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Multiplication Model (Integer/Fractions)

3D model description

This is created in response to a math teacher's request for a 3D printable model for multiplication (K-8). It can be used to model both integers and fractions, depending on the choice of wording and definition of the whole.

Example 1: What is 3 x 5?
Example 2: What is the area ( in term of sq cm) of a rectangle that measures 3 cm by 5 cm?
Example 3: Assuming the board is 1 square unit. What is the area of a rectangle that is 3/12 unit by 5/12 unit?

3D printing settings


FlashForge Finder









Please use a higher infill rate for the slider for strength.

Put the two sliders carefully on the board. Please note one is slightly higher than the other for overlapping. If it gets too difficult to slide across, you can remove the right or the bottom end.

How I Designed This
I did everything on 123D Design.

Overview and Background
Models for Multiplication

Multiplication has multiple meanings. For integers, it can be repeated addition, splitting (tree, product rule for counting), or area. For fractions, it can be area or a sequence of steps for partitioning. The 3D model allows for both integer and fractional multiplications. Context matters a lot in making sense of multiplication!

Lesson Plan and Activity
Please define or describe units (non-dimensional, linear, 2D, or even 3D) clearly.
To model integer multiplication, please use the small square as a non-dimensional unit for counting. For an area model, please use the small square as a 2D unit (unit square).
To model fraction multiplication, please define the whole board as a 2D unit (square unit). Each small square is thus 1/144 (square unit).
To model fraction multiplication as a sequence of actions, please use the small square as a non-dimensional unit. Example: John has 144 toys car. He gives 3/12 of them to Mary. Mary then gives 2/12 of what she gets to Katie. How many toy cars does Katie get?
Of course, it can be used in other ways, depending on the context.

  • 3D model format: STL


STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides:




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