Monday, March 18, 2019

How to Make Fraction Multiplication Model Sun Catchers



I had intended this math enrichment activity for both girls, but to target primarily Syd, who is reviewing multiplying and dividing fractions in her math curriculum and is having trouble keeping the algorithms straight.

Unfortunately, you'll see only Will in this tutorial, as Miss Syd is having a chronic case of the tweens, and school is such a great outlet for a power struggle when one is feeling tween-ish. I'm declining to participate in this battle, because tweens generally come back around--I mean, look at Will! I wasn't sure we'd both survive her middle school years, and now she's a very dedicated student--so instead of two kids completing a craft project that is math review for one kid and math enrichment for another, we have one kid sulking somewhere else and one kid being crafty.

Eh, Will always needs more fine motor skills practice, anyway.

To make these fraction multiplication model sun catchers, you need the following:

1. Make the templates. The most accurate fraction multiplication model is the ten square or hundred square. We did do a couple of fraction circles, too, but I told Will that we had to know the product we wanted and then construct the model to fit it when we worked with the circles. 

When you work with the squares, the models construct themselves in a really cool way.

Trace several ten or hundred squares or pie circles onto a piece of clear acrylic using black Sharpie. They can be any size you choose.

2. Trace and cut out the fraction models. To make a fraction multiplication model, you need to cut out two fraction representations, one each in a different primary color.

Each fraction representation should be in tenths.

So, for instance, Will cut out one fraction in red--


--and another in blue:



3. Glue the fraction representations to the clear acrylic template. Place them perpendicular, with one edge of each representation lined up on the adjacent side to the other. This way, they will naturally overlap--


--and the area of their intersection is the product.

I like this model because it shows a different way of problem solving than my go-to explanation, that the x stands for "of" and the expression 1/2 x 1/2 can be translated as 1/2 OF 1/2. The visual is also a terrific memory aid, as it's colorful and striking and fun:


I haven't figured out a way to make the pie circle model come together as naturally as the square model does; there's no simple construction method that I can pick out that makes the product neatly assemble itself the way it does with the square model.

It can, however, be done--you just have to know what product you're looking for and then assemble the fractions so that the intersection represents that product:


Even though Syd refused to participate in the creation of the fraction multiplication model sun catchers, she can't help but see them on the window every time she's in the family room, mwa-ha-ha:


They look especially lovely when the setting sun shines through them, and I think they're a nice example of how naturally beautiful mathematical representation can be.

P.S. The next time Syd is amenable (perhaps when she's fourteen?), here is how to model fraction division in a way that makes it actually make sense.

P.P.S. Curious about all the other awesome stuff we get up to whenever a kid's not grumping out? Check out my Craft Knife Facebook page for more WIP pics and resources.

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