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

Hints for the Patty Paper Trisection

Posted on by Denise Gaskins
drafting tools

No peeking! This post is for those of you who have given the trisection proof a good workout on your own.

If you have a question about the proof or a solution you would like to share, please post a comment here.

But if you haven’t yet worked at the puzzle, go back and give it a try.

When someone just tells you the answer, you miss out on the fun. Figure it out for yourself — and then check the answer just to prove that you got it right.

Continue reading Hints for the Patty Paper Trisection