What are some ideas for math topics to teach to gifted second and third grade math circle students? Let's assume the math circle meets for one hour every week.

One example activity is learning about various types of ciphers that can be used to send secret messages.

I know I can look at math circle archives online (and I have), but I think it'd be useful to compile a list of topics here. I'm curious to see what suggestions this community comes up with.

Edit: Archives for the Los Angeles Math Circle can be found here.

Also, a little background on math circles from Wikipedia:

Mathematical enrichment activities in the United States have been around for at least thirty years, in the form of residential summer programs, math contests, and local school-based programs. The concept of a math circle, on the other hand, with its emphasis on convening professional mathematicians and secondary school students on a regular basis to solve problems, has appeared only within the past twelve years. This form of mathematical outreach made its way to the U.S. most directly from Russia and Bulgaria, where it has been a fixture of their mathematical culture for decades. (The first ones appeared in Russia during the 1930s; they have existed in Bulgaria for a century.)

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    $\begingroup$ For those of us not familiar with "math circle" can you tell us more about it, and also give links to these "math circle archives" you mention? $\endgroup$ Commented Sep 24, 2014 at 15:29
  • $\begingroup$ great question! $\endgroup$
    – celeriko
    Commented Dec 20, 2014 at 16:25

5 Answers 5


I've created a gallery of math activities, aimed at learners and children, with descriptions and images. You can see it at http://mariuskempe.net/Activities/.

  • $\begingroup$ great link! to improve your answer maybe briefly describe some of these activities here, in case the URL changes or goes down the in the future! $\endgroup$
    – celeriko
    Commented Dec 20, 2014 at 16:24
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    $\begingroup$ This is awesome, thank you. Keep it up! I'll be using some of these ideas. $\endgroup$
    – littleO
    Commented Dec 21, 2014 at 22:16

Have you seen Rodi Steinig's blog? She does lots of very cool math topics. Her stuff may not fit your audience, though.

I haven't yet worked with groups of gifted kids, but I'd start out with an intriguing topic, and see where it took us. You might like rational tangles, or one of the many other topics on Tom Davis' page.

  • $\begingroup$ Great links, thank you. $\endgroup$
    – littleO
    Commented Dec 21, 2014 at 22:21

some things that i did in my elementary math circle (we called it math enrichment)

  • Fibonnaci Numbers (there are a plethora of activities involving Fib. with a simple Google search)
  • Curve Stitching (Link shows the basics. We took shoeboxes and stitched curves using thin string from one side of the box to another. Very cool!)
  • Pascal's Triangle a la the way it was presented in The Number Devil
  • Pico, Bagel, Fermi
  • SET Card Game
  • Symmetry (mostly involving making snowflakes and other fun hands-on activities)
  • Origami (relating it to geometry and symmetry)
  • Basic Geometric Constructions (expose students to using compass and straightedge)
  • "Mathy" board games such as Connect Four, Mancala, or Othello
  • Infinite series (have a student walk half way across the room, then walk half way across the remaining part of the room, then half way and half way etc. and discuss why they will never actually reach the other wall)
  • Mobius Strips
  • "Non-standard" functions (factorial, absolute value, modular arithmetic)

I hope this list helps, i know some of these topics seem way to advanced for elementary students but all of these can be introduced in very basic, and easy to understand terms. Gifted students should have a natural predilection for math so if you can just spark their interest in any one of these topics they will be willing to push their thinking to the limits in order to learn more. Again, these were all things that I did in my elementary math circle and i am now a secondary math teacher :)

  • $\begingroup$ Awesome, thank you! $\endgroup$
    – littleO
    Commented Dec 21, 2014 at 22:25
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    $\begingroup$ Peter Engel's book on Origami from Angelfish to Zen is a great introduction to the math (and patterns) in origami. $\endgroup$
    – Jasper
    Commented Dec 24, 2014 at 20:18
  • $\begingroup$ With the infinite series example, let them point out that they will get "close enough" as literally makes "no difference". After how many divisions are you 10^-10 meters away? If a hydrogen atom is only 2 * 10^-10 meters across, then you overlap with the wall, so you are touching. $\endgroup$
    – Jasper
    Commented Dec 24, 2014 at 20:39

I've had some success using basic kirigami at that age, in particular, cutting out snowflakes:

          (Kirigami snowflakes link)
Memorably, I had one nearly mute kid who could cut out the most amazing designs, but could not explain what he was doing. It was as if kirigami was a language in which he was fluent, but he was decidedly not fluent in English (his native and only language).


How high can you count on your fingers?

  • Most people can count from 1 through 10.

  • I use roman numerals to count from 1 through 99. (right fingers = Is; right thumb = V; left fingers = Xs; left thumb = L)

  • Basketball referees can count from 0 through 35. (They use base 6. Each hand is from 0 through 5, and the uniform numbers don't include any digits from 6 through 9.)

  • Some people can use binary to count from 0 through 1023. (Warn them they'll get in trouble if they go around flashing the numbers 4, 128, or 132.)

How to do Check-By-Substitution

  • As I have explained in other answers, you can teach them to check their work (especially on story problems). This will give them a huge advantage going forward.

How to write out very big numbers

  • thousands, millions, billions, trillions... decillions
  • 1,000; 1,000,000; 1,000,000,000; 1,000,000,000,000...
  • 10^3, 10^6, 10^9, 10^12, ...
  • kilo-, mega-, giga-, tera-, ...
  • Ask the students to provide examples of real-world big numbers, and real-world words that use the prefixes, and figure out what they mean.
  • 1 googol (10^100)
  • 1 mole (the number of carbon-12 atoms in 12 grams of carbon-12. Or the net number of electrons that go past a point in one second when a one Amp current is flowing. About 6x10^23, or 602 sextillion.)

How to write out very small numbers

  • thousandths, millionths, billionths, trillionths... decillionths
  • 0.001; 0.000 001; 0.000 000 001; 0.000 000 000 001...
  • 10^-3, 10^-6, 10^-9, 10^-12, ...
  • milli-, micro-, nano-, pico-, ...
  • Ask the students to provide examples of real-world small numbers, and real-world words that use the prefixes, and figure out what they mean.

What is a negative number?

Tricks for setting up story problems

  • Draw a picture
  • What is a variable?
  • Label what you know
  • Keep your units
  • Solve the problem
  • Write out your answer in words
  • Check-by-substitution

How to Lie with Statistics

Maps, Areas, and Volumes

  • Measure the classroom's length, width, and height
  • Calculate the classroom's floor area
  • Calculate the classroom's volume
  • Draw a "map" of the classroom
  • Ditto for a desk (or other object)
  • Use an atlas or big map to measure the distances between cities, or calculate the areas of states. Look up the "official" answers, and see how close you were.
  • $\begingroup$ Google is a company, the number $10^{100}$ is googol. $\endgroup$
    – Ruslan
    Commented Feb 1, 2015 at 7:53

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