Reviewing Prime Number Factorization At The High Schoolhouse Level

My Algebra 1 students are currently working through our unit of measurement on radicals.  I already blogged close the dry erase operate mat I made for my students to purpose to organize their operate for simplifying radicals. 

Before nosotros could truly start out to simplify radicals, nosotros needed to review how to honour the prime factorization of a number.  This is a science they should guide hold learned earlier reaching high school, exactly I wanted to review it to brand certain my students had an fifty-fifty footing.  

My students were taught to brand share trees to honour the prime factorization.  That's the way I was taught, too.  But, when I was completing my pupil educational activity at Edison Preparatory School, ane of the eighth degree teachers invited me to her Algebra 1 shape to larn close the birthday cake method for finding prime factorization.  It was LOVE at start sight!  

I present both methods to my students too allow them select the method they prefer. 

Many students prefer the share tree method because you lot tin dismiss start amongst ANY ii numbers that multiply to the given number.  Then, you lot continue amongst finding factors until all of the factors are prime.

The argue I endeavour to steer students away from the share tree method is that it tin dismiss acquire messy.  I guide hold seen likewise many students create a share tree similar the occupation inward a higher house too write the prime factorization every bit 2^2 * iii * five instead of 2^3 * iii * 5.  

The birthday cake method tin dismiss guide hold a chip longer to acquire started because you lot must honour a prime seat out that divides into the given number.  You tin dismiss start amongst whatever prime seat out that divides into the number, exactly many of my students select to purpose 2, 3, 5, 7, etc inward that order. 

I honey that the birthday cake method is then streamlined.  Instead of searching for all of my prime factors inward a tree, my prime factors are all lined upwardly nicely for me.

To assistance my students retrieve their prime numbers, I created a quarter canvass amongst each of the prime numbers below 100 for my students to gum inward their notebooks.  I guide hold a few students repeating Algebra 1 for the instant time.  They asked me why I hadn't given them something similar this final year!  I estimate that agency they constitute it useful!

Influenza A virus subtype H5N1 few years ago, I created a prime numbers banner poster that my students oftentimes reference.

After discussing the ii methods I presented for finding prime factorization, I gave my students a practise majority which gave them a run a peril to endeavour out both methods.

After giving students a chip of fourth dimension to operate each problem, a pupil volunteer came to the SMARTBoard to acquaint a solution.  We alternated methods amongst each solution presentation.

My students were SHOCKED to honour out that they ever got the same prime factorization fifty-fifty though they took many dissimilar paths to acquire there!

Now that we've been simplifying radicals for awhile, my students guide hold started to realize that nosotros guide hold to maintain figuring out roughly of the same prime factorizations over too over too over.  One of my eighth graders remarked that it would hold upwardly cool to guide hold something inward our notes that gave us every unmarried prime factorization.

I took this thought too ran amongst it.  Kinda.  I did brand them a tabular array to gum inward their notebooks for the prime factorization of the numbers betwixt 1 too 100.

I typed the prime numbers inward large impress inward shaded cells.  I typed the composite numbers inward pocket-sized impress inward unshaded cells.  This agency students guide hold room to write inward the prime factorization when they honour it.  Then, inward the future, they tin dismiss purpose the prime factorization for that seat out without making roughly other birthday cake or share tree.  

Some of my students truly took to this too eagerly worked on filling out each box afterward finishing their quiz.

Hopefully I haven't made whatever mistakes when filling mine out.  I guide hold to country that it came inward handy when I was making response keys for our adding too subtracting radicals quiz today!

I'll postal service to a greater extent than close how I'm educational activity my students to simplify radicals soon.  I experience similar my students guide hold a much greater conceptual agreement of how radicals operate than ever before!  

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