Math = Love: Logic Puzzle Love: Shikaku Edition

## Thursday, April 30, 2015

### Logic Puzzle Love: Shikaku Edition

I'm not sure why I'm still surprised when the #MTBoS comes through for me.

Last week, I tweeted about doing griddler logic puzzles with my students.  Bowen Kerins tweeted back with a suggestion of a different type of logic puzzle that could be tied to the math curriculum: shikaku.

Guess what type of puzzle we did the next day in class?

A quick google search revealed an article in NCTM's Mathematics Teaching in the Middle School May 2010 issue by Jeffrey J. Wanko.  Dr. Wanko wrote about a process of introducing students to logic puzzles by first showing them a completed puzzle and having them determine the rules of the puzzle.

I placed the unsolved shikaku puzzle from the article on the SMARTBoard.  I asked students to speculate as to what the rules of the puzzle were.  After a few suggestions, I asked students if it would help to see a completed puzzle.  They were eager to see this.

At first several students proclaimed that this was too hard or impossible.  And, of course, I followed this up with "This will take some time and effort."  In some class periods, a student said this second line instead of me.  #growthmindset  It was really cool to see the light bulbs going off as students studied the screen.  Soon, they decided that the circles told how many boxes were in each section.

Though, the room quickly erupted when one student claimed that each section must be a rectangle.  Other students argued that squares were also allowed.  Some students claimed that every square was a rectangle.  Several classmates were less than convinced.

We also discussed the fact that the rectangles could not overlap, and the circle could be placed anywhere in the rectangle.  With these rules, students were antsy to start a puzzle.  I put up a puzzle on the board to do as a class from the same NCTM article.  Students came up one at a time and drew a rectangle where they thought it went.  Some students were not using logic to place their rectangles.  But, I didn't say a word.  I figured the class would figure this out eventually.  And, they did.  They worked together to fix the mistakes.

After doing one puzzle as a class, I gave students an activity sheet with 4 more shikaku puzzles.  To receive their points for the day, they had to successfully complete two of the puzzles.  Most of the students agreed that they liked these puzzles better than the griddler puzzles from the previous day.

It was eye-opening to listen to students' thinking as they worked these puzzles.  One student claimed that if the circled number was odd, the boxes would always be in a straight line.   I hope they eventually realized that 9 broke this pattern.  What they were actually noticing was the difference between prime and composite numbers!

I could see using this as a fun introduction to factoring.  A 12 rectangle can have dimensions 1X12, 2X6, or 3X4.  Students had to consider each of these possibilities when solving the puzzle.  I can also see using this as part of an investigation into comparing area and perimeter.

These got my students thinking which is exactly what I want them to be doing during these last few weeks after testing and before the end of school.  Several students came in the next day and asked for more of these puzzles to do.  I even have students who aren't enrolled in my classes coming to me and asking for logic puzzles because they see their friends doing them.  These puzzles are definitely a keeper!

Here's a link to a pdf file by the author of the NCTM article with more logic puzzles (including some shikaku puzzles!) to use in the classroom.  Enjoy!