How to Think like a School Math Genius

Posted on by Denise Gaskins
Teen student thinking

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

    “There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

      “Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

      —James Tanton

      James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.

      But his wonderful, old-fashioned site full of great insights and interesting problems is gone.

      😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.

      Continue reading How to Think like a School Math Genius

      Fun New Math Story

      Posted on by Denise Gaskins
      Characters from Modultown math story

      Hey, look! A new book from the folks at Natural Math, now on Kickstarter:

      Modultown! A Math-Inspired Children’s Book

      Experience a whimsical puzzle hunt in a new fantastic world full of friendship and surprises, from the authors of Funville Adventures.

      When human siblings Emmy and Leo find themselves magically transported to Modultown, they make new friends and combine their different perspectives to solve challenges that flesh out the mechanics of modular arithmetic.

      Playing in Modultown unlocks pathways into number theory, computer science, genetics, and other essential modern fields.

      Continue reading Fun New Math Story

      Notice, Wonder, Discover: The Foundation of Learning Well

      Posted on by Denise Gaskins
      Notebook on desk, with the words "Notice. Wonder. Discover."

      Most of us were never taught how to teach. And we certainly weren’t taught what to do when NOTHING is working.

      My friend Sonya Post is offering a free orientation course that will help you rethink how learning actually works, how you can stop second-guessing yourself and start seeing real growth.

      I’ve taken the earlier iterations of her course, and I’d recommend it to all parents.

      Truly wonderful insights!

      Find More Information

      Continue reading Notice, Wonder, Discover: The Foundation of Learning Well

      Mental Math: Advanced Addition

      Posted on by Denise Gaskins
      photo of kids having fun with math

      Mental math is doing calculations with our minds, and perhaps with the aid of scratch paper or a whiteboard to jot down notes along the way.

      But we cannot simply transfer the standard pencil-and-paper calculations to a mental chalkboard. That’s far too complicated.

      We still want to follow our basic strategies of using friendly numbers, estimating, and adjusting the answer. So how can we help children do math in their heads as the numbers get bigger and the problems more challenging?

      How might kids figure out a multi-digit addition like 87 + 39?

      Here are three useful strategies…

      Continue reading Mental Math: Advanced Addition

      Mental Math: Early Division

      Posted on by Denise Gaskins
      Boy doing mental math calculation

      Mental math is doing calculations with our minds, though we can use scratch paper or whiteboards to make notes as we work.

      Doing mental math, children use the basic principles of arithmetic to simplify problems so they can think about number relationships, mastering the basic structures of how numbers work, the same structures that underlie algebraic reasoning.

      As always, we rely on two key mental-math strategies.

      • Use friendly numbers.
      • Estimate, then adjust.

      Division is the mirror image of multiplication, the inverse operation that undoes multiplication, which means we are scaling numbers down into smaller parts. Important friendly numbers include halves, thirds, and tenths, plus the square numbers and any multiplication facts the student happens to remember.

      Continue reading Mental Math: Early Division

      Two Hands-On Craft Projects

      Posted on by Denise Gaskins
      photo: Cutting a paper square

      Here are a couple of fun foldable projects to try with your kids.

      Both of the projects below start with squares of paper. Do you know how to convert any piece of paper into a square? Here are two methods.

      • Can you tell why they work, how each method creates a true square?
      • What if you didn’t have a rectangular page to start with — could you still create a square?

      Continue reading Two Hands-On Craft Projects

      Mental Math: Early Multiplication

      Posted on by Denise Gaskins
      mother and daughter talking math together

      Children learn best through interaction with others, and mental math prompts can lead to fascinating conversations, listening as our kids apply their creativity to the many ways numbers interact.

      With mental math, students master the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

      And these 3Rs are the foundation of algebra, which explains why flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

      Let’s Try an Example

      Multiplication involves scaling one number by another, making it grow twice as big, or three times as much, or eightfold the size. Multiplication by a fraction scales the opposite direction, shrinking to half or a third or five-ninths the original amount.

      The key friendly numbers for multiplication and division are the doubles and the square numbers. As with addition and subtraction, students can estimate the answer using any math facts they know and then adjust as needed.

      How many ways might children think their way through the most-missed multiplication fact, 8 × 7?

      Continue reading Mental Math: Early Multiplication

      FAQ: How To Start a Homeschool Math Club

      Posted on by Denise Gaskins
      Denise Gaskins reading math with preschoolers

      The question hits my inbox whenever parents start planning for a new school year:

      “Hello! I am on the board of a homeschool co-op. We have had requests for a math club and wondered if you have any tips for starting one. We service children from K-10th and would need to try to meet the needs of as many ages as possible.”

      There are several ways you might organize a homeschool math club, depending on the students you have and on your goals. I think you would have to split the students by age groups — it is very hard to keep that wide of a range of students interested. Then decide whether you want an activity-oriented club or a more academic focus.

      When I started my first math club, I raided the math shelves in the children’s section at my library (510-519) for anything that interested me. I figured that if an activity didn’t interest me, I couldn’t make it fun for the kids. Over the years we have done a variety of games, puzzles, craft projects, and more — always looking for something that was NOT like whatever the kids would be doing in their textbooks at home.

      Let’s look at the possibilities by grade level…

      Continue reading FAQ: How To Start a Homeschool Math Club

      Playful Math 182: The Storytelling Carnival

      Posted on by Denise Gaskins
      two children digging in the yard

      Would you like some great ideas for reading and playing math with your kids?

      Sue VanHattum put together a delightful collection of mathematical fiction in honor of Math Storytelling Day:

      What are you waiting for? Come join the fun!

      Click Here to Read the Carnival Blog

      Continue reading Playful Math 182: The Storytelling Carnival

      Mental Math: Early Subtraction

      Posted on by Denise Gaskins
      mother and child doing math homework

      By doing mental math, we help our children use the basic principles of arithmetic to simplify problems so they can think about number relationships, mastering the basic structures of how numbers work.

      And the more our children practice these structures in mental math, the better prepared they will be to recognize the same principles in algebra.

      The basic idea of subtraction is finding the difference between two quantities: comparing a larger amount to a smaller one, figuring out what’s left when you remove a part, or finding the distance between two measurements (or two points on the number line).

      When you work with young children learning subtraction, remember our two key mental-math strategies.

      • Use friendly numbers.

      For early subtraction with numbers less than 20, the most important friendly numbers are 5 and 10, the pairs of numbers that make 10, and the doubles.

      • Estimate, then adjust.

      When children apply their creative minds to reasoning about math, they can use friendly numbers to get close to an answer, and then tweak the result as needed.

      Continue reading Mental Math: Early Subtraction