Question

Dear Mitch,

I am going to start teaching the grade 8 fraction unit and I've been thinking of fun ways to introduce LCM, GCF, and multiplying and dividing fractions so that my students are fully engaged. My students are highly interested in video games, Facebook, anime, and music, and I was thinking of ways to get them to do some sort of investigation connected to these math topics and to make it worthwhile and meaningful.

I was also wondering if you had any ideas for an end-of-the-unit project that can be done with grade 8.

Thank you,

Ms. V.

Answer

Dear Ms. V.,

Well, in your impressively succinct letter, you manage to squeeze in a VERY broad range of interesting ideas and topics -- truly enough to inspire a response that could approach book-length!

So, allowing for the fact that this format prohibits such a response, I find myself forced to leave out about 97% of the suggestions that occur to me. And so, with that in mind, here, in no particular order, are a few possibilities:

Regarding multiplication and division of fractions, finding LCM and GCF, i.e., all the topics you mention, when it comes to practice problems, either for homework or in-class assignments, I strongly suggest that, rather than assigning a lot of the typical "small" problems teachers tend to assign, such as 1/3 x 7/19 = ?, I suggest that you assign only a few, but make each problem HUGE. For example: 5/8 x 20/16 x 80/3 x 1000/900 x 15/60 DIVIDED BY 1/4 DIVIDED BY 16/180 x 1/625 x 1/45 x 1/2 x 1/2 x 18 x 120 = ?

Why?

Because by working it out, the students will actually discover for themselves how powerful it is to UNDERSTAND the way numbers work as they learn to factor, look for multiples, and sharpen their arithmetic skills. Rather than be bored by lots of 'drill-type' problems, students have actually reported that they find it "fun" to try a long problem like that and discover that -- rather than 'need' a calculator to do all the computations -- after a little cancellation here and there, they easily come to the nice, neat answer of 5.

Yes, as you probably figured, the solution to the 'long' problem you see above is actually the "neat" and compact answer of 5. So, that's the kind of thing I would assign for practice/homework.

If you'd like to get some music in, you might try amusing them with some "really outdated" technology: an old-fashioned casette tape or even -- if you have it -- a vinyl record and a turn-table. Try to use a song/album that still has some appeal (or, at the least, a song that has an element of recognition, such as something from a Beatles' album), and then, using the time-lengths printed after each song, and the length of time that one side of a tape/album lasts, such as 45 minutes or 30 minutes, have groups of students use math to predict how many centimeters of tape or how much of the area of the round record will have to play before their chosen song begins/ends. Obviously, this one's easier for the tape because, although they both involve circumference (with the tape winding around one of its interior circular wheels, when you consider the area of a circle and its relationship to temporal fractions, the album's surface area presents a wider range for error. It also requires a basic understanding of circles and the rate of change of circles as the record rotates and the circle shrinks, but, at the least, you can bypass that area of math by using it as an opportunity to have the students practice estimation.

You mention FACEBOOK. Have the students count their "friends", decide on a number of hours per day/week/month/year they wish to socialize with their "friends", and envision that FACEBOOK enacts a new rule that requires all members to spend a roughly equal amount of time with each of their "friends". Now, using their new mathematical skills, they have to determine how many hours or minutes or seconds they will be able to socialize with each "friend" per day/week/month/year...

Next, they get to double their quantity of friends and repeat the exercise. Next, triple, then quadruple...

Another potential musical assignment: Each student selects a favorite song or piece-of-music. At home, they tally up the number of times the drummer strikes a beat. Then, using the length of time the piece lasts, the students are to calculate the number of beats the drummer's rate would mean per minute, per second, per hour, per day, per... -- I think you get the idea!

And then -- How many beats would there be if the drummer wished to speed the rhythm up by a third? A half?

Finally, using each other's calculations, students could be required to investigate and analyze each other's musical selections to see if they can match up their classmates' beat-counts with their chosen tunes. . . The students can do this project in groups, and I can easily imagine such an investigation lasting a week or more.

That's it for now, so good luck!

If you'd like more, you know where to find us, and please, do let us know how it goes!

-- Mitch