Categories

## Put(t)ing Rational Numbers in Order

Many of my friends and followers have caught onto one of my guilty pleasures: my wierd fascination with The Price is Right (read about Price is Right and counting principles in this old post).  Here’s how a pricing game made for a fun review activity, and also made my life flash before my eyes (read to the end for that).

Here in Pennsylvania, we use the PA Core Standards.  For Algebra 1, here is a standard under “Anchor 1”:

A1.1.1.1.1 Compare and/or order any real numbers.  Note: Rational and irrational may be mixed.

Seems innocent enough.  Here is a sample “open-ended” task used to assess understanding on our state’s Keystone Algebra 1 exam:

Exciting….now let me go over here and watch the paint dry….

But during the NCTM conference, a lightning bolt hit. I was checking out a putting game at one of the booths, and I suppose rational numbers were on my brain….Hey – Golf + ordering rationals = feels like Hole in One to me!

In the Price is Right Hole in One game, contestants place groceries in order from least to greatest by price.  The number of items they can order until they are incorrect determines where they putt from. After a quick trip to the sporting goods store to find a putting cup, and some time with a Google Doc, we’re all set!

To start, I created a Google Slides presentation with 6 games.  Each game has 6 numbers for students to put in order:

During the game, all students in the class had about 2 minutes to place the numbers in order.  They, we randomly drew our “contestant”, who came to the board to fill in the 6 boxes on the board.

Next, we went through the numbers from left to right, and determined how far the contestant had gone in successful ordering.

On the floor, 6 lines were taped.  Line 1 was on the other side of the room, and the lines were closer and closer to the hole. If a student had 4 numbers correctly ordered, they were allowed to putt from line 4.  Two students were able to order all of the numbers and tried their putt from about 2 feet away.

Those who made their putts earned candy to share with their group.  In about 20 minutes, we got through 4 games – not bad for ending a Friday on a fun note.

But be careful! My last “contestant” – one of my less cooperative students and a sometimes hot-head – was able to putt from line 6 with the help of his group.  After missing the first putt, I reminded him that the game is really Hole in One – OR TWO, and had a second chance. Lining up the putt…he took it easy…and missed again.  This is when he raised the putter up and, for a brief second, it looked like the putter could end up flying in my direction.

“Sean, just pick up the ball and put it in the hole….here’s some candy…”

Categories

## Rock, Paper, Scissors and 2-Way Tables

Last weekend, the evil Michael Fenton posted a link to an online applet which will now occupy you for the next 2 hours.  It’s not too late to run away now…

Still with me? An adventurous soul, you are.  Anyway, the NY Times online Science section has shared an online game of “Rock, Paper, Scissors”, where you can play against a choice of computer opponents.  The “Novice” opponent has no understanding of your previous moves or stratgey.  But, the “Veteran” option has gathered data on over 200,000 moves, and will try to use its database to crush your spirit.

My Advanced Placement Statistics class today was preparing for their first chapter test, where topics include 2-way tables and marginal distributions.  Time to abandon my planned review and play!  Here’s what we did:

Each group (I have 6 groups of 4) was given a netbook computer and the NY Times site.  Half of the groups were told to play against the “Novice” player, while the other half challenged the “Veterarn”.  Each group played 20 times, and pride was on the line as groups considered their moves carefully.  Class data was gathered and compiled into a 2-way table.

But just how good are we at outsmarting the computer opponent?  In round 2 of this activity, groups again played 20 games, switching their opponent.  This time, however, I directed groups to choose their moves RANDOMLY.  Groups used their graphing calculator to generate a random number from 1 to 3, which determined their move.  The NY Times site provides some info regarding randomization:

A truly random game of rock-paper-scissors would result in a statistical tie with each player winning, tying and losing one-third of the time. However, people are not truly random and thus can be studied and analyzed. While this computer won’t win all rounds, over time it can exploit a person’s tendencies and patterns to gain an advantage over its opponent.

Groups played 20 more times, and a new table was created for this “random” round.  Last round strategy was labeled the by “guts” round.

With the data now on the board, groups were given a few minutes to summarize their findings.  Did we improve by being random?  Did we improve in any particular area?  This turned out to be an engaging review of marginal distributions, and a good opportunity to discuss ribbon graphs, which come up in AP Stats as a useful graphical display.  Below, Excel can be used to compare the “Veteran” opponent results.

Thanks Mike, for sharing such a cool link!

Categories

## The Take-Away Game

A recent visit to a 6th-grade classroom gave me a chance to introduce a simple game I have used in the past as an-going challenge.  Even after a few pop-ins to this 6th grade class, I am still undefeated, and don’t plan on giving up my championship belt anytime soon!

THE TAKE-AWAY GAME – Rules

On a board, or piece of paper, draw 23 X’s.  Players will alternate turns, and on each turn a player must erase 1, 2 or 3 X’s.  The winner is the player who erases the last X.

It’s an easy game to understand.  An example is given here:

With a class, I will give students a chance to use dry-erase boards and play against each other.  Then, as students begin to understand the game, they are allowed to challenge me.  This usually ends badly (for them), as I know the tricks to the game.  I start by asking the player if they would like to go first, or allow me to go first.  Since kids are usually nice, they will allow me to go first, and this sets them up for certain doom.  Also, I will use my best poker skills to agonize over my moves, though I know exactly where I want to go with my moves.

Eventually, students will gather around to suggest moves.  Their first realization is that if I get the board down to 4 Xs, I will win.  This will then extend to 8 remaining.  With some classes, I have placed a fist behind my back, and done a thumbs-up to signal those watching when I know I have the game won.  Shoot me an e-mail if you need thorough instructions on how to win.

As students master the game, we can ask some extension questions:

• Does the number of X’s we draw change the game?  What if we use 25, 35, or 50 X’s?
• What if we could erase 4, 5, 6 or n number of X’s?  How would the strategy change?

For now, play the game with your students, and I look forward to retaining my Inter-Galactic Take-Away Game Championship Belt!