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Dragons, Gryphons, and Math Mistakes

statue of a gryphon

Let's Play Math by Denise GaskinsThis post is adapted from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It.

Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.

Even teachers are human.

In this case, it was a multi-step word problem, a barrage of information to stumble through. In the middle of it all sat this statement:

“…and there were 3/4 as many dragons as gryphons…”

My eyes saw the words, but my mind heard it this way:

“…and 3/4 of them were dragons…”

What do you think — did I get the answer right? Of course not! Every little word in a math problem is important, and misreading even the smallest word can lead a student astray. My mental glitch encompassed several words, and my final tally of mythological creatures was correspondingly screwy.

But here is the more important question: Can you explain the difference between these two statements?

Continue reading Dragons, Gryphons, and Math Mistakes

Thinking Thursday: Success

Thinking Thursday math journal prompt

Writing to Learn Math: You can spark creative thought by removing any need to worry about spelling or punctuation rules.

Do you want your children to develop the ability to reason creatively and figure out things on their own?

Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.

Continue reading Thinking Thursday: Success

Conversion Factors: How Old Are You in Nanoseconds?

birthday cupcake with sparkler

Homeschool Memories

[Based on a problem I made up for my co-op students, once upon a time…]

Conversion factors are special fractions that contain problem-solving information. Why are they called conversion factors?

  • “Conversion” means change, and conversion factors help you change the numbers and units in your problem.
  • “Factors” are things you multiply with. So to use a conversion factor, you will multiply it by something.

For instance, if I am driving an average of 60 mph on the highway, I can use that rate as a conversion factor. I may use the fraction:

Or I may flip it over to make:

It all depends on what problem I want to solve.

After driving two hours, how far have I gone?

But if I am planning to go 240 more miles, how much longer will it take?

Any rate can be used as a conversion factor. You can recognize them by their form: this per that. Miles per hour, dollars per gallon, cm per meter, and many, many more.

Of course, you will need to use the rate that is relevant to the problem you are trying to solve. If I were trying to figure out how far a tank of gas would take me, it wouldn’t be any help to know that an M1A1 Abrams tank would get about 1/3 mile per gallon. I won’t be driving one of those.

Continue reading Conversion Factors: How Old Are You in Nanoseconds?

Podcast: Charlotte Mason’s Living Math

family doing math together

Cindy Rollins, Dawn Duran, and I had a delightful chat about my new book, Charlotte Mason’s Living Math, which is now available in ebook (print editions coming soon!) at my Playful Math Store.

We talked about how math is a whole world full of big, living ideas that we can explore with our children. What it means to have a living education in math, opening our children’s minds to big ideas about the relationships of numbers, shapes, and patterns. And how to tell if our kids really understand what they are doing, or if they’re just parroting back the steps we taught them.

And lots more — listen for yourself:

“Math doesn’t have to be a drudgery, a chore that we finish so we can check it off of our list. Math can be a delight when we give children things to think about, ideas to wonder about. When we explore the world of numbers and shapes together, math can be a playful delight for the whole family.”

—Denise Gaskins

For full show notes, see Season 11, Episode 144: Charlotte Mason’s Living Math with Denise Gaskins.

 
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Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my free email newsletter on Substack.

This blog is reader-supported. If you’d like to help fund the blog on an ongoing basis, then please join me on Patreon (or choose the paid level on Substack) for mathy inspiration, tips, and an ever-growing archive of printable activities.

Column Jumping: An Investigation

man jumping on rock columns

Charlotte Mason's Living Math ebook editionIn my new book, Charlotte Mason’s Living Math, I encourage families to explore the world of math by asking big, open-ended questions.

[Now available exclusively in my Playful Math Store! Ebook only at the moment, but print editions are coming soon.]

Here’s an example of such a question, an excerpt from my earlier book, 70+ Things To Do with a Hundred Chart: Number, Shape, and Logic Activities from Preschool to Middle School.

Have fun exploring math with your kids!

Continue reading Column Jumping: An Investigation

Make Your Own Nim Games

tower of rocks on a beach

Nim is a pure strategy game for two players. On each turn, players remove an option until finally no choice remains.

Game options might include:

  • How many stones to take from a pile.
  • Which position to claim on a gameboard.
  • How far to count in a given sequence.

The rules can vary at the players’ whim (as long as both players agree). How many possibilities do you start with, what are the rules for removing options, and how do you win or lose the game? Everything is open to change. And with every tweak, players must reanalyze their strategy.

Continue reading Make Your Own Nim Games

FAQ: Doing Math His Own Way

FAQ learning subtraction math

Isn’t it fun when children surprise us with their understanding?

All my children have figured out ways to do things in math that I would never have expected, and I’ve learned quite a bit from listening to their explanations.

But what if the child’s creative method makes it hard for them to learn what our textbook wants to teach?

Continue reading FAQ: Doing Math His Own Way

This Puzzle Is Murder

cartoon detective

Do you sometimes mourn (in a small way) the loss of a favorite website? I still miss the Daily Set puzzle, which was part of my morning routine for years.

But lately, I’ve added a new teaser to wake up my brain for the day.

While Set was a visual-logic puzzle, this one is straightforward (though not simple) deduction. I think you’ll enjoy it.

Continue reading This Puzzle Is Murder

Tasty Treats from the Moscow Puzzles

basket of apples

“Problems stressing deduction rather than calculation have a special appeal and value. They teach you to analyze, and to seek unorthodox ways of solving a problem.”

—Boris Kordemsky

Today I’m sharing a few treats from The Moscow Puzzles by Boris Kordemsky, which mixes classic brainteasers and original stumpers.

Recreational math expert Martin Gardner called Kordemsky’s book “the outstanding puzzle collection in the history of Russian mathematics.”

Have fun playing logic with your kids!

Continue reading Tasty Treats from the Moscow Puzzles

Rescuing Cool Math for Older Kids

mother and teen daughter do homework together

Do you have math dreams for your children?

Here are some dreams shared the authors of Avoid Hard Work!

For our children, we dream that mathematics…

  • … makes sense.
  • … is more than just arithmetic.
  • … is joyous.
  • … makes them strong.
  • … is meaningful.
  • … is creative.
  • … is full of fascinating questions.
  • … opens up many paths to solutions.
  • … is friendly.
  • … solves big problems and makes the world better.
  • … is a powerful tool they can master.
  • … is beautiful.
  • … lets them learn in their own ways.
  • … is connected to their lives.
  • … asks “why” and not just “how.”
  • … opens the world.

Continue reading Rescuing Cool Math for Older Kids