Nick,
I'll give both some non-techie and techie examples of how I use math:
Shopping and cooking:
* Determining which product and/or size to buy for greatest economy:
Although unit pricing is required where I live and shop, there is no requirement for the unit pricing to use the same units among products in a given type. For instance, my sister likes a certain kind of sweetener in packets. One item on the shelf was priced in dollars per 100 packets, another was dollars per ounce. Being able to divide (or even estimate division) let me figure out which was the better deal. Note: with most phones containing at least a rudimentary calculator, I think it's far more important to understand what operations(s) to perform -- to get the desired result -- rather than being able to perform them in one's head (or on paper.)
* Scaling a recipe up or down:
Oftentimes, I want to cook from a recipe, but I want to make more (or less) than the recipe is for. So multiplying all the quantities by the same scale factor enables me to cook the quantity I want.
* Synthesizing among recipes:
Often, when thinking about what to cook, I'll look at several recipes online, and synthesize them into my own version. In order to make this work well, I look at the ingredient ratios (e.g. milk/egg in custard recipes), and use that as my basis for proportions in my hybrid recipe.
* Calculating minimum postage:
I work with a non-profit organization,
www.nesfa.org , to do mass mailings. Sometimes, such as when we're asked to include a flyer or similar that we didn't print ourselves, we need to get an accurate weight per piece, so we can use enough postage, but no more than needed. To get more accuracy (and resolution), we typically weigh twenty or twenty five pieces, and divide the total weight by the number of pieces.
* Determining how much paint to buy:
I just helped a friend paint her room. We measured the ceiling height and the length of each wall, and used those measurements to get a (conservative, because we left out doors and windows) estimate of the area. Armed with that info, we were able to buy just enough paint to do the job, but no more.
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Technology/Engineering uses:
* Calculating resistor values and/or power ratings, via good old Ohm's law -- especially when modifying a circuit to work from a different supply voltage than the original.
* Calculating resistor and capacitor values to make an analog filter select the frequencies I want a filter to pass.
* Calculating the volume of a part -- and, via the material density -- how much it'll weigh. (Or if reprapping, how much filament would be needed to print the part.)
If the horse hasn't already left the barn, please pass the above examples on to your teacher.