Get a Weekly Dose of Playful Math

Our leaves haven’t started to turn yet, but summer’s on the wane, farmers are busy with harvest, and the back-to-school rush has calmed down into a daily routine.

But if you’re like me, you keep tweaking that routine, constantly looking for the perfect balance for your family or classroom. I especially love to discover easy ways to add more playful math to our schedule.

So here’s a collection of sites that offer fresh math resources on a weekly or monthly basis throughout the school year.

Which one will you try?

KenKen Classroom

Every week, they’ll email you a set of free KenKen arithmetic puzzles for all ages. As the challenge level subtly shifts week to week, students develop their math and logical thinking skills without even knowing it.

Subscribe ❯

#MathStratChat

Pose an interesting math problem. How can you figure it out? What else could you do? How many different ways can you find? Which strategy do you like best for this problem?

Follow Pam Harris on your favorite social media site to get a new problem every Wednesday.

Choose a Problem ❯

The Parallel Universe

Dr Simon Singh, author of the No. 1 bestseller Fermat’s Last Theorem and The Simpsons and Their Mathematical Secrets has created a set of weekly maths challenges – just 15-30 minutes of interesting, fun and challenging tidbits of mystery and history, activities and oddities, puzzles and problems.

Help students expand their mathematical horizons beyond the school curriculum and build strong mathematical thinking skills. Stretch your brain every week!

Learn More ❯

Problem Solving with James Tanton

At the back of my new Word Problems from Literature book, I’ve included an appendix with links to recommended online resources.

Check in on the Kickstarter

So I thought this week, I’d share some of my favorites with you. First up: Problem Solving Tips from James Tanton.

You may know Tanton from the popular Exploding Dots and other activities at the Global Math Project website. But he’s been busy for decades sharing the delight and the beauty of the subject. He currently serves as the Mathematician-at-Large for the Mathematical Association of America.

Read on to discover several of Tanton’s best problem-solving tips for middle school and older students.

Have fun exploring math with your kids!

How to Think like a School Math Genius

In this 4-video series, Tanton presents five key principles for brilliant mathematical thinking, along with loads and loads of examples to explain what he means by each of them. A call for parents and teachers to be mindful of the life thinking we should foster, encourage, promote, embrace and reward — even in a math class!

Watch the Videos

Two Key — but Ignored —Steps to Solving Any Math Problem

How many degrees in a Martian circle?
Every challenge or problem we encounter in mathematics (or life!) elicits a human response. The dryness of textbooks and worksheets in the school world might suggest otherwise, but connecting with one’s emotions is fundamental and vital for success — and of course, joy — in doing mathematics.

Read the Article

MAA AMC Curriculum Inspirations

Essays and videos showing how to approach math puzzles in a way that a) is relevant and connected to the curriculum, and b) revels in deep, joyous, mulling and flailing, reflection, intellectual play and extension, insight, and grand mathematical delight.

Scroll down and start with the Ten Problem-Solving Strategies.

Download the Puzzles

Think Puzzles and Think Cool Math

Here are some essays illustrating astounding tidbits of mathematical delight. And here are some purely visual puzzles to surprise.

Explore and Enjoy

“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.

    “There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.

      “Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”

      —James Tanton

      CREDITS: Feature photo (top) by Ian Stauffer via Unsplash.com.

      How Will You Celebrate this Epic Twosday?

      Tomorrow is Tuesday 2/22/22 (or 22/2/22, if you prefer). What a wonderfully epic Twosday!

      Here’s a puzzle your family or class may enjoy…

      The “All 2s” Challenge

      Use only the digit 2, and try to use as few of them as you can for each calculation. You may use any math operations you know.

      For example:
      0 = 2 − 2
      8 = 2 + 2 + 2 + 2

      • Can you find a way to make 8 using fewer than four 2s?
      • What other numbers can you make?
      • Can you calculate all the numbers from 1–20? 1–100?

      Putting 2 in Perspective

      You might enjoy practicing your math art skills with this 2-digit challenge from Steve Wyborney.

      How many blocks make the digit 2? How did you count them?

      Playful Math #152: Auld Lang Syne Edition

      Welcome to the 152nd edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

      Bookmark this post, so you can take your time browsing. There’s so much playful math to enjoy!

      We didn’t have a volunteer host for January, so I’m squeezing this in between other commitments. This is my third no-host-emergency carnival in the last year, which is NOT sustainable. If you’d like to help keep the Playful Math Carnival alive, we desperately need hosts for 2022!

      By tradition, we start the carnival with a puzzle or activity in honor of our 152nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

      Math Journaling with Prime Numbers

      Cool facts about 152: The eighth prime number is 19, and 8 × 19 = 152. When you square 152, you get a number that contains all the digits from 0–4. You can make 152 as the sum of eight consecutive even numbers, or as the sum of four consecutive prime numbers.

      But 152 has two real claims to fame:

      • It’s the smallest number that is the sum of the cubes of two distinct odd primes.
      • And it’s the largest known even number you can write as the sum of two primes in exactly four ways.

      So here’s your math investigation prompt:

      • Play around with prime numbers. Explore their powers, their sums, and anything else about them you like.
      • What do you notice? What do you wonder?
      • What’s the most interesting number relationship you can find?

      Continue reading Playful Math #152: Auld Lang Syne Edition

      Advent Math Activity Calendars

      Once again, the delightful Nrich Maths website offers a seasonal selection of activities to encourage your children’s (and your own!) mathematical creativity.

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

      For Primary Students

      Here are twenty-four activities for elementary and middle school, one for each day in December during the run-up to Christmas.

      2021 Primary Advent Calendar

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

      For Secondary Students

      Here are twenty-four favorite activities for middle and high school, one for each day in December in the run-up to Christmas.

      2021 Secondary Advent Calendar

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

      More Holiday Math

      I encourage you also to explore my HUGE holiday math post:

      Or check out these pages for more ideas:

      Have fun playing math with your kids!

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

      Playful Math Education Carnival 147

      Welcome to the 147th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

      Bookmark this post, so you can take your time browsing. There’s so much playful math to enjoy!

      By tradition, we start the carnival with a puzzle in honor of our 147th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

      Continue reading Playful Math Education Carnival 147

      Playful Math Carnival 144: Anniversary Edition

      Welcome to the 144th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

      Bookmark this post, so you can take your time browsing.

      There’s so much playful math to enjoy!

      By tradition, we would start the carnival with a puzzle/activity in honor of our 144th edition. But this time, I want to take a peek back at the history of our carnival.

      But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.

      Continue reading Playful Math Carnival 144: Anniversary Edition

      FAQ: Playful Math for Older Students

      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…

      Continue reading FAQ: Playful Math for Older Students

      The Gerrymander Math Project

      With a big election on the horizon, now is a great time to talk about the math of politics.

      Does “One person, one vote” make a fair democracy?

      Or does it give the majority license to trample a minority?

      How can planners arrange voting districts to give everyone the best representation? And is that really what politicians would do, if they had the choice?

      Try the Gerrymander Project with your students to investigate these questions and spark real-world mathematical discussion.

      First, Create a Map

      [Or buy a copy of my printable activity guide, The Gerrymander Project: Math in the World of Politics, which includes a prepared city map with more detailed instructions, answers, and journaling prompts. My publisher has extended the 10% discount code TBLTOP10 through to Election Day, 3 November 2020.]

      • Print a blank hundred chart or outline a 10×10 square on grid paper. This represents your city. Give it a name.
      • Pull out your colored pencils. Choose one color for your city’s Majority Party and another for the Minority Party.
      • Color 10 squares in a neutral color for non-voting areas. These might be malls or parks or the downtown business district — your choice.
      • Color the remaining 90 blocks in a random distribution so that 60% are the Majority color and 40% the Minority. How will you choose which squares to make which colors? Can you think of a way to use dice or playing cards to make your choices random, yet still get the right proportion?

      Slip your finished map into a clear page protector, so you can mark on it with dry-erase markers. Or make several copies, so you can write on them without destroying the original.

      Then Gerrymander Your City

      “Gerrymandering” is the American political tradition of adjusting the voting district boundaries to favor one’s own party at the expense of one’s opponents.

      The city has hired you to mark out 10 new voting districts of 9 squares each (not counting the neutral squares, which can go in any district). The squares in each district must touch side-to-side, not just meet at a corner.

      So now you get to play “political hack.”

      First, see how fair you can make the map:

      • What happens if you ignore the party colors and make your districts as compact as possible, so the people living nearest to each other vote together? Will the Majority Party always win?
      • Can you give all your voters a proportional representation? Both parties should win the number of districts that most closely matches their percentage of the voting population.

      Next, try your hand at gerrymandering, but make sure all the squares in each district stay connected. Can you create ten voting districts that will guarantee:

      • A come-from-behind triumph for the Minority Party? They need to carry at least six districts to wrest control of the City Council from their opponents.
      • The greatest possible margin of victory for the Majority Party? Can you keep the Minority from winning any districts at all?

      Share Your Thoughts

      I’d love to hear your students’ reaction to this project. Please share in the comments section below.

      For myself, the more I play with this project, the more I admire the work done by the framers of the U.S. Constitution. Our Electoral College divides the country into “districts” based on state boundaries, giving each a vote roughly proportional to its population — but in a way that slightly strengthens the Minority Party. The system may not be perfect, but it’s done an amazing job through the centuries of maintaining a balance of power, making sure that neither major political party can destroy the other.

      Which is NOT to say that our country always protects the rights of true minorities. Clearly, that’s an ongoing struggle.

      But overall, the political parties stay relatively balanced, making for a stable government. After more than two centuries, we still have, as Ben Franklin said, “a republic, if you can keep it.”

      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 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!

      Continue reading Math Game: War with Special Decks