One Variable Inequalities Inb Pages (Algebra 1)

My Algebra 1 students simply finished upwards a mini-unit on graphing as well as solving 1 variable inequalities.

As usual, every novel unit of measurement starts amongst a tabular array of contents.  Last year, I had students proceed 1 tabular array of contents at the get-go of their notebook.  I similar the private unit of measurement tabular array of contents SO much better!  Almost all of my students proceed them upwards to date!

Table of Contents

This foldable was inspired yesteryear a foldable I saw on Coffee Cups as well as Lesson Plans.  I started this unit of measurement yesteryear drawing the unlike inequality symbols on my Smart Board.  I wrote numbers inward a higher house each symbol.  Then, I asked a simple question, "Who tin tell me which number is inward a higher house the symbol that way less than?"  Hands shot upwards inward the air.  Some students gave me the right number.  Others had confused the symbol for less than amongst the symbol for greater than.  Still others had confused it for the less than or equal to symbol.  One pupil argued that in that place was no way of knowing because in that place were no numbers for the alligator to eat. 

Graphing Inequalities Foldable - Outside

Oh, the alligator.  I retrieve learning almost the alligator inward unproblematic school.  The alligator is a genuinely hungry animal.  He ever chooses to swallow the largest number of fish possible.  I fifty-fifty did a projection for my ed psych degree inward college where I taught a kindergartner almost inequality symbols using the alligator.  Now that I'm educational activity algebra, I can't stand upwards the alligator.  The alligator doesn't aid my students interpret symbols into words.  The alligator holds my students back.  So, I told them that they had to accept everything they ever learned almost the alligator as well as throw it out the window.  I idea in that place was going to live a revolt inward my classroom.  One pupil proclaimed, "That's one-half of my life!  You can't await me to simply throw away one-half of my life because y'all don't similar the alligator."       

When I expression at an inequality symbol, I simply know its name.  I estimate I simply memorized them somewhere along the way without realizing it.  Last year, 1 of my college algebra students was having a terrible fourth dimension remembering which symbol meant less than as well as which symbol meant greater than.  One day, she had an epiphany.  If y'all brand an L amongst your hand, it looks similar the less than symbol.  Less than starts amongst L.  This was perfect!  So, making a backwards L amongst your paw creates the greater than symbol.  If y'all are familiar amongst sign language, y'all could also brand an declaration that in that place are similarities betwixt a sign linguistic communication G as well as the greater than symbol.  My pupil who discovered the paw play a joke on was therefore proud of herself!  Her exact words were "This simply made my day!"  And, she never had to inquire me almost what a symbol meant again.  

Since then, I've been educational activity this paw play a joke on to my students.  After a distich of days, they commonly acquire to where they simply know what they symbol is without thinking almost Ls as well as backwards Ls.    

Graphing Inequalities Foldable - Inside

I had my students create the examples for each inequality symbol.  I would allow 1 pupil selection the variable as well as or therefore other pupil selection the constant.  Some students were pretty mad at me because they didn't acquire a adventure to selection a variable for the class.  We graphed each instance as well as talked almost the divergence betwixt opened upwards circles as well as unopen circles.  My favorite intelligence was on how to graph sec is non equal to 3.  

I instruct my students that the club y'all write an inequality inward matters.  Does it really?  No.  However, on standardized tests, inequalities are ever (almost always?) written amongst the variable initiative of all as well as constant last.  Of course, chemical compound inequalities are the exception to this rule.  But, to a greater extent than almost them later.  As presently every bit I passed out this half-sheet of paper, I had the amount attending as well as curiosity of my students.  Why are in that place flip flops on my paper?  Don't y'all realize it's winter?  

I know, it's a lilliputian corny, but I told that "If y'all receive got to flip flop the sides of the inequality (to accomplish the right order), y'all must also flip flop the inequality symbol."  They affectionately called this the "Flip Flop Rule."  

Inequalities INB Page: Order Matters - The Flip Flop Rule

This side yesteryear side page was effort to modify the page I created concluding yr for graphing two-variable inequalities.  I don't similar it quite every bit well, but I estimate it did the job.

This belike isn't the best thing to admit, but I didn't instruct my students why it was necessary to flip the inequality symbol when y'all multiply or dissever yesteryear a negative concluding year.  I mean, I taught them to exercise it.  I simply never explained why.  This year, 1 of my Algebra 2 students asked.  I wrote 2 < iv on the Smart Board.  Then, I divided both sides yesteryear -1.  If nosotros proceed the inequality symbol the same, nosotros acquire -2 < -4 which is a faux statement.  Light bulbs went off.  It was a beautiful sight.  I am constantly becoming a improve teacher.  I've heard earlier that sense is the best teacher.  I don't think I quite realized how truthful that is until I started teaching.  

This year, I wrote 5, a large space, as well as a seven on the board.  Then, I asked, "Who tin tell me what symbol should acquire betwixt these 2 numbers?"  The degree agreed that a less than symbol belonged inward the middle.  Next, I asked for volunteers.  Tell me something nosotros could exercise to both sides of this inequality.  Add 2.  So, nosotros added 2 to both sides.  Guess what?  The inequality symbol is withal true.  What else could nosotros exercise to both sides of this inequality?  Subtract 7.  The inequality symbol is withal correct.  Give me something else nosotros could do.  Multiply yesteryear 2.  The inequality symbol is STILL correct.  By now, my students were convinced that the inequality symbol would ever stay the same.  So, I issued them a challenge.  The initiative of all individual to come upwards up amongst an functioning that would require us to alter the inequality symbol would win a Tootsie Pop.  I bribe my students amongst H5N1 LOT of candy...

It took quite a land to come upwards up amongst multiplying or dividing yesteryear a negative, but I similar to think it was fourth dimension extremely good spent.  I must receive got withal been half-asleep when I typed upwards these notes because I called it The Golden Rule of Inequalities: Whenever y'all multiply or dissever both sides of an inequality yesteryear a negative number, y'all must flip the inequality symbol.  In retrospect, the shout makes no sense.  My kiddos didn't seem to notice, though.

Solving as well as Graphing Inequalities inward One Variable

The concluding role of our unit of measurement focused on chemical compound inequalities.  I used the topic of Christmas presents to motivate the divergence betwixt AND as well as OR Compound Inequalities.  After completing our bellwork, I sat downward on my stool at the front end of the classroom as well as announced, "Today nosotros are going to verbalize almost Christmas."  I called on a pupil as well as asked them what was on their wishlist for Santa.  There were snickers.  I estimate high schoolhouse students are also cool for Santa Claus...

The initiative of all fourth dimension I did this, I lucked out.  The initiative of all pupil I called on said that he wanted a PS4 or an X-Box One for Christmas.  I became incredibly excited as well as started peppering him amongst questions.  What gaming organization exercise y'all currently have?  If y'all acquire this novel gaming system, volition y'all receive got to acquire all novel games or volition your erstwhile games withal work?  Finally, I asked him which organization he was leaning towards.  "So, all y'all desire for Christmas is an X-Box One?"  "You'd live happy if the alone thing y'all got for Christmas was an X-Box One."  See what I'm edifice towards here?

Does the gaming organization exercise y'all whatsoever proficient if y'all don't receive got whatsoever games to play?  So, I told him that what he genuinely wanted was an X-Box One AND or therefore games for Christmas.  Another pupil said my declaration should genuinely say "I desire an X-Box One, or therefore games, AND or therefore controllers for Christmas."  If y'all acquire the gaming organization but no games, y'all volition live disappointed.  If y'all acquire the games but no gaming system, y'all volition live genuinely disappointed.  The minute fourth dimension I did this during the day, I had to inquire 3-4 students earlier I institute someone that wanted a novel gaming organization for Christmas.  With my concluding degree of the day, I asked almost every unmarried individual inward the degree earlier I institute someone who mentioned video games.  That was a shocker!

Then, I wrote an OR declaration on the board.  I desire an X-Box One or a PS4 for Christmas.  We had a similar conversation.  If this was your wish, would y'all live happy if y'all institute an X-Box One nether the tree?  Would y'all live happy if y'all institute a PS4 nether the tree?  What if y'all institute both nether the tree?  With an AND statement, y'all had to acquire both of your wishes to live happy.  With an OR statement, y'all alone receive got to acquire 1 of your wishes to live happy.  If y'all acquire both of them, y'all volition simply live ecstatic.  This was the perfect transition for looking at AND as well as OR inequalities.

Compound Inequalities Foldable - Outside

The within of this foldable didn't photograph the best where I wrote inward pencil on this nighttime regal paper.  Sorry almost that!

Compound Inequalities Foldable - Inside

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