entire book about this paradox of choice.  Click here to see that.  (I did not read this book, so I have no opinion).


Monday, July 20, 2015

Watch What You Say

I don't know why, but lately I've been thinking about things that have happened in my classroom in the past in an attempt to learn and move forward.




Student talking at inappropriate times drives me crazy.  One of my favorite sayings is, "Please be quiet."  Just this past year I had to keep repeating this to one particular student.  Please be quiet, please be quiet, please be quiet.  Finally, I asked him why he wouldn't be quiet when I directly asked him multiple times.  He response?  "I am talking quietly".

He got me.  You could tell by his reaction that he was clearly surprised by my anger.  I asked him to be quiet, not to stop.  I need to watch what I say.

Friday, July 17, 2015

Tug of War - Evaluating Expressions Game

@mathhombre pointed me in the direction of this interesting Tug of War game.  Click here.  I was playing around with the idea to make it more mathy, and here is what I came up with.

I thought trading cards would be fun and each card looks something like this:






Each card would have a function in the top left corner.  The game could start with linear functions, and then mix in cards with other functions.

In the top right is the suit.  The suits would be a letter (A, B, or C) and a color (Orange, Blue, or Green).

In the middle is the character.  He/she is wearing a shirt that indicates what makes them stronger for the tug of war battle.  This character is looking for Bs.  (If he was wearing a blue shirt, then he is looking for blue suits)

The arrows indicated in which direction the character can get his strength.

Each player places up to 9 characters in a 3x3 array.  (Just like in the Daniel Solis' post above).



Let's suppose that this card is placed on the bottom left of your 3x3 array.  I wrote in the suits for some other cards.


Since this character is looking for B in the indicated directions (up and right), we count the Bs in those directions.  There is 1 B to the right and 3 Bs up, for a total of 4.  This means that the value of x for this card is 4.  Determine f(4), to get the strength of this character.  f(x) = 3x + 2, f(4) = 14.



The players do this for each of their 9 cards to determine their strength.  Then, they determine the strength of their 3 characters in each column.  If their 3 characters are stronger than their opponent's 3 characters, they win that Tug of War. 



Some Thoughts

Playing this game requires a lot of book-keeping.  I have a strong feeling that all this computation will take the players out of FLOW if they even get there.  Also, there is little feedback for the players as to who is winning throughout the game (unless they are doing the problems the whole time or the game was digital).  At the end of the game the players would complete the 9 math problems and then determine the winner.  

I like Daniel's mechanic of each player taking a card from the deck, placing it face down on the 3x3 array, and then both revealing their card at the same time.

What if this were a 4 player game?  Tug of war up-and-down, side-to-side, and 2 diagonal wars????

The characters could be people in the school.  The Superintendent might have 4 arrows for strength, and maybe even a higher coefficient of x.  Next most powerful would be the Principal, etc.

What if the students earned their own set of cards?  and could trade them with each other???

What if the suits were classifications of triangles rather than letters and colors?  The suits are classified by angle (right, acute, or obtuse) and by side length (scalene, isosceles, or equilateral).


However, I think this game is worth a shot.  Hopefully, I remember this idea come September and play a few rounds with the students.  Hmm...maybe they could even make their own cards with some constraints.


Wednesday, July 8, 2015

Absolute Value INEQUALITY Game

A few weeks ago I asked Twitter what math topic they thought could use a game.  



Challenge accepted!  I do have an Absolute Value EQUATION game (click here to read about that) but she is asking for inequalities.  

Since I'm at home creating games rather than my classroom, I do not have access to a large white board.  You'll have to use your imagination with my photos about playing this with a whole class.


Who, What, When, Where, Why?

2 - 5 Players or Teams

Algebra 1 Students

After learning about Absolute Value Equations and Inequalities.
BUT....you could use this game leading from student Abs Val Equations to Inequalities

Classroom with a large magnetic whiteboard.

Because you want your students to love math.


Game Objective:

Work together as a class to get the highest score possible.


Materials:

A standard deck of cards with all the face cards removed (Jacks, Queens, and Kings)



Two arrows.  On one side you want an open circle and on the other side a filled in circle.
You will need magnets on both sides.


You'll need to keep track of the classes score.  I recommend posting the table of possible points for all groups to see.  The class starts with 6 points.



You will need to draw a number line from -20 to 20.

You will need 32 2-sided circles (or squares, or stars, or whatever shape you want).  Hint: squares are easier to cut.  My circles are yellow on one side and red on the other.  I used a 3/4 inch hole punch for each of the colors and then glued them together.  However, your circles will need to be much larger if you are playing with the whole class.  Place magnets on both sides of the circles.





Set Up:

Place one circle at each integer on the number line from -15 to 15.  There will be one circle remaining.  Use that circle to keep track of what color you are working on.  

The 'extra' circle lets players know that they are trying to make all the circle red.

Deal 5 cards to each team.



Game Play:

On a teams turn, they will create an Absolute Value Inequality using at least 2 of their cards.  Teams may choose to use a plus or minus sign.  They may also decide which of the 4 inequalities they want to use.  (<, <=, >, >=)

Once they create their inequality, they place the arrows to match their inequality.  All the circles that are within the domain of the inequality are flipped to the other side and showing the other color.

The team hands in their 2 cards and receive 2 new cards from the deck.

Once there are only a few of the unwanted color remaining, points are given as follows.
4 circles remaining: 1 point
3 circles remaining: 2 points
2 circles remaining: 3 points
1 circle remaining: 4 points
0 circles remaining: 5 points

If a team is able to get the unwanted color down to say 4, then next team can decide if they can keep going to add more points, or try to flip the circle back to the other color.

At the end of class, see how many points are accumulated and try to beat that score next time.  Or try to beat another class.  Or keep track and beat that score next year.

** Teams are able to add the cards together to get a required higher number.  Each extra card used will cost 1 point.  All cards will be replaced at the end of the round so that each team still has 5 cards.

Some Examples of Game Play:

Here are the five cards that team 1 has. 


They decide to use 10 and 2 to create the following inequality.




They position the arrows.  Positive 10 is the 'middle' and 2 is the distance.  They picked <, so the arrows will points toward the middle.
I like to remind the students that since the distance is less than 2, they can't flip circles that are farther away than 2.


They flip over the circle in that domain.


Since there are more than 4 yellow circles showing (the unwanted color), no points are awarded.

Team 2 has the following cards.



They decide to use 6 and 2 to create their inequality. 


The arrows...


Flip the circles...


Back to team 1...


The inequality...


The arrows....


Flip the circles...


Back to team 2...


They are going to use 3 cards to create their inequality.  I will cost them 1 point for each extra card used.


The class point total goes down to 5 since an extra card is used.


Place the arrows...


Flip the circles...


Internal thought (okay, someone should have made some points by now).  Anyway back to player 1.


The inequality...


The arrows...


The flip...


At last!  We are down to 4 yellow circles, and the class has scored 1 point.  If the next team is able to flip over some of those yellow, the class could earn even more points.  If not, we flip the 'extra' circle to show that we are now trying to make them all yellow.


And here is the point we earned!  We went from 5 to 6.







Here is another example, because I noticed that I didn't use > in the above example.

We are trying to make the red circles yellow.

The 5 cards...


D'oh!  I forgot to take a photo of the inequality.  Let's see, it looks like |x-6| >= 1

The arrows...


The flip.  This was great because I was able to flip over all the circles except for 1 and the class scored 4 points.  The next team is unable to flip that last circle over, so now we are trying to make them all red.




The cards...


The inequality...


The arrows...


The flip...



I guess you get the idea.  


Other Thoughts:

You might be wondering why the circles aren't placed to the end of the number line.  I was play-testing it that way, but it was difficult to flip the circles between 16 and 20 (and -16 and -20).  Even with the whole adding-two-cards-together rule, it wasn't easy to get those high numbers needed.  The arrows can still be placed from 16 to 20 (and -16 to 20).

I did play-test this as a competitive game, but it's too easy to sabotage the board so that no one gets points.  I thought working together was the best way.

This can be a tabletop game for your students as well.  Instead of each class trying to get the highest score, each group of students playing could be trying to get the highest score.  

I wish I had access to some students, but I'll have to wait and see if this is even fun when school is back in session.  Anyway, this gives me plenty of time to keep tweaking and get your ideas...which are appreciated.  


Thursday, June 25, 2015

Operations with Monomials Game - Version 3

If you missed them, here are links to Version 1, Version 2, and the original game, Polynomial Pirates.

Who, What, When, Where, Why?

3-5 Players

Algebra 1 Students

After learning about operations with monomials

Anywhere you want

Because you want your students to practice operations with monomials.


Game Objective:

Be the first player to get rid of all his cards.


Materials:


  • 70 expression cards.  I wrote the expressions on index cards there were cut in half.  
Here are the 70 expressions that I used:


0, 1, 2, 1/2, 3, 1/3, 3/2, 2/3

x, 2x, 3x, 4x, 5x, 6x, x^2, 2x^2, 3x^2, 4x^2, 6x^2, 9x^2

y, 2y, 3y, 4y, 5y, 6y, y^2, 2y^2, 3y^2, 4y^2, 6y^2, 9y^2

x+y, x+2y, x+3y, 2x+y, 2x+2y, 2x+3y, 3x+y, 3x+2y, 3x+3y

x-y, y-x, x-2y, 2y-x, x-3y, 3y-x, 2x-y, y-2x, 2x-2y, 2y-2x, 3y-2x, 3x-y, 2y-3x, 3x-3y

xy, 2xy, 3xy, 4xy, 6xy, 9xy

x/y, y/x, 2y/x, x/3y, y/2x, 3y/2x, 2x/3y, y/3x, 3x/2y



  • 3 blank dice with these monomials written on each one.  x, 2x, 3x, y, 2y, and 3y





Set Up:

Deal all the cards to the players.  Make sure each player has the same amount of cards, the remaining ones can be set to the side.

Each player places their cards in a pile facedown in front of them and turns over the first three cards.

Place the three dice in the middle of the table.




Game Play:

Roll the three dice.  

Every player tries to create the expressions on their three face-up cards with two of the dice that have been rolled by adding, subtracting, multiplying, or dividing.  

Once a player is able to create an expression, he announces how to do it (add, subtract, multiply or divide the two monomials), places it to the side, then flips over another expression card from his pile.  
Players continue to do this until there are no moves left.  

Re-roll the dice and continue the process.



Example of game play:



Player 1 has the following expressions:


3x/2x gives up 3/2.  Player 1 moves that card to the side and replaces it with another one from his pile.



Player 1 uses 2y-3x to remove the middle card and replace it.
There are no more moves for player 1.







Winning the Game:

The first person to get rid of all his expression cards is the winner.