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

      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

      November Math Calendars

      High school math teacher Chris Rime has done it again. Check out his November 2015 printable math calendars for Algebra 1 (in English or Spanish), Algebra 2, and Geometry students. Enjoy!


      Things to Do with a Math Calendar

      At home:
      Post the calendar on your refrigerator. Use each math puzzle as a daily review “mini-quiz” for your children (or yourself).

      In the classroom:
      Post today’s calculation on the board as a warm-up puzzle. Encourage your students to make up “Today is…” puzzles of their own.

      As a puzzle:
      Cut the calendar squares apart and trim off the dates. Then challenge your students to arrange them in ascending (or descending) order.

      Make up problems to fill a new calendar for next month.
      And if you do, please share!

      Math Calendars for Middle and High School Students

      High school math teacher Chris Rime posted three wonderful review calendars for middle and high school students on his blog.

      The links at Chris’s blog will let you download editable Word docx files. If you’re cautious about internet links and prefer PDF, here you go:

      Chris writes:

      There are no explicit instructions about process being more important than the answer on these, so you’ll need to stress that in class.

      I remind students that everyone already knows the answer to each of the questions, and that one of the things we’re practicing is explaining our reasoning…


      And if anyone else has a math review calendar to share, for any grade level, please add your link in the comment section below.

      Infinite Cake: Don Cohen’s Infinite Series for Kids

      Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits
      Prerequisite: able to identify fractions as part of a whole

      This is how I tell the story:

      • We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. An 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.

      Bobby Flay German Chocolate Cake

      • How big is your piece compared to the whole, original cake?
      • But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your new piece? Color it in.
      • How much of the whole, original cake do you have now? How can you tell?
      • I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?
      • Now how much of the whole, original cake do you have? How could we figure it out?
        [Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below‌—‌identify how much of the cake is left out.]
      • Even for being on a diet, I still don’t feel very hungry…

      Continue reading Infinite Cake: Don Cohen’s Infinite Series for Kids

      Happy Birthday, General Relativity

      Don’t forget that Pi Day is also Albert Einstein’s birthday! And this year marks the 100th anniversary of his Theory of General Relativity. So Science Magazine has a special Einstein issue online, featuring this interactive comic:


      You may also enjoy:

      Pi and Buffon’s Matches

      From Numberphile: Dr Tony Padilla’s unique (and low budget) twist on the Buffon’s Needle experiment to learn the true value of Pi.

      For a kid-friendly version of this experiment, try throwing food:

      Do you have a favorite family activity for celebrating Pi Day? I’d love to hear it!

      The Math Student’s Manifesto

      [Feature photo above by Texas A&M University (CC BY 2.0) via Flickr.]

      Note to Readers: Please help me improve this list! Add your suggestions or additions in the comment section below…

      What does it mean to think like a mathematician? From the very beginning of my education, I can do these things to some degree. And I am always learning to do them better.

      (1) I can make sense of problems, and I never give up.

      • I always think about what a math problem means. I consider how the numbers are related, and I imagine what the answer might look like.
      • I remember similar problems I’ve done before. Or I make up similar problems with smaller numbers or simpler shapes, to see how they work.
      • I often use a drawing or sketch to help me think about a problem. Sometimes I even build a physical model of the situation.
      • I like to compare my approach to the problem with other people and hear how they did it differently.

      Continue reading The Math Student’s Manifesto

      2015 Mathematics Game

      [Feature photo above by Scott Lewis and title background (right) by Carol VanHook, both (CC BY 2.0) via Flickr.]


      Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the Annual Mathematics Year Game Extravaganza!

      For many years mathematicians, scientists, engineers and others interested in math have played “year games” via e-mail. We don’t always know whether it’s possible to write all the numbers from 1 to 100 using only the digits in the current year, but it’s fun to see how many you can find.

      Math Forum Year Game Site

      Rules of the Game

      Use the digits in the year 2015 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 2-0-1-5 order are preferred, but not required.
      • You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.
      • 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. Math Forum allows these, but I’ve decided I prefer my arithmetic straight.

      Click here to continue reading.