Additional Math Pages & Resources

Wednesday, October 17, 2012

A Tribute to Martin Gardner & Brainteasers

Martin Gardner was born on October 21, 1914 and died in May 2010 at the age of 95. Read more about him in this interesting profile by Philip Yam. Mr. Gardner was a fan of mathematics, puzzles, magic tricks, gag gifts, and feral cats. In his honor, October 21 (his birthday) is set aside as Celebration of Mind Day. Since it falls on a weekend this year, you may want to celebrate all week long. As you might expect, this celebration encourages a fun and playful approach to math. Students can mark the day by doing fun math puzzles, performing illusions, and even sharing math stories.  Read our previous post about Math Storytelling Day for additional math story ideas for the classroom.

Martin Gardner was fascinated by mathematics, magic and Alice in Wonderland. He was a prolific American writer who had interests in music, philosophy, scientific skepticism, religion and literature. Mr. Gardner enjoyed creating mathematics and logic puzzles and writing about them. You can find some of those puzzles in his ebook, Fractal Music, Hypercards and more . . . Mathematical Recreations from Scientific American Magazine at This book is an anthology of Gardner's Mathematical Games columns from the 1978 and 1979 issues of Scientific American Magazine (the 14th in his series of such collections). Try some of Martin Gardner's brainteasers and play some puzzle games online or download them for your students at

One of Mr. Gardner's most famous puzzlers was the onion (sometimes changed to a cherry) in the glass. This was originally demonstrated using matchsticks. For the classroom, you could use a bead or counter for the cherry (or whichever food your students prefer in their lemonade or soda—lime, orange slice, raspberry, etc.) with 4 toothpicks for the glass. Some of your students may have played the ball in the cup tossing game. If so, you could change the puzzle from a cherry in a glass to a ball in a cup. The object then would be to try to toss the ball out of the cup by rearranging two toothpicks. Here's how to arrange the toothpicks and the ball or bead:
The problem is to move just two toothpicks so the cherry (or ball) ends up outside the glass (or cup). The finished glass may be turned left, right or upside down as long as the cherry is outside it. Try it yourself before looking at the solution below.

The Excel Math Teacher Editions for Grades 2-6 include a variety of math brainteasers and logic puzzles called Stretches. Stretches teach students various kinds of thinking skills and, like the rest of Excel Math, carefully spiral through math concepts. Here's a Stretch from the third grade Teacher Edition in the style of Martin Gardner:
Draw the figure below on the board or have your students use 13 toothpicks to create it. Ask the students if they can remove 1 toothpick (or one line) so it forms 3 squares instead of 4. The answer appears below.

Stretches can be used as math warm-ups or bell work to get the students focused on solving problems before they begin the daily lesson. Read more ideas for math class warm-up activities in our July 23 blog post.

This is the answer to Mr. Gardner's cherry in the glass puzzle. We've color coded the toothpicks so it's easier to see how they move. If you slide the green toothpick right instead of left, the cherry ends up on the outside left of the glass. To see some of the incorrect moves your students might try, read Philip Yam's blog.

Here's the answer to the Excel Math puzzle from above. Simply remove the top center toothpick (or line):

Because Excel Math uses a unique spiraling strategy, the lessons build upon each other and need to be taught sequentially within each grade level (including Guided Practice, stretches, and interactive activities) in order to get the concepts into your students' long-term memory. Try out some sample lessons but then use it for a full year in your classroom to see the amazing results.

Since an entire year of Excel Math curriculum is as low as $11.00 per student, many schools use it as their core curriculum. Other schools find it's a powerful supplement to their adopted curriculum. In both situations, students gain confidence in mathematics as test scores soar.

Visit our web store to order Student Lesson Sheets (155 lesson sheets plus tests) and a Teacher Edition set of 155 Lessons with brainteasers, teaching suggestions, the answer key, activities, and reproducible manipulatives for each grade level. Excel Math is available for Kindergarten through Grade 6.

Interested in finding out more about Excel Math? Take a quick tour here.

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