Math Teachers at Play #58

[Feature photo (above) by Alex Kehr. Photo (right) by kirstyhall via flickr.]

Welcome to the Math Teachers At Play blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college. If you like to learn new things and play around with ideas, you are sure to find something of interest.

Let the mathematical fun begin…

PUZZLE 1

By tradition, we start the carnival with a pair of puzzles in honor of our 58th edition. Click to download the pdf:

PUZZLE 2

A Smith number is an integer the sum of whose digits is equal to the sum of the digits in its prime factorization.

Got that? Well, 58 will help us to get a better grasp on that definition. Observe:

58 = 2 × 29

and

5 + 8 = 13
2 + 2 + 9 = 13

And that’s all there is to it! I suppose we might say that 58’s last name is Smith. [Nah! Better not.]

• What is the only Smith number that’s less than 10?
• There are four more two-digit Smith numbers. Can you find them?

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my Google Reader. Enjoy!

EARLY LEARNING ACTIVITIES

[Image © Nevit Dilmen.]

Teacher: If you had 5 apples in one hand and 7 apples in other hand, what would you have?

Student: Very large hands!

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Teacher: If I had 5 coconuts, and then I gave you 3 of them, how many coconuts would I have left?

Student: I don’t know.

Teacher: Why not?

Student: Because all of our practice problems were about apples!

• Lilac and her preschoolers explore the world of logic in Number Conservation / Conservation of Mass and Venn Diagrams for Little Kids.

• Jennifer’s family has fun with logic, too: Logic Cards for Preschoolers and the sequel, Logic Cards for Older Kids.

• The Relentlessly Fun, Deceptively Educational Mom tells how to make and measure snowflakes in It’s Snowing Angles!

• Moby Snoodles plays with iconic numbers in 1+1=2 but Mostly it Doesn’t, and your children can join in by contributing to A scavenger hunt game about unitizing.

• Are there times you doubt that anything is sinking in, or wonder if you’re not doing enough of the “right” kind of math? Malke finds reassurance in Found Math: How My Kid Shows Me She’s Learning.

• Yelena says, “Like so many other kids, my son loves listening to stories. So I try to find or make up stories of mathematical adventures for him. This particular one, about two lonely Moebius Ants, was inspired by Vi Hart’s video Wind and Mr Ug.”

• David shares a variety of ways to nurture our children’s sense of wonder about the world of numbers in Raising mathematicians. And a different Dave encourages us to Challenge all our children beyond what we think they can do.

ELEMENTARY EXPLORATION AND MIDDLE SCHOOL MASTERY

[Image by kaʁstn Disk/Cat.]

Q: Why was ¹/₅ sent to a counselor?

A: Because he was two-tenths.

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mal·e·frac·tion
(noun) an illegal mathematical move when working with rational numbers, such as dividing by 0 or assuming that a/b + c/d = (a + b)/(c + d)

• The Piwi Kids’ Mom says, “It is hard for any Mama to watch their child struggle with something. The ‘I hate Math’ comment still happens but we hear it less.” She explains how in What works for us…Math.

• Mama Squirrel enjoys a recent thrift store treasure in Praise for The Number Devil (book review). And Malke finds a “gold mine” in Ten Times Better, Longer, Faster, Farther: Understanding Scale.

• Michelle’s students try out different strategies to solve word problems in Introduction to Math Problem Solving.

• Alicia shares 22 Fun ways to help kids learn their math facts.”Remember that some kids naturally memorize math facts much easier than others. Kids who are right brained learners are often ‘late’ in memorizing math facts but are capable of doing very advanced math despite it. Don’t obsess over the fact that your kids don’t know it all by heart, and don’t wait to get into higher math until they know it all by heart.”

• Rachel reviews Mathtopia – Best Math Facts App Ever.

• Julie created the skip-counting game Speed! to help her homeschooled daughter learn multiplication. Now she’s excited that Speed! is in the iPad App Store.

• Middle- to upper-elementary students love to collect facts about their friends, books, pets, or whatever else catches their interest. Heather offers advice on sharing that data in How to Make a Good Graph.

• Cindy turns some Dollar Store clothespins into a hands-on activity/math center for fractions.

• Jeremiah gives us a fun way to practice order of operations (and a bit of pre-algebra) with The Ultimate B-Day Expression.

• For my contribution to this month’s carnival, I challenge your children to join us in the 2013 Mathematics Game, an arithmetic puzzle for all ages. Elementary students can start with the numbers 1-20, middle school 1-50, and high school students can take on the full 1-100.

ADVENTURES IN BASIC ALGEBRA & GEOMETRY

[Image by Maschen.]

Student: In the expression x³, what do you call the 3?

Teacher: An exponent.

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Teacher: In the expression y², what do you call the 2?

Student: A y‑ponent.

• Jena’s students finished their first quarter on coordinate plane geometry, and now they’re dreaming of vacations in Geometry Project.

• Drafting can be a great way to learn the basics of geometry. Check out Julie’s daughter’s creations in Math Art – Geometry.

• Willa examines the advantages and challenges of Teaching Euclid in the Homeschool (and Part 2).

• Fawn challenged her geometry students: “Can you locate the square root of 7 on the number line?” She shares the results of their investigation in The question was mine, but the answer was all his.

• Analyzing mistakes is a great way to learn. Can your algebra students explain what went wrong in these Algebra 1 Math Mistakes? Can your geometry students make sense of these Geometry Math Mistakes?

• The Mathematical Association of America’s American Mathematics Competitions feature algebra puzzles, geometry problems, and much more. Try your hand at their daily puzzle at MAA Minute Math.

ADVANCED MATHEMATICAL ENDEAVORS

[Image by Timboliu.]

After a logic exam…

Student: “Sir, did I pass or fail the exam?”

Professor: “Yes.”

• A former student of mine returns to blogging: Gecko plays around with number series in Fibonacci Multiplication.

• Pat investigates square pyramid numbers in Some Notes on the Sum of Squares of the Integers.

• Sam uses GeoGebra to play with Families of Curves. Beautiful!

• Speaking of curves, Amy Sextupled the Time It Takes To Teach End Behavior of polynomial functions to her Algebra 2 students.

• Are your students ready for advanced math? Sue reviews several important Algebra Skills for Calculus.

• Guillermo introduces an intriguing curve in The Cycloid and the Pendulum Clock.

• Professor Arthur Benjamin in a recent TED talk claims that AP Statistics should be the new summit of the high school curriculum. John disagrees in Why Calculus still belongs at the top.

• Sue has to teach Centroid (Center of Mass) to her calculus students. She says, “The textbook explanation is inadequate, and I found nothing good online. So I wrote my own explanation. I now understand it better than I ever did before. (Not surprising, huh? If you’re a student, this is an important principle of learning. After you think you understand something, try to write an explanation of it and see how much deeper your understanding can get.)”

• And finally, don’t miss the Carnival of Mathematics 94.

PUZZLING RECREATIONS

[Image by Rob Zako.]

Take a positive integer n.
No, wait; n is too large.
Take a positive integer k …

• John and his son Xavier investigate conjectures about an origami cube in Family Math: Origami.

• Getting “the answer” is only the beginning of mathematics. The real fun comes in extending the puzzle and asking new questions, as Bon demonstrates in 8 Digit Puzzle – Rules, Downloadable & Questions to Ponder.

• To program a computer, one must solve plenty of puzzles, as Christy explains in What I want my children to practice through computer programming. Jimmy reviews a Homeschool Programming Curriculum. I would also recommend Invent Your Own Computer Games with Python (free download available here), which Kitten is enjoying.

• “For 450 years, puzzles that can be rearranged to change the area have been keeping us spellbound.” Pat explores Geometric Vanishes, A Little HIstory.

• Guillermo invites us to calculate The Kaprekar Constant 495.

TEACHING TIPS

[Image by Proferichardperez.]

The cannibal family was eating dinner. One son says, “I really hate my math teacher.”

The other son says, “I know. He’s so tough!”

The mother tells them, “Quit complaining. If you don’t like the meat, just eat the noodles.”

• Tammy offers excellent suggestions in Five Strategies for Teaching Mathphobics.

• Kalid shares a wealth of insights about learning and teaching math in his How to Develop a Mindset for Math series.

• David reminds us that a tiny thing can have a large effect on student understanding in A Small But Significant Decimal Point.

• Colleen’s thoughts turn to New Year Resolutions in This year I will …

• Sue thinks learning math should be like a back float.

• Do you use journals for teaching or reviewing math? Check out these math notebooking pages on Pinterest: Teaching: Math Notebooking, and Math Notebook.

• Are your students limiting their own mathematical potential? Watch out for these Math Myths to Muddle the Mind.

GIVING CREDIT WHERE IT’S DUE

The Smith numbers puzzle is from Terry Trotter at Trotter Math, and the other quotations are from Patrick Vennebush at his Math Jokes 4 Mathy Folks blog.

Math diagrams are courtesy of Wikimedia Commons: Mathematics, except for the book image, which is from Amazon.com (where I receive a small commission through Skimlinks if you actually click through and buy it no longer, thanks Illinois!).

And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.

The next installment of our carnival will open sometime during the week of February 11-15 at Learners in Bloom. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival information page.

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!