A two-part project, which can be taken on together or as separate parts. The main part is a series of 3D objects for use in learning and practicing volume equations. The second is a short course detailing how they were made so that students can make their own for use in class. Combined, these will make up a good primer for students in learning and understanding 3D space and engineering.
The objects are provided in both Metric and Imperial units. The walkthrough, lesson plan and solutions are included as PDFs.
What follows are the first two lessons I've made for this project. The full set of six lessons, which cover everything required to replicate all the designs in the project, is fourteen pages long and is available as a PDF in the Thing files as Tutorial.pdf.
When I tried to enter more, the site seemed to stop working properly. I appreciate the understanding on this.
In this we'll go over the techniques I used to create this project and assuming zero experience. My preferred program is 123D Design because it's free and works using primitives rather than coordinates. I find primitives somewhat restrictive, but far easier to use. Lessons 2 - 5 will recreate blocks 1 - 4, demonstrating the necessary functions and techniques and then allow you to complete the block on your own. You will need either a print or to be able to view the STL files of the blocks to complete this tutorial.
Any similar program should work fairly similarly, so use what you're comfortable with.
If you don't have 123D, you can get it here: http://www.123dapp.com/design
Lesson 1: The Environment
If this is your first time opening 123D, a pop up tips window will be the first thing you see. For now, close this. The picture below will be what you see.
For the purposes of this walkthrough, these five icons are all we will be focusing on. Others will be mentioned when pertinent.
1) Transform: Moving, rotating and scaling (resizing) pieces
2) Primitives: The shapes we'll be using
3) Combine: Merge parts and subtract pieces from parts using others. That's make more sense later.
4) Snap: A function to align and connect the faces of two parts
5) Grid: Snap linear controls accuracy when adding new primitives. Angular snap controls fine accuracy when rotating parts (I like to set mine to five).
The environment defaults to millimeters. If you'd like to work in inches, click 'Edit Grid' in circle 5 and select it from the units dropdown. I prefer working in metric, so I'll keep to millimeters, but things will work the same. Remember that, for the purposes of this project, all metric dimensions will divisible by 5mm and all inches will be divisible by 0.25.
Take a minute to get comfortable moving around the environment.
Left-click: Selects an object
Right-click: Rotates the environment
Middle button (click down on mouse wheel): slide the environment sideways or up and down.
Mouse wheel: Zoom in and out.
Now, hover your mouse over the primitives button. A new pane will open.
Select the box. You will see this.
Note the dot. Virtually all positioning in 123D is centered and objects will try to snap to the center, edge or vertex of objects they're placed on. Plan your math accordingly. The three entries at the bottom are the three dimensions of the box and can be changed. The number of dimensions will depend on the primitive used.
You can normally tab through these to change them, but if they lose focus (the blue part winds up grey), you will need to click on the entry box to work with them again. The object will stay attached to the cursor until you click where you want it. Do so now.
Click on the box to select it again. Don't click your mouse while doing this, but intentionally move your cursor off of the box and then back on again. Doing this allows you to select individual parts of box, like the edge shown below.
Select a part of the box if you'd like.
Note the panel that pops up under the selected part. This is a contextual menu. It'll bring up the most commonly used options for whatever you have selected. A face and an edge will have different options. Feel free to play with these and get a feel for them. This is the end of lesson 1.
Lesson 2: Positioning and Merging
In this lesson, I'll be demonstrating how to replicate Block #1.
Open a file in 123D Design. Do this by either opening the program, or hitting the 'new' option under the main menu.
As before, select and place a box. This time, however, give it the dimensions of Length 30, Width 30 and a height of 5. If you're using inches, use 1.25 x 1.25 x 0.25. Place this in the environment, preferably somewhere near the origin.
Now, do this again, but with a box measuring 25 x 25 x 5 (1 x 1 x 0.25) and place it on the other box. Notice where the center of the new box will snap to. Experiment with this, then place it centered on first.
Select the new box again and click the first icon in the context menu.
This is the transform option. Three arrows and three rotation axes will appear along with an entry box. Move the top box to one corner. Given the size difference, this will be 2.5mm or 0.125". For now, use the arrows to drag the box into place. The distance per 'click' will be determined by how closely you're zoomed in.
If you're following along using inches, you've just hit a problem. No matter how closely zoomed you are, the program will not allow you to drag in increments past the second decimal place. This is one of the main reasons I prefer using metric. Because Imperial units break down by halves and computers will use decimal, using anything more precise than a 1/4" in 123D will require you to enter it manually. It will still work fine, but it is something to be aware of.
If you make a mistake, hit the Escape key. Until you click off of what you're doing while in a transform function, hitting Escape will reset the part. If you want to undo something after clicking off, hit Ctrl + Z.
Once your top piece is located properly, hover over the Combine icon in the top menu and select Merge. A new panel will open. Ignore the panel and click on both pieces, then hit enter. You should see this:
The faces at the corner should have merged cleanly. If they're still two separate faces, they were misaligned. Merging pieces isn't necessary, but is useful for manipulating many pieces as they're built. This is just to familiarize you with the function.
Complete the piece to finish.
Save the part when you're done. Note: When you go to save under the main menu, there will be two options. "Save" and "Save a copy." Save a copy functions like "Save as" in most programs. When hovering over them you'll get an option to save to projects or to your computer. "Projects" is a cloud save and requires an account. I tend to just save to the computer. To get a printable file, choose "Export as 3D" and choose STL
There are two purposes of this project.
1) to provide students with visual and physical aids for calculating volume while learning the formulas in math. Having physical examples will help provide a practical understanding of the subject rather than just the theoretical.
This project provides students with six examples of small objects that can be produced relatively quickly and cheaply; all of which have been designed with this project's methods in mind. Blocks 5 and 6 include a practical example for trigonometry.
2) building on the first, this project is intended to give students a primer on how objects exist in 3D space and to learn the basics of 3D modeling. If computers are available, this project was made in 123D Design, a free design program that uses primitives. A walkthrough is provided with this project that shows the techniques used to make these objects, but do not complete them. In this section, completing the first four objects is given as the assignment.
Students are then encouraged to make their own objects, under some constraints, for further volume exercises.
I admit that I don't know what's currently taught at what grades. Students should have a reasonable grasp of the mathematical equations for calculating volume. This project would be ideal as a proof for students learning those.
As will be mentioned again later, two of these blocks require a require a working knowledge of trigonometry.
An appropriate number of the blocks should be printed out ahead of time, along with an appropriate number of the depth gauges. While the parts are small and will print out relatively quickly, supplying a class with these will take days a prep time. The gauges are printed in batches because objects as tall and thin as them have a tendency to melt if printed on their own.
The lines on the gauges are faint, so marking them with a marker is a good idea.
The students will need calculators, rulers and scratch paper.
If used as a course on 3D modeling, or if this will be a component of the project, students will need access to computers with 123D Design or a similar program installed on them.
Whether or not students will be using computers in this project, they should start off by being given the physical objects to calculate. Students should be given one of the depth gauges to keep. The project blocks should be given to the students one at a time, and in order.
Inform the students that the purpose of the assignment is not so much about measuring, but about the calculations and that the assignment can be completed using only the depth gauge, if needed.
Inform students of the following:
1) All necessary measurements can be evenly divided by 5mm (or 1/4"). All other dimensions must be calculated. For round objects like spheres, this number relates to its diameter.
2) All round objects (cylinders/spheres) can be assumed to be regular.
If an object is given as homework, ask the student to look up the density of three different materials (IE: Water, iron and tungsten) and calculate what the object would weigh if it were made of those materials.
Blocks 5 and 6 were designed to be challenges, not a core part of the project. Both require knowledge of at least basic trigonometry to solve and can be quite frustrating. Inform students of this before they start. These can be omitted if necessary or just given as extra credit.
Suggested methods for solving all six blocks are included in the Solutions PDF included in this
If students have access to computers, and after they've completed at least the first four blocks, provide them with the tutorial and allow them to work through it.
- As a final project for this, students should create a similar object that can be used in future classes. This object should meet the following requirements:
1) As above, divides cleanly into either 5mm or 1/4" units.
2) All round objects are regular
3) Physically measuring should not be difficult (no hidden recesses, etc)
4) Must be able to print without supports
5) The student who created the object must be able, and first, to solve it.
From the use of the objects alone, the students will have gained some insight into how volume and real-world dimensions work in a way even word problems can't convey.
If taken through the tutorial, they will have designed a fairly basic object, but done so with a creative purpose as well as functional limits in mind. They will have gained some working knowledge of a modeling program that they can then expand on, should they want.
For finding the volume of the original objects, they should be graded as a normal question. Accuracy and an ability to show their work are key. The ability to solve blocks 5 and 6 should be a form of extra credit, unless the class is of a level where they'd be expected to understand and work through these kinds of problems.
For the design aspect, I would suggest that each of the five sections that replicate a block be worth 12% each, totaling 60%. These should be graded on with marks removed for accuracy and symmetry. Uneven pips on the same face of the die, for example, or the smooth faces of block #1 having a seam. These should be examined in the program rather than the solid piece. The ability to meet deadlines should also be a factor of these.
Of the remaining 40%, a quarter should go to attendance. One day given as grace, but with 2% deducted (to a max of the 10%) per class missed; excluding legitimate sickness, bereavement or school function, of course.
The remaining 30% should be given to the final piece designed by the student. Any student who hands in a build that meets all five points stated above, including being able to solve for it, should receive a passing grade on this part. The rest should be given on creativity (either artistic or interesting math), accuracy of what they designed (as above) and complexity.