Tuesday, January 26, 2016

What I'm Looking For

     Last year Jo Boaler's multiplication task How Close to 100? caught my eye. I decided to bring it to our grade 3 teachers, and it quickly found its way into the rotation.

Roll two dice.  Use the numbers as factors and generate corresponding rectangular arrays.  Place them on a 10 x 10 grid, and see how close you can get to filling it up.  I liked color coordinating the equation with the array.  Colored pencils worked best.

     Although designed to build fluency with basic multiplication facts, we found the activity had other benefits.  In order to maximize your chances of filling up the grid, rectangles needed to be placed strategically.  Also, in order to calculate your final "score", you needed to do some computation.

Students experimented with different computation strategies, from adding up all their products to subtracting the total number of blank squares from 100.

The activity provided inspiration for a number talk:

     And when we experimented with a 20 by 20 grid, and dice that would generate higher factors, things got a bit more difficult...

And a little messier...


We also challenged the kids to find different ways fill up the grid using exactly 10 rolls:

     The rectangles came in quite handy when we got to studying area and perimeter:

There's really no escape from the scissors.

We had them cut out the rectangles, find their perimeters and areas...
...and sort them based on their relationship.

     I'm often asked, "What do you look for when choosing a game or activity to bring to a class?"  Once it passes through the first, most important test of might a kid who doesn't like math find  this engaging, I look for its potential to be extended or repurposed.  There's something about the idea of  becoming familiar with the way something works, then using that familiarity to build on or connect to something different, that appeals to my sense of how we grow and learn.  How Close to 100? is a good example of an activity that checked off those boxes.

Wednesday, January 6, 2016

"I Like This Game Because You Have to Think Hard."

    A Monday afternoon, working with one of my second graders, helping him fill in a blank hundreds grid.  Suddenly it hit me.  What if...

...using different colored pencils, players alternate capturing squares on a hundreds grid...

...while trying to get 4 squares in a row, column, or diagonal.

It would work  just like tic-tac-toe.

Each tic-tac-toe is worth a point, and you can keep track with tallies.  Play until the board is filled up.

   Theresa and I played a practice round:

Initially we tried 3 in a row, but things got very confusing and we decided that 4 in a row was better.  We also tried a game where a square could be used in multiple tic-tac-toes, but didn't like that either.  We also decided that the 0 and 100 would not count towards any player's tic-tac-toe.

And then it was time to take newly christened Number Grid Tic-Tac-Toe for a test drive.  (Apologies if someone holds the patent on this!)  Jane's class was first, and we decided to get crazy and use a grid that went from 1 to 120.  It took only about 5 minutes playing a demo game with a volunteer under the document camera and they were ready to rumble.

"Hmmm.  Where should I go?"

"I think I can figure this out in my head."

Playing it safe.

Using a number grid to help is so SMP 5.

A barn-burner.  You can see here that 34 was used twice, as was 46. 
   Over the next several weeks I tried it out with 3 more second grade classes and 1 third grade class.  I asked each to write down their reflections and reactions on the back of their game boards.  Here's a sample:
  • I liked this game because it was fun to figure out where the numbers go.
  • I like this game because you need strategy.
  • I loved it so much but hard.  So hard!!!
  • I think the game helps because to put the right number in the right place you have to count by numbers and learn to do that in the game.
  • I liked it because I outsmarted (my opponent) when he tried to outsmart me.
  • I like this game because you have to think hard.
The kids came up with some awesome suggestions for modifying the game, including:
  • If someone gets stuck, the other player gets a point.
  • If you get three in a row you get half a point.
  • Add a few numbers scattered around the board.  (Love it!  This child wants it differentiated!)
  • If you get five in a row you get 2 points.
Jane's class experimented with a 3 player game:

They found that 3 in a row was better with 3 players.

Maggie's class tried something a little more difficult:

"What goes here?"

Many possibilities...

If it's green's turn, where should he go?  Why?  Defend your answer.

     I'm happy to report that the game is wildly popular; for some reason it hits that elusive kid sweet spot.  I suspect it's because the cognitive demand is just right. (I like this game because you have to think hard.  Unspoken: But not too hard?)  And because the kids already know how to play tic-tac-toe, they can expend their mental energy on strategy and on figuring out which number goes in what square without worrying about a bunch of rules.   The teachers love it too because it's easy to explain and takes almost no effort to prepare.
   So grab a blank grid and some colored pencils and have some fun!

Sunday, January 3, 2016

Standards for Mathematical Practice and the Cinema, Part 3

    In the first two installments of the series Standards for Mathematical Practice and the Cinema, I  explored how SMP 6 (Attend to Precision) played out in two classics: This Is Spinal Tap and March of the Wooden Soldiers.  I'd like to turn my attention to a different practice standard, SMP 5 (Use Appropriate Tools Strategically), and one of my favorite movies of all time, Hoosiers.
   The film, released in 1986, is loosely based on the true story of tiny Milan High School's Cinderella run to the 1954 Indiana state basketball championship. It stars Gene Hackman as Norman Dale, a disgraced, temperamental ex-college coach seeking redemption...

Barbara Hershey as Myra Fleener, a small-town teacher with unfulfilled dreams...

And the late, great Dennis Hopper as the alcoholic assistant coach "Shooter" Flatch.

   The Hickory High basketball team responds to Dale's unorthodox coaching methods.  They make an improbable march to the state basketball championship, and face increasingly more difficult competition along the way from schools much larger than their own.  The team is used to playing in their small, claustrophobic high school gym...

...and are visibly shaken upon entering cavernous Hinkle Field House, on the campus of Butler University in Indianapolis, where the championship final is to be held.  Afraid that his team will be intimidated by the size of the arena and become mentally psyched out before the game even begins, Coach Dale employs a wily teaching move:

So was the tape measure responsible for Hickory's last second 42-40 win over South Bend Central?  If so, it played a very small part.  Because we all know who the real hero was:

Jimmy Chitwood!