Playful Math Education Carnival 171: Modern Math Artists

Posted on by Denise Gaskins

Welcome to the 171st 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 over the next week or so.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 171st edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle/Activity

171 is a triangular number, the sum of all the numbers from 1 to 18:

  • 1 + 2 + 3 + … + 17 + 18 = 171.
  • Can you think why a number like this is called “triangular”?
  • What other triangular numbers can you find?

Also, 171 is a palindrome number, with the same digits forward and backward. It’s also a palindrome of powers:

  • 171 = 52 + 112 + 52
  • 171 = 23 + 43 + 33 + 43 + 23

So in honor of our 171st Playful Math Carnival, here is a palindrome puzzle that leads to an unsolved question in math:

  • Does every number turn into a palindrome eventually?

palindrome number activity

Click here for all the mathy goodness!

Gameschooling Math

Posted on by Denise Gaskins

Games are fun, building a positive attitude toward math. They give students a refreshing break from textbook work and make kids willing to practice their math. Games make math practice enjoyable, something children want to do. We can happily work through many more calculations during a game than anyone would ever want to do on a homework page.

Benefits of Math Games

But more important than the fun, math games push children to think about what numbers mean and how they work. The numbers in a math game are not just meaningless abstractions, but tools that players can use to gain an advantage over their opponent.

A good math game reinforces the idea that math is about reasoning, using the things you know to figure out what you need. Math is not just about getting the right answer. It’s about what goes on in your head on the way to that answer. The answer itself is merely a side-effect. of what really matters, your thinking.

A good math game helps students develop flexibility, the ability to adapt, applying what they have learned to new situations, finding a way to work out the things they haven’t mastered yet. All these add up to a more robust type of mathematical fluency than what many people imagine possible.

Continue reading Gameschooling Math

Math Musings: When Should We Work on Memorization?

Posted on by Denise Gaskins

Having knowledge in long-term memory can be very helpful in solving problems.

But master problem-solver Sherlock Holmes was concerned that if he had too much knowledge in his mind, new facts would crowd out the old and cause him to forget something important:

Continue reading Math Musings: When Should We Work on Memorization?

Carnival 170: A Plethora of Playful Math

Posted on by Denise Gaskins

Welcome to the 170th edition of the Playful Math Education 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.

There’s so much playful math to enjoy!

By tradition, we start the carnival with a puzzle/activity in honor of our 170th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

Puzzle: Prime Permutations

According to Tanya Khovanova’s Number Gossip, 170 is the smallest composite number where exactly four permutations of its digits make prime numbers.

To find permutations, think of all the different ways you can arrange the digits 1, 7, 0 into three-digit numbers. (When the zero comes first, those permutations actually make two-digit numbers, which DO also count.)

Can you figure out which permutations make prime numbers?

Hint: The permutation that makes the number “170” is not prime, but it is the product of three prime numbers. Which ones?

For Younger Children: The 170 Square

A Latin square is a grid filled with permutations: letters, numbers, or other symbols so that no row or column contains more than one of any character. You’ve probably seen the popular Latin-square puzzle called Sudoku. A Graeco-Latin square (also called an Euler square) is two independent Latin squares overlapping each other.

Can you complete this Euler square made by overlapping permutations of the digits of 170 with winter colors? Don’t repeat the same color OR the same number in any row or column.

Click the picture to get a larger image you can print.

Click here for all the mathy goodness!

FAQ: The Necessity of Math Facts

Posted on by Denise Gaskins

Ah, math facts — the topic that just won’t stop giving grief to students and anxiety to their parents. So it happened that I got another question, but this one leaned in a more philosophical direction…

“I enjoyed your podcast interview on Cultivating Math Curiosity and Reasoning in Kids. I love the idea that we don’t have to make our children memorize everything in math. We can give them freedom to make mental connections for themselves.

    “But on the other hand, we don’t have unlimited time for them to figure things out on their own, do we? What about children who can’t make these connections for themselves?

      “For example, what about the math facts? If my kids aren’t picking them up, don’t they just have to memorize them?”

      Continue reading FAQ: The Necessity of Math Facts

      FAQ: Memorizing the Math Facts

      Posted on by Denise Gaskins

      It came up again this week, one of the most frequently asked questions about homeschooling math:

      “I believe it’s important for children to memorize the math facts, but my kids are struggling with mental math. How can I help them master these important number relationships?”

      We all want our children to own the math facts, those basic relationships between small numbers that form the foundation of all arithmetic.

      But I don’t think emphasizing memorization will develop the sort of fluency your children need.

      The human brain remembers what it thinks about, so we want children using their brains and thinking as deeply as possible about number relationships from as many different perspectives as we can get, noticing patterns, finding connections, making sense of the math.

      Continue reading FAQ: Memorizing the Math Facts

      Homeschooling Math: Start Where You Are

      Posted on by Denise Gaskins

      There’s a well-known quote attributed to tennis champion Arthur Ashe (and to President Theodore Roosevelt, and probably others):

      “Start where you are, use what you have, do what you can.”

      How does this apply to learning math?

      Many homeschoolers fear that their students have fallen behind grade level in math and worry about how to catch up.

      We have an educational myth that math is a steady progression of topics arranged by ever-increasing complexity with regular signposts like mile markers that identify what students must learn at each stage along the way.

      For example, first-grade students can add one-or two-digit numbers, but three-digit numbers are beyond them. Second-grade students can add three- or four-digit numbers, but never wander off into millions and billions. And so forth.

      That is one valid path to learning math.

      Continue reading Homeschooling Math: Start Where You Are

      5 Tips for Better Homeschool Math

      Posted on by Denise Gaskins

      Many homeschoolers hate or even fear math. It’s the topic most likely to bring our children to tears.

      In my last several posts, I’ve indulged my theoretical muse letting my thoughts wander over topics that may seem esoteric to parents in the midst of a daily struggle to help their child learn.

      So today, let’s put away the theory and get practical:

      • What can you do today to make learning stick?
      • How can you transform tears of frustration into the satisfaction of “Aha! I get it”?

      You don’t have to invest in a new curriculum to revolutionize your child’s experience of math. Just change how you use the math program you have.

      Here are five tips that will help you and your child work together to build mathematical understanding.

      Continue reading 5 Tips for Better Homeschool Math

      Math Musings: Lies My Teacher Told Me

      Posted on by Denise Gaskins

      I mentioned last time that the common phrase “Multiplication is repeated addition” is a mathematical lie we tell our children. And it’s not the only one.

      Did you ever say, “Subtraction means take-away”? Or how about “Division is sharing”? I know I have, but both of those statements are also mathematical lies.

      One of the reasons I like Cuisenaire rods so much is that they can help us avoid lying to our children about math.

      Continue reading Math Musings: Lies My Teacher Told Me

      Math Musings: Teaching the Big Ideas

      Posted on by Denise Gaskins

      Earlier, I wrote that “the big ideas of number relationships are found in algebra, not in arithmetic. If we want to bring our children into direct contact with these ideas, we need to teach with algebra in mind from the very beginning.”

      Whether we teach the traditional way, beginning with counting and whole number arithmetic or take the road less traveled and explore algebra first — either way, we need to look at number relationships with an algebraic mindset.

      So you might wonder, what are these big ideas of number relationships? How can we recognize them?

      Continue reading Math Musings: Teaching the Big Ideas