With MathType installed, you should have a MathType tab on Word's Ribbon. In the Format group of the MathType tab, there is a Convert Equations command. Click this.
Notice on the left side of the Convert Equations dialog is a list of "Equation types to convert", and one of those types is "Word 2007 and later (OMML) equations". If there's not a checkmark in this box, check it. Make sure beneath that, the Range is set to "Whole document" (unless of course, you want only to convert a few). Don't click Convert yet.
Now you have 2 choices. If your institution's Moodle has the TeX Filter turned on, the best (IMO) option is to click the dropdown list in the "Text using MathType translator" section, and choose Moodle:TeX filter. When you click Convert, all of the equations, both MathType equations and Word 2007 equations, will be converted into a format that Moodle can use and can convert them into images. If you choose to go this route, please review this information first: http://www.dessci.com/en/products/mathtype/works_with.htm?target=moodle.
Your second option is to let MathType convert all the equations in the document to GIFs, then insert the GIFs into Moodle. Since you're using Word 2007 equations, this is a 2-step process, but it's easier steps than your "convert to Word 2003/convert to HTML" process that you were using. At this point, you should still have the Convert Equations dialog open, and the options on the left are set. In the "Convert equations to" section, choose the top option: "MathType equations (OLE objects)". Click Convert. MathType will go through and do the conversion (you can watch the progress in Word's Status Bar), and when it's finished, it'll tell you how many equations it converted. Dismiss that dialog, and in the MathType tab of Word's Ribbon, click on the Export Equations command. A full description of using this command is available in MathType Help (just click the Help button on the dialog).
Let us know what you decided to do, and how well it worked (or what didn't work). If you need to write back because something didn't work, be sure to let us know what version of MathType you're using, and what version of Moodle.
