Unit 1: Section 0: Vocabulary

Unit 1

Section 0: Vocabulary

Welcome to the first unit, scholars! In this unit, we will be discussing the foundations of geometry. By far, the most important part of mathematics is your understanding of vocabulary! That's right; your understanding of the meanings of words is the single most important skill you can have, so thank your English teachers now for the language skills that you have that will help you pass this Geometry class.

That being said, let's dig into some vocabulary. Shall we...

Plane

A plane is a flat surface with infinite length and width, and no height.

Now, it is quite easy to determine whether a plane is 1D, 2D, or 3D. We just look at the definition, which clearly states that a plane has infinite length and also width, and no height. Well, I count: one, two dimensions. Planes are 2D.

Unfortunately, there are very few true examples of planes in the world.

Let me give you an example:

Foundations

When someone constructs a building, they need a flat surface to build on. This surface is called a foundation. This is a limited example, since foundations do not extend forever. However, since they are nearly perfectly flat by design, they serve well as examples of a plane. See below:

Figure 1: A building's foundation

When two or more points are on the same plane, they are called coplanar points. Naturally, when points are not on the same plane, they are called non-coplanar points.

Point

A point is an exact location in space.

If you ever wondered if a point is 1D, 2D, or 3D, it is none of these; a point has no dimensions. It is simply a location. Some variations on the vocab word point are:

• Endpoint
• Midpoint
• Center Point
• Intersection Point
• Vertex
• Collinear Points

Let me give you an example:

Locations on GPS

When you want to walk or drive somewhere, you use your phone or a GPS app. My old grumblings aside - about how we have no sense of direction and are therefore crippled by the very technology we invented in order to make our lives simpler (I'm rambling now) - this illustrates a handful of extremely useful Geometric objects. The first of these is a point. When you type in a desired location, your app drops some kind of marker - a pin, a dot, etc. - on that location. This is a point. Does that pin or dot have any length? Of course not. Does it have any width? Of course not. It only exists to serve as an indicator of that place's exact location in space. See below:

Figure 2: Hogwarts on Maps

Line

A line is an object that is straight and infinitely long.

Lines extend forever in both directions. A line happens to be 1D; that is to say it has one dimension. It has an infinite length, sure, but does it have any width? Of course not. Same goes for height.

When two or more points are on the same line, they are called collinear points. Naturally, if points are not on the same line, they are called non-collinear points.

Unfortunately, there are very few true examples of lines in the world.

Some variations on the vocab word line are:

• Line Segments
• Rays

Line Segment

A line segment is a part of a line that is bounded on both sides by endpoints.

Unlike lines, line segments do not extend forever. This means they have a finite length. They are still 1D, though.

Let me give you an example:

GPS... Again

When you finally get around to setting our for Hogwarts - from your home in, say, 4 Privet Drive in Bristol, your phone or computer will give you a nice little layout of all the roads and turns you will have to take. Most of these small road paths that you take are line segments. They have starting points and ending points, and they are laid out in a straight path. See below:

Figure 3: Google Maps directions from 4 Privet Drive to Hogwarts

Figure 4: A section of the directions from Figure 3

The parts of Figure 3 that are important here are the sections of road on Privet Drive and Fulford Road, as these are straight paths with clear endpoints. This makes both of these sections great examples of line segments.

Ray

A ray is a part of a line bounded on only one side by an endpoint.

No, I am not talking about the baseball team, or of undersea life, or of the famous pianist and songwriter famously portrayed by Jamie Foxx in 2004. I am speaking of a geometric object. A ray is something between a line and a segment. It has a single endpoint (like a segment) and the other end continues on forever (like a line).

Let me give you and example:

LASER Pointers

Have you ever used a LASER pointer? Have you noticed how the beam seems to go on forever? That is, if it a quality LASER, since some crappier ones are rip-offs that are made with not-so-real LASER technology with weaksauce ranges? If you have, then you've probably asked yourself, "if there were no wall here (or building, or person, or whatever), would this beam actually go on forever?" Long story short, in a perfect vacuum - like space - the answer is yes. This is a perfect example of a ray, since it has a definite point of origin (the device itself) on one end, and since it continues forever in the other direction. See below:

Figure 5: A long-range LASER pointer

Intersection

An intersection is the point (or points) that two geometric objects have in common.

You may be wondering if an intersection is 1D, 2D, or 3D, and honestly, that will depend entirely on what the objects are that are intersecting. I think this one would be easiest to describe using examples.

Let me give you an example:

Street Intersections

When we see intersections in the street, this most closely resembles an intersection of lines. This is because these two 1D objects are legitimately crossing, which means that they are going to have some point or points in common. Since they are both our equivalent of lines, and therefore would have no width or height, then their intersection will not have width or height either. It is a single point. This is a 1D intersection. See below:

Figure 6: The intersection of Mill Rd and Fire Rd is a single point

Mouldings

In houses, there are objects called mouldings. These are decorations that cover the places where a floor and wall (floor moulding) or a ceiling and wall (crown moulding) meet - hint: "where two things meet" is a very easy way to spot intersections; see also "where two things overlap". We discussed in a previous definition how a flat surface is our best example of a plane, and so the floor, wall, and ceiling are all planes - 2D objects. Where they intersect is usually some form of crack, which is why we use a moulding in the first place; that crack is in the form of a line. This is a 1D intersection. See below:

Figure 7: Moulding is used to cover the lines where walls and ceilings meet

Lighting Gels

When you work in theater production, sometimes you have to create colored light. To do this, you use color gels over your lights to give it a tint of color. A gel is a sheet of translucent paper/plastic that is tinted a color and then secured over a light. Most of these come in the primary light colors - red, green, blue - and sometimes you have to get creative to make shades like purple. This is when overlapping two color gels over a single light becomes very useful (see? called it: "overlapping" = intersection). These two gels represent planes, since they are both flat surfaces, and where they intersect is also another flat surface or plane. This is a 2D intersection. See below:

Figure 8: Assorted overlapping lighting gels

Angle

An angle is a geometric object formed by two rays or line segments sharing an endpoint.

You may be wondering if an angle is 1D, 2D, or 3D. Let's consider what it is made of: two line segments or rays that share an endpoint. Since this is the case, an angle has to be at least 1D. But, let us also consider that there is some kind of, well, angle between them, so they aren't "in line," so to speak. Since this is how angles are made, then we must conclude that angles are 2D

One important thing about an angle is that the shared endpoint is called a vertex. So, to be clear, a vertex is a specific type  of point.

Let me give you an example:

Hinges

Every pivoting door has a hinge that secures it to the wall and also enables it to move. This hinge is a great example of a real-world angle. A hinge simply connects two pivoting pieces of metal to a single rod, and that rod serves as the vertex of the angle. The pieces of metal are the two segments that make up the angle, which we will call the sides of the angle. See below:

Figure 9: A working hinge.

Attache Work

Make sure that you practice your vocabulary skills, and don't forget to take the online quiz for this section.

Syllabus: Expectations For The Year

Syllabus

Expectations For The Year

This first post is simple; it is an online version of the syllabus I will hand out in class, and this online portion just serves as a reminder of all of the things I will be going over from the syllabus. For any references necessary, I will also attach a copy of the syllabus to the class Weebly and Blackboard pages.

Who Am I?

I am Mr. Sciacchitano. For those parents reading, that's Andrew Sciacchitano, and I am most commonly called Mr. Shock (or sometimes Coach Shock). I can be found in classroom 1025, where I hold class and tutoring sessions. My email address is andrew.sciacchitano@tuhsd.org, and my office phone number is (623) 478-4494, so that you may contact me in the case of any questions or concerns. I look forward to a year full of cooperation and success.

Course Goal And Description

The goal of this course is to demonstrate mastery on formative and summative assessments along with the End of Course Assessment with a 60% or higher.

This Geometry course is a mastery-based program. The course is divided into key objectives, written in the form of an "I Can" statement. Students will be taught the math content and skills using the "I Can" statements and will practice the material both inside and outside of class. Once complete, the students will need to demonstrate mastery of the "I Can" statement on a formative assessment. After all of the "I Can" statements in a given unit are completed, students will take a unit summative assessment requiring completion of all of the statements. Class mastery will be recorded on a chart in the classroom.

Course Outcomes

Topics that will be covered first semester include:

Unit 1: Geometric Foundations

• I can apply the Segment Addition Postulate and the Angle Addition Postulate.
• I can determine the measure of complementary, supplementary, linear pair, and vertical angles.
• I can apply properties of segment and angle bisectors.

Unit 2: Parallel and Perpendicular Lines

• I can identify the relationships in space between lines, planes, and angles.
• I can identify and solve for missing angles formed by transversals.
• I can apply theorems about parallel lines and perpendicular lines.

Unit 3: Triangle Congruence

• I can classify and solve for missing angles in triangles.
• I can apply properties of isosceles and equilateral triangles.
• I can prove triangles are congruent.

Unit 4: Similarity

• I can determine if triangles are similar using similarity postulates and theorems.
• I can solve problems and prove relationships in geometric figures.
• I can identify and apply properties of dilations.

Unit 5: Triangle Properties

• I can apply properties of perpendicular and angle bisectors.
• I can apply properties of medians and altitudes of triangles.
• I can solve problems using properties of triangles.

Topics that will be covered second semester include:

Units 6: Right Triangles and Trigonometry

• I can identify and write a trigonometric ratio and explain their relationships.
• I can use trigonometric ratios to solve right triangles in applied problems.
• I can apply trigonometric ratios to solve special right triangles.

Unit 7: Circle Concepts

• I can calculate the measure or length of an arc and its related angle.
• I can apply properties of angles to calculate or construct inscribed and circumscribed circles.
• I can apply properties of chords, tangents, and secants.

Unit 8: Transformational Geometry

• I can identify and describe a transformation in words or using an equation.
• I can construct a transformation and determine its new coordinates.

Unit 9: Properties of Polygons and Quadrilaterals

• I can identify and apply properties of quadrilaterals and parallelograms.
• I can apply properties of rhombi, rectangles, and squares.
• I can apply properties of trapezoids and kites.

Unit 10: Three-Dimensional Measurement

• I can calculate the surface area of a figure and use to model or solve relevant problems.
• I can calculate the volume of a figure and use to model or solve relevant problems

Grades

Grades will be on a standard "A-B-C-D-F" scale, and will be weighted as follows:

• Homework/Other Assignments      13%
• Formative Assessments                  23%
• Summative Assessments                54%
• End of Course Assessment             10%

Other Topics of Note

Tutoring

Tutoring will be offered on Thursdays from 2:15 to 3:30 or by appointment ONLY. Tutoring buses are available on Tuesdays and Thursdays to accommodate this schedule.

Formative and Summative Assessments

Students may take an alternate version of a formative assessment (quiz), and are encouraged to do so when needed. This is to be done before the unit Summative Assessment. Any time after, the formative remains as it was in the gradebook.

Students may perform corrections on a summative assessment. This is to be done no later than two weeks after the summative assessment was assigned. Any time after, the summative remains as it was in the gradebook.

Absences

A student may make up formative or summative assessments missed due to absences, but is subject to the same deadlines as those above.

Homework

All assignments in a unit are due before the summative assessment for that unit. Late work will result in the loss of half of the credit.

Necessary Resources

It is of the utmost importance that you prepare yourself for class. In order to properly do so, you will have to acquire the following items:

• Notebook: you will need a notebook in this class. In this notebook, the first five pages must be used as a glossary/index of useful definitions
• Folder/Binder: This must have pockets! This is to hold on to all of the handouts and notes from class.
• Pen/Pencil/Highlighter/Marker: These are essential for taking notes and for labeling them.

Rules and Procedures

All La Joya Rules and procedures apply. Please be aware of these specific topics, as they will be consistently enforced by staff:

Sweep: Student's entire body is in the door before the bell finishes ringing.

Bathroom Passes: No passes will be issued the first and last ten minutes of class, as well as during lunches.

Headphones: Headphones are patently not allowed during class (see Student Handbook).

Dress Code: Inappropriate dress will result in student reporting to Principal's office, can result in OCR (see Student Handbook).

ID's: Student identification cards are to be worn and visible at all times by students (see Student Handbook).

Phones/Technology: Unapproved technology, such as tablets and smart phones, are patently not allowed during class (see Student Handbook).

Attached Work

Now that you've read all of the information for my class, check your understanding with the online quiz on the Weebly page.

Introduction: What To Expect From This Blog

Introduction

What To Expect From This Blog

Welcome to the blog for Mr. Sciacchitano's (or as you no doubt call him, Mr. Shock's) Geometry class. This entry serves as an introduction to the kinds of things you can expect from me - Mr. Shock - and this blog, this year. I will start with the purpose and mission of this blog.

Purpose and Mission

This blog exists specifically to give students a pseudo-textbook of geometric fact, and to serve as a means to stay connected to the class even on days when they are absent. The mission of this blog is to instill in students a stronger sense of connection between all the material we will learn this year, as well as provide a (hopefully) interesting learning platform for them.

The mission of the blog is simple: education for all. Whether a student is healthy or sick or home or on vacation or working or busy or a babysitter or a parent, they can learn Geometry. This blog exists as a means of learning geometric content at home or work, or just life. No more excuses; just learning.

*      *      *

The purpose and mission can seem a bit sweeping, so I will break it down for you. The next part of this introduction consists of the expectations of both myself - the teacher - and of you - the student.

Expectations Of The Teacher

As the teacher, it is my job to teach, and you can still expect that every day in the classroom. The teaching itself will, however, look a bit different than you're used to. As follows are a list of things I will not do as your teacher:

Things I Won't Do

1. Give Definitions: We're all big boys and girls with the power to look things up on our own. Plus, all important definitions will be on this blog, so I will not be taking class time to read a definition from a math glossary.

2. Do A Problem Start-To-Finish: As you are all (or most) in tenth grade at this point, there exists a certain expectation that you can pay attention and follow along, and that you can do basic algebra. In class, if an example is too difficult, I will of course help break it down with you, but I will not be spoon-feeding anyone any answers.

3. Issue Quiz Re-Takes: You are perhaps used to the notion that, in math class, you are allowed to take a quiz or assessment more than once. I do not believe in this. If you did not perform to your best abilities, then study up and ask for another version of the quiz; I will not re-issue a quiz.

All of this being said, it is of course expected that I do my best to ensure your learning and the expanding of your mind. What follows is a list of things I will do as your teacher, to the best of my abilities:

Things I Will Do

1. Real-World Examples: The world is full of real-world Geometry examples, and as often as I can, I will relate all of this class' content to you in a manner that reflects that, using as many examples from real life as possible.

2. Explain Concepts: Being ignorant of  a definition is never an excuse; however, not knowing how to apply that definition in order to solve problems is a difficulty that I can level with. I will always explain how a concept works in class if it is needed. It should be noted, however, that the ideal time to get help with conceptual things is during tutoring sessions.

3. Offer Test Corrections: I understand that from time to time you are not in your best state of mind for a test, and so you will occasionally earn a grade on a test that you did not want. In those times, I will offer the opportunity to do test corrections. These corrections must be done on your own time after school on days that have tutoring sessions.

Expectations Of The Student

First and foremost, you are a part of the Lobo PACK here at La Joya Community High, and as such, you are expected to follow the guidelines of PACK:

PACK

Positive

This means that your attitude, behavior, and decisions are positive. We understand that everyone has bad days or even weeks, but the manner in which you carry yourself on the campus should be a positive one, and this is a daily decision you make.

Accountable

This means that you are responsible for your actions and behavior. This also means that, as a student, there are people that you "answer to." These people are teachers, administration, coaches, parents, and even study partners or groups. Accountability means that there are people looking out for your best interests and that you are working with them.

Connected

This means that you are a part of the greater La Joya community, and beyond that, the community of Avondale and Maricopa. Participating in sports, drama, choir, band, open-mic nights, community events, community service, clubs, youth groups, etc. is expected of you. It is important that you become an active member of your community.

Knowledgeable

This means that you know what you are doing, and that you know the school rules, at all times. Having this understanding, you would never pull your cell phone out in class, because you know that there is a rule against it in your Student Handbook and you also know that the consequence for disobeying this rule is a referral for misuse of technology.

As the student, it is understood that you are trying to understand the content, as well as learn skills such as problem solving and critical thinking. Your actions as a student should in all ways reflect this desire to learn and think. As such, here are the expectations of you, the student:

Expectations

1. Come Prepared: In the next post, titled "Syllabus," you will read of the three basic necessities for this class. It is your responsibility to acquire or purchase these basic necessities and bring them to class every day. I will not provide notebooks, pencils, or folders for students. This is your job.

2. Stay Up-To-Date: This blog will have every lesson, vocab word, homework assignment, and example that we do from class. As such, even if you are absent, it is expected that you stay up-to-date with lessons and assignments. It is also expected that if you miss a quiz or test, you come in on your own time to make it up.

3. Respect Your Teacher: We work best as a class when my students understand that I am in charge. Once that understanding sets in, we can focus on learning our content and expanding our minds. Parts of respecting me are also turning in homework, doing your best on tests, asking questions during class, respecting your fellow students during class, and arriving/leaving on time (no arriving late, no leaving early).

4. Pay Attention: Believe it or not, you can't soak up math knowledge just by being here. The more attention you invest, the better you will do in my class and in life.

5. Obey Class Rules: I have very specific rules about backpacks, cell phones, purses, and food. These rules will be posted on the walls and discussed on day 1. Please make yourself aware of these rules and follow them.