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.

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.

How to Succeed in Math: Answer-Getting vs. Problem-Solving

You want your child to succeed in math because it opens so many doors in the future.

But kids have a short-term perspective. They don’t really care about the future. They care about getting through tonight’s homework and moving on to something more interesting.

So how can you help your child learn math?

When kids face a difficult math problem, their attitude can make all the difference. Not so much their “I hate homework!” attitude, but their mathematical worldview.

Does your child see math as answer-getting? Or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, and then goes on to the next question.

Problem-solving asks “Why do you say that?” and listens for the explanation.

Problem-solving is not really interested in “right” or “wrong”—it cares more about “makes sense” or “needs justification.”

Homeschool Memories

In our quarter-century-plus of homeschooling, my children and I worked our way through a lot of math problems. But often, we didn’t bother to take the calculation all the way to the end.

Why didn’t I care whether my kids found the answer?

Because the thing that intrigued me about math was the web of interrelated ideas we discovered along the way:

  • How can we recognize this type of problem?
  • What other problems are related to it, and how can they help us understand this one? Or can this problem help us figure out those others?
  • What could we do if we had never seen a problem like this one before? How would we reason it out?
  • Why does the formula work? Where did it come from, and how is it related to basic principles?
  • What is the easiest or most efficient way to manipulative the numbers? Does this help us see more of the patterns and connections within our number system?
  • Is there another way to approach the problem? How many different ways can we think of? Which way do we like best, and why?

What Do You think?

How did you learn math? Did your school experience focus on answer-getting or problem-solving?

How can we help our children learn to think their way through math problems?

I’d love to hear from you! Please share your opinions in the Comments section below.

CREDITS: “Maths” photo (top) by Robert Couse-Baker. “Math Phobia” photo by Jimmie. Both via Flickr (CC BY 2.0). Phil Daro video by SERP Media (the Strategic Education Research Partnership) via Vimeo.

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.

Mindset for Learning Math

Playing with a new image editor, I came across this Winston Churchill quote. What a great description of how it feels to learn math!

If you have a student who struggles with math or is suffering from a loss of enthusiasm, check out Jo Boaler’s free online course on developing a mathematical mindset:

Or explore some of the playful activity ideas for all ages in her Week of Inspirational Math.

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.

How to Talk Math With Your Kids

A friend shared this video, and I loved it! From Kent Haines, a father who happens to also be a math teacher…

“I hope that this video helps parents find new ways of interacting with their kids on math topics.”

Kent Haines

More from Kent Haines

Advice and Examples of Talking Math with Kids

Danielson-Talking Math

If you enjoyed Kent’s video, you’ll love Christopher Danielson’s book and blog.

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.
“You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.
“In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.
“The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.”

— Christopher Danielson
Talking Math with Your Kids

CREDITS: “Kids Talk” photo (top) by Victoria Harjadi via Flickr (CC BY 2.0). “Parent Rules” by Kent Haines.

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.

Even a Math Workbook Can Be a Game

Homeschooling Memories…

My youngest daughter wanted to do Singapore math. Miquon Red was her main math text at the time, but we added a bit of Singapore Primary Math 1B whenever she was in the mood.

We turned to the lesson on subtracting with numbers in the 30-somethings.

The first problem was pretty easy for her:

30 − 7 = _____

I reminded her that she already knew 10 − 7.

She agreed, “Ten take away seven is three.”

Then her eyes lit up. “So it’s 23! Because there are two tens left.”

Wow, I thought. She’s catching on quickly.

Mom Always Talks Too Much

We went to the next problem:

34 − 8 = _____

“Now, this one is harder,” I said. “But you know what ten minus eight is, right? So we could take one of these tens and—”

She waved at me to be quiet.

I was just getting started on my standard speech about how to turn a tough subtraction like 34 − 8 into the easy addition of “2 + 4 + two tens left.” But her mind was still on the last problem, specifically on the two tens and the seven.

“If you have 27,” she said, “and you add three more, you get 30. And four more is 34.”

“Um, yes, but…” I interrupted.

She shushed me again.

“And then you can take away the four. And then you can take away the three. And then you can take away one more…It’s 26!”

Mom Learns a Lesson

She continued through the next page that way. For every problem, she started with whatever number struck her fancy, usually containing at least one digit from the problem before. She added enough to get up to the 30-something number in the book.

Only then would she deign to subtract the number in question.

I don’t think she ever saw the point of the mental math technique the book and I were trying to teach, but she did have a lot of fun playing around with the numbers.

In the long run, that’s much more important.

Feature photo: “Laughing Girl” by ND Strupler via Flickr (CC BY 2.0).

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.