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 of the project we will be charting our data from part 1 that we verified in part 3. This will allow students to make predictions on the outcome of the rest of our project.
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 5 of this project I started out with our product from the part 2. 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. We then made this into a mold by adding a channel around the base and extending the flaps.
The objective of this part of the project is to take the data that we have collected so far and put it in a usable form. By the end of this part, students should be able to make educated guess as to the X value that will allow for maximum volume.
Even though the overall project is designed for Calculus students, this part of the project can be used for algebra and statistics students as well.
- Teachers and students will need access to a computer with a spreadsheet program, preferably excel.
- Teachers should be comfortable answering questions about the spreadsheet program.
- Students don't need any prior experience with excel.
- This project is easier if students stay in their groups of 2-3.
Step 1: Calculate
assign all groups an even number from 2-30, and have them solve for the volume of the lidless container with X equal to that container
Step 2: Chart
Write down the values on the board of all of the volumes. If you are using the same numbers I am, the results should be as follows:
Lidless Box Volume
Step 3: Use excel to enter data
This step will also verify the math in step 2. Type "X Values" into column A1, and "Volume" into column B1. Next type all X values into the "X value" column. In box B2 (to the right of the X value "2") use the equation from part one of the project to have excel automatically find the volume. You should type in something that looks like this:
Sorry about the $ signs but formatting would not let me use asterisks there. Just substitute in an asterisk anywhere you see a $.
Step 4: Graph
Use the graph (scatter) feature to make a graph of your data.
Step 5: Make predictions
Based on the spreadsheet and the graph, have students make predictions as to what value(s) of X will give the greatest volume.
It should be easier now for students to see exactly what the volume is doing based on a given value of X. This will give them a firm base to start to learn exactly what a derivative is, in part 6!