Making a 3D dynamic model in Scratch


I want to make a dynamic model of the Montessori Trinomial Cube, but I’m not sure how to do this in Scratch. One of the things about the physical Montessori manipulative that bothers me is that it suggests there is a fixed proportionality between the variables. I’m hopeful Scratch would be suitable medium for illustrating otherwise.

Any guidance will be very appreciated, thanks!

Note: to clarify, I want to make a 3d illustration that is dynamic.

Help with Scratch? :smiley_cat:
¿Han usado Scratch, para crear proyectos en 3D?

Maybe Scratch is not the right tool to illustrate that if you want show the 3D models.
I remember that some used minecraft (@Bice_Rapaccini were you?)
Othervise you can use Processing / Java
Maybe you can try also tinkercad just to see if can help you


Thanks for the suggestions for other software and approaches!

When I studied the Montessori apparatus, I built a .xls model that dynamically managed data and calculated the volume of the blocks given other variable sizes, and produced a 2-d rendering which was, as a proof, adequate.

I considered using CAD to model and then print differently proportioned cubes. (Don’t know if one could build the CAD model using variables rather than fixed inputs. I have very limited experience with CAD, and I’m not a programmer.)

My revised question for the community is: Can this possibly be done in Scratch, so that younger students can explore/remix within the Scratch environment?



BLOCKSCAD can be the solution for 3D models using variable

Scratch cannot show 3d models (no Z axes) unless you simulate it somehow


With Scratch it could be hard to experiment, I have to think more.
I asked my students for representing and explaining a binomial cube in different way:
2D Cad
3D Cad
Minecraft ( but I am promoting Minetest in school)
3D printer (they prepared the model with 3d cad)

Here a video:


You need a parametric Cad


I have seen many clever approaches to 3D in Scratch, even raytracing!

3D Model Projects in Scratch

You could start with the following article:


Thanks for the BlocksCAD link!


I love the multiple approaches you’ve taken to presenting and exploring the binomial. Thank you for the ideas!


Thanks for pointing out that wiki; precisely the guidance needed to open up this dimension of Scratch!


@Bice_Rapaccini @cyberparra @breenworks @Aldo_Arbore I built a dynamic 2d representation of Maria’s cube . For those of you who are involved in Montessori, I’d love suggestions on how this might be made more useful for students.


Hi, great work, but I am often full of doubts in using virtual representations when we talk about Montessori. Developing sense of touch, sight, hearing (the pieces could falling and make noise), smell (the cube should be in wood) are very important in early age, in general in the developing age. Montessori trinomial cubes are a sort of 3D puzzle to develop math but also visual skills.

I don’t understand why you wrote
"the purpose of this project is to illustrate that, in contrast to what the physical Montessori trinomial manipulative suggests, there need not be a fixed proportionality between the variables a b & c."
Trinomial cube is (a+b+c)^3 and in the original Montessori cube dimensions are a=4, b=3, c=2 (9x9 cube), but there are many other examples. Why you wrote in contrast?

Thanks, Beatrice


Hi Beatrice, difficult questions, thanks! First, I made a new Scratch model of this overnight that better achieves what I wanted, and with less code. It updates in real time as you move the sliders:

To your question, why I wrote “in contrast to what the physical manipulative suggests”, maybe there is some presumption on my behalf about this; however, some Montessori experts, and math professors, have agreed with me that the apparatus implies a fixed proportionality. I researched the Montessori trinomial for over a year for my graduate thesis. Primarily, I studied the language and word choices used by children (Montessorians and non-Montessorians, before and after engagement with the apparatus) to describe and make sense of the apparatus; I also asked about the relationship of the manipulative to the accompanying algebraic notation. Generally, I found that children who had familiarity with the apparatus had difficulty describing and perhaps noticing its properties as physical substance; instead they spoke about what one does with it, often demonstrating as they spoke, and sometimes speaking, as if about doctrine, of its utility as equipment. Non-Montessorians, lacking familiarity with the apparatus, would speak about its properties as physical substance, e.g. “it’s blocks, it’s red/blue/yellow, it’s cold, it’s wood”, etc. (I have ~80 pages of transcribed interviews on the topic). Alongside my research I recorded my evolving questions. One of my first questions was Could you change the value of one variable - thus the proportions between the three variables - and still build a solid cube that expresses the trinomial? Today I can visualize this in my mind, but at first, like many of the children I interviewed, I couldn’t relate to the algebraic notation (is it a formula? a tautology?), but only to the static, physical apparatus. And the analogies suggested by that apparatus will always be fixed at 4 : 3 : 2. Does that make sense?

Absolutely agree with you that these Scratch projects wouldn’t easily find their way into an orthodox Montessori approach :thinking:


Hi, thanks for sharing.
I agree with @Bice_Rapaccini about ‘virtualisation’ of Montessori tools and activities.
About your scratch project, at a first look, I just notice a little lack of text/voice comment during
the development of the animation: maybe it could be useful to avoid neither a ‘contrast’ nor a direct referral to Montessori, but just a hint in the ‘instructions’ area about the process.
I know/use a different color coding for mathematical hierarchies in Montessori.
A presto,




@Bice_Rapaccini @Aldo_Arbore Thank you both for the feedback!. :slightly_smiling_face:

I appreciate the suggestion of framing the digital manipulative in its own terms, neither within nor outside of Montessori. At the same time, I am wondering how AMS would respond differently than AMI to such a digitization (?). To be clear, I greatly value the original manipulative, and bring a treasured Gonzagarredi edition into all kinds of non-Montessori environments (robotics classes in Boston Public Schools, etc.).

Aldo’s comment about lack of text / voice provoked another Scratch idea: creating animations of the story of 3 kings that accompanies this manipulative. Are either of you able to share the Italian text to that story?

Grazie mille,