Reflections On A Futurity Lesson: Rationalizing The Denominator

I genuinely wrote this inward answer to the Week 1 topic of Walk the Plank Wednesdays.  I'm then excited close what I wrote that I decided to intermission my unintended weblog hiatus alongside this post.  I actually have yet to read Teach Like H5N1 Pirate.  I'm hoping to acquire to it this weekend.  Most of my reading of belatedly has been either Embedded Formative Assessment (amazing!) or non-school related reading. 

Note to self: deal back-to-back week-long math instructor conferences is inspiring in addition to really, genuinely draining.  I saw all kinds of genuinely cool ideas that I desire to weblog about, but my motivation has been extremely lacking.  So, without farther ado, I present: Why I'm Actually Excited About Teaching My Students to Rationalize the Denominator Next Year

Until I went to a Pre-AP Math Conference concluding week, I had no persuasion why it was customary to rationalize the denominator of a fraction. I never questioned the practise when I learned it inward school. Last year, I but taught my students that “mathematicians don’t similar to select radicals inward the denominator.” They complained in addition to weren’t quite satisfied alongside that explanation.

Next year, I volition innovate the concept of rationalizing the denominator yesteryear taking away my students’ calculators in addition to providing them alongside foursquare source charts similar those institute inward quondam math textbooks. I volition enquire them to uncovering the numerical approximation of 1/sqrt(2). After suffering through having to dissever 1 yesteryear 1.414, I promise they volition enquire for a amend way.

Then, nosotros tin beak close how a fraction remains equivalent equally long equally the numerator in addition to denominator are multiplied yesteryear the same value. I volition enquire students what they recollect nosotros should multiply the numerator in addition to denominator by. Hopefully, individual volition advise that nosotros multiply the numerator in addition to denominator yesteryear sqrt(2). (Of course, I’m going to brand my students crusade out all the other possibilities that are suggested, too. They are going to absolutely honey me!) Then, nosotros volition exercise our nautical chart to dissever sqrt(2) yesteryear 2 or 1.414 yesteryear 2. This partitioning work is much, much nicer. Most students should last able to produce this inward their heads.

I tin meet myself bringing out the stopwatches in addition to breaking the shape into 2 groups. I volition set an appear on the board that involves a radical inward the denominator. The finish is to uncovering the numerical approximation of the value. One grouping volition solve the work using the foursquare source nautical chart without rationalizing the denominator. The other grouping volition solve the work using the foursquare source nautical chart alongside rationalizing the denominator. What is the fourth dimension difference? If you lot had a homework sail of twenty problems, how much fourth dimension would you lot relieve yesteryear rationalizing the denominator?

I desire my students to meet that rationalizing the denominator does select a purpose. Or, it did select a piece of work inward the days earlier calculators. Yes, inward this electrical current solar daytime of technology, nosotros exactly type 1/sqrt(2) into our information processor in addition to allow it produce the piece of work for us. Hopefully, seeing the historical argue behind the mathematical procedure volition help my students empathise why nosotros rationalize the denominator in addition to the procedure volition last to a greater extent than meaningful to them.

With Common Core in addition to the increased emphasis on writing, I'm e'er on the sentry for creative ways to fit to a greater extent than meaningful writing into my math lessons.  Oklahoma's electrical current Algebra 1 EOI features specific questions on rationalizing the denominator.  I recollect I volition select students write a memo/letter/speech/etc to the State Department of Education expressing their toughts on whether students should or should non nevertheless last required to rationalize the denominator inward calorie-free of technological gains.  I quest to await into the Common Core Language Arts standards in addition to pose this interrogation inward such a trend that it matches what students volition last required to write on their cease of twelvemonth test.

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