GT Unit 1: Foundations in Geometry

Notation and the language of geometry

FOUNDATIONS OVERVIEW

 Download the Foundations Assignment

The study of mathematics and geometry requires precision in language.  As we work on and discuss geometric principles, it’s essential that we use common language to describe the relationships between points, lines, and planes.  As we begin our study of geometry, we want to build a foundation of notation and vocabulary that will help us clearly describe geometric relationships.  To do this, we’ll go through three major steps:

  1. Define basic geometry vocabulary and notation
  2. Begin proving and calculating properties of lines
  3. Design an illustration for how geometric constraints work in engineering design

When you’re done, you’ll be ready to study transformations, translations, and symmetry!

PART 1: NOTATION

(40 pts)  About 3 days

Any study of geometry has to start with a clear discussion of notation.  In order for any math to make sense when communicated between people, the mathematicians involved need to use common language and vocabulary.  In this first part of the unit, we’ll agree on common vocabulary and notation for points, lines, and planes as well as their common relationships.

PART 2: LINES & PROOF

(65 pts)  About 3 days

With some basic vocabulary out of the way, you get to turn your attention to various calculations about lines: distance, midpoints, slopes, and angles.  These form the basis of most work in geometry, and will even set the stage for our first simple mathematical proofs!

PART 3: CONSTRAINTS

(40 + 100 pts)  About 3 days

Finally, you’ll get to create something new!  Autodesk Inventor is a tool used by engineers when trying to create 3D models in a computer.  Autodesk has many tools for creating geometric objects, and the geometric constraints are some of the most important.  Here, you’ll use geometry to describe the geometric constraint tools before taking your unit test!

PART 1: Notation

Agreeing on the proper notation and vocabulary of geometry

Bug Bot Wiring Diagram

Our unit starts with a review of the different notation and vocabulary that will be used in our entire year of geometry.  It’s important to start here because this language is the one we’ll use to explain the complex relationships between different geometric objects like points, lines, planes, and shapes.  The videos and practice for this first part of the unit are pretty straight-forward, but do require careful attention to detail.

GRADING & PROCESS

 Use your Engineering Notebook to take good notes on the different videos presented here.

 Complete all three homework assignments using the information from the videos.  Take time after completing each homework assignment to check your work using Mr. Benshoof’s answer key.

 Talk to Mr. Benshoof and take Quiz 1: Notation

Bug Bot Wiring Introduction

How To Solder

Troubleshooting Wiring Problems

What’s Due In Foundations Part 1: Notation

  • Notation Notes
  • Homework 1
  • Homework 2
  • Homework 3
  • Quiz 1: Notation
  • Questions for Benshoof

Here’s what’s due in Part 1: Wiring

  1.  Notes on the three videos about geometric notation
  2. Homework Assignment 1
  3. Homework Assignment 2
  4. Homework Assignment 2
  5.  Quiz 1: Notation
  6.  Talk to Benshoof about geometry questions!

PART 2: Design & Draw

Brainstorm ideas for your Bug Bot and draw a careful picture

Now that we’ve covered some of the very simple vocabulary for geometric objects, and also talked a little bit about different relationships like collinear, coplanar, parallel, and perpendicular, it’s time to get a little more mathematical.  In this second part of the unit you’ll focus in more on how to do some relatively simple calculations on lines and line segments.  Things like finding distance, midpoints, angles, and slope might seem like very simple things, but they form the basis of all the other measurements and calculations throughout geometry!

Here we’ll watch a variety of videos that talk about these starting calculations, and then we’ll even get to look at how to formulate some of the first two-column proofs that we’ll make.

Absolute Value as Distance

Parallel & Perpendicular Lines

Distance Formula

Measuring Angles

Midpoint Formula

Example Proof

What’s Due In Bug Bot Part 2: Design & Draw

  • Brainstorm
  • Research
  • Pick Design & Draw
  • Benshoof’s Check-Off

Here’s what’s due in Part 1: Wiring

  1.  Brainstorm at least 10 ideas for what your Bug Bot might look like or be made of
  2.  Look up “Bug Bot Designs” on Google and see what other designs are out there.  Add 5 more ideas to your brainstorm list.
  3.  Pick what your final design will look like, and make a careful drawing in your engineering notebook
  4.  Have Benshoof check-off your careful drawing

PART 3: Build It!

Put your plan into action and build your Bug Bot in our workshop

Soldering – how to!  Give some thoughts and notes that summarize the big ideas

Check out this video on how to solder

Check out this video on how to wire your bugbot

Check out this extra video on troubleshooting

What’s Due In Bug Bot Part 3: Build It!

  • Build It
  • (Extra Credit) Decorate it
  • Benshoof’s Check-Off

Here’s what’s due in Part 3: Build It!

  1.  Get into the makerspace and build your Bug Bot!  Make sure it functions properly!
  2.  If you have extra time, give your Bug Bot that special touch by painting, lasering, or making stickers to customize it!
  3.  Have Benshoof check-off your finished, working Bug Bot

Double Check: Unit Expectations

Check what you need to have completed by the unit deadline

The purpose of this unit is to use the Engineering Design Process to wire, design, and build a working Bug Bot.  You should have had the chance to do some soldering, design your own Bug Bot, and use the tools in our makerspace to build your Bug Bot.  If you were really on-task and working hard, you should have also had time to decorate your Bug Bot to make it look super cool.  By the unit deadline, you should have completed and be able to submit the following items:

Engineering Notebook:

 (Part 1) Definition of problem, criteria, constraints, and Bug Bot Overview notes

 (Part 1) Wiring diagram, soldering notes, and wiring reflection

 (Part 2) Bug Bot Design brainstorm, notes, and careful drawing

 (Part 3) Final drawing/picture, half-page written reflection on Bug Bots

Building & Making:

 (Part 1) Wiring should work, soldering should be clean and complete

 (Part 2) Bug Bot design should be carefully drawn out including labels and diagrams

 (Part 3) The Bug Bot should be assembled and should function properly

Benshoof Checkpoints

 (Part 1) Benshoof should have seen your working wiring before you moved on

 (Part 2) Benshoof should have seen your careful drawing before you moved on

 (Part 3) Benshoof should have seen your working Bug Bot