Equivalent Fractions teaches multiplication. It all goes together so while they learn fractions concepts they learn multiplication or in this case they get to practice it...but when we get to the higher numbers they'll be learning the higher multiplication tables.
It's easy to see that 1/3rd and 6/18ths are the same. They can see it.
People often ask the ridiculous question: "Do they need to have the blocks with them to do math?"
The other night without blocks or even symbols just verbally I asked him what the factors of x2 + 3x + 2 where and he looked up for a moment and said X plus one and X plus 2...then before naps today I asked him, "if the sides are x plus 2 and x plus 3 what's the whole thing?"
He thought out loud and said, "one x square, three and two...five x's and four...no I mean six...six would fit in there cuz it's three and two."
No blocks or symbols. It's the same when you teach any language to babies: they hear it FIRST before they ever see an ABC...just because they can't write symbols doesn't mean they can't learn math.
Further the average student can't multiply 15 x 17 in their heads...because they need to have the symbols and a pencil and something to write on. My students can see the answer is 255 or at worst can add 100, 120 and 35...
Here in this video they have seen this a couple of times before without symbols and for the first time they see the symbols for fractions today, and the symbols make sense and are easy to comprehend because they have heard them before.
You can see their progress with multiplication if you have been following this blog...they still can't tell you 4 x 5 off the top of their heads but give them a little time and they can figure it out...and the more we learn fractions the better they'll get.
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“Men must be taught as if you taught them not, And things unknown proposed as things forgot.” ~Alexander Pope
Beautiful job illustrating how easy equivalency can be if we first begin building the conceptual understanding. In research with 5th graders who did not know their multiplication facts, we found working with fractions improved their automaticity in both multiplication and division. Imagine if they used your approach prior to fifth grade. Bravo!ReplyDelete
Lauri, have you published that research or made it available?ReplyDelete