Saturday, January 28, 2017

Proving Math Formulas to High School Students

I am teaching PreCalc this year.  We are knee deep in our trig unit and I am planning to teach Trig Angle Addition formulas on Monday.  I seriously dread this day because I don't see any motivation for it.  I mean we have a calculator to figure out what sin 75˚ or cos 165˚ is...who cares about the exact value???

So, I checked around the internet to see if I could find some motivation and I seriously still haven't found too many reasons why we are still actually teaching this topic, BUT I did find some motivation for me!  I found several different (but similar) proofs of the formulas:

sin(x+y) = sin x cos y + cos x sin y

cos(x + y) = cos x cos y - sin y sin x

Can I tell you a secret?  I never had any idea where these formulas came from.  As a math teacher, I'm embarrassed to say that, but it is true!

So, I decided to give this proof a try during class last Monday.  It went about as I expected - some students appreciated the proof...some students' eyes started to glaze over.  But, I felt like I had done my duty and showed them some of the the beauty of mathematics.  Formulas that we use come from unlikely places - someone had to think of them...they didn't just appear out of thin air.

Here are links to a few products that I have that encourage students to see the "proof" in mathematics.  What proofs do you show your class?

Friday, January 20, 2017

Using a Desmos Card Sort in High School Math - Ambiguous Case

We are a 1:1 ipad school and I try to incorporate the iPad into class whenever it works.

I have used Desmos for graphing and to make a Christmas graphing project (see post here: Using Desmos to Graph).

But, I just recently noticed a new feature [new to me at least!] on the teacher side of Desmos.

You can make your own Card Sort!  I am currently teaching the Ambiguous Case in PreCalculus.  Ugh....seriously complicated and sometimes difficult for students to understand.  Plus...I was getting observed during this lesson :)

Sunday, January 1, 2017

Fun Systems of Equations Activities

I enjoy teaching systems of equation in Algebra One - it is an important skill that students need to understand for future math classes.  But, there is only so much I can say!  Students need and should have a wide variety of practice on this topic.

A new approach that I've used lately is called Color My Math.  Students solve problems and then color according to a pattern given.  In the end, they make a cool design or picture.  My students love the opportunity to color :)

Check it out in my TPT store...

Another way my students love to practice is by using Task Cards.  Why - it seems the same as a worksheet, but hey...put one problem on a card with a cute graphic and they are busy for the entire 45 minutes :)

AND...if I put QR Codes on the task cards that they can scan with their phones to see if they are correct...Awesome!

Check out these cute solving systems task cards.

Are you teaching Systems of Equations?  Whatever level you are teaching - Algebra One, Algebra Two, PreCalculus - there are activities below that could help make your teaching more fun and easier!  Check them out!