0 Radical Radicals

We are currently learning about radicals in Algebra 2.  I am loving this unit!  I'm building this unit off of a short unit I did on radicals with my Algebra 1 kiddos towards the end of last year.  After all, there's no need to reinvent the wheel...  We're still working on this unit, so there will be more pages posted sometime in the future.

Radical Functions Table of Contents

I'm doing something else radical with this unit on radicals.  I'm trying out SBG.  To be honest, I was disgusted with my Algebra 2 students' performance on the previous unit.  I have quite a few students who CANNOT factor a trinomial.  They bombed their last test.  But, they are still passing my class.  Therefore, they have no motivation to actually learn to factor.  I've always loved the idea of standards based grading, but I've always written it off before as too time consuming.

I take it all back.  Do you know what is too time consuming?  Spending almost an entire month on a unit and having students not master key concepts because your grading system tells them they don't have to.  Grades in my class have become almost meaningless.  I hate it.  When I look at a students' test score, I don't know what they know well and what they don't know at all.  I don't know if they completely mastered one topic and left another topic blank.  Or, maybe they made little mistakes on all of the topics.

It's gotten to the point where I hate to grade.  I let the pile of papers to grade sit there, growing, all week long.  Eventually, I bite the bullet and have a marathon grading session.  When I pass back papers and tests, very few students look to learn from their mistakes.  I hear other teachers talk about writing comments all over their students' papers.  I don't even do that.  Why?  I know they won't read them.

In a desperate measure, I threw this together in about an hour.  I wrote 6 learning goals for our unit on radicals.  I decided to grade on a scale from 0-4.  Is this the best scale?  I have no clue.  This was totally last minute.  Once a student achieves a 4 on a learning goal, they are exempt from questions that cover that learning goal on all future quizzes.

I had my students glue in a score tracking sheet on the page facing their table of contents for Unit 4.  Every day, I pass back the previous day's quiz.  Students update the sheet in their notebook.  Then, I review the questions students have questions on.  I like that this new method is forcing me to teach in layers, not lumps.

If a student doesn't get a 4, they immediately start looking for their mistake.  I have rarely been writing comments on the quizzes.  I just put a number.  It makes students think.  Where did I go wrong?  How can I avoid making this mistake on today's quiz?  They get mad at me when I give them a 3 for a tiny, tiny mistake.  But, by forcing them to retake the quiz, I am ensuring that they will never make that mistake again.

This system is a work in progress.  I'm liking it so far.  And, my students are liking it, too.  I still have a handful of students who aren't trying on the quizzes.  I'm not so sure what to do about that.  The only complaint from students is that now they can't get their name on the Star Student Bulletin Board for making an 85 or above on our unit tests since the quizzes are replacing the unit test.

I love looking through my grade book.  I can scroll down the columns and instantly know who needs work with each aspect of the chapter.  I'm still trying to figure out how to do homework with sbg.  And, I'm toying with trying out SBG with my Algebra 1 kiddos during our linear functions unit.  Decisions, decisions, decisions...

SBG Tracking Chart and Table of Contents

Before we could delve into simplifying radicals, I needed to refresh my students' memories regarding prime and composite numbers.  We color-coded a hundreds chart to keep in our notebooks for reference.

On the sides of the chart, we wrote definitions for prime and composite numbers.  Two of my students decided we should color our prime number definition the same color as our prime numbers on the chart and likewise for the composite numbers.  Color With A Purpose.  I like it!

Prime and Composite Numbers Chart

We used highlighters that I had ordered from Amazon.  They worked well for this activity.

Highlighters!

I'm still in love with the birthday cake method for prime factorization.  I've written before about why I like this method better than factor trees.

The Birthday Cake Method for Finding Prime Factorization 

I typed out the steps for finding the prime factorization for my students to save time.  We also did examples together in our interactive notebooks.

Prime Factorization Birthday Cake Examples

Vocabulary is a very important part of this chapter.  When I started teaching algebra, I didn't know the terms index or radicand.  I'm sure my algebra teacher taught those words to me, but I never had to use them.  I will not let my students go down this same path.  We are constantly talking about the index and radicand!

Parts of a Radical - Index, Radicand, Radical Symbol

For practice, students had to determine the index and radicand of these radicals.  This further emphasizes the necessary vocab for this unit.

Parts of a Radical Examples

I also typed out the steps for simplifying radicals.  Last year, I had students write this out by hand, and it took WAY too long.

Steps for Simplifying Radicals

Then, we did examples of simplifying radicals in our notebooks.

Simplifying Radicals Examples

After simplifying radicals, we moved on to adding and subtracting like radicals.

Adding and Subtracting Like Radicals Notes

And, this was soon followed by multiplying radicals.

Multiplying Radicals Notes

  

We still have yet to cover dividing radicals, rationalizing the denominator, and converting between radical form and rational exponent form.

PDF Templates to Download:

Unit Table of Contents (PDF)


SBG Tracking Sheet for Interactive Notebook (PDF)


Prime and Composite Numbers Chart (PDF)


The Birthday Cake Method for Prime Factorization Notes (PDF)


Parts of a Radical Notes (PDF)


Steps for Simplifying Radicals (PDF)


Adding and Subtracting Radicals Notes (PDF)


Multiplying Radicals Notes (PDF)