This is the second part of a series of projects intended for first year calculus students. In this series, students will learn how to use different mathematical equations to assess the properties of solids and containers. My apologies if the "X" and "x" thing is confusing, but in some situations formatting makes using an asterisk impossible, so big X is a variable, and little x is multiply.
In this part we will be creating molds that we can use to allow students to see the negative space they are solving for, as well as to create 3D castes of the volume.
I optimized this thing to be printed in ABS with maximum settings. I would recommend a skirt with an offset of 0mm (otherwise known as a brim) with 2-5 loops for ABS. I would also suggest an increased infill ratio.
For this project I used a free program from Autodesk called TinkerCAD. I have long been a user of AutoCAD which is a desktop drafting program from the same company. I used TinkerCAD to make it easier for educators and learners to be able to more easily replicate what I did. TinkerCAD is awesome because it's not only free, but it's easy to use. It also runs in your browser and has built in instructional lessons.
For part 2 of this project I started out with our product from the part 1. If you remember, we used X=20mm which gave us a base of 60x20mm, two flaps with dimensions of 60x20mm, and two flaps with dimensions of 20x20mm.
I used what we learned from part one to break down our different parts
(Remeber that the height of the base is 2.0mm)
To make this into a mold, I created a channel around the base that consisted of:
- a border sunk down to 1.0mm that was 2.1mm thick (extra .1mm makes all the pieces fit together real nice on max resolution, but you may need to add more if you will be using low resolution)
- a border around the first border that was 2.0mm thick and 2,0mm tall
Remember that you can adjust your snap to .1mm in the lower right hand corner of TinkerCAD.
Next I extended all the flaps from being 20mm tall to being 21mm tall to make up for the channel. I also had to extend the width of the small sides to 22mm (from 20mm) to fill in the rest of the space.
At the end of this project teachers and students will have a way of creating molds to assist them in understanding derivatives.
Even though the overall project is designed for Calculus students, this part of the project can be used for algebra students as well.
- Teachers and/or students who are creating a lidless box using their own values of X will need to have access to a computer with internet access and be logged on to a free TinkerCAD account.
- Tinkercad is easier to use with a mouse than with a tablet or trackpad, so computer mice are recommended.
- No previous 3D design experience is required for the students, although familiarity with Tinkercad would be helpful.
- The instructor should be comfortable answering modeling questions about Tinkercad and be able to advise students to avoid design features that might cause printing difficulties (overhangs, delicate features, etc).
- It is helpful to have students form into working groups of two or three so that they can collaborate on the design process. Having students work in groups is also helpful if you have a limited number of computers and/or limited 3D printer access.
Establish your X value. For the following parts of this project, you may want to make models with X = to 10mm, 20mm, 30mm, etc... Or you can make them for X = 5mm, 10mm, 15mm, etc... depending on how many groups of students there are or how precise you would like your data to be.
Use what we learned in part one of this project to make your representation.
Either review my process for making this project and make your own, or download the one(s) I have made (I will post more soon).
Print out your thing(s). For tips on settings, see the top of this project. After you things are done, pop them off your print bed and remove the loops if you used them. Sometimes some slight sanding of the edges with a high grit sand paper may be useful in getting the "flaps" to sit in place better. Also, I designed this thing so the addition of rubber-bands would add to the stability as well as hold the flaps together better.
Fill your mold with your choice of substrate. Some fun things to try:
You can add silicone to the bottoms and sides of your flaps to make your thing water tight if you would like to add a liquid.
You have now created a mold that you can use to make positive representations of the negative space that students will be solving for. For a lot of students, being able to interact and create is a big part of learning. The more hands on projects like this that they get to do, the more likely they are to succeed.