Playful Family Math on Facebook

If you want to know more about my playful math books, check out my new author page. You can post comments or send me a message. I’d love to hear from you!

Visit Denise Gaskins on Facebook

You can also join the Playful Family Math discussion group or find plenty of online mathy goodness at my original Let’s Play Math Facebook page.

🙂 See you there!

Funville Adventures: Blake’s Story

Today we have a guest post — an exclusive tale by Sasha Fradkin and Allison Bishop, authors of the new math storybook Funville Adventures. Enjoy!

Funville Adventures is a math-inspired fantasy that introduces children to the concept of functions, which are personified as magical beings with powers.

Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. Some Funvillians have siblings with opposite powers that can reverse the effects and return an object to its original state, but other powers cannot be reversed.

In this way, kids are introduced to the mathematical concepts of invertible and non-invertible functions, domains, ranges, and even functionals, all without mathematical terminology.

We know about Funville because two siblings, Emmy and Leo, were magically transported there after they went down an abandoned slide.

When they came back, Emmy and Leo shared their adventures with their friends and also brought back the following manuscript written by their new friend Blake.

Blake’s Story

Hi everyone! My name is Blake and I live in Funville. Before I met my new friends Emmy and Leo, I didn’t know there were places outside of Funville, but now I do! Emmy explained to me that people from her world don’t know about Funvillians and our powers, so she suggested that I write to you and tell you a bit about myself.

Each Funvillian has a special power. My friend Doug’s power is to make things twice as big. He can look at a cookie and make it double in size! Which really isn’t fair but it’s still nice, since he’s good at sharing the now mega-cookies with the rest of us. His brother Harvey can make things twice as small. Sometimes when Doug and Harvey are arguing, they make the same thing big and then small and then big and small over and and over again, which is really quite funny to watch.

My power is to erase things. In comes in very handy when I want to redo a drawing or clean up a spill. But it gets tricky sometimes when I play games.

Games in Funville are the best! I imagine they must go somewhat differently where you are, since in Funville everyone uses their powers while playing. Emmy calls this “cheating,” but we think it’s all in good fun! It makes games very exciting, but it also makes it hard to decide who wins. If my friend Heather uses her power to make the soccer ball too heavy to move when the score is 1-to-1, we usually have to declare a tie and play something else (I suspect she does this whenever she’s bored of playing soccer).

For a while, every time I tried to use my power to play a game, it didn’t work very well. The first time I played checkers I accidentally erased the checkerboard. We drew it back on, but it took awhile, because we had to guess how many squares there should be, and we had to try it a few times before it looked right again. The second time I erased the scoreboard in the fifth inning of a baseball game because I wanted to start over, but then it got dark before we could finish the game.

I don’t even get invited to play Scrabble anymore because I always erase letters I don’t like. I know I probably shouldn’t do this, but I just can’t help myself! And then sometimes I even forget what the letters were by the end of the game, so now we have too many blank scrabble tiles and we don’t know what they should be.

But then Emmy and Leo taught me about games you can play on paper, which we hadn’t been playing in Funville before. Leo taught me how to play tic-tac-toe, and soon everyone in Funville was playing it! Well, I guess not the original version — we had to change it to tic-tac-elephant, so that my friend Constance could play (her power is to turn anything into an elephant).

And Emmy taught me how to play hangman, where you come up with a word and the other players have to try to guess it one letter at a time. Harvey always beats me at that one when he’s guessing, because he keeps making the parts of the hangman so small that I can’t see them and I forget they are there, and so I keep drawing the same arm over and over again while he gets more guesses. And I always beat him when I’m guessing, because I can erase the parts and he forgets, too!

Whenever we play these games, it’s mine to shine — whenever a game is finished, I can erase the paper, and we get to play all over again!

Sometimes it’s tough having a power that can’t be reversed, and I wish I was like Harvey and Doug, who can always undo each other’s mistakes. But other times I’m proud I can erase things. It’s not always what we want, but sometimes a clean slate is exactly what we need.

Your Turn to Play

Dear reader, now it’s your turn to have fun with powers!

Talk with your children about ideas inspired by the Funville Adventures story.

For example, think of one of your favorite games to play on paper. (If you don’t have any, you can think of board games instead.) Would having Blake’s power help in the game?

Blake also mentions his friends Doug, Harvey, and Constance in his story. Would one of their powers be more useful? Or funnier?

Come up with your own powers that you’d like to have while playing each of your favorite games.

For inspiration, enjoy this father’s conversation with his son after reading Funville Adventures.

And if you’d like, you can play The Function Machine Game to experiment with functions of numbers. Be sure to let your kids have a turn making up function rules for you to solve!

Ready for More?

About the Authors

Sasha (A.O.) Fradkin has loved math from an early age and seeks to share that love of math with others. After receiving her PhD in mathematics from Princeton University, she worked for several years as a professional mathematician and taught enrichment math to children ages 4-10 at the Golden Key Russian School. Currently, Sasha is the Head of Math at the Main Line Classical Academy, an elementary school in Bryn Mawr, PA. She develops their math curriculum and teaches children in grades K-5. She writes a blog, Musings of a Mathematical Mom, about her teaching as well as various math adventures with her two daughters, and enjoys pondering exciting and engaging ways to present the beauty of mathematics to young children.

Allison (A.B.) Bishop grew up with a passion for writing and initially disliked math because it was presented as formulaic. She belatedly discovered the creative side of mathematics and science, and now sees it as a vital component of the curiosity that drives her life. She is currently a professor of computer science at Columbia University as well as a quantitative researcher at the Investors Exchange. She remains an avid fiction enthusiast and writer, and is always seeking new ways to expose young minds to creative mathematical thinking and fuel their scientific curiosity.

Giveaway: For the Love of Math

Wow, what a deal!

To celebrate Valentine’s Day, Sonya at Arithmophobia No More and Lacy from Play, Discover, Learn (two of my favorite homeschooling bloggers) teamed up to offer a HUGE set of hands-on mathy goodness.

As a bonus, I’m throwing in a signed copy of one of my books — winner’s choice.

But you have to act fast. The giveaway ends Saturday, February 17, 2018, at midnight (CT).

Click the links.

Drool over the prizes.

Submit your entry today.

Enter to Win!

[Shipping to U.S. addresses only.]

Cultivate Mathematical Curiosity

“Cultivating thinking skills is the main reason for teaching math. It is the mind’s perfect playground for shaping up.

To begin developing thinking, you must first have a child who is curious. For without curiosity, there is only forced thinking.

The problem with traditional math is it jumps to the punchline.

Absolutely no mystery or suspense is developed in traditional math books. Why? Apparently, someone thought math was without mystery. That math is a definitive subject of rules and algorithms that all have been discovered.

We must persuade children that math is a worthy pursuit through interesting stories, examining quirky math properties, and asking good questions.”

— Lacy Coker
5 Tips to Cultivate Math Curiosity

The Mind’s Perfect Playground

My K-2nd-grade homeschool co-op math class will be following many of the tips in Lacy’s article.

Our topic is “Math Storytime,” so we’ll be starting with picture books, exploring the ideas they bring up, and finding things to notice and wonder about.

I’m looking forward to it.

But picture books aren’t just for little kids. They can be great discussion-starters at any age. Have you enjoyed math books with your students?

I’d love to hear your suggestions!

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Bekah Russom on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Learning Mathematics Is a Deep Mystery

Of all the myths about mathematics, the one I find most blatantly wrong is the idea that some people are just born knowing the answers. In my experience, when you confront a genuine puzzle, you start out not knowing, no matter who you are.

Moreover, “knowing” the answers can be a trap; learning mathematics is about looking at what you thought you understood and seeing that there’s deeper mystery there than you realised.

— Dan Finkel
A Mathematician at Play Puzzle #1

Puzzles for Learning Mathematics

If you’d like to practice learning mathematics by confronting genuine puzzles, Dan’s “A Mathematician at Play” series looks like a wonderful place to start.

Some of these puzzles are classics, others are original. All of them involve some kind of thinking or insight that strikes me as pretty, or surprising, or delightful.

— Dan Finkel
A Mathematician at Play Puzzle #1

Dan plans to post new puzzles on the Math 4 Love blog every Monday for the next few months. And sharing spoilers on each following Friday, if you want to verify your answers.

Check it out!

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Amy on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Learning Math Requires Imagination

“Teach mathematics the way we learn any other subject: Make it visual, make it concrete, not dependent on meaningless, abstract symbols, employ all the senses!

If math is such an important subject (and it is) why teach it in a way that is dependent on a child’s weakest mental ability: memory, rather than her strongest mental ability: imagination?”

— Geoff White
The Grade 10 Math Crunch, or Hitting the Wall at Grade 10

Mathematics and Imagination

How can we stir up our students’ imagination?

Teachers have struggled with this question for years — perhaps since the beginning of the profession.

Consider these comments by W. W. Sawyer in Mathematician’s Delight:

“Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.

“People often make mistakes when they reason about things they have never seen. Imagination does not always give us the correct answer. We can only argue correctly about things of which we have experience or which are reasonably like the things we know well. If our reasoning leads us to an untrue conclusion, we must revise the picture in our minds, and learn to imagine things as they are.

“When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination.

“Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.”

Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo by Mehmet Kürşat Değer on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

2018 Mathematics Game — Join the Fun!

Let’s resolve to have fun with math this year. Ben has posted a preview of 2018’s mathematical holidays. Iva offers plenty of cool ways to think about the number 2018. And Patrick proposes a new mathematical conjecture.

But my favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.

Math Forum Year Game Site

Rules of the Game

Use the digits in the year 2018 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

  • You must use all four digits. You may not use any other numbers.
  • Solutions that keep the year digits in 2-0-1-8 order are preferred, but not required.
  • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
  • You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

  • You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
  • You MAY use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.

Click here to continue reading.

A Beautiful Puzzle

This lovely puzzle (for upper-elementary and beyond) is from Nikolay Bogdanov-Belsky’s 1895 painting “Mental Calculation. In Public School of S. A. Rachinsky.” Pat Ballew posted it on his blog On This Day in Math, in honor of the 365th day of the year.

I love the expressions on the boys’ faces. So many different ways to manifest hard thinking!

Here’s the question:

No calculator allowed. But you can talk it over with a friend, as the boys on the right are doing.

You can even use scratch paper, if you like.

Thinking About Square Numbers

And if you’d like a hint, you can figure out square numbers using this trick. Think of a square number made from rows of pennies.

Can you see how to make the next-bigger square?

Any square number, plus one more row and one more column, plus a penny for the corner, makes the next-bigger square.

So if you know that ten squared is one hundred, then:

… and so onward to your answer. If the Russian schoolboys could figure it out, then you can, too!


Simon Gregg (@Simon_Gregg) added this wonderful related puzzle for the new year:

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.