Math Teachers at Play 63

Hmm… let’s see… now where did I put my notes? I know that this is supposed to be the Math Teachers at Play blog carnival… but which one?

Maybe the following puzzle will help. In the grid below, do the following:

• Circle any number, then cross out the other numbers in the same row and column.
• Of the remaining nine numbers, circle one, then cross out the other numbers in the same row and column.
• There should now be four numbers remaining; circle one. Then cross out the other numbers in the same row and column.
• There should now be one number remaining. Circle it.
• Calculate the sum of the four circled numbers.

Pretty cool, huh? Try it again, and you’ll find that the sum of the four circled numbers will always be 63. Can you figure out why it works?

Ah, yes! That’s it! This is Math Teachers at Play 63! Good day! Welcome one and all!

You might wonder why I’d start this carnival with so many questions. Maybe it’s because 63 is the ASCII code for a question mark.

• 63 = 7 × 9.
• 63 = 26 – 1 = 1 + 2 + 4 + 8 + 16 + 32.
• The record for the longest field goal in NFL history is 63 yards–kicked by Tom Dempsey, Jason Elam, and Sebastian Janikowski.
• 63 = 62 + 33.
• ‘Rule 63’ is an online adage, which states that every fictional character has a counterpart of the opposite gender.
• In Roman numerals, 63 is written as LXIII; and if you add the position of those letters in the alphabet, you get 12 + 24 + 9 + 9 + 9 = 63. It is the smallest number with this property. (Can you find the only other number with this property?)

Pre-School

Trying to help little kids see the fun and usefulness of math, Beanie N Us shows her daughter Learning about Numbers at the Car Park and having Fun with Math.

Elementary School

At the New Hope Elementary School, kids of all ages do M&M Math to learn about graphs, measurement, and area. Yum!

Fraction Folding, Discovery Learning is the first in a series of 16 blog posts that documents what a fourth-grade teacher at the Fourth Grade Studio did to help students develop conceptual understanding of fractions.

Navigating by Joy shares A Living Maths Approach to Angles using the book Sir Cumference and the Great Knight of Angleland and also shows how to have Fun With Tessellations.

When the Math Mama Writes, you better listen, especially when she’s questioning how and why we teach vocabulary in Writing, Vocabulary, and Teacher Inquiry.

Middle School

Offering straightforward and practical advice, The Numerist explains How to Write an Equation of the Line.

Who doesn’t love a story about student success? 4mulaFun shares such a story from a lesson that has students Reviewing Proportions with WKU. (Don’t know WKU? Neither did I! Read on.)

Miss Math Dork shares One of Her Favorite Activities for teaching measurement to middle schoolers, which is sure to become one of your favorites, too!

High School

Watch what happens when Mr. Chase alternately adds and multiplies in Arithmetic-Geometric Hybrid Sequences.

In Probabilities in a Painted Cube, Cut the Knot examines solutions to a problem about painting and cutting a larger cube into unit cubes and then  considers the historical problem of constructing a line that halves the area and the perimeter of a triangle in Area and Perimeter Splitters in a Triangle.

Math and Multimedia share 5 Fascinating Facts About Triangles That Will Surprise You.

Did you know that a Quadrilateral with Congruent Opposite Sides is a Parallelogram? Proofs from the Book will show you why.

Let’s Play Math tells us How To Master Quadratic Equations, with some assistance from James Tanton’s G’day Math Courses.

Potpourri

Are vectors too tough for mental math? Not according to White Group Maths, whose Vectors Mental Quiz demonstrates all the stuff you can calculate in your head without reaching for a computing device.

A mom and her kid at Moebius Noodles used concept maps to create Free To Learn by Peter Gray: Review and Infographics.

Charlotte Mason and Louis Benezet’s Thoughts on Math are documented by Triumphant Learning.

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• 1. Shaun @ The Numerist  |  June 14, 2013 at 10:43 am

Nice collection of math links! Thanks for including mine! 🙂

• 2. venneblock  |  June 14, 2013 at 9:40 pm

De nada, Shaun! Yours was totally worthy of inclusion. I hope lots of folks enjoy your post.

• […] for Friday! Let’s celebrate by visiting this month’s Math Teachers at Play blog carnival, featuring mathematical activities, lessons, and games for all […]

• 4. Denise Gaskins  |  June 14, 2013 at 11:26 am

Thank you for hosting! Looks like I have a great weekend of reading ahead. 🙂

• 5. Sue VanHattum  |  June 14, 2013 at 11:40 am

My posts are sometimes hard to classify. Although my post on Writing, Vocabulary, and Teacher Inquiry starts out in the 4th grade classroom, it ends up with some thoughts on graduate-level mathematics. But I hope I wrote it in a way anyone can think about the questions I asked.

• 6. venneblock  |  June 14, 2013 at 9:41 pm

Yeah, yours was a hard one, Sue. Let me know if you think I should move it to a different category.

• 7. xander  |  June 14, 2013 at 4:17 pm

Oi! What a nifty variation on the magic square. It took me a minute to figure out what was going on, too. Hint: it was easier for me to see the trick after subtracting 15 from each entry in the grid.

• 8. venneblock  |  June 14, 2013 at 9:45 pm

Nice strategy, Xander. But why 15? Seems subtracting any number would help… just wondering why that one.

• 9. xander  |  June 15, 2013 at 2:52 pm

It was the average of the min and max. I figured that by subtracting this amount, some positive and negative numbers might pop out in an obvious looking manner. It also has the advantage of changing the sum obtained from 63 to 3 (63-4*15=3), which is a bit easier to work with (I have a touch of dyscalculia, and try to simplify things to single digit operations when I have to do mental arithmetic). Subtracting 16 would have been my next thought, as that would have changed the sum to -1, which is also easy enough to work with.

From there, one can simplify further: reduce the problem to 4×4 blocks, figure out what is going on, increase the block size and repeat.

• 10. venneblock  |  June 16, 2013 at 4:11 pm

Got it. Subtracting 16 is what seemed natural to me, since 4 × 16 = 64, the magic sum in a 4 × 4 magic square. But I think the brilliance of what you did is realizing that all numbers could be changed to ones that are easier to work with. Perhaps should all have a touch of dyscalculia, if it means we’d come up with strategies like this!

• 11. Guillermo Bautista  |  June 15, 2013 at 10:19 pm

Thank you for this excellent collection.

• 12. Carnivalia — 6/12 – 6/18 | Sorting out Science  |  June 19, 2013 at 8:45 am

[…] Math Teachers at Play 63 […]

• 13. Lula B @ www.navigatingbyjoy.com  |  June 22, 2013 at 1:34 pm

Thanks for hosting the carnival so entertainingly! I’m happy to have come across your site 🙂

• 14. A Living Maths Approach to Angles  |  June 22, 2013 at 1:41 pm

[…] For more hands-on maths ideas, visit the Math Teachers at Play Carnival #63. […]

• 15. Bloggers: Time to Submit Your Post! | Let's Play Math!  |  July 2, 2013 at 1:24 pm

[…] Last month’s MTaP 63 at Math Jokes 4 Mathy Folks […]

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MJ4MF (offline version)

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