## Tuesday, February 18, 2014

### Domain and Range: Nailed it!!!

A while ago, I told you about the game I created called Domain Ranger.  I played the game with my students this past week and it was AWESOME!!  I mean awesome.  Every student was engaged, multiple students were overheard saying how much fun the game was.  I was on cloud 9.  The next day I introduced the topic of domain and range with graphs and the students got it.  In one lesson (well, three if you count game play).  Either way, it has never happened so fast and accurately for me before.  So I can't keep all this math goody-ness to myself.  It's time to share...

### The Game:

You can read my original post about the game here.  But a lot has been updated...

For a two-player (or two-team) game:

Start by printing out 2 sets of these.  These are the cities.  There is one that is crossed out, and some blank ones; throw those away.  Cut out each graph and attach each set to it own color paper (i.e. one set in blue, the other in green).

Next print out the weapon double sided.  You will need two of these.

Print out one set of the number cards and cut apart.

Each student will need scrap paper and a pencil/pen.

You will need items to represent shields (I used eight buttons)
.
You will also need items to represent the capital (I used two pennies).

#### The Cards:

Shield -->  Discard the Shield card to place a shield on one of your cities.  OR  Discard the Shield card to remove a shield from one of you opponent's cities.  Each city can have at most one shield.

Change Army Formation --> Discard this card to replace one of your city cards with a city card from you pile.

Move Capital -->  Discard the Move Capital card to move your capital to another city.

#### Game Set Up:

Each player/team sets out any 9 city cards in a 3x3 array so that 3 of their cities are adjacent to 3 cities of his opponent.

Each player places their capital indicator (penny) on one of their cities.  Players should pick a city that is as far away from their opponent as possible.

Shuffle the deck of cards, hand out 7 cards to each player, place the remaining cards on the table and turn over the first card next to the pile to start the discard pile.

Give each player a weapon.  If students are new to domain and range, have them begin with the side of the weapon that used 'up, down, left, and right'.  Students who are more familiar with domain and range will use the other side.

Shields (buttons) are placed to the side until needed.

#### Overtaking an opponent's city:

Players load the weapon with the 4 numbers necessary to enclose the army formation (left, right, down, and up).  To load the weapon, players simply place the 4 numbers in the correct space on the weapon.  Opponents check to see that they are correct.
If the 4 numbers are correct, the opponent's city is removed and replaced with one of your cities.
Discard the 4 number cards in the weapon and pick up 4 new cards.
Note - players may only overtake cities that are adjacent to their own (no diagonal takeovers).
The 4 numbers:  The 4 numbers used to defeat a city are the 4 numbers in the domain and range.  For instance, the numbers needed to defeat the city below are:  Left -6, Right 4, Down -2, and Up 3.

On a player's turn, he takes either to top card from the discard pile or the top card from the card pile.  The player now has 8 cards in his hand.  The player organizes what cards he wants to keep, and/or load the weapon.  When the player is finished, they discard one card to end their turn.  He now has 7 cards in his hand again.

Only number cards can be picked up from the discard pile.  Shield, Change Army Formation, and Move Capital cards cannot be picked up from the discard pile.

#### Removing Shields:

There are two way to remove a shield from an opponent's city:
1. Discard a Shield card to remove a shield from an opponent's city.
2. Load the 4 numbers into your weapon to remove a shield from an opponent's city.

#### How to win:

The winner of the game is the person who defeats the opponent's capital.
If there is not enough time to finish a game completely, the winner is the player with the most cities.

### In class:

We played this game in class for two days.  Well, the first day was on a 2-hour delay schedule, so let's say 1.5 days.  I started by having 4 volunteers (two teams of two) walk through the game with me as the rest of the class watched.  Next, the class split up into groups of four to start to play the game.  The first thing I have students do it write down the 4 numbers they need for each of the 3 cities they are adjacent to on their scrap paper.  Whenever a city is defeated, or an army formation changed, the numbers on the scrap paper will have to change as well.

On the third day, we took a formal look at domain and range.  Throughout the two days that we played the game, not once did I mention the words domain or range.  However, it was such an easy transition from the game to the lesson that I was floored.  Here are the materials that I used in class that day.

#### Some Photos:

1. Dear Simplify With Me,
As a proponent of math education in the United States, we need your help to promote our nationwide math competition by blogging or posting about it on your blog/forum.

As you probably already know, despite the fact that the US spends the most money on education per capita, our students are ranked 25th globally for math proficiency. The MATHCOUNTS Foundation is a nonprofit dedicated to improving that statistic. MATHCOUNTS’ third annual “ Math Video Challenge” is a math competition for 6th to 8th graders that encourages student innovation as they create and star in their own math videos, thus exciting them to pursue higher education in math.

As the webmaster of Simplify With Me, we are asking you to help support this effort by mentioning us in your next blog or forum post or promoting our logo with a link to the site. So far this contest has gathered over 500
submissions and millions of views on the videos. Our goal this year is this year is to do even better. With your help, we are confident we will reach this goal.