Synthetic is better!

If you do anything with cars, you’ve probably heard about the big push for using synthetic oil in vehicles. It runs cleaner, lasts longer, etc. But have you heard of synthetic division in regards to polynomials?

In Algebra II, we learned just that – Dividing Polynomials using Synthetic Division. We we started learning it, most were giving me the “stank face” as if to say, “And how is this any easier?” But, by the time we were finished, I think everyone came around to see that this really is easier than long division. If you still don’t know what I’m talking about, see the notes.

In Geometry, we looked at Parallel Lines cut by a Transversal. This is the second half of our third unit because I mean, did you seriously think you’d get away with not having any “math” in a unit? It’s somewhat hard to explain in words, so see the notes for the deets.

Flashback Monday

We’ve all heard of flashback Friday, but have you heard of Flashback Monday? If not, then you were obviously not in my class today.

In Algebra II, we looked at long division. For many, this is where the flashback comes in because most haven’t seen long division since their elementary days. But, SURPRISE! It’s back! There’s not really much to say on this one other than that it’s one of two methods to divide polynomials.

In Geometry, we had a practice day to combine everything we’ve done these past three days into one nice, complete package. This meant looking at inductive reasoning, conditional statements, converses, inverses, contrapositives, and biconditional statements. Again, there’s not much to say here, so see the notes.

Power Rules!

We all like to have a little bit of power over something, right? Well today, we have had just that…power over powers.

In Algebra II, we added one more exponent rule to the mix, bringing our grand total to 4 exponent rules. The new rule today was called “Power to a power”. I told them this clever saying that when you have a “Power to a power, you multiply the powers.” There’s even a little hand signal that goes along with it. After learning that new rule, we combined all four rules and had different moving pieces in the problems. See the notes for more details.

In Geometry, we looked at conditional statements and their variations. We saw that the converse is of the form q -> p, the inverse is of the form ~p -> ~q, and the contrapositive is ~q -> ~p. That’s all on that topic too, so see the notes for more details.

Exponentially True

While something may not be exponentially true, one thing that is for sure – we have more Fridays left in the school year than Mondays.

In Algebra II, we started our new unit by looking at multiplying and dividing monomials and then dealing with negative exponents. There are three basic rules to remember from today’s lesson and if you can remember those, you’ll be doing pretty good.

  1. If you are multiplying like bases, then you add exponents.
  2. If you are dividing like bases, then you subtract exponents.
  3. If you have a negative exponent, you move it to the opposite side of the fraction.

In Geometry, we started our Logic and Parallel Lines unit today by looking at patterns, writing conjectures, and disproving those same conjectures. This is to get us set up for conditional statements, which we will get to have fun with over the next few days.

Day Late and a Dollar Short

If I wait any longer to put up the notes from Friday’s class, that’s just what I very well may be – a day late and a dollar short due to having to get some caffeine in me.

Anyways, in Algebra II, we looked at the last of the new material for Unit 2, which involves our fourth and final way of solving a system of equations – Matrices. This method is usually the most beloved because it can be 100% done on the calculator, except for the small part where you have to write out the matrix equation. Just remember that when you put it in the calculator, you have to raise the coefficient matrix to the -1 power.

In Geometry, we had a calculator activity that helped us to review the concepts taught in Unit 2. So, that meant two things – 1.) No Notes and 2.) No Homework. You’re Welcome.

Algebra II Notes – Lesson 2.7 Solving Systems Using Matrices
Algebra II Assignment – Day 7 A – Solving Systems Using Matrices

Scaling Mount Everest

When you introduce a third unknown and equation into the mix of things, that’s exactly what it seems like we are doing…climbing Mt. Everest. How am I ever going to solve that?

Well, if you were in Algebra II today, you should know the answer now. We need to modify the equations and get them to play nice with us. Then, we can conquer even the most difficult of system of equations! Tomorrow, things are about to be breezy now from the top!

In Geometry, we had a practice day over all the concepts covered in the 2nd unit. It was a long notes day, but that’s about the only way to get a whole unit into one lesson.

It’s Hoppin’ Up in Here!

We are getting the heat cranked up in the Math hallway! That’s the reason for posting these notes so late – Tutorials were hoppin’!

Anyhow, in Algebra II, we had a review day of sorts in the sense that we looked at solving systems of equations using all three methods that we have talked about thus far. That is, solving by either graphing, substituting, or eliminating.

In Geometry, we looked at different ways to write equations of lines and then graphing those lines on the coordinate plane. This was the last day of new material. So, tomorrow is a Practice Day and Friday is a calculator day.

Sleep Works Miracles!!

Did you know that the average person sleeps for 1/3 of their life? So if you live to be 75 years old, you would have spent 25 years doing nothing but sleeping! After not getting a lick of sleep Sunday night, I’ve come to the conclusion that those 25 years would be well spent and much needed.

In Algebra II, we looked at yet a third method of solving a system of equations – Solving by Substitution. This is just like it sounds, you will substitute one equation into the other and then solve. There’s not really too much more I can say because it’s that simple, so see the notes.

In Geometry, we looked at Slope. Then we took that slope and applied it to see if a pair of lines were parallel, perpendicular, or neither. Remember, parallel lines have the same slope, while perpendicular lines have opposite reciprocals for their slope.