Math with Young Children

The question came up again:

“What is the best curriculum for my children? They are four and six years old, and I’m afraid of letting them fall behind.”

I remember being a young parent, eager to start homeschooling. I used to get mad (without letting it show, like a true introvert) when people told me, “They are young. Just let them play.”

Now I see the wisdom in it.

The most important thing for your children right now, by far, is for them to enjoy learning. The joy of learning is a child’s natural state. As a parent, your primary job is to keep yourself from stomping it out.

But our parental fears can push us into joy-trampling before we realize it.

And our own experience of school makes it hard for us to see how much of our children’s play really is learning. We expect education to look like schoolwork, but natural learning looks nothing like that.

Natural Learning Looks like Conversation

“The lesson here is that children are brilliant. They build math out of their everyday experiences, and when you offer them opportunities they apply the math they know to make further sense of their worlds.”

—Christopher Danielson
Counting in downtown Saint Paul

Natural Learning Looks Listening to Your Children

It Looks Like Free Play

“The children who receive the least instruction from parents, volunteers, or me are the most likely to persist. These are the children who will spend 20 minutes or more exploring the possibilities. But when we tell kids to ‘make a pattern’, we are asking the children to fill that carton with our ideas, rather than allowing them to explore their own.”

—Christopher Danielson
Let the children play

Let children play with blocks or other math toys, or with anything they find around the house or outdoors.

Free play, without any direction or instruction from you.

And Playing Games Together

“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”

Peggy Kaye
Games for Math

CREDITS: “Two children” photo (top) by Kevin Gent on Unsplash.

Play Math with Your Kids for Free

One of the most common questions I get from parents who want to help their children enjoy math is, “Where do we start?”

My favorite answer: “Play games!”

And in this time of pandemic crisis, it’s even more important for families to play together. So my publisher agreed to make my ebook Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play free for the duration.

When you’re stuck at home and getting bored, it’s a great time to play math with your kids.

Math games meet children each at their own level. The child who sits at the head of the class can solidify skills. The child who lags behind grade level can build fluency and gain confidence.

And both will learn something even more important: that hard mental effort can be fun.

The Let’s Play Math Sampler contains short excerpts from my most popular books, including a preview of two games from my work-in-progress Prealgebra & Geometry Games.

Don’t miss it: Download your copy today.

Free Online Preview

Ebook available FREE at most bookstores:
Amazon-logo google-play-badge Barnes-Noble-logo kobo-logo apple-books-badge Scribd_logo and other online retailers.

NOTE: Has your favorite store refused to adjust its price? (I’m looking at you, Amazon!) Try this link, and the good folks at BookFunnel will help you load the ebook file to your reading device (phone, Kindle, etc.): https://bookhip.com/SAATAW.

Or you can order the paperback by special request at your favorite local bookshop.

“Denise Gaskins is that sound voice of reason that comes into my head when I get agitated teaching. This isn’t performance — this is play. My kids aren’t on trial, they are learning to learn.”

—Sonya Post

“By exploring math in a playful way, your kids will be happy to learn and will discover an enjoyment of math in the process. You might even have fun, too! ”

—Olisia Yeend

NOTE: In many locations, you can get the rest of my playful math books free if you request them on your library app or through your local librarian.

Playing Math with A.A. Milne

Halfway down the stairs
Is a stair
Where I sit.
There isn’t any
Other stair
Quite like
It.
I’m not at the bottom,
I’m not at the top;
So this is the stair
Where
I always
Stop.

Halfway up the stairs
Isn’t up
And isn’t down.
It isn’t in the nursery,
It isn’t in the town.
And all sorts of funny thoughts
Run round my head:
“It isn’t really
Anywhere!
It’s somewhere else
Instead!”

—A.A. Milne
When We Were Very Young (affiliate link, see details)

The Stair-Counting Game

Play on any set of stairs where you won’t get in other people’s way. Start at the halfway step.

  • Roll one 6-sided die. Go up that number of steps.
  • Roll again. This time, go down that number of steps.
  • Keep rolling the die, alternating movements up and down.

Will you ever escape the stairs?

Fill the Stairs Game

Each player draws 11 stair steps (counting the top and bottom floors) on a piece of paper. Write zero on your middle step.

Remove the face cards and jokers from a deck of playing cards. Mix the remaining cards face down in a fishing pond.

  • On your turn, choose one card. Red cards are negative numbers, and black cards are positive.
  • Write the number from your card on one of your stair steps.
  • Then mix your card back into the pond.
  • The first player to fill their stairs with numbers in order wins the game.

The numbers have to grow as you go up the stairs and get smaller going down. But you can skip numbers. For instance, you could put +2 on the stair above zero, if you like. Or you could write −4 two steps below zero, leaving only one blank in between.

If you draw a card that will not fit on your stairs, you lose that turn. Mix the card back into the pond without writing anything.

If you make a mistake — like putting +9 too close to the middle, so there’s no way to fill the higher stairs — you can use a turn to erase one number on your stairs. You don’t get to choose a new card on the same turn as erasing a number.

Fill the Stairs Variations

Help young students understand negative numbers. A stairway makes an excellent number line visual.

Download the place value version (no negative numbers) of the stairway game from Math for Love.

Or discover variations for all grade levels at Math Hombre blog. I especially like John’s Decimal Point Pickle game. And the exponential version looks like a fun challenge.

Your Turn

Do you play stairway math? Please tell us your games and variations in the comment section below.

Or share other ideas for playing math with children. I love to hear new ways to play!

Playing with Math: My Favorite Posts

The articles that attract a browsing reader aren’t the same as the ones that pull on my heart. Yesterday, I shared my most-visited blog posts of 2019. Today, I give you my most-loved posts of the year.

#12

A fun challenge, based on an old family-favorite game.

Math Game: Six Hundred

Players around the world have played poker-style dice games for ages. Reiner Knizia included this mathematical version in his book Dice Games Properly Explained

#11

Math art — what a delightful way to learn!

Updated Geometric Coloring Designs

I created these coloring pages for my homeschool co-op math kids, and then collected them into a downloadable 42-page PDF coloring book for your family to enjoy…

#10

I could watch this video every day.

Math That Is Beautiful

Do you have trouble believing that math can be beautiful?

In “Inspirations,” artist Cristóbal Vila creates a wonderful, imaginary work studio for the amazing M.C. Escher…

#9

One of my favorite hobbies is collecting inspirational quotes as I read.

Find the Sweetness in Math

Good problems can help us fall in love with math and make a delicious meal of it, sinking our teeth into tough problems, tenderized by their intrigue…

#8

From the beginning of this blog, more than a decade ago, my desire has been to help homeschooling parents (and other teachers) change how they look at math.

Math Makes Sense — Let’s Teach It That Way

Annie Fetter is talking to classroom teachers, but her message is just as important for homeschoolers. Math is all about making sense. Let’s help our kids see it that way…

#7

An excerpt from the draft of my coming-someday-it-always-takes-longer-than-I-expect Prealgebra & Geometry Games book.

Math Activity: Polite Numbers

Did you know that numbers can be polite? In math, a polite number is any number we can write as the sum of two or more consecutive positive whole numbers…

#6

A sweet little game that was a big hit with my K–2nd grade homeschool co-op math class this year.

Playing with a Hundred Chart #35: The Number Grid Game

You’ll need a 6-sided die, a hundred chart (printables here), and a small token to mark each player’s square. A crumpled bit of colored construction paper works well as a token…

#5

This number-pattern activity was so much fun with my upper-elementary class.

A Puzzle for Palindromes

Here’s a math puzzle for palindrome week — or any time you want to play with math…

#4

For years, I’ve been meaning to create an email series about learning math through play. This year I finally did.

8 Weeks of Playful Math for Families

Yes, your kids CAN learn to love math. Keep your children’s math skills fresh with my 8-week email series of math games and activities…

#3

Not a single blog post but a whole new feature, which I hope to continue in the new year.

Morning Coffee

One of the best ways we can help our children learn mathematics (or anything else) is to always be learning ourselves…

#2

The Playful Math Blog Carnival is a labor of love for all our volunteer hosts. This year, August was my month to play.

Playful Math Education Carnival 130

The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math. It’s back-to-school time in the U.S., so this month’s edition focuses on establishing a creative math mindset from preschool to high school…

#1

But the work closest to my heart this year wasn’t math at all. My daughter finally concluded her fantasy novel series, the major project of her teen homeschooling years. When she gave me the manuscript to edit, I didn’t get any sleep that night. She had me hooked — I had to find out how it ended!

The Final Books from a Homeschooled Teen Author

Do you enjoy binge reading tales of epic fantasy? Love exploring magical worlds wracked by the struggle of good against evil? Then don’t miss Teresa Gaskins’s four-book serial adventure, The Riddled Stone

How About You?

Do you play math with kids? Please tell us one (or a few) of your favorite things. What touched your heart this year?

CREDITS: “Sparkling heart” photo (top) by Jamie Street on Unsplash.

Math Game: Place Value Fish

Math Concepts: addition, subtraction, place value to six or seven digits.
Players: two or more.
Equipment: pencil and paper.

Set-Up

Each player needs a sheet of blank or lined paper, and a pencil.

At the top of your page, write a 6-digit number. All the digits must be different, and none of them can be zero.

How to Play

On your turn, you go fishing for points. Ask one other player, “Give me your _____’s.” The blank is for the single-digit number of your choice.

The other player answers, “You get _____.” This blank is for the value of that digit in the other player’s number.

For example, suppose you asked for 5’s. If the other player has a 5 in the tens place of his number, you get 50 points. But if 5 was in the ten-thousands place, you would get 50,000. And if there is no 5 at all, you get zero.

You add those points to your number. The other player subtracts the points from his number.

Then it’s the next player’s turn to go fishing.

Notice These Rules

Your number may change with each turn (except when you get zero). Always use your most recent number to add or subtract the fishing points.

If you have more than one of the digit asked for (like the player on the left above, who has two 7’s), you may choose which one to give away. That is, you can give the other player 70 points and not even mention the 7,000.

Endgame

Keep taking turns until every player gets five chances to fish for points. After five rounds, whoever has the highest score wins the game.

UNLESS the winner made an arithmetic error.

Be sure to check each other’s math, because any player who makes a mistake automatically loses the game.

Share the Fun

If you try this math game with your kids, I’d love to hear how it goes. Please drop a comment below.

And tell us about your favorite math game, so we can all play that, too. 😀

CREDITS: This game comes from Michael Schiro’s book Mega-Fun Math Games: 70 Quick-and-Easy Games to Build Math Skills. Feature photo (top) by Ruben Ortega via Unsplash.

Mathematics: An Acrostic

What Is Your Child’s Experience of Math?

If your children made an acrostic for the word “Mathematics,” what would they include?

Would they think of adjectives like artistic, mysterious, or sublime?

Or would they focus on words like answers, maddening, and stress?

I love taking a playful approach to mathematics. Puzzles, games and art projects lay down a foundation of wonder and enjoyment. This creates a strong, positive base to support our kids through the inevitable difficulties of learning an abstract subject like math.

There are many rich math resources these days! So different from back when I started homeschooling. If you need ideas to help you transform your child’s experience of math, check out my Free Math on the Internet pages.

Internet Math Resources

In fact, I have a huge folder of even more bookmarks and links that I hope to add to my resource pages, whenever I find the time…

Does your family have a favorite way to play with math?

CREDITS: Water background photo by Ishan via Unsplash.