Puzzle: Exploding Dots

I’m planning ahead for my fall semester homeschool co-op math class. Definitely going to try this with the kids…

Encourage your children to have some fun this week with this Exploding Dots math puzzle from The Global Math Project. What do they notice? Does it make them wonder?

More Explosive Math

You may recognize the connection between Exploding Dots and binary numbers. Or not — the puzzle is accessible to people at almost any age and level of mathematical sophistication.

But what I find amazing is that this puzzle can help us understand all sorts of topics in elementary arithmetic and algebra. So cool!

If you’d like to investigate Exploding Dots in depth, check out James Tanton’s free G’Day Math online course.

5 thoughts on “Puzzle: Exploding Dots

  1. I disagree that this should be used in elementary school. It takes away from base ten number sense. If kids can follow the 2:1 concept they can follow the 10:1 concept (and we have all kinds of manipulatives to use) . I know as my kids loved maths and did very well on provincial testing. I am not sure why anyone thinks this is even a choice for elementary kids. I don’t have a PhD but I do have BSc in maths and have taught this age group. I do not believe James has done the latter.

    1. That’s an interesting perspective, Judy. Do your students get confused by puzzles like this? My elementary math club kids find the Exploding Dots puzzle intriguing, and it helps them see place value in ways they hadn’t before.

      1. My students love puzzles. I just do not see why you would introduce the binary system before base ten is well understood. I do not see it as having value to teaching place value. It can be used later to gain a more in-depth understanding of why we use any system at all. The creator of the exploding dots seemed to agree with me. This is the relevant part of his response to my concern. ”
        Apologies for the brevity of this response — very busy right now — but I should let you know that I am in complete agreement with you and have been warning against using Exploding Dots for the elementary grades. This is an experience for middle-schoolers and above once the context of place-value, base-ten place-value, is firmly in grasp. The idea of Exploding Dots is to take the opportunity to reflect on that place-value understanding, probe into more deeply, and see what full story-line then unfolds that connects the base-ten algorithms, other place values, base x and all of high-school polynomial algebra, some infinite series and undergraduate mathematics, and some unsolved research work.”

        My fear, and I know it has been realised, is that it is taken as a way to first teach place value in grades K-3 say, and I vehemently warn against that.

        1. No matter what age you are teaching, you don’t introduce Exploding Dots as “the binary system.” That is a conclusion that happens through play, as kids notice the patterns created by the dots.

          Rather, you introduce it as a game that creates a secret code. My middle-elementary students didn’t have any trouble with that and were not at all confused by it.

          I haven’t tried the puzzle with K-3rd grade students. My expectation would be that most K-1st kids would find it rather abstract and boring — except perhaps for children who are used to playing a variety of board games. I think 3rd-graders would do just fine, and in 2nd grade I’d guess it would depend on the student’s interests.

          If you have younger students who want to participate in the Global Math Project, but you’re afraid Exploding Dots is over their heads, there are some alternate online activities through the Matific website.

    2. Actually, I use Exploding Dots in Elementary School to help solidify my students’ understanding of Place Value. Amazing how quickly, they understands why we have a tens, 100s, 1000s, and beyond place when they did not understand it prior. I have 2-11 yr olds in my class and they did not understand why we call it a tens place, but through exploring other “machines” they are understanding the place names and now that we visited 10 –> machine, they have that missing understanding. In fact, today one of my 8 yrs olds commented that the larger the machined (3–> vs 7–>) the fewer place values needed. Then the 10-11 yr olds figured out the value of 96 from our 10–>1 machine in 5, 6, and 7 machines. It was the 9 year old who figured out the 2–> machine and then an 8 year old who asked, “If we were using a 1–>1 machine, would it be 96 ones? ” Yes, my 7-11 years are really growing understanding because of ED.

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