## Tuesday, December 30, 2014

### Bounty Hunter: Rise Up and Run

Click here to see our website about Bounty Hunter: Rise Up and Run

I have this game that helps students with the concept of slope.  I can't count the times in my career where I have reminded students the slope is rise over run.  I have tried to help them make the connection between rise over run with the change in y over the change in x with the slope formula.  My methods include lecture, worksheets, activities, projects, and finally games.

This is what the paper prototype looks like and what students have been using in my classroom to play Bounty Hunter:

Bounty Hunter: Rise Up and Run, is the first game that I created that wasn't quiz-based.  In other words the game is not where a students gets to do something if he answers a question correctly.  Bounty Hunter was just the beginning for me.  I have created more and some I have shared here on this blog.  Games such as Domain Rangers, Conic Capture, Polynomial Pirates, A River Runs Through It, Tornado Inequality, Snakes on a Coordinate Plane, etc.  But I've run into a few problems with sharing these games:

1) It's time consuming for other teachers to recreate my games in their classroom.
2) It's expensive for other teachers to recreate my games in their classrooms (for some games).
3) It's difficult to explain all the rules for some of my games.
4) It's difficult to teach a room full of students how to play a board game.
5) I'm running out of storage room for all of my games, and you might be as well if you're making them too.
6) I (we) lose a lot of class time going over rules before even getting to the actual learning part of the game.

That's quite a few hurdles to overcome. But I can think of one way to scale them; make the games digital.

I was hopeful back in 2011 when a small computer gaming company wanted to write an SBIG grant to make a digital version of Bounty Hunter.  For whatever reason, that grant was never meant to be and I was back to square one.  I started looking around for a programmer to take on my game and I was told that I would need the likes of \$30,000 to make that happen.  Things did not look good for me.
Then in 2013 the local community college was awarded a grant to match up their computer programming and art students with teachers to program their games.  This is when my luck started to change.  Out of the three teams that were formed, my team is the only one that created a working version of the game.  And by team, I mean one person, the other members of the team were "let go".

Through this process I found a programmer that I trust and jumped at the chance to continue working with him.  We have decided to start our own business to share these games online.  Time and funds are a little low right now, so we will be asking for help to get this endeavor started through sites like Kickstarter.

## Friday, December 26, 2014

### Family Game with No Name

Warning -->  This post will be off topic.  No math education stuff here.  I comfort myself with the realization that since it's Christmas you are all at home with your families and not with your students, so you will want a game to play with your families and not your students.

## Objective:

I wanted a game that would create a sense of togetherness, especially with my sons (ages 4 and 9).  Those two are spending the break fighting and playing video games so far.  I want them to work together and spend time with the rest of us.

## Who Can Play:

Ages: 4+
Number of Players: 4

## Materials:

108 cards.  I used 27 large index cards, cut into quarters.
3 color pencils (red, green, and blue)
4 rubber bands
Container.  I used an old granola container.
Something to keep score.  I used bottle caps, but anything will do; coins, pretzels, buttons, etc)

## The Cards:

Each player will play with their own deck of cards.

On the cards, draw the following:

1 red triangle
2 red triangles
3 red triangles
1 red circle
2 red circles
3 red circles
1 red square
2 red squares
3 red squares

Create the same shapes and quantities with two other colors, I used green and blue, for a total of 27 cards.

This makes one set of cards.  You will need to do this three more times.

On each set of cards, I wrote our family members' names.  On my 27 cards I wrote "Nora" on the back.  This way if decks get mixed up, you can easily sort them.  I thought about color index cards, but it may be distracting with the different color pencil shapes.

## Game Play:

Create teams of two.  Teammates sit across from each other.
Each player shuffles his deck and places it face down in front of himself.  Take the top three cards from the deck and hold in your hand so no one else can see your cards.
The youngest player goes first.

Player 1 places one card in the middle of the table.

Player 2 places a card in the middle of the table like this.

The third player looks at the card his teammate played and tries to match as many things as he can with the cards in his hand.  Cards can match by color, shape, and/or number of objects.  He selects one of his cards and places that in the middle of the table.

The fourth player does the same thing, trying to match his teammate, player 2.

Each team counts how many categories they matched.  Players 1 and 3 matched the shape only (circle), so they get one point, or in this case bottle cap.  Players 2 and 4 matched the color (red) and the number (two objects), so they get two points (bottle caps).

Each player takes back his card and places it on a discard pile and picks a new card off their face down pile to have three in their hand again.

Player two starts the next round.

Game play continues in this manner until the end.

## The End:

Game play can end when you run out of bottle caps or when all players use their 27 cards.
Score can be kept with tally marks instead of bottle caps, but with my youngest son I think the visual scorekeeping was best.

## Winning:

The team with the most points/bottle caps, wins.

## The Need:

I created the game Polynomial Pirates because I realized there was a need for students to focus on the difference with certain polynomial operations.  For instance, students were confusing (x+x) with (x*x).  I could 'reason' with them until I was blue in the face and nothing changed.  Then I realized that I needed to come up with a game.

## The Story:

You are one of four pirate captains searching for a sunken treasure. Not only are you competing against the other pirates to get to the treasure before they do, you will need to defeat the fire-breathing treasure-guarding sea monster first.  Battling other pirates and surviving the open seas will prove to be too difficult for the weak of heart; only the strongest will be victorious.

## The Materials:

You will need 8 dice with these 6 monomials written on them; x, 2x, 3x, y, 2y, 3y.
A plate will be helpful because the players will roll the dice then pass them to the next player.
Frugal Options: Put stickers on dice you already own.

At least 2 sets of polyhedral 7 set dice will be needed.  These will be needed when your pirates either battle each other or the sea monster.
Frugal Option:  Use a random number generator.

Players use two forms of currency; coins and gems.  Pirates use these to buy and upgrade the cannons and shields for their ships.
Frugal Option:  Print out paper coins and gems.  Or use pennies and buttons or whatever you have lying around.

You will also need something to represent the treasure chest.  I was fortunate enough to find this lying around my house.
Frugal Option:  Print a paper 2-D treasure chest.

Here are the pawns that I use.  They are stickers placed on bottle caps.
Frugal Option:  Use any ol' pawns you have lying around from other games.  Or even different color bottle caps.

(Seriously, why is this sideways?  It's right-side-up in iPhoto.)

To keep track of how many cannons and shields and their respective levels, players will need the cannon/shield cards and 6 paperclips per player.  I glued the player cards to large index cards.  On the front are the shield and cannon indicators.  On the back of the index cards are the rewards for winning.

In this game the game cards make up the board.  When you add, subtract, multiply for divide any two of the 6 monomials used in this game (x, 2x, 3x, y, 2y, 3y) there are 52 unique outcomes if I did my math correctly.  I bought a deck of pirate cards, printed my cards on sticker paper, and then stuck them to the playing cards.

Frugal Option:  print the cards and glue to index cards.

(Again, not sure why this is sideways)

## Game Play:

Set up your "game board" like this.  It's a 5 by 5 array with the middle card missing.

Place the treasure chest in that middle spot.

Each player starts their pawn in a corner.

Each player is given a player card, 5 coins, and 5 gems to start the game.

Suppose that the monkey is the first player.  He will roll all 8 dice on to the plate.  Looking at the cards adjacent to him, he can either move to xy or 3xy.  The monkey can use two or more dice to create any adjacent statement.

The monkey decides to use 2y, y, 3x, and 2x to create xy.  (2y - y)*(3x-2x) = xy
The monkey moves to that card and does what it says.  In this case it reads, "Buy a cannon 4 coins, or collect 2 coins, or collect 2 gems".  Once he is finished with his turn, he passes the plate to the next player.

*Once a player moves his pawn and uses a card, that card is put on the bottom of the card pile and the top card is put in that spot.

Now it's pirate girl's turn.  Her options are x-2y or 2.  Looking at the remaining dice, I can't find a way for her to create either of those statements (remaining dice:  2x, 2x, 3y, 3y).  She will have to pay one gem to re-roll all 8 dice.  If she is unable to create either of those statements again she can pay another gem to re-roll or pass to the next person.  Note - re-rolls are free if there are three or less dice on the plate.

## Battles:

In order for players to battle each other they need to be on the same space.  The person who was on the space first is the defender, the player who lands on the space second is the attacker.

In this case the pirate girl is the defender and uses her shields and the monkey is the attacker and uses his cannons.  At this point in the game the pirate girls has 2 shields; one level 8 shield and one level 6 shield.  So, she uses an 8-sided die and a 6 sided die, rolls both, and adds them together.  Her total is 4.  The monkey has two cannons; one level 8 cannon and one level 4.  So he uses an 8-sided die and a 4-sided die and adds those together.  His sum is 7.
The monkey won 7 to 4 and wins by 3.

Turn a player card over to see his reward.  Since he won by 3 he can take a combination of 2 gems or coins from the pirate girl.  Since the pirate girl lost she teleports back to her starting corner while the monkey can stay on that spot.  The pirate girl may not collect what is on that corner card.

If there is a tie, the defender is the winner.  He would collect nothing but the other player would need to go back to his starting corner.
If the losing player in a battle does not have enough coins or gems to pay out, they are required to lose levels with their shields and/or cannons to equal the number of coins/gems they were to pay out. If things are dire enough, they may lose cannons and shields.

## Winning the Game:

In order to win the game, the sea monster must be defeated.  The sea monster is a level 20 fire-breather, meaning he uses a 20-sided die.

To attack the monster, a player must be adjacent to the monster.  Please note that players may attack the monster individually.  In the photo below, the players have teamed up to attack the monster.

Attacking the monster is different from players attacking each other.
To attack the monster, the player will roll their cannon dice and find their sum., then roll the monster's 20-sided dice.  If the player has a higher sum than the monster, he wins the game and the treasure.  However, if he does not have a higher sum there is a second part to this.  Then the player rolls his shield dice and the monster rolls his 20-sided die again.  If the monster has a higher number, the player must forfeit the corresponding loot and return to his starting corner.  If the player successfully defends himself, he only moves to his starting corner.

Cooperative play:  Attacking the monster is the same.  Each pirate would roll their cannon/shield dice and add them all together.  The only difference would be the amount of loot lost is paid by each player attacking.

## Other Stuff:

Players can trade in coins and gems for half the amount.  For instance; a player can trade in 2 gems for 1 coin or 2 coins for 1 gem.

Players may form alliances and freely give loot to other players.

## Next Steps:

I am in the process of creating pre- and post-tests in order to determine if the game is even worth it.  Stayed tuned for that information.

## Tuesday, November 25, 2014

### Hidden Squares Activity - Equations with Variables on Both Sides

I did this activity last year with the snowflake posters if you want to check that out here.

#### To start class:

Tell the students there are a total of 32 small blue squares on this poster.  Some are hidden under the purple flaps.  Let them know that there are the same amount of square hidden under each flap.  How many blue squares are hidden under the flaps?

Most of my students noticed that there were 17 exposed blue squares and that meant that 15 were hidden.  If there are 5 flaps that means there must be 3 under each flap.

Me:  When we don't know the quantity or value of something what do we do?
Student:  We use x.
Me:  Right a variable.  Can we represent this poster as an expression using constants (numbers) and a variable?

The students were able to come up with 5x + 17 = 32, and then noticed that they needed to take exactly the same steps they took when they solved the poster problem above.

Me:  Do you see the "bubbles"?  What do you notice about the bubbles?
Student:  They have the same things inside them.
Me:  Let's use this information to write an equation.

With a little prodding the students came up with 2(2x+5) + x + 7 = 32
As we wrote each line of the solution, we made the connection with the poster to see where the numbers were coming from.

#### Taking Things Up a Notch:

Show the students this poster (without the algebra at first) and ask if they can determine how many squares are hidden under each flap.
They need to know that both posters have the same amount of small blue squares on them and the same amount are hidden under each purple flap.

All of my students used trial and error for this at first.  But then as a class we were able to solve with algebra.  I like that after we finish the algebra, we are able to lift a flap to see if we're right.

#### Now It's the Students' Turn:

I put students into groups of 2 to 3 and had them create their own posters.  The requirements were:
1) There must be the same number of small squares on each poster.
2) There must be the same number of small squares hidden under each flap.
3) Each poster must have a different amount of flaps.
I also wanted them to have "bubbles" on at least one of their posters.

The last image is very interesting.  The students and I had a nice discussion about it.  At first they said the answer was 1.  I agreed.  But then I asked if it could be 2.  They agreed.  3? 4? 5?  Why?  How can we write what all the answers are?  What does this look like algebraically?

#### Next time:

I enjoy this activity.  It's such a concrete way to talk about equations, the distributive property, combining like terms, and even consistent and inconsistent systems.  Next time I will focus more on the "why" on the poster requirements.

1) The posters must have the same amount of small squares.  Why?  What would happen if they didn't?

2) There must be the same number of squares under each flap.  Why?  What would happen if they didn't?

3) There must be different amount of flaps on each poster?  Why?  What would happen if they did?