Wax Newspaper Parabolas

This year, my Algebra 2 interactive notebooks are easily a hundred times improve than lastly year's Algebra 2 notebooks!  I'm serious.  Last year, I did a pretty expert task amongst Algebra 1.  And, Algebra 2 form of got the curt terminate of the stick.  This year, I made a commitment to set inwards extra fourth dimension to brand sure our Algebra 2 notebooks were good idea out in addition to comprehensive.

I experience similar the agency I am approaching my Algebra 2 cast this twelvemonth is also agency better.  Of course, at that spot are a lot of things that I would similar to alter in addition to do differently adjacent time.  I'm soundless non only satisfied amongst the ordering of my units.  They don't precisely current into i some other the agency I would similar them to.  Next year, when I learn to the CCSS (or Oklahoma Academic Standards - my field decided they needed a novel name) for the starting fourth dimension time, I volition possess got plenty of opportunities to alter things up!  I'll start out stressing over that this summer.

As a high schoolhouse student, I was smart.  Really smart.  I was valedictorian.  I made it my goal to brand the highest grade inwards every unmarried class.  I fifty-fifty had teachers brand bets amongst each other close whether I would earn the transcend score inwards every cast that semester.  And, I did.  If I didn't possess got a 100% inwards a class, it was a sign that I could live doing better.  I went to TU on a full-ride scholarship for National Merit.  I don't country this to brag.  I country this to brand a point.  In high school, I was smart, but I wasn't curious.  Whenever a instructor taught something, I didn't interrogation it.  I cataloged it inwards my retention in addition to accepted it.  Teaching is changing that practice, however.

I possess got students who are incredibly curious.  When I learn them something, they inquire me why it works.  And, I'm non talking close the students who inquire questions inwards an assay to move out of doing an assignment.  These students genuinely desire to know the why behind what I am teaching.  For example, I've never questioned why the alter of base of operations formula for logarithms works.  It simply does.  I've never genuinely wondered why natural logarithms possess got a base of operations of e.  They simply do.  The to a greater extent than I enquiry the math behind their questions, the to a greater extent than I realize how much to a greater extent than I could/should live doing inwards my classroom.  

I've started pedagogy my students things that I never learned inwards high school.  And, I for certain never learned them inwards college.  Last year, I skipped in addition to thus many things because it wasn't on the test.  But when I only learn to the test, I'm cheating my students.  It's taken me a spell to realize this.  Teaching this agency takes to a greater extent than time, but I'm realizing it's worth it.

Here are the supplies nosotros used inwards Algebra 2 before this week.  Wax paper.  Rulers.  Colored Paper.  Sharpies.  Can y'all jurist what unit of measurement nosotros are in?  

Wax Paper Parabola Supplies

We simply started quadratic functions.  Last year, my students performed worse on the quadratic role questions than whatever other theme on the field test.  They performed improve on the conic department questions than whatever other topic.

This summer, I got the conduct a opportunity to create a parabola using a slice of newspaper at the mutual nub workshop I attended (OGAP).  I had never experienced anything similar that, in addition to I idea it was genuinely cool.

Confession Time.  A calendar week ago, I didn't know what a parabola was.  Oh, I knew what they looked like.  I could graph one.  I could tell y'all if an equation belonged to a parabola.  But, I didn't genuinely know what a parabola was.  Last twelvemonth when my Algebra 2 students did Conic Cards, I had null clue what a focus in addition to a directrix were.  I simply knew it wasn't going to live on the test.  And, lastly twelvemonth that was enough.  But, non this year.

I tailored this projection in addition to thus that our wax newspaper parabolas could fit inwards our interactive notebooks.  If you're non doing interactive notebooks (or y'all desire to display your parabolas), y'all could easily usage a total sail of newspaper in addition to a larger sail of wax newspaper for this activity.

Start past times trimming your wax newspaper to check the size y'all desire your finished parabola to be.  We used a half-sheet of missive of the alphabet sized paper.  I instructed pairs of students to conduct grip of a sail of paper, cutting it inwards half, in addition to portion it amongst their partner.

Wax Paper in addition to Colored Paper

I tore the wax newspaper off in addition to thus it was every bit unopen every bit possible to the size of a missive of the alphabet size sail of paper.  Less trimming equals less potential trash to live left inwards my room.

So, you're in all probability wondering.  Why the wax paper?  Well, y'all tin post away do this amongst paper, but it's a hundred times harder.  Wax newspaper is perfect for folding a parabola.  You tin post away come across through the paper, in addition to that volition brand all the divergence inwards this activity!  Plus, wax newspaper is only $1.28 at Wal-Mart.    

But, first, I intend I mightiness demand to remind y'all close what a parabola is.  I can't live the only i who didn't know the exact Definition of a parabola.

H5N1 parabola is a exceptional arch-shaped curve.  This is where my previous cognition stopped.  It's non simply whatever arch-shaped curve, though.  Each in addition to every request on a parabola is at an equal distance from a fixed request (called the focus) in addition to a fixed line of piece of occupation (called the directrix.)  Once I learned this, the conic cards from lastly twelvemonth started to brand to a greater extent than sense!  I promise.  I genuinely do possess got a bachelor's grade inwards math.    

Lay the wax newspaper over the colored newspaper in addition to thus y'all tin post away come across what y'all are doing easier.

I modeled these steps nether my document camera.  This allowed students to come across precisely what I was doing in addition to to follow along.

Draw a direct line of piece of occupation on the wax newspaper using a permanent marker.  I placed this line of piece of occupation at the bottom of my wax paper, close a ruler's width from the bottom.  This volition live the directrix of your parabola.  

Drawing the Directrix

Be sure to permit the line of piece of occupation dry out for at to the lowest degree xxx seconds or in addition to thus before folding.  Otherwise, the permanent marking volition smudge in addition to transfer during the folding process.

Wax Paper Parabola - Directrix

Next, nosotros demand to create upwards one's heed where the focus of our parabola volition be.  Instruct students to assay to pump their focus over the directrix.  They are allowed, however, to house their focus every bit roughly or every bit far away from the directrix every bit they choose.  It simply needs to live centered.  If it's non perfectly centered, the Blue Planet volition non come upwards to an terminate or anything.  But, y'all volition non terminate upwards amongst a centered parabola.

The placement of the focus volition determine what the parabola volition expect like.  I told students this, but I didn't tell them how it would behave upon the parabola.

Wax Paper Parabola - Focus

If every request on a parabola is at an equal distance from the focus in addition to the directrix, nosotros tin post away notice points on the graph past times folding the wax newspaper in addition to thus that the directrix in addition to the focus intersect i another.  The crease volition live half-way betwixt the focus in addition to the directrix.  Thus, that request must live at an equal distance from both.

Folding the Wax Paper Parabola

Repeat the process.  Fold the wax newspaper a dissimilar agency in addition to thus that the focus in addition to the directrix intersect.

Second Fold of my Wax Paper Parabola

After making several folds, many students volition start out to intend that they possess got run out of possible folds.  I encouraged them to choke along trying dissimilar folds.

One side of the parabola is starting to convey shape. 

Soon, a few students realized that nosotros could brand some folds on the other side of the focus/directrix.

Folding the other side of the wax newspaper parabola

The to a greater extent than folds y'all make, the to a greater extent than obvious the parabola volition become.  If students complain that their parabola looks jagged, encourage them to brand to a greater extent than folds.

Parabola Progress

When y'all are satisfied amongst the bend formed past times the folds, halt folding in addition to usage a permanent marking to draw over the parabola.

Finished amongst Folding

Here is i parabola I created.

The Finished Parabola

In some other cast period, I created this beauty.  Notice the divergence made past times changing the location of the focus!  It is also quite obvious that I did non possess got my focus centered over the directrix.  Oops.

A dissimilar parabola amongst a dissimilar focus

To choke along the wax newspaper from moving, I had students staple the transcend of their wax newspaper to the colored newspaper below.

Stapling the wax newspaper to the colored background paper

Here are 2 of the parabolas I made, side past times side.  Next fourth dimension I do this, I desire to possess got students choke through a see/notice/wonder activeness where they expect at everyone's parabolas.  Or, perchance I should tell students how many inches higher upwards their directrix to house their focus.  Then, nosotros could possess got a cast intelligence regarding the divergence made past times the location of the focus.  

Comparing Parabolas

On the colored newspaper (under the wax paper), nosotros labeled the focus, directrix, in addition to created parabola.  Then, nosotros stapled the bottom of the wax newspaper to our colored paper.  By stapling this to colored paper, nosotros tin post away come across the parabola to a greater extent than easily.  And, nosotros are genuinely able to mucilage our creation inwards our notebook.  I couldn't intend of whatever other agency to attach wax newspaper to our notebook.  

Parts of a Parabola Notes

 Here's a close-up of the parabola I made that made it into my interactive notebook.  (This i is dissimilar from the ones pictured above.)

One of my students got genuinely creative amongst his labeling.  He made the focus into the "o" inwards his label of focus.  And, he made the intelligence "parabola" precisely follow the bend of his parabola.  I was impressed!  I for certain wasn't that creative.

Creating H5N1 Parabola Notebook Page

After creating our parabola out of wax paper, nosotros took notes over the parts of a parabola.  Our notes covered the parabola, focus, directrix, axis of symmetry, in addition to vertex.  

Parts of a Parabola Vocabulary Notebook Page

On the twenty-four hours next this lesson, I finally introduced them to the term "quadratic function."  Now that nosotros had learned what a parabola was, nosotros were finally ready to larn what type of role produces a parabola when graphed.  we organized our notes on quadratic functions inwards a Frayer Model.

Quadratic Function Vocabulary Frayer Model

After having my students create their ain parabolas out of wax paper, I realized they weren't quite every bit excited close the procedure every bit I had hoped they would possess got been.  The reward came a twenty-four hours later, however.  I possess got an Algebra 2 pupil who has made it pretty clear that she does non desire to live inwards my class.  She does simply plenty piece of occupation to acquire by.  Many days, she is the prototype of disinterested.  So, I'm pretty sure my jaw was on the flooring when I overheard the conversation she was having amongst mortal who had been gone the twenty-four hours before when nosotros made the parabolas.  She was literally gushing close the activeness nosotros had done in addition to how fun it was.  She was trying to explicate the procedure of making a parabola out of wax paper, in addition to it was clearly going over the caput of her classmate.  I looked at her inwards shock.  "I didn't intend your cast was also thrilled past times the parabolas nosotros made yesterday."  "Oh, I loved it! I beloved it when nosotros do hands-on things similar that inwards class."  

After some quick research, I possess got establish tutorials for making all of the conic sections out of wax paper.  I intend I know what we'll live doing inwards the adjacent unit!  

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