Trigonometry Interactive Notebook Pages - Unit Of Measurement Two 2016-2017

We're currently wrestling amongst the unit of measurement circle inwards trig class, in addition to hence it's fourth dimension to postal service pictures of all of our trig interactive notebook pages for unit of measurement 2.  Unit 1 was a review of the algebra in addition to geometry concepts necessary for trig.  Unit 2 covered the 3 basic trig ratios in addition to each of the pre-requisite concepts for the unit of measurement circle.  You tin honour my pages for Unit 1 here.  

Unit 2 started amongst our unit of measurement divider.  

Here's a close-up of our SBG skills for the unit:

To start off the unit, each pupil had to cutting a right triangle out of colored newspaper in addition to gum it into their notebooks.  We labeled 1 of the non-90 marking angles every bit theta.  Then, nosotros discussed how to seat the side past times side in addition to contrary sides every bit good every bit the hypotenuse.

This is my students' initiatory off sense amongst these price because the geometry instructor they had did non learn whatsoever right triangle trig.  It's a long story, but this trig cast is the initiatory off fourth dimension my students withdraw maintain ever seen whatsoever trig.

My greek alphabet posters are perfect for showing my students where theta comes from.  

I tried my manus at doing a uncovering activity to assistance them regain sin/cos/tan past times themselves.  This failed MISERABLY.  In the end, I just defined the 3 trig functions for them inwards a foldable.  I had my students bend their colored newspaper inwards one-half in addition to dissever it into 3 doors.  

They labeled the exterior of each door amongst the abbreviation for a trig function.  

On the within of the foldable, they wrote the equations for the trig functions in addition to drew triangles showign the given sides for each function.

Students used the following page inwards their notebooks to create problems from a pizzazz worksheet.

I withdraw maintain given my students intelligence problems whenever possible on their quizzes this year.  So many of the problems involve angle of elevation in addition to angle of depression, in addition to hence I printed an illustration off the meshwork of this for students to gum inwards their notebooks.

Next, I showed students the Gettin' Triggy Wit It video on YouTube.  You tin spotter this video here.  Because some of the lyrics are a flake difficult to understand, I gave them a re-create of the lyrics to gum inwards their notebooks.

Next, nosotros used sin, cos, in addition to tan to honour missing angles of triangles.

My students were a flake miffed that they had to just write these equations.  They thought I should withdraw maintain given them a foldable for these!

I did brand them a do book, though.  These pocket-size do books are 1 of my go-to ways to having them efficiently house do problems inwards their notebooks.

Each majority holds half-dozen do problems.  Here they are:

After practicing finding missing sides in addition to angles of right triangles, I decided to give the cast some hands-on do past times having them construct their ain clinometers.

I printed a clinometer template off of VirtualMaths.org for them to use.

You tin honour this template online here:
http://www.virtualmaths.org/activities/topic_shapes/theod2/resources/height-of-building.pdf

I mistakenly assumed that they would live on able to pose together their clinometers, withdraw maintain their measurements, in addition to finding the missing heights all inwards 1 50 infinitesimal cast period.  I was WRONG.  Somehow, it took my trig students almost forty minutes of the 50 infinitesimal menses to construct a unmarried clinometer.  With a template.  I'm notwithstanding non sure enough why this took that long.

Here's what the clinometers looked similar when they were completed:

I created this template for students to organize their piece of work inwards their interactive notebooks.  They were required to occupation trig to mensurate the acme of 3 dissimilar objects about the schoolhouse grounds.

After roofing basic trig ratios, it was fourth dimension to delve into the exciting the world of radians!  We started out past times discovering "What is a radian?"  I blogged almost this activity inwards exceptional concluding fourth dimension I taught trig, in addition to hence I'm going to ship y'all to that postal service for the step-by-step details.  I did brand a tiny alter this year.  Instead of tracing jounce lids to acquire a circle shape to cutting out, I borrowed my husband's novel security compasses.  I dear that my hubby in addition to I acquire to learn inwards the same schoolhouse in addition to percentage resources!

If y'all didn't click the link higher upwardly to read how this activity works, the pipage cleaner is cutting to the length of the circle's radius.  Then, the pipage cleaner is placed about the circumference of the circle to brand wedges inwards the circle.

If everything is done correctly, y'all *should* halt upwardly amongst 6 total wedges in addition to a partial wedge.  This represents the fact that in that location are 2pi radians inwards a circle, or 360 degrees.

We educate a proportion to determine just about how many degrees are inwards 1 radian.

After figuring out what inwards the the world a radian was, nosotros started converting betwixt radians in addition to degrees.  At the kickoff of the year, nosotros spent a span of days on unit of measurement conversions.  You tin read almost that here.  I was hoping that would pay off large fourth dimension when nosotros got to converting betwixt radians in addition to degrees, in addition to it did!  

We ended upwardly playing radians in addition to degrees nation of war to do our unit of measurement conversion fifty-fifty further.  I blogged almost that activity here.

To hash out sketching angles inwards criterion position, nosotros made a spinner.  Since the initial side is ever on the positive x-axis, nosotros glued the initial side arrow to the positive x-axis.  The terminal side of the angle was attached past times a brad in addition to hence it could easily spin.

My favorite affair to withdraw maintain students create afterwards putting together their angle spinners is to inquire them to brand a ninety marking angle.  Some students volition house their terminal side on the positive y-axis.  Other students volition house their termal side on the negative y-axis. Which is right?!?  This leads to a give-and-take of positive/negative angles.   We depict arrows on our papers every bit a reminder.

We wrote definitions for criterion seat in addition to quadrantal angles.

We finished this off past times completing 2 do books.  We did the do majority for sketching angles inwards criterion cast amongst DEGREES first.  I did this because students are most comfortable working amongst degrees.

Students were able to consummate these relatively easily.  There was a flake of confusion amongst some students on positive/negative angles in addition to remembering which goes clockwise in addition to which goes counter-clockwise.

In retrospect, I wishing I would withdraw maintain given my students some angles that were larger than 360 degrees or smaller than -360 degrees.  This would withdraw maintain led inwards to coterminal angles to a greater extent than perfectly!

When students finished this do book, they assumed nosotros were done amongst this science in addition to begged for their quiz.  Instead, I passed out the following do book: Sketching Angles inwards Standard Position inwards RADIANS.

Their initiatory off instinct, of course, was to occupation what they had learned almost converting betwixt degrees in addition to radians to convert all of the radians to degrees.  I told them to non create that YET.  There was an easier way.  They didn't fully believe me, but they did pose away their aspirations to convert away all of the radians for at to the lowest degree a lilliputian bit.  

I did tell them that if they didn't similar the method I showed them that they could convert the radians to degrees on their quiz.  I am happy to denote that non a unmarried pupil chose to convert the radians to degrees on their quiz.  They decided working amongst radians wasn't that bad afterwards all.  Yay :D  

Here's how nosotros did it.  

We already knew that pi was equivalent to 180 degrees.  So, when we're given something similar -2pi/3, nosotros tin withdraw maintain a -180 marking  angle in addition to dissever it into 3 pieces.  We desire 2 of those pieces.  And, in that location nosotros withdraw maintain an angle.  If y'all await at my angle, I did non dissever my -180 marking angle inwards to just 3 equal sections.  Oops.  I told my students that nosotros were "SKETCHING" angles.  It was okay if our sketches are non alone precise.  If I wanted them to withdraw maintain precise angles, I would brand them leave of absence the protractors.  

For pi/6, nosotros divided our positive 180 marking angle into 6 sections.  This meant each quadrant was divided into 3 sections. The invisible 1 inwards front end of the pi tells us that nosotros demand just 1 of these sections.  Bam.  Pi/6.  No degrees necessary.  After sketching each angle, nosotros did speedily convert the radians to degrees to come across if our answers made sense.  I did this to demo students that this method genuinely was working!  

After a few of these, they decided radians genuinely aren't all that bad.  I'm in addition to hence impressed amongst how my students withdraw maintain taken to working amongst radians this year.  It's been in addition to hence much amend than the concluding fourth dimension I taught trig.  I believe the argue this yr is going in addition to hence much smoother is because I'm making my students to a greater extent than responsible for agreement the "why" behind things.  Maybe it's because I, myself, empathise the "why" behind the things nosotros are doing better.

After sketching our angles inwards criterion position, nosotros began our give-and-take of coterminal angles.

Due to a lack of fourth dimension to create a novel activity, I decided to occupation the same coterminal angle menu sort that I created the concluding fourth dimension I taught trig.  This was non my master copy innovation because this menu sort went HORRIBLY concluding fourth dimension I used it.

Here's what I wrote almost this activity on my weblog concluding fourth dimension I used it:

"I had the brilliant thought to brand a menu sort for my students over coterminal angles. They were going to write the Definition of coterminal angles. Then, I was going to give them a page amongst all kinds of angle measures. They would sort them into groups that were coterminal amongst 1 another. Then, they would withdraw maintain a blank foursquare in addition to write an additional angle that was coterminal amongst the other angles inwards the group. 

This. Did. Not. Go. Well.

And, I'm non genuinely sure enough why. "

So, why did I create upwardly one's heed to occupation the same activity that did non become well?  Because I'm a dissimilar instructor instantly than I was 2 years ago.  Two years ago, I had my students write notes for how to honour coterminal angles.  Then, I gave them the menu sort in addition to laid them free.  

That was non my approach.  Instead, I gave my students the menu sort.  I didn't withdraw maintain them cutting apart the pieces YET.  Instead, I had them acquire into groups in addition to acquire 1 of our novel giant, grouping sized white boards that I got courtesy of my schools' foundation which awards grants to teachers.  

I asked each grouping to withdraw maintain the nine marking measures inwards the menu sort in addition to to sketch the angles on their dry out erase boards.  

Their piece of work was messy in addition to beautiful at the same time. 

This pupil decided he wanted a whiteboard all to himself.  

After sketching angles for a while, I asked students if they had noticed whatsoever similarities betwixt the angles. They genuinely hadn't because dissimilar students were sketching their angles a flake differently.  I gave them the Definition for coterminal angles to assistance them out a bit. Then, I asked them to await at their sketches in addition to determine which angles were coterminal.

I did give them a pretty large hint.  There are nine angle measures.  They tin live on sorted into 3 groups of 3 coterminal angles.

With this novel information, students kept working.  Some groups began to acquire a flake frustrated when they couldn't jibe their nine angles into 3 groups.

I took agree of this frustration in addition to used it to encourage my students to think almost what coterminal angles would withdraw maintain inwards common.  I started past times sketching a xx marking angle on the dry out erase board.  Then, I asked students to come upwardly up amongst 2 coterminal angles of that xx marking angle.  They came upwardly amongst -340 degrees in addition to 380 degrees.  Upon this discovery, I asked them how they could tell if 2 angles were coterminal based on this.  One pupil piped upwardly that coterminal angles were ever 360 degrees apart.  I challenged this.  Are they ever just 360 degrees apart?  Then, a pupil corrected the statement.  Coterminal angles are ever multiples of 360 degrees apart.

And, that's what is making the departure this year.  I am non giving my trig students facts to memorize.  I am giving them experiences that allow them to regain things for themselves.  And, it is making ALL the difference!

When I directed my students to await at the radian measures in addition to honour the coterminal angles, they 1 time again wanted to convert all of the radians to degrees first.  Again, I encouraged them to think almost how nosotros could bargain amongst the radians without turning to degrees.

We already know that coterminal angles are multiples of 360 degrees apart.  So, how many radians are they apart.  360 degrees is equivalent to 2pi, in addition to hence coterminal angles are also multiples of 2pi apart.  So, nosotros did some review of adding in addition to subtracting fractions, in addition to nosotros were good on our way.  No degrees needed!

Up next: Reference Angles!

The initiatory off epitome I gave students every bit a reference was from TutorVista.com.  The 2d epitome I gave my students was from RegentsPrep.org.

On the within of this booklet foldable, I had students sketch the angles (given inwards both degrees in addition to radians!) in addition to honour the reference angle.  I am happy to written report that my students did non inquire to convert the radians to degrees!!!

In grooming to motion toward the unit of measurement circle inwards the following unit, I ended this unit of measurement past times having students honour the sine, cosine, in addition to tangent of a betoken on the coordinate plane.  This pose together in addition to hence many of the concepts nosotros had learned inwards this unit of measurement in addition to the previous unit.  It's in addition to hence exciting to come across all of the pieces start to autumn together.  

Here are the step-by-step directions I gave my students

I gave them a do booklet to, well, give them some practice.

My students were quick to betoken out that the graphs for our concluding 2 examples were upside downwards inwards the book.  Oops...

After students took their quiz over finding the sine/cosine/tangent of a point, I assigned them this task:

Create a foldable that summarizes whether sine, cosine, in addition to tangent are positive or negative inwards each quadrant.  They were quick to inquire how they should create this?  I but told them to alternative a betoken inwards that quadrant in addition to honour the sine/cosine/tangent value.  I didn't give them whatsoever to a greater extent than guidance than that.

When I studied trig inwards high school, I was taught the "All Students Take Calculus" mnemonic device for remembering which trig functions were positive inwards which quadrant.  I am trying my hardest to non occupation a mnenomic device for this at all this year.  I desire my students to know why sure enough trig functions withdraw maintain sure enough signs.  In the past, I taught it to my students every bit a affair to memorize.  It's non something that has to live on memorized.  It's something that tin live on understood.

To my trig students of 2 years ago, I am so, in addition to hence pitiable for taking away in addition to hence many chances for y'all to create some thinking on your own.

And, that wraps upwardly Unit 2 of Trigonometry.  You tin honour the files for these interactive notebook pages here.  (I withdraw maintain a few files on my schoolhouse information processor that I volition upload on Monday!)  

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