Balance puzzle

Screen shot of the balance puzzle

I created a new puzzle, based on something I played with when I was at the New York Hall of Science. The idea of the puzzle is that given three numbers, you are trying to balance both sides of the equation, with the constraint that different positions on each side of the equation are worth different amounts. At this stage, this is a prototype, so the numbers are chosen randomly, but the eventual plan is to build this balance puzzle into a series of challenges, each of which will probably have multiple solutions.

One hope is that a puzzle like this helps bridge the gap between arithmetic and algebra, by providing an activity which uses arithmetic operations but embeds algebraic reasoning. I also hope that this app helps reinforce that the equal sign (and the inequality symbols) are not indicators that one should do an operation, but rather that they represent a relationship between the two sides of the equation.

Check out the puzzle here:

I’d love feedback before I move onto making this puzzle more robust.



  • 1. I would make the x2 x3 etc a bit bigger.
    2. This is more than arithmetic and algebra, it is physics. This has to be connected with balancing real objects on a stick,especially since you have chosen the numbering and spacing accordingly. (they could have been all jumbled up!!!!). Leads on to levers etc.
    3. You could next give them just two disks, some of which will have an answer (oops, sorry!), and some,like 3 and 7, which wont, in which case “What do you need, would you like to get, etc ???”

  • David Wees wrote:

    Yeah, it is absolutely physics. This is essentially a digital version of a physical balance beam located in the NY Hall of Science. It would also be interesting to create a model where the x1, x2, etc… is not made explicit, but the bar is more continuous, and people could attempt to balance the weights anywhere along the line. That would lose some of the connection to arithmetic, but increase the connection to physics.

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