12 models of multiplication

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These models come from 24×36 inch full-color glossy poster.

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Posted in Grow
9 comments on “12 models of multiplication
  1. Shannon B. says:

    I was wondering if I need to purchase or somehow print the 12 models of multiplication?
    Thank you

  2. I’m delighted to say that I can add another model of multiplication to your list: prime factor concatenation.
    For example, 6 = 2 * 3 and 10 = 2 * 5, so 6* 10 = 2*2*3*5 = 60

    This was inspired by the game Prime Climb, so I really can’t take much credit for it. They use this to build a pretty multiplication table which illustrates the model nicely.

    Unfortunately, this makes 13 models of multiplication, which we know doesn’t allow us to create a nice array of models.

    • MariaD says:

      Joshua, thank you for your comment! I have good news and more good news :-)

      First, we do have plan to redesign the poster, something like “Even more models of multiplication” (since people suggested new ones since it came out). And the structure will be different – clustered by types of models and their relationships. I think it will come out first in our book on multiplication.

      Second, we need to separate “models and models” so to speak, and find good terms for them. What we have in that poster are bridges to the physical world: how objects (arrays, reflections, stretchy things) represent multiplication. What we need to have, separately, is how we can represent multiplication by other symbolic mathematics. Repeated addition will leave the original poster and go into that second collection. So will your concatenation.

      Do you know a good physical model of concatenation?

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  4. Joshua says:

    This collection of models for multiplication remains one of my all-time favorite webpages for elementary school math. Taking a look again, I have the inkling of a pedagogical structure, so I am curious to hear other people’s thoughts:

    Models that can substitute for knowing multiplication facts: skip counting, repeated addition, array (maybe sets?). These are models where, if the student doesn’t know a multiplication fact, they can use the model to calculate a fact.

    Models that extend multiplication beyond positive integers: sets (one factor non-integer), number line (one factor non-integer), area (fractions and decimals, neither factor needs to be an integer, but both positive), scale (fractions and decimals, at least one positive factor), time and money (fractions, decimals, negatives).

    Models that connect multiplication to other math: combinations (combinations), fractals (exponentiation), symmetry (geometry), scaling (geometry), area (geometry), sets (division), splitting (fractions, division).

    Any thoughts?

2 Pings/Trackbacks for "12 models of multiplication"
  1. […] see what multiplication looks like in real life, explore the multitude of Multiplication Models collected at the Natural Math website. Also available as a poster for easy […]

  2. […] a model as fragile as “repeated addition.” Instead, explore the many real-life Multiplication Models collected at the Natural Math […]

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