Monday, January 30, 2006

Multiply, Schmultiply

Today, on a homeschooling discussion board, I posted this complaint, er ... question:

I'm looking for some real life applications for my daughter for multiplying fractions ... something she can grasp, something beyond the very unreal examples in math books.

Here's how my daughter and I would both respond to the following problem in her math book:

"Larry ordered 3/8 of a pizza. He gave Pat 1/3 of his pizza. How much of a pizza did Pat get?"

She and I would both say this sort of thing:

"Do you think Pat is a guy? Or his wife? And why would someone order 3/8 of a pizza? That's ridiculous. I might order by the slice, but never in fractions. Pat must be a guy friend, because Larry certainly would give his own wife more than 1/3 of 3/8 of a pizza. Are you hungry? Let's get something to eat. Then maybe we could write a story about a hungry mother and daughter who abandon math, join forces to open a pizzeria and hire people to do all the stuff that makes them lapse slowly into comas ... i.e., the measuring, the math ...."

... I do think doubling or tripling is easy for her to see, but what we're missing is when will one use things like this:

1/3 x 3/8
3/4 x 2/3
4/21 x 7/9

and the countless other examples in any math book? What's the point of these? Who uses them?

... When in real life do we do this? When in life do I do this? Or shall we chalk it up to "needed to move on and pass SATs down the road ...."

As you can see, we're big on the living books, literature, history, and oohing and aahhing over science that involves life forms, but the math? Not so much.

The only things I've been able to figure out in answer to my question:

I can think of instances in which we'd need to divide a fraction, and since in the universe of math we divide by inverting and multiplying, we just have to know how to do the pluttification before we can do the division.

Anyone? Anyone?


  1. Karen,

    I asked my daughter (who's good at math - at least higher math) your question. She said recipes which usually involve 1/3, or 1/4, or 1/2, but that she has had to do sort of weird calculations when mixing up only one bottle of lamb milk replacer instead of the pint for which the container gives directions. I think I've had to do some rather strange calculations when dyeing yarn. Abby also said that she'll need this for chemistry later on. She also said that "in real life we often have to do things we don't understand the application of now, its's good to get that concept out of the way while practicing fractions." She says that only now is she beginning to see the value in the Latin I made her learn earlier. That from a former ecletic homschooler. Just do the fractions, Anne, pretend you're Anne Shirley working for Miss Stacy and trying to earn a scholarship to Queens.

  2. Oh, and remember, Anne, you're trying to beat Gilbert Blythe for top honors in math.

  3. When you are multiplying fractions you are normally (in real life anyway) doing as division of a fraction by a whole number.

    As in I had 3/8 of a pizza left and want to divide it among 3 people. Hence the multiply by 1/3 (reciprocal of 3).

  4. Ron said, "When you are multiplying fractions you are normally (in real life anyway) doing as division of a fraction by a whole number."

    ... Yes ... just about every example I could think of (or that I was given) is actually the need to divide, which we end up doing by multiplication.

    And, Liz, Anne is actually being quite a good sport about this ... I'm the one with the attitude. :-)

  5. So, your job, if you choose to accept it is to pretend you're Miss Stacy!

    Actually I do have a real life sort of problem that works for this kind of thing. Decide that you want to take a recipe that is designed for an 8 x 8 pan and make enough of it for a 9 x 13 pan (or a 9 x 9 for a 9x13). First you have to figure the volume of your pan, then you have to take all of those 1/4 cups, teaspoons etc. and convert them into whatever you need for the larger pan. Or you can do the reverse, figure out how to reduce a recipe from a 9 x 13 pan to fit into an 8 x 8 or a 9 x 9. If you're really up for a challenge work all of these sorts of calculations for various sizes of round pans (where you end up having to use pi, etc). This actually isn't all that impractical. You might someday find yourself doing this for a wedding cake or a shower cake (if you actually bake that is).

    Or you could set up this sort of problem: If you have x number of triops eggs and Ramona dumps 5/8 of them on the floor how many hatched triops does each girl get?

    But I agree 1/3 of 3/8 of a pizza is just plain dumb.

  6. Liz said: "Or you could set up this sort of problem: If you have x number of triops eggs and Ramona dumps 5/8 of them on the floor how many hatched triops does each girl get?"

    This could work. :-)
    Miss Stacy

  7. Karen tell Anne that she has to learn fractions so she can someday find a cure for the things that ail all her relatives, especiall her Aunt Nancy!

  8. Oh, Aunt Nancy, I think that will do it!
    :-) She'll do anything for one of your hugs.

  9. I can never figure these sorts of things out. And I wonder if I spent more time learning those sorts of things over and over again (i.e., I have to look up every single time how many pints are in a quart), if my life would be a little easier.

    In fact, this morning I found myself wondering how much money I'd save in a year if I bought a vehicle that got better mileage. Needless to say, I turned up the volume on my iPod after 2 minutes of frustration.