I’m posting this at around 8 o’clock, which means I’m still up here at the school at 8:00 PM! Therefore, I’m keeping it short because I’m tired and ready to go home, if I’m being quite frank here.
Algebra II learned how to solve absolute value inequalities algebraically using a 4-step process.
Geometry had a fun calculator activity.
In both classes today, we built a little more on topics that we discussed yesterday.
For Algebra II, we looked at how to solve absolute value inequalities using a graph or table. This built on yesterday’s in the sense that we still had to remember how to graph and find where the function is some value, but now we will need to use those values to write an inequality. Enter “Legs” and “Vertex”. If what we are wanting can be found with the “legs” of the function, then we have an “or” inequality. If what we are wanting can be found with the “vertex” portion of the function, then we have an “and” inequality.
In Geometry, we took classifying angles to another step higher. Now, we know what complementary, supplementary, and verticals angles all are, in addition to angles being adjacent and/or forming a linear pair. This is all technical jargon that can best be seem in the notes. So, without any more adieu, here they are below.
I’m not sure what all to say today other than the fact that both classes talked about something that was bent. In Algebra II, it was the absolute value function and in Geometry, we talked about angles.
With that in mind, let’s get into the content. As mentioned above, we looked at solving absolute value equations two different ways. The first way was by graphing, while the second way was algebraically. When doing the second way, remember to get the absolute value “stuff” by itself and then if the resulting number on the other side of the equal sign is positive, you can split it into each a positive and negative answer. If not, then there is probably no solution.
For Geometry, we learned how to draw, measure, and name angles. Then we used the Angle Addition Postulate to find various values, whether it was the x or an angle, we could do it. Also, that word bisector came back to greet us again.
I think it is safe to say that there is a love-hate relationship with Mondays, at least in the world of academia. While Monday means we have to get up and come to school, it also means that there is one less day before being out for the summer. Besides, if no one worked on Monday, then Tuesday would become our proverbial Monday that no one likes. Nonetheless, it’s time to get back to the grind…who knows, if we do well, we may be rewarded with a three-day weekend coming up!
In Algebra II, we looked at transforming the absolute value function using a, h, and k. We “discovered” their impacts on Friday, but today we actually put them into practice. They are so AWEsome because they allow us to graph these functions without even needing a calculator! The sooner we befriend them, the easier our life will be.
In Geometry, we looked at measuring segments. This means the Segment Addition Postulate was introduced along with the topics of a midpoint and bisector. In short, the thing to remember is that “Part + Part = Whole”.
The things that we find and think to do when we get bored are unbelievable. I was bored over Christmas break and have unearthed my percussion set that I had in middle school band (which alone makes the set 14 years old!) but haven’t practiced on since I was a sophomore in high school (8.5 years). So, this great idea struck me – Let’s dust off our skills and play in front of 80 students and look like a fool! However, I think it went pretty well, if I say so myself, other than the 2-3 times I messed up in a 30 second song 😀
In Algebra II, we shifted gears to look at our first family of functions – the Absolute Value functions. Today was more of an exploration exercise to see what happens when different parts of the equation are changed. This leads to the discovery of a, h, and k, who are the bestest of friends and will stay with us throughout the semester taking us on all kinds of journeys.
- a – shape (stretched or widened AND normal or flipped)
- h – horizontal movement (left or right)
- k – vertical movement (up or down)
In Geometry, we got into our first “geometry”-esque material. We learned about naming points, planes, lines, segments, and rays. With so many topics, it’s hard to put a summary here for those, so see the notes for the details.
Depending on the class you are in, you either heard enough of the word “Inequality” or “Equality” for a year…or at least that’s what YOU think *Evil Laugh*. That’s because in Algebra II, we looked at compound inequalities, which means you have two inequalities that you have to worry about. The general rule, however is that the “and” inequalities mean that x could be anything between those two numbers, while the “or” inequalities mean that they have to be outside of that range.
On the other hand, in Geometry, we had a good detailed looked at different properties of equality and properties of congruence. Well, I maybe exaggerated the “detailed” part, but you at least should know enough definitions to do a basic proof with justifications. The way to think of a proof is like having a three year old constantly asking you why you did something and you having to give a true answer (“because I just did” isn’t acceptable).
Even though you may be in high school, you need to be thinking about what you want to do after school is finished. That was the motivation behind today’s warm-up. Also, I liked hearing your most and least favorite things about being in a math class. Unfortunately, I have some bad news for y’all – Math requires work, it’s sad but it’s sooo true. Also, if you’re struggling with something, ASK!! Don’t do like me and bang your head into the wall because then you just may end up with my twisted sense of humor…you’ve been warned!
As far as classwork goes, Algebra II looked at solving linear inequalities and graphing their solutions on a number line. These pretty much work like normal equations, but you just have one more thing to keep track of – the sign! See the notes if you need more details or a review of what was covered in class.
For Geometry, y’all just finished the assignment that was started on the first day of class over solving basic equations. This should have been turned in before you left class, so that means NO Homework!
Notes – Lesson 1.2 Solving Linear Inequalities
Assignment – Day 2 A – Linear Inequalities
I hope everyone enjoyed their much-deserved Christmas break over these past 2.5 weeks! While it may not be a new school year, it sure does feel like it, but I guess that’s what you get when you are on a semester basis. With that being said, that means the likes of Math Models has gone away and is replaced by Algebra II and Geometry. So, without further adieu, here’s what you may have missed today:
Usually, I will break this section up into their respective class, but today is one of the rare occasions where we pretty much covered the same thing in both classes. What is that thing? I’m glad you asked! We started simple by trying to solve an equation for “x” because I know y’all have a few cobwebs that need to be knocked off before getting to the good stuff. The thing to remember here is to do the opposite of what the current operation is to “undo” the equation (i.e., If it is x + 1 = 2, you would SUBTRACT 1 from both sides), just like you would probably do if your parents told you not to do something. For all the deets, see the notes for your respective classes: