My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?
Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)
But that’s definitely not the only way to learn. For most students, it’s not the best way, either.
Here are a few ideas to get your older children playing with math…
Just updated my blog post Math Game: War with Special Decks to add a couple of games I missed the first time around:
And…
If you’d like more ways to play with math from preschool to high school, check out My Favorite Math Games.
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Which I am going to say right now. Thank you!
“More Math War with Special Decks” copyright © 2020 by Denise Gaskins. “Red playing cards” photo by José Pablo Iglesias via Unsplash.com.
My book Prealgebra & Geometry: Math Games for Middle School is scheduled for release to regular bookstores in February, 2021. Because no publisher wants to send a new book into the world during such hectic, unsettled times as a big election, the winter holidays, or during inauguration season.
But preorder links are beginning to appear at several of the major online booksellers. And more stores will join them, as the information filters through their website systems.
The paperback will also be up for preorder, whenever the sites catch that update.
And remember: If you don’t favor a particular bookstore, you can buy the early-release ebook right now at my publisher’s webstore — and get a 10% discount if you order before 15 October.
I believe this was the first math game I ever invented. Of course, ideas are common currency, so I’m sure other math teachers thought of it before I did. But to me, it was original.
I’ve blogged about the game before, but here’s the updated version as it appears in my new book Prealgebra & Geometry: Math Games for Middle School — scheduled for publication in early 2021. Sign up for my newsletter to get updates.
Math Concepts: integer addition, absolute value.
Players: two or more.
Equipment: playing cards (two decks may be needed for a large group).
The all-time most-visited page on this site is my post about Math War: The Game That Is Worth 1,000 Worksheets. It’s easy to adapt to almost any math topic, simple to learn, and quick to play. My homeschool co-op students love it.
But Math War isn’t just for elementary kids. Several teachers have shared special card decks to help middle and high school students practice math by playing games.
Take a look at the links below for games from prealgebra to high school trig. And try the Math War Trumps variation at the end of the post to boost your children’s strategic-thinking potential.
Have fun playing math with your kids!
Here is a math problem in honor of one of our family’s favorite movies…
Han Solo was doing much-needed maintenance on the Millennium Falcon. He spent 3/5 of his money upgrading the hyperspace motivator. He spent 3/4 of the remainder to install a new blaster cannon. If he spent 450 credits altogether, how much money did he have left?
Stop and think about how you would solve it before reading further.
If you haven’t seen the meme going around, this is a palindrome week because the dates (written American style and with the year shortened to ’19) are the same when reversed.
Here’s a math puzzle for palindrome week — or any time you want to play with math:
What do you think: Will all numbers eventually turn into palindromes?
You can find all sorts of hundred charts on my Free Math Printable Files page.
Read about the history of palindromes on Nrich Math’s Palindromes page.
Find out more about the Palindromic Number Conjecture in Mark Chubb’s article An Unsolved Problem your Students Should Attempt.
Or play with Manan Shah’s advanced palindromic number questions.
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.
(Consecutive means numbers that come one right after another in the counting sequence.)
For example, five is a polite number, because we can write it as the sum of two consecutive numbers:
5 = 2 + 3
Nine is a doubly polite number, because we can write it two ways:
9 = 4 + 5
9 = 2 + 3 + 4
And fifteen is an amazingly polite number. We can write fifteen as the sum of consecutive numbers in three ways:
15 = 7 + 8
15 = 4 + 5 + 6
15 = 1 + 2 + 3 + 4 + 5
How many other polite numbers can you find?
Are all numbers polite?
Or can you find an impolite number?
Can you make a collection of polite and impolite numbers? Find as many as you can.
How many different ways can you write each polite number as a sum of consecutive numbers?
What do you notice about your collection of polite and impolite numbers?
Can you think of a way to organize your collection so you can look for patterns?
Make a conjecture about polite or impolite numbers. A conjecture is a statement that you think might be true.
For example, you might make a conjecture that “All odd numbers are…” — How would you finish that sentence?
Make another conjecture.
And another.
Can you make at least five conjectures about polite and impolite numbers?
What is your favorite conjecture? Does thinking about it make you wonder about numbers?
Can you think of any way to test your conjectures, to know whether they will always be true or not?
This is how mathematics works. Mathematicians play with numbers, shapes, or ideas and explore how those relate to other ideas.
After collecting a set of interesting things, they think about ways to organize them, so they can look for patterns and connections. They make conjectures and try to imagine ways to test them.
And mathematicians compare their ideas with each other. In real life, math is a very social game.
So play with polite and impolite numbers. Compare your conjectures with a friend.
Share your ideas in the comments section below.
And check out the list of student conjectures at the Ramblings of a Math Mom blog.
CREDITS: Numbers photo (top) by James Cridland via Flickr (CC BY 2.0). I first saw this activity at Dave Marain’s Math Notations blog, and it’s also available as a cute printable Nrich poster. For a detailed analysis, check out Wai Yan Pong’s “Sums of Consecutive Integers” article.
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 hope you enjoy them, too!
Click here for more information
So, what can your kids do with a math journal?
Here are a few ideas:
I’m sure we’ll use several of these activities in my homeschool co-op math class this fall.
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.
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:
Create math art. Check out my math doodling collection on Pinterest and my Dot Grid Doodling blog post. Can you draw an impossible shape?
I’d love to hear your favorite math explorations or journaling tips!
Please share in the comments section below.
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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.
Which I am going to say right now. Thank you!
“Math Journals for Elementary and Middle School” copyright © 2018 by Denise Gaskins. Photos of children © original artists / Pixabay.
This lovely puzzle (for upper-elementary and beyond) is from Nikolay Bogdanov-Belsky’s 1895 painting “Mental Calculation. In Public School of S. A. Rachinsky.” Pat Ballew posted it on his blog On This Day in Math, in honor of the 365th day of the year.
I love the expressions on the boys’ faces. So many different ways to manifest hard thinking!
Here’s the question:
No calculator allowed. But you can talk it over with a friend, as the boys on the right are doing.
You can even use scratch paper, if you like.
And if you’d like a hint, you can figure out square numbers using this trick. Think of a square number made from rows of pennies.
Can you see how to make the next-bigger square?
Any square number, plus one more row and one more column, plus a penny for the corner, makes the next-bigger square.
So if you know that ten squared is one hundred, then:
… and so onward to your answer. If the Russian schoolboys could figure it out, then you can, too!
Simon Gregg (@Simon_Gregg) added this wonderful related puzzle for the new year:
Denise Gaskins' Let's Play Math 