IED Unit 4: Modeling

The basics of modeling systems with math and computers


One of the jobs that engineers need to be able to do is to create models of their work.  Sometimes this means creating a mathematical model for the motion in a system, or using a computer to create and assemble a 3-dimensional model of their work. As we look at modeling, we’ll focus on modeling in three ways:

  • Mathematical Models
  • 3-dimensional part models using Autodesk
  • 3-dimensional assemblies using Autodesk

The skills we work on in this unit will carry us through a lot of our work this year.  Not only do we need to be able to investigate graphs and mathematical models to make smart design decisions, we also need to be able to make computer models of parts and assemblies to facilitate the design of our prototypes.  In this unit we will have three main parts:

  1. STEP 1: Create some simple mathematical models to demonstrate motion, and to investigate your puzzle cube further.
  2. STEP 2: Create Autodesk models of your puzzle cube pieces that accurately depict your puzzle.
  3. STEP 3: Create fully dimensioned Autodesk drawings of your puzzle pieces as well as a complete Autodesk assembly of your puzzle cube.

When you’re done, you should have a few new ways to model different situations: mathematically, as an Autodesk part, drawing, or assembly.  You’ll also have all the experience you need to tackle our semester’s toughest Autodesk challenge in the next unit!


(25 pts) About 3 days

Mathematics is an important tool for engineers because it helps quantify the decisions we have to make.  If an engineer wants to know which choice is most efficient, least costly, or has the biggest impact, chances are they’ll need a mathematical model.  In this part of the unit you’ll create some simple mathematical models of real-world situations.


(25 pts) About 3 days

Autodesk Inventor Professional 2017 is a great software package that will let us build and create a wide range of 3-dimensional models. In this part, we’ll use Autodesk to create models of each of your puzzle-cube pieces. You’ll follow some basic steps to make some precise models.


(20 pts) About 3 days

In addition to making individual parts, Autodesk can also make nice drawings with dimensions.  Autodesk can also let us put multiple pieces together into an assembly.  In this part you’ll confirm that all your pieces fit together correctly to make a cube, and you’ll make an answer key to your puzzle as a drawing.

Part 1: Mathematical Models

Create graphs and equations to describe mathematical relationships

Mathematical Models

Whether an engineer is working with a simple or complex system, a mathematical model can help give insights into relationships. Mathematical models are used by engineers to define motion, connections, and various parameters.  In our class, we’ll use mathematical models to confirm our designs and to help with creating things that move.  In this first part of the unit, we’ll create a few simple mathematical models that help describe motion of different kinds.  We’ll also create a graph to model the relationship between size and weight of our puzzle cube.


Watch the presentation on mathematical models and take 1 full page of careful notes!

 Complete the Motion Modeling assignment

 Collect data on the size and weight of your team’s puzzle cubes and complete a linear regression using Excel

 Have Mr. Benshoof confirm your completed activities and data collection

Ferris Wheels

Graphing Motion

Puzzle Cube Regression

What’s Due In Part 1: Mathematical Models

  • Math Modeling Notes
  • Motion Modeling Assignment
  • Puzzle Cube Analysis
  • Mr. Benshoof’s Confirmation

Here’s what’s due in Part 1: Mathematical Models

  1.  Notes on mathematical modeling in your engineering notebook
  2. Complete the Motion Modeling assignment
  3.  Complete puzzle cube analysis
  4. Have Mr. Benshoof confirm your activities and data collection

Part 2: Autodesk Parts

Use Autodesk Inventor to create models of your puzzle cube pieces

Autodesk Reference

This unit includes our first introduction to Autodesk and the modeling of different parts and components.  For this first introduction, we’ll focus on very square objects and our puzzle cube pieces.  You’ll start by following a short tutorial to build a few simple 3-dimensional shapes, then you’ll models of each of your puzzle cube pieces.


 Start by taking careful notes on Basic Parts in Autodesk

 Follow the tutorial to make a basic shape

 Create each of your puzzle cube pieces one at a time in Autodesk; save each as a separate .ipt part file on your jump drive

 Have Mr. Benshoof check-off your completed Autodesk puzzle cube parts

Basic Puzzle Cube Part in Autodesk

Sketch Plane Cube Tutorial

What’s Due In Part 2: Autodesk Parts

  • Autodesk Notes
  • Tutorial Shape
  • Puzzle Cube Parts
  • Benshoof’s Check-off

Here’s what’s due in Part 2: Autodesk Parts

  1. Watch the “Basic Parts in Autodesk” video and take detailed notes in your engineering notebook
  2. Create the tutorial model to practice basic shapes in Autodesk
  3. Carefully create all of your puzzle cube pieces as separate part files in Autodesk
  4. Benshoof’s check-off of your completed Autodesk puzzle cube parts

Part 3: Autodesk Drawings & Assemblies

Using new features in Autodesk to make dimensioned drawings and full assemblies

Autodesk Reference

As you do more and more engineering, you’ll learn that Autodesk can do an amazing range of things.  Not only can we use Autodesk to build individual 3-dimensional models, we can also use it to create nice drawings of those models or even assemble them into working systems.  In this final part of the unit, we’ll do just that!


 Take a page of notes on creating drawings in Autodesk – be sure to include notes on how to add dimensions and multiple views

 Create and print a single-page drawing of your most interesting puzzle cube piece

 Take a page of detailed notes on creating assemblies.  Be sure to include specific notes on how to “Mate” and “Flush” faces

 Create an assembly of your puzzle cube by joining the necessary faces of each piece – it might help if you make each piece a different color

 Create a drawing of your completed puzzle cube

 Have Mr. Benshoof confirm your Autodesk drawings and assembly

Assemblies in Autodesk

Puzzle Cube Assembly Tutorial

Drawings of Assemblies

Drawings in Autodesk

What’s Due In Part 3: Puzzle Cube

  • Puzzle Cube Notes
  • Puzzle Piece Sketches
  • Build Your Puzzle
  • Excel Analysis
  • Mr. Benshoof’s Confirmation
  • + Decorate & Package!

Here’s what’s due in Part 3: Puzzle Cube

  1. Take a page of notes on creating and dimensioning diagrams in Autodesk.
  2. Create a complete and dimensioned drawing of a puzzle cube piece in Autodesk
  3.  Take a page of notes on creating assemblies of parts in Autodesk
  4.  Create a full assembly of your puzzle cube in Autodesk
  5.  Create a Multiview diagram of your puzzle cube assembly
  6. Have Mr. Benshoof confirm your Autodesk drawings and assembly

Double Check: Unit Expectations

Check what you need to have completed by the unit deadline

The purpose of this unit is to look at different ways to create models of more complicated things.  We start by using graphs and mathematics to show how we can model both motion and rates of change.  We then move in to Autodesk where the computer can help us make 3-dimensional models of the physical things we’re working with.  For this unit we stick with our puzzle cube pieces because they’re relatively simple – in the next unit we’ll get lots of practice with Autodesk modeling of much more complex features and objects.

Engineering Notebook:

(Part 1) You should have used your engineering notebook to take a page of notes on mathematical models including both graphs and regression

(Part 2) You should have taken good notes on how to make basic shapes in Autodesk

(Part 3) You should have taken a page of careful notes on creating diagrams with Autodesk

(Part 3) You should have taken detailed notes on creating assemblies with Autodesk

Building & Making:

(Part 1) Complete the puzzle cube modeling activity with regression

 (Part 1) You should have completed the Mathematical Modeling Assignment

(Part 2) You should have completed the basic Autodesk tutorial

(Part 2) You should have completed the puzzle cube Autodesk models

(Part 3) You should have made an Autodesk drawing of one of your puzzle cube pieces

 (Part 3) You should also have put your puzzle cube pieces together in an Autodesk Assembly of your completed puzzle, and made a drawing of your puzzle too

Checkpoints & Quizzes:

(Part 1) Mr. Benshoof should have checked-off your activities & data collection

(Part 2) Mr. Benshoof should have confirmed your Autodesk puzzle cube parts

(Part 3) Mr. Benshoof should have confirmed your Autodesk drawings and assembly