A good way to start once you finished the tutorials (always do those first) is to make some quick shapes and objects. Try to make them simple yet have features that use lots of inventors functions. A good example of this is isometric drawings. You can find some
here (just a google images search). Try to use the ones that have dimensions but if you are feeling adventurous try to model one that doesn't have dimensions and make up you own.
On a more realistic note, its probably not a good idea to try and depend on CAD this year if no one on your team understands it yet. It takes most people 2-3 weeks or at least a week if they have the
"knack" to get to the point where they can model something without directions. I know this from my experience teaching new members on my team and from watching/ assisting in my schools engineering classes (where we get taught inventor through the curriculum). But don't let this discourage you. Inventor or any CAD program is really powerful and the sooner you learn it the faster it can help you.
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2010 Midwest Spirit award
2010 Midwest Quarterfinalists
2010 Wisconsin Quarterfinalists
2009 Midwest Finalists
2009 Wisconsin Quarterfinalists
2008 Midwest Rookie AllStars