Math as a Verb

Posted on by Denise Gaskins

Here’s the full quote:

I like to play games. Almost any type of game.

I also like to play math.

If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

—John Golden
Yes, Playing Around

CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

Master Your Tools

Posted on by Denise Gaskins

As I’ve mentioned before, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s my version of SMP5…

Math Tip # 5: Master Your Tools.

  • Collect problem-solving tools.
  • Practice until you can use them with confidence.
  • Classic math tools: pencil and paper, ruler, protractor, compass.
  • Modern tools: calculator, spreadsheet, computer software, online resources.
  • Physical items: dice, counters, special math manipulatives.
  • Tools for organizing data: graphs, charts, lists, diagrams.
  • Your most important weapon is your own mind. Be eager to explore ideas that deepen your understanding of math concepts.

Continue reading Master Your Tools

Look Beneath the Surface

Posted on by Denise Gaskins

So, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s the fourth installment…

Math Tip # 4: Look Beneath the Surface.

  • Notice the math behind everyday life.
  • Examine a complex situation. Ignore the parts that aren’t relevant.
  • Pay attention to the big picture, but don’t lose track of the details.
  • Make assumptions that simplify the problem.
  • Express the essential truth using numbers, shapes, or equations.
  • Test how well your model reflects the real world.
  • Draw conclusions. Explain how your solution relates to the original situation.

Continue reading Look Beneath the Surface

Know How to Argue

Posted on by Denise Gaskins

You may remember, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

My kids loved to argue. Do yours?

Math Tip # 3: Know How to Argue.

  • Argue respectfully.
  • Analyze situations.
  • Recognize your own assumptions.
  • Be careful with definitions.
  • Make a guess, then test to see if it’s true.
  • Explain your thoughts. Give evidence for your conclusions.
  • Listen to other people. Ask questions to understand their point of view.
  • Celebrate when someone points out your mistakes. That’s when you learn!

Continue reading Know How to Argue

Don’t Panic

Posted on by Denise Gaskins

As I mentioned last Saturday, I decided to try my hand at rewriting the Standards for Mathematical Practice into student-friendly language.

Here’s the second installment…

Math Tip # 2: Don’t Panic.

  • Don’t let abstraction scare you.
  • Don’t freeze up when you see complex numbers or symbols.
  • Break them down into simpler parts.
  • Take each problem one step at a time.
  • Know the meaning of the math, how it relates to the “real world.”
  • But if it gets in your way, ignore the “real world” situation. Revel in the abstract fantasy.

Continue reading Don’t Panic

Never Give Up

Posted on by Denise Gaskins

Have you read the Standards for Mathematical Practice? Good idea in theory, but horribly dull and stilted. Like math standards in general, the SMPs sound as if they were written by committee. (Duh!)

I’ve seen several attempts to rewrite the SMPs into student-friendly language. Many of those seem too over-simplified, almost babyish.

Probably I’m just too critical.

Anyway, I decided to try my hand at the project. Here’s the first installment…

Math Tip # 1: Never Give Up.

  • Fight to make sense of a problem.
  • Think about the things you know.
  • Ponder what a solution might look like.
  • Compare this problem to those you solved in the past.
  • If it seems too hard, make up a simpler version. Can you solve that one?
  • If one approach doesn’t work, try something else.
  • When you get an answer, ask yourself, “Does it truly makes sense?”

Download the poster, if you like:

What do you think? Would this resonate with your students?

What changes do you suggest?

You can find the whole SMP series (eventually) under the tag: Posters.

Update: I Made a Thing

I had so much fun making these posters that I decided to put them into a printable activity guide. It includes the full-color poster shown above and a text-only version, with both also in black-and-white if you need to conserve printer ink.

Here’s the product description…

Join the Math Rebellion: Creative Problem-Solving Tips for Adventurous Students

Take your stand against boring, routine homework.

Fight for truth, justice, and the unexpected answer.

Join the Math Rebellion will show you how to turn any math worksheet into a celebration of intellectual freedom and creative problem-solving.

This 42-page printable activity guide features a series of Math Tips Posters (in color or ink-saving black-and-white) that transform the Standards for Mathematical Practice to resonate with upper-elementary and older students.

Available with 8 1/2 x 11 (letter size) or A4 pages.

Check It Out

Playful Math Carnival #142: Math Art Edition

Posted on by Denise Gaskins

Welcome to the 142nd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

Bookmark this post, so you can take your time browsing.

Seriously, plan on coming back to this post several times. There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 142nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Activity: Planar Graphs

According to the OEIS Wiki, 142 is “the number of planar graphs with six vertices.”

What does that mean?

And how can our students play with it?

A planar graph is a set of vertices connected (or not) by edges. Each edge links two vertices, and the edges cannot intersect each other. The graph doesn’t have to be fully connected, and individual vertices may float free.

Children can model planar graphs with three-dimensional constructions using small balls of playdough (vertices) connected by toothpicks (edges).

Let’s start with something smaller than 142. If you roll four balls of playdough, how many different ways can you connect them? The picture shows five possibilities. How many more can you find?

Sort your planar graphs into categories. How are they similar? How are they different?

A wise mathematician once said, “Learning is having new questions to ask.” How many different questions can you think of to ask about planar graphs?

Play the Planarity game to untangle connected planar graphs (or check your phone store for a similar app).

Or play Sprouts, a pencil-and-paper planar-graph game.

For deeper study, elementary and middle-school students will enjoy Joel David Hamkins’s Graph coloring & chromatic numbers and Graph theory for kids. Older students can dive into Oscar Levin’s Discrete Mathematics: An Open Introduction. Here’s the section on planar graphs.

[“Geöffneter Berg” by Paul Klee, 1914.]

Click here for all the mathy goodness!

FAQ: I’ve Ruined My Daughter

Posted on by Denise Gaskins

My daughter is only eleven, but I’m afraid I’ve ruined her chance of getting into college because she is so far behind in math. We’ve tried tutors, but she still has trouble, and standardized testing puts her three years below grade level. She was a late reader, too, so maybe school just isn’t her thing. What else can I do?

Standardized tests are not placement tests. They cannot tell you at what level your daughter should be studying. They aren’t designed that way. The “placement” they give is vague and general, not indicative of her grade level but rather a way of comparing her performance on that particular test with the performance of other students.

There can be many different reasons for a low score. I’ve listed a few of them in my post In Honor of the Standardized Testing Season.

Continue reading FAQ: I’ve Ruined My Daughter

To Badger a Child

Posted on by Denise Gaskins

Here’s the full quote:

Audrey seemed, for once, at a loss for words. She was thinking about the question.

I try to stay focused on being silent after I ask young children questions, even semi-serious accidental ones. Unlike most adults, they actually take time to think about their answers and that often means waiting for a response, at least if you want an honest answer.

If you’re only looking for the “right” answer, it’s fairly easy to gently badger a child into it, but I’m not interested in doing that.

—Thomas Hobson
Thank You For Teaching Me

CREDITS: “Pismo Beach, United States” photo by Tim Mossholder on Unsplash.

Math for Star Wars Day

Posted on by Denise Gaskins

May the Fourth be with you!

Here is a math problem in honor of one of our family’s favorite movies…

Han Solo was doing much-needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?

Stop and think about how you would solve it before reading further.

Continue reading Math for Star Wars Day