Math Game: War with Special Decks

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 algebra, geometry, and trig games. 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!

War Decks for Algebra & Geometry

War Decks for Algebra 2 & Trigonometry

Math War Trumps

The biggest problem with Math War is that it’s really just a worksheet in disguise. Children enjoy it more than a worksheet because of the social interaction, but there’s no choice or strategy to the game.

But you can bring strategic thinking into your number practice by playing Math War Trumps:

  • Players draw three cards from their deck and look at them.
  • The player whose turn it is calls the trump: High or Low, for which answer takes the trick. Or “closest to zero,” or any other winning value that makes sense with your card deck.
  • Then all players choose a card to reveal, and the winner collects the other cards as prisoners.
  • In case of a tie, the winners choose one of their remaining cards for a head-to-head competition (with the same trump).

Then all players draw enough cards to replenish their hand for the next turn.

Your Turn

Do you have a favorite way to play math with your kids? Please share in the comments below!

CREDITS: “Man shuffling cards” by ammiel jr and “Red playing cards” photo by José Pablo Iglesias via Unsplash.com.

How to Homeschool Math

Far too many people find themselves suddenly, unexpectedly homeschooling their children. This prompts me to consider what advice I might offer after more than a quarter-century of teaching kids at home.

Through my decades of homeschooling five kids, we lived by two rules:

Do math. Do reading.

As long as we hit those two topics each day, I knew the kids would be fine. Do some sort of mathematical game or activity. Read something from that big stack of books we collected at the library.

Conquer the basics of math and reading, then everything else will fall into place.

Learning math is an adventure into the unknown. The ideas we adults take for granted are a wild, unexplored country to our children. Like any traveler in a strange land, they will stumble over rocky places and meet with unexpected detours.

Many parents long to find a perfect math curriculum that will smooth over those rocky places. There is no such thing. Stumbles and detours are a necessary part of learning.

But you can help your children along the journey. Here are my top five tips for navigating the mathematical wilderness:

  1. Start with Play.
  2. Read Books Together.
  3. Consider Your Own Perspective.
  4. Listen to Your Children.
  5. Focus on Making Sense.

Click those links for a variety of ideas and resource links to help you with each of these areas.

Do you want to get started right away? Download a free copy of my Sampler ebook featuring ten family-favorite math games you can enjoy with your children today.

Join the Conversation

In the meantime, I’d love to hear from you!

  • What are your most pressing questions about helping your children with math?
  • Or what tips would you share with other parents?

Please add your ideas in the Comments section below.

Photo by Simon Rae on Unsplash

CREDITS: Photos generously supplied via Unsplash.com by Sandy Millar (top) and Simon Rae.

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.

(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?

You can build polite numbers (like fifteen) with a staircase of blocks.

What Do You Notice?

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?

What Do You Wonder?

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?

Real Life Math Is Social

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.

Advent Math Activity Calendars

Once again, 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.

Including an especially tough Advent meta-puzzle for truly determined problem-solvers…

Click the images below to visit the corresponding December Math Calendar pages.

For Primary Students

Easier activities for elementary and middle school.

A problem or game that uses dice for each day in the run up to Christmas.

2018 Primary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Secondary Students

Activities for middle and high school.

Most of the tasks require dotty paper or circles which you can find on the Nrich Printable Resources page.

2018 Secondary Advent Calendar

When you get to the Nrich website, click a number to go to that day’s math.

For Teens and Adults

“Because sometimes, in the midst of all the family fun, it’s good to put your headphones in and retreat into a word of your own, this year’s advent calendar brings you some of our favourite Plus podcasts. From the secrets of the Universe to the maths of football stadiums, there should be something there for everyone. Happy listening and happy Christmas from the Plus team!”

When you get to the +Plus Magazine website, you can tell which links are live because they jump to a larger size when you tap or mouse over the picture.

Plus Advent Calendar 2018

One link becomes live each day — so come back tomorrow and discover something new!

Christmas Meta-Puzzle

Or try your hand at the biggest mathematical mystery of them all — and save Christmas!

“It’s nearly Christmas and something terrible has happened: one of Santa’s five helpers — Jo Ranger, Fred Metcalfe, Kip Urples, Meg Reeny, and Bob Luey — has stolen all the presents during the North Pole’s annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.”

Christmas Logic Puzzle

If you solve all the clues and enter the answer on Christmas day, you may win a present for yourself, too.

Still More Mathy Fun

Colleen Young has collected several more holiday math calendars — enough to keep your kids playing and learning well into the New Year. Take a look!

Mathematical Advent Calendars

CREDITS: “Peanuts Christmas Panorama” photo [top] by Kevin Dooley via Flicker. (CCBY2.0)

A Beautiful Puzzle

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.

Thinking About Square Numbers

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!

Update

Simon Gregg (@Simon_Gregg) added this wonderful related puzzle for the new year:

Playful Math Education Carnival 106

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 106th edition of the Math Teachers At Play 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. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

  • How many times would you have to slice the pizza to get 106 pieces?

Click here for all the mathy goodness!