Base 10 blocks (units, rods, flats and cubes) are a widespread manipulative material for teaching place value.

However, piling rods on top of each other is not very stable, so it is not easy to build one single tower with all pieces that represent a number.

As an alternative, one can use flat pieces for rods, cubes and beyond, exploiting the fact that 10 is a triangular number.

Using this system, 9999 looks like this:9999 with vertical sum

I would like to know whether this system has been described before.

  • $\begingroup$ Why is the "900" layer a 10x10x9 cube? $\endgroup$ Sep 10, 2020 at 12:56
  • $\begingroup$ Well, it is not exactly a cube, but 9 slices of 100 cubes each. $\endgroup$ Sep 10, 2020 at 14:02
  • $\begingroup$ So, the even powers of ten are all flat squares and the odd powers of ten are all flat, jagged "half-squares"? Interesting idea. $\endgroup$
    – Nick C
    Sep 10, 2020 at 16:42
  • 3
    $\begingroup$ The whole point of decimal system is not to "pile rods", but to hide ten needles inside of an egg, then hide ten eggs inside of a duck, then hide ten ducks inside of a rabbit, then hide ten rabbits inside of a chest, buried under an oak tree on an island. Your approach is needlessly complicated to be used as a manipulative for teaching place value. $\endgroup$
    – Rusty Core
    Sep 10, 2020 at 18:05
  • 2
    $\begingroup$ @Rusty_Core, I love your image of hiding things inside other things. Although I agree that this system won't help teach place value, this new contributor is having fun thinking about math, and that is way cool. $\endgroup$
    – Sue VanHattum
    Sep 11, 2020 at 3:09


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