Mr. L's Math» Puzzle

KenKen Presentations at NCTM 2011 Annual Meeting

Bill Lombard — Fri, 08 Apr 2011 00:59:57 +0000

I’ve asked for the information download link for the conference handouts and other information from the presenters below. I’ll post the link as soon as it is available. I’m glad to see so much interest in this fabulous puzzle.

KenKen is now the main topic at two independent presentations at the National Council of Teachers of Mathematics (NCTM) 2011 Annual Meeting & Exposition in Indianapolis, April 14-16

KenKen: A Logical Marriage between Sudoku and Arithmetic
April 14, 8:00 am – 9:00 am
Sagamore Ballroom 2 (Indiana Convention Center)
Pamela D. Martin & Kathie O. Smart, Instructors of Mathematics, University of Louisiana at Monroe
Description: How the simplicity and effectiveness of KenKen allow young learners to quickly excel, while challenging their logical thinking.

Using KenKen to Enhance Students’ Learning
April 14, 10:30 am – 12:00 pm
Room 124 (Indiana Convention Center)
Harold B. Reiter, Professor of Mathematics, University of North Carolina at Charlotte
Description: Using KenKen with children and teachers. Professor Reiter will talk about his experiences using the puzzle at a camp in Bangalore, India, and at various teachers’ workshops.

Video – Reverse the Math Puzzle, Part 2: Using 1, 3, and 5

Bill Lombard — Wed, 06 Apr 2011 00:27:28 +0000

Here’s Part 2 of the Reverse the Math Puzzle: Using the numbers 1, 3, and 5, and mathematical operations, create expressions that equal the numbers from 1 through 10. This puzzle increases number sense and reinforces the concepts of exponents, factorials, and operations. You can see Part 1 here.

Video – Sum Equals Product Puzzle Part 2 – Solution

Bill Lombard — Sun, 27 Mar 2011 18:31:09 +0000

The Sum Equals Product Puzzle Part 2 – Solution shares the video showing the approach I took to solve this puzzle, which asks “Can you find a set of positive integers whose sum equals their product?” The original problem some extensions, and the generalization are shown, along with the algebra proof.

You can play the video here or find it on my youtube channel, mathvideouniversity: Sum Equals Product Puzzle Part 2 – Solution

Line by Line – A Mathematical Puzzle Poem Made of Numbers

Bill Lombard — Sat, 26 Mar 2011 00:17:46 +0000

Line by Line – A Mathematical Puzzle Poem gives the reader clues about a mathematical poem made up of numbers. Each line gives a clue about the line following. Line by Line, Part 2 will present the solution.

Here is where you can find this (somewhat ) classic poser on youtube: A Mathematical Puzzle Poem

Video – Sum Equals Product Puzzle – Part 1

Bill Lombard — Fri, 25 Mar 2011 19:20:09 +0000

Sum Equals Product video screenshot

Here’s a puzzle from the California Math Communicator, the quarterly math journal for California’s math teachers from the California Math Council.

The Sum Equals Product Puzzle asks the question, “Can you find two positive integers whose sum equals their product?” Bill Lombard shares this problem and shows several extensions of this puzzle about number sense. Part 2, the next video in this series, will show the solution, Bill’s method of solving, extensions, the generalization, and some pedagogy of teaching problem solving in the math classroom.

Here’s the link to Sum Equals Product Puzzle as posted on my mathvideouniversity Channel on youtube.

Best wishes as you explore this puzzle either on your own or with your classroom of inquiring minds.

Reverse the Math Puzzle Using 2, 3, and 4

Bill Lombard — Tue, 22 Mar 2011 18:59:16 +0000

I’ve just posted a new video at my mathvideouniversity site on youtube called Reverse the Math Puzzle Using 2, 3, and 4. This puzzle uses the numbers 2, 3, and 4, along with standard operational symbols of mathematics to create the numbers 1 – 10.

The reason it’s called Reverse the Math is that the numbers from 1 – 10 are the target numbers, or essentially the answers to problems that must be created; so students and puzzle enthusiasts are given the answers, but must come up with problems that have the answers from 1 – 10.

Not only is this a great puzzle that builds number sense, it also reinforces a great deal of number properties and provides examples of algebra concepts in a fun way. You can find solutions using exponents, factorials, and square roots, and in most cases there are a number of different ways to express numbers using the given “ingredients.” I’ve used this type of puzzle for years, often spending a week on this as warmups or part of homework. Each day I change the ingredients and watch students’ number sense and enthusiasm grow.

Magic Square Products Solutions – a New Twist on an Old Puzzle Pretzel

Bill Lombard — Mon, 21 Mar 2011 00:35:09 +0000

Magic Square product - 3 solutions

Here are some solutions for the puzzle I posted last week, that of finding a solution to making a magic square not using addition, but with multiplication. The first solution, using powers of ten, occurred to me since multiplying numbers with the same base simply amounted to adding the exponents. This is a great way for teachers to reinforce exponent facts. This is, of course, just one of many solutions; other bases can be used.

The second solution came from a colleague of mine, Joe Loverde, who created a more general version with a’s and b’s, with a and b relatively prime; the magic product is a³b³. He also supplied the “real live example” that you see as well, with a = 2, b = 3, and the magic product = 216.

This new puzzle twist arose recently when I read one of my favorite RSS feeds from The Math Nexus: Mathematics Portal – News and Ideas for Teachers and Learners of Mathematics at http://mathnexus.wwu.edu/.

If you have other solutions or variations to this puzzle, please let me know; puzzles grow better with more input and variety.

Historical note: After posting the puzzle last week, I sent an email to Jerry Johnson at Math Nexus and thanked him for all the quality work that he and his group do. He related the following:

Thanks for the encouraging words. A side note: The problem was first given to me in 1973 by my graduate adviser…I think you know him, Jack Beal at the University of Washington. When meeting in his office, he handed me the problem and said “Go play with it a while….” That is great advice….and now I have handed on the problem…and you the same…
Jerry Johnson

Magic Square Products – a New Twist on an Old Puzzle Pretzel

Bill Lombard — Mon, 14 Mar 2011 00:09:42 +0000

Magic Square 3x3 sum

Most of us are familiar with magic squares. They are square arrays of numbers such as the one shown here. The sum of each row, column, and major diagonal is the same, hence the name. The first time students are posed the challenge of creating one, they invariably say “It’s impossible.” After seeing one such as the one at the right, they are entranced. Magic squares exist for all sizes of squares from 3×3 on up, and there are simple rules to create them.

The new twist arose recently when I read one of my favorite RSS feeds from The Math Nexus: Mathematics Portal – News and Ideas for Teachers and Learners of Mathematics at http://mathnexus.wwu.edu/. I look forward to reading each edition of their online newsletter for great math nuggets.

The problem Math Nexus posed was to find a 3×3 Square that was magic, not using addition, but multiplication. In other words, the product of each row, column, and major diagonal must be the same. I had seen this problem posed before, but had never pursued it. This time I wanted to give it a good try. So I made several 3×3 grids, played around with factors, multiples, and so forth, before I realized that I wasn’t going to be successful right away. So I did what I’ve always suggested to my students: set my intent to solve it and let my subconscious know that this was important, did my best to wrestle this puzzler to the mat, and then left my desk. About two hours later, while sitting in my recliner, the solution just presented itself. And not just one solution, an infinity of them. Those who have played around with magic squares know that there are many different solutions to magic square puzzles, and the Magic Square Product puzzle is no different.

I pose this problem today, and will share at least two different solutions to this product puzzle in seven days. As always, there is much to be gained by studying this puzzle, and teachers can look forward to using many math concepts in the explanation of the puzzle solution.

Mr. L’s YouTube KenKen Video

Bill Lombard — Tue, 14 Dec 2010 20:19:38 +0000

KenKen 4x4

I got an email from YouTube a few days ago asking if I was interested in YouTube’s Partnership Program. This program allows video makers the opportunity to place ads next to their videos and receive a share of the revenue.

I was surprised at this, so I visited my KenKen video, KenKen 4×4 Introduction and Strategy, and found out that it’s been watched over 13,000 times as of this date (mid-Dec 2010). That’s pretty cool for a math/puzzle video. It’s nice to see so many people interested in puzzles, especially one that is so math oriented. So I guess I’ll make some more vids showing how to use puzzles in and out of the classroom to improve logical and mathematical thinking.

I recently bought a Canon T2i dSLR camera, and one of its nicest features is the ability to record HD video. My plan is to use this camera to record vids showing classroom lessons and pedagogy. Since winter vacation is coming up, I’ll have some time to make progress on this idea. The dSLR is a big step up for me, and all the menus may take awhile to master, but the end result should be great. Here’s hoping to make some more vids with even larger viewership!

Games and Puzzles that Reach the Kids and Teach the Standards

Bill Lombard — Fri, 27 Nov 2009 16:19:28 +0000

The title of this post is from a conference session at the California Math Council conference at Asilomar in December, 2009. You may download the handout, with instructions for some activities, through the following link:

Games and Puzzles that Reach the Kids and Teach the Standards – download file

Puzzles and Games are a great way to build enthusiasm, excitement, and skills in a math classroom. When these are used properly, there is always an underlying mathematical theme that is being explored or reinforced. Students learn the value of logical thinking, proper planning, and long-term focus.

Mathematical games can develop a lot of creativity and number sense in students. Many times a game or puzzle at first looks overwhelming, but becomes manageable after focusing on the key concept. Motivation is almost always inherent in a game or puzzle; this creates conceptual emotion which is a key to successful learning.

Opportunities for transitioning from number sense to algebra thinking abound with puzzles. Number properties show their strength in supporting algebra throughout puzzle activities. It’s always a pleasure to watch the enthusiasm and skills grow in students!

Some of these activities are from Teacher to Teacher Press books:

Simply Great Math Games

Simply Great Math Activities: Algebra Readiness

Simply Great Math Activities: Number Sense

Put these activities, puzzles, games, and ideas into regular practice, you will find increased skills and motivation in your students and more joy in your teaching.

Best wishes,

Bill Lombard (a.k.a. Mr. L)