Math = Love: Trigonometry - Unit 1 Interactive Notebook Pages 2016-2017

## Thursday, October 13, 2016

### Trigonometry - Unit 1 Interactive Notebook Pages 2016-2017

Today I want to share my interactive notebook pages for our first unit in trigonometry.  Our first unit of the year is a review of the algebra and geometry concepts needed for success in trig.

Like with every unit, we start out with a unit divider.  This lists all of the SBG skills for the unit.

This year, I opted to do unit conversions as our first review topic in trig.  I chose to do this based on the fact that we will be converting between degrees and radians later.  I want to make sure my students understand how units cancel before we start converting "weird" units like radians.

This is actually a foldable I used with my Algebra 1 students last year.  I blogged about it here.

To practice some real-life unit converting, I had my students go out in the lobby and measure their speed doing various activities such as walking, running, hopping, or skipping.  Then, we converted our speed to miles/hour and compared our speed to the speeds of various animals.

Here's the animal speed chart I gave my students:

Radicals are something that get covered in depth in Algebra 2, but some of my students took stats last year which means they haven't seen radicals for a year.  Another student is currently enrolled in Algebra 2 along with trig, so she hasn't covered radicals either.

I always love to emphasize radical vocabulary:

I found a simplifying radicals puzzle online for my students to complete and glue in their notebooks:

I made a poof book for my students to use to practice rationalizing the denominator.

Here are the problems we worked through together:

Here is our operations with radicals foldable:

My students chose to only do one example under each flap.  I guess that means they actually remember stuff from Algebra 2!

Instead of just telling my students that the sum of the angles in a triangle is always 180 degrees (something I hope they remember from geometry!), I decided to have them cut out a triangle and illustrate it themselves.

We folded one angle down to the other side to create a fold that was parallel to the side we were folding towards.  Some students really struggled with this step!

Then, we marked where each angle ended up after being folded.

If students followed the directions properly, all of the angles should have formed a straight line!

Finally, I asked them what geometric concept this proved.  This was definitely not an original idea.  I found an example of folding a triangle to illustrate the fact that the sum of the angles in a triangle is 180 degrees in this blog post.

To review this concept, I had students find the missing angles in this diagram that I found online.  Here's a link the original source.

To review the Pythagorean Theorem, I had my students work through this book from Jessie Hester.  I love how this shows students a visual of what the Pythagorean Theorem looks like.

I decided my students needed a Pythagorean Triples reference page in their notebooks to go along with the posters I have hanging in my classroom.  Here's a link to download the posters! Here is the page.  You will notice that 6, 8, 10 is not included on the list because it is related to 3, 4, 5.

To give my students a bit more practice with word problems, I typed up these Romeo and Juliet themed problems.  These are slightly modified from this Weebly site.

I'm a rebel and chose not to teach the distance formula since it's way easier to just use the Pythagorean Theorem instead.

Instructions for Finding the Distance Between Any Two Points on the Coordinate Plane:

We made a poof book of practice problems.  The problems I created in this book were just random points.  That was a mistake...

Here's the first problem that ended up being a right triangle with sides of length 2 and 8.

Here are the second and third triangles with the same side lengths!!!  Note to self: Try out the problems before giving them to your students!

Our last topic of the unit was special right triangles.  The page I'm showing you FIRST is actually what we did LAST.  Yes, I'm that teacher who makes my students discover the pattern for themselves.  Here's the summary we wrote as a class AFTER we discovered the relationship that holds true for all 45-45-90 right triangles.

Here's the first thing my students saw.  Yes, it's a page with 12 squares that are cut by a diagonal.

Students had to determine the angle measures and use the Pythagorean Theorem to solve for the diagonal.  They continued to keep chugging along with the Pythagorean Theorem until someone in the class noticed a pattern.

After about the first four problems, students started to notice something peculiar.  Soon, they were racing through each question.  No Pythagorean Theorem needed.

We really did have to stop and think about how to do the problem when we were given the diagonal of the square instead of the length of the sides.  But, we persevered and figured it out!

To give my students some practice with 45-45-90 special right triangles, I gave them this task to do in small groups.  I found this task in the Open Curriculum Task Database.  I loved listening to the conversations my students had as they struggled through this problem.  And, I mean "struggle" in the best possible way!

Finally, I wanted students to discover the pattern for 30-60-90 triangles the same way we discovered it for 45-45-90 triangles.  Here's the summary sheet we filled out AFTER discovering the pattern ourselves:

Here are the problems I posed for my students in order to help them see the relationship for 30-60-90 right triangles.

For each equilateral triangle, students had to use the Pythagorean Theorem to solve for the altitude of the triangle.  We did this over and over and over until the pattern began to emerge.  Students were on a lookout for a pattern from the get-go because of their experience with the 45-45-90 activity.

You're probably not surprised that I made a poof book for my students to practice special right triangles.  I'm kinda obsessed with these mini-books!

I found this dragon puzzle online, and I fell in love with it.  Each of the triangles is a special right triangle.  I'm not sure of the original source, but I found it online here.

My students got really involved in this problem, but they really complained about the size.  I downsized it to fit in our notebooks, but there was so much going on in the problem that they soon ran out of room to label sides and angles.  In the future, I'd do this problem again, but I think I would print the dragon on an 11x17 sheet of paper so students can write ALL over it.

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