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!”
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 (as Peggy Kaye pointed out in her book Games for Math) both will learn something even more important — that hard mental effort can be fun.
Now I’ve put together a short, inexpensive book to help families begin playing with math.
Let’s Play Math Sampler: 10 Family-Favorite Games for Learning Math Through Play contains short excerpts from my most popular books, including a preview of two games from my work-in-progress Prealgebra & Geometry Games.
“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! ”
My goals are to continue playing with math (1) in my homeschool co–op classes and (2) on this blog — and (3) hopefully to publish a couple of new books as well.
My favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
Rules of the Game
Use the digits in the year 2019 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
You must use all four digits. You may not use any other numbers.
Solutions that keep the year digits in 2-0-1-9 order are preferred, but not required.
You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.
My Special Variations on the Rules
You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
You may NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. The Math Forum allows them, but I feel much more creative when I can wrangle a solution without invoking them.
For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find.
Hapollonian Holiday Greetings from my co-op class kids, and best wishes for a grace-filled holiday season.
Do you know of any great math-related seasonal games, crafts, or activities I missed? Please add them to the comments section below.
As you scroll through the links below, you find several puzzle graphics from the wonderful Visual Patterns website.
Use them as conversation-starters with your kids: What do you notice? How does each pattern grow?
For older students: Can you write a formula to describe how each pattern? What will it look at stage 43?
Pattern #7, Trees
A Bit of Fun
Setting the mood: Enjoy this bit of seasonal fidgeting from Vi Hart. If you don’t understand some of the references, that’s normal! Pick a phrase, Google it, and enjoy the fun of learning something new.
Every year, some of my favorite websites offer a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity, one for each day in the run-up to Christmas.
Colleen Young updates the list every year, so check out her pages:
Clarissa (@c0mplexnumber) demonstrates how to make beautiful, challenging origami snowflakes. She recommends beginners try the first few folds — which create a pretty cool design on their own. Let it Snow…
K (@Ms_Kmp) reviews the distributive property with Algebra snowflakes and links to a make-your-own puzzle generator for math review at any level. Or download one of Craig’s (@mrbartonmaths) pre-made Tarsia Jigsaws.
Speaking of Christmas carols, the Christmas Price Index shows the current cost for one set of each of the gifts given in the song “The Twelve Days of Christmas.” I wonder what’s the cumulative cost of all the gifts, when you count each repetition in the song?
Alexandria Jones and her family are fictional characters from my old Mathematical Adventures newsletter. Their stories appear sporadically as I find time to transcribe them from the back-issues. You can find them all on this blog page.
Here are all the Alexandria Jones stories Christmas stories, with activity and craft ideas…
The Playful Math Carnival is like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school. This month’s edition features articles from bloggers all across the internet.†
You’re sure to find something that will delight both you and your child.
By tradition, we start the carnival with a puzzle in honor of our 123rd edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.
†Or more, depending on how you count. And on whether I keep finding things to squeeze in under the looming deadline. But if there are more, then there are certainly 36. Right?
Check out my new printables for playing math with your kids:
The free 50-page PDF Hundred Charts Galore! file features 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more. Everything you need to play the activities in my new 70+ Things to Do with a Hundred Chart book.
Math Concepts: number symbols, numerical order, thinking ahead. Players: two or more. Equipment: one math deck of playing cards (remove face cards and jokers), or a double deck for more than four players; additional cards to use as train cars.
Set-Up
Give each player four to six miscellaneous cards (such as the face cards and jokers you removed from the card deck) to serve as the cars of their number trains.
Lay these cards face down in a horizontal row, as shown. Shuffle the math card deck and spread it on the table as a fishing pond.
Line up the cars of your train.
How to Play
On your turn, draw one card and play it face up on one of your train cars. The numbers on your train must increase from left to right, but they do not need to be in consecutive order. If you do not have an appropriate blank place for your card, you have two choices:
• Mix the new card back into the fishing pond.
• Use the new number to replace one of your other cards, and then discard the old one.
The first player to complete a train of numbers that increases from left to right wins the game.
Two of the train cars have passengers. Which numbers could you put on the other cars?
Variations
House Rule: Decide how strict you will be about the “increases from left to right” rule and repeated numbers. Does “1, 3, 3, 7, 8” count as a valid number train? Or will the player have to keep trying for a card to replace one of the threes?
For older players: You can adapt Number Train to play with more advanced students:
If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.
This fall, my homeschool co-op math class will play with math journaling.
But my earlier dot-grid notebooks were designed for adults. Too thick, too many pages. And the half-cm dot grid made lines too narrow for young writers.
So I created a new series of paperback dot-grid journals for my elementary and middle school students.
I’m sure we’ll use several of these activities in my homeschool co-op math class this fall.
Noticing and Wondering
Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.
So more than anything else, we need to teach our kids to think mathematically — to make sense of math problems and persevere in figuring them out.
Help your children learn to see with mathematical eyes, noticing and wondering about math problems.
Whenever your children need to learn a new idea in math, or whenever they get stuck on a tough homework problem, that’s a good time to step back and make sense of the math.
Kids can write their noticings and wonderings in the math journal. Or you can act as the scribe, writing down (without comment) everything child says.
For more tips on teaching students to brainstorm about math, check out these online resources from The Math Forum:
Problem-solving is a habit of mind that you and your children can learn and grow in. Help your kids practice slowing down and taking the time to fully understand a problem situation.
Puzzles Are Math Experiments
Almost anything your child notices or wonders can lead to a math experiment.
For example, one day my daughter played an online math game…
A math journal can be like a science lab book. Not the pre-digested, fill-in-the-blank lab books that some curricula provide. But the real lab books that scientists write to keep track of their data, and what they’ve tried so far, and what went wrong, and what finally worked.
Here are a few open-ended math experiments you might try:
Explore Shapes
Pick out a 3×3 set of dots. How many different shapes can you make by connecting those dots? Which shapes have symmetry? Which ones do you like the best?
What if you make shapes on isometric grid paper? How many different ways can you connect those dots?
Limit your investigation to a specific type of shape. How many different triangles can you make on a 3×3 set of dots? How many different quadrilaterals? What if you used a bigger set of dots?
Explore Angles
On your grid paper, let one dot “hold hands” with two others. How many different angles can you make? Can you figure out their degree without measuring?
Are there any angles you can’t make on your dot grid? If your paper extended forever, would there be any angles you couldn’t make?
Does it make a difference whether you try the angle experiments on square or isometric grid paper?
Explore Squares
How many different squares can you draw on your grid paper? (Don’t forget the squares that sit on a slant!) How can you be sure that they are perfectly square?
Number the rows and columns of dots. Can you find a pattern in the corner positions for your squares? If someone drew a secret square, what’s the minimum information you would need to duplicate it?
Does it make a difference whether you try the square experiments on square or isometric grid paper?
I’d love to hear your favorite math explorations or journaling tips!
Please share in the comments section below.
* * *
P.S.: Do you have a blog? If you’d like to feature a math journal review and giveaway, I’ll provide the prize. Send a message through my contact form or leave a comment below, and we’ll work out the details.
This blog is reader-supported.
If you’d like to help fund the blog on an on-going basis, then please head to my Patreon page.
If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.
Welcome to the 115th edition of the Playful Math Education Blog Carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.
In honor of Women’s History Month, this carnival features quotes from fifteen women mathematicians.
They came from many countries and followed a variety of interests.
They conquered new topics in mathematics and expanded the world’s understanding of old ones.
They wrestled with theorems, raised children, published articles, won awards, faced discrimination, led professional organizations, and kept going through both success and failure.
Some gained international renown, but most enjoyed quiet lives.
They studied, learned, and lived (and some still live) as most of us do — loving their families and friends, joking with colleagues, hoping to influence students.
I think you’ll find their words inspiring.
“What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.”
—Julia Robinson (1919–1985)
“All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”
—Karen Uhlenbeck (b. 1942)
But my favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.
So grab a partner, slip into your workout clothes, and pump up those mental muscles!
For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find. This year may prove to be a challenge.
Use the digits in the year 2018 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.
You must use all four digits. You may not use any other numbers.
Solutions that keep the year digits in 2-0-1-8 order are preferred, but not required.
You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.
You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.
My Special Variations on the Rules
You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.
You MAY use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. I’m including these because Math Forum allows them, but I personally try to avoid the beasts. I feel much more creative when I can wrangle a solution without invoking them.
Now I’ve put together a short, inexpensive book to help families begin playing with math.
articles from bloggers all across the internet.†
I’d love to hear your favorite math explorations or journaling tips! 
Welcome to the 115th edition of the Playful Math Education Blog Carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. 
Denise Gaskins' Let's Play Math 