Geometry

This is for students who have completed Algebra 1 and will be taking Geometry in the 2024-25 school year

Introduction


Since you aren't skipping any grades, your summer assignment is intended to get you back into the mathematical groove and feel comfortable about what you are about to start. 


You must have this assignment completed by the first day of school, August 20.  It would be great if everyone procrastinated and waited until August to complete this but we know summer schedules vary and some just like getting it done early.

Part 1:  Get Your Supplies 


General Supplies

Here are the supplies that you will need for Geometry starting on the first day.  These are the supplies that you will be using EVERY DAY!


Required


Optional (nice to have, but not necessary)

Special Supplies For Geometry

In the middle of the first 9 week grading period we will start constructions.  You will need a compass and a straight edge to do constructions.  Any ruler will work as a straight edge as long as it isn't some weird wavy ruler.  

We will have compasses for you to use in class.   However, if you would like to get your own compass, There are some things you will need to consider or you may cause yourself a lot of frustration.

A good compass will:


Types of Compasses

Below are some common styles of compasses that you'll find out in stores and online.

Recommended 

This is called a "Circle Master Math Compass."  It holds a radius very well, has few parts that can get lost or broken and allows you to use basically any writing utensil that will fit.  They are also easy to hold and easy to adjust.  This is the type that we will have available for in class use because they are practically impossible to break.   However, it is hard to find these sold individually because the people who buy these are usually Geometry teachers wanting a class set, not students who just want one.   

Pretty Good

The Bow Compass is pretty good, but can be expensive.  In addition, parts get lost easily and they require specialized lead (as seen in the image).  This is why we won't have class sets of these.   You need to be careful.  You will find that most bow compasses come with a case.  If you get one that does not, get a sturdy pencil case to keep the compass safe.   Put it in a pocket of your backpack, not in the main compartment.  They ring on the top will break if weight is put on it.  Screws will loosen as the compass jostles in your backpack and parts will get lost.  As a matter of fact, Ms. Hill has a container of compass parts she found on the floor.

Absolute Trash

Ball Bearing Compasses are a waste of money.  You can't  fix a radius and they get looser over time.  It will frustrate you to the point of wanting to throw it.  This is dangerous because they have a really sharp point which will poke through your backpack or stab you whenever you reach in to grab it.   We honestly don't know why these are still on the market.  However, there are newer versions made of plastic that have a little button that will fix a radius that aren't terrible, at least not with light use.  We don't know whether or not the newer models are sturdy enough for a semester of heavy use.

Part 2:  Setting Up Your Notebook


This part is the same as it was for Algebra.  You will be keeping all of your notes and work in composition books.  Most people will use 2 in a school year, one if you write tiny, more if you write big or leave a lot of space.  They are plentiful and inexpensive in the fall during back to school sales so get as many as you think you'll need.


We don't have a preference about college, wide ruled, graph paper, dot grid, dot lined, blank.... but we do want it to be a bound journal (sewn), like composition books.  Glued binding, like in most journals, are okay.   No spiral notebooks. They are terrible!  No perforated pages.   We need the pages to stay inside the notebook over time and daily use.


Decorate it to your heart's content.  You will be using it every day so you should like the way it looks.


You will need to:


Do not create a pocket if you plan on using a folder to hold handouts and assessments.   


Ms. Hill was too busy making new videos for Geometry and did not have time to create a new notebook set-up video.   Below is the link to the one from Algebra 1 just in case if you forget how to set up your notebook or you will be new to the Ways of  Kealing Math.  Just make sure to write "GEOMETRY" on the title page.


Video:  Setting up your journal 


NOTE:  We will actually check to make sure you are maintaining your notebook.  There will be notebook checks throughout the school year and they will be counted as assessment grades.  Make sure you set your notebook up correctly now or you will lose points on those notebook checks!  

Perforated pages have a line of tiny shallow cuts on the paper.  They are there to help you tear out pages cleanly.  If you get a notebook with this feature, invest in tape because your pages will start to fall out after a week or so.  

From Ms. Hill:

The only spiral notebooks with perforated pages I've been able to find that would have any chance of surviving a year in a middle school student's backpack are expensive and  from Japan.   Just say no to spiral bound notebooks and perforated pages!

Part 3:  Making A "For Reference" Section


The following are concepts that you should know before entering Geometry.  These are things we will be using throughout the year and will haunt you if you forget them.  So, you will be making yourself a "For Reference" section in your notebook that you can refer back to as needed.  You can put it in the front of the notebook or in the back, your choice.  


Please note that we are going to try to limit your "screen time" during class and there will be many days that all computers, phones, ipads, calculators and other electronic devices will be banned from use in class.  Don't assume that you will be able to "look things up" or watch videos during class time.   Your notebook, tools of construction, a pencil and your brain will be all you have.  


If you anticipate using 2 (or more ) notebooks, they each will need a "For Reference" section.  However, these do not have to be identical for every notebook you use.   Later, you may choose to include some Geometry concepts in your second notebook's "For Reference" section, for example.


In the first week of school (probably the first day), you will have a quiz where you will be able to use your Geometry notebook.  This quiz will be your first grade in Geometry and it will be an assessment grade.  Because it is open notes, there will be no retake and no corrections.  Your "For Reference" section will be helpful for this quiz, but only if you take this part of the summer assignment seriously.


Now, we will be giving you freedom when it comes to what to add to your notebook's "For Reference" section.  Here are the criteria you must meet for credit during notebook checks:



1.  Rounding 

Yes, that says rounding.  I'm assuming you all know the correct way to round a value to a certain place-value.  That isn't the issue. Read this document  Problems with Rounding and Exact vs. Approximate.  No joke y'all!  Kealing Geometry students have lost MANY points on several assessments, including final exams, because they ignored the information in this document!


2.  Dimensional Analysis 

Units and unit conversions will be a thing in Geometry and dimensional analysis is a technique that helps you make sure you did the conversions correctly.    Here are some notes with conversion factors .   This contains examples and some practice problems.  You are not required to do the problems.  But you must know how to convert complex units and you must know some conversion factors.   If you actually choose to learn how to do dimensional analysis, it will serve you well in Physics and Chemistry.  


3.  Slope 

Be able to calculate the slope of a line given 2 points on the line, a graph, or a table.  In addition, be able to solve problems involving slope. WITHOUT DESMOS or any other calculator!!!!!  


4.  Linear Equations 

Be able to write equations for a line in point-slope and slope-intercept forms.   This will include lines that are parallel and perpendicular to different lines that may be given to you in a problem set-up!  Remember the SMOL Floof problems?  Well those were examples of Analytical Geometry, which you will have to do throughout the entire year.    WITHOUT DESMOS or any other calculator!!!!!  FYI Analytical Geometry is a way to study Geometry through Algebra.  Ordered pairs are used a vertices.  Lines are described by equations.  Properties are described in terms of patterns that emerge in equations.  For example, in Analytical Geometry parallel lines are "distinct lines with the same slope."  Our primary focus is on Euclidean Geometry, but we do like to sprinkle in the Analytical.


5.  Solving Systems of Equations

I'm going to assume you will remember how to solve one variable linear equations because we did that ALL year in Algebra 1.  But, we didn't spend as much time on solving systems, so you may want to include this in your "For Reference" section.  


Be able to set up and solve systems of linear equations using either substitution or elimination methods.   Sometimes you will need to find intersection points when doing Analytical Geometry and other times a system is just going to be part of a larger Geometry problem.  WITHOUT DESMOS or any other calculator!!!!!


6.  Simplifying Radicals 

You will need to find some lengths and distances when we do Analytical Geometry in the first semester.  However, exact and simplified answers become more of an issue in the second semester when we hit the Pythagorean Theorem and start to look at areas, volumes, etc.   Make sure you can simplify a radical in general and can deal with fractions and radicals.  


7.  Solving Quadratic Equations

You will need to solve quadratic equations to for some Geometry problems, especially when we get to the calculation heavy second semester.   You must be proficient in one of the universal solving methods either the quadratic formula or completing the square.   Being able to solve by factoring is cool and might save you time on some problems, but sometimes we'll give you problems that can't be solved via factoring.  


8.  Factoring and Multiplying Polynomials

You won't see this much in the first semester because the early concepts of Geometry don't require much polynomial knowledge.   Second semester is very different so make sure you can multiply polynomials and factor them before we end the much feared circles unit.


Part 4:  A Preview of Geometry


Geometry is a very different course.  You'll have to read carefully and remember definitions and properties exactly.  It isn't a course that has you just learn and practice specific skills by following algorithms.   Geometry requires you to observe, think logically and pull pieces together to solve various problems, building strong chains of reasoning backed up by the laws of mathematics



An Axiomatic System

"Science is operated according to the judicial system. A theory is assumed to be true if there is enough evidence to prove it 'beyond a reasonable doubt'.

On the other hand, mathematics does not rely on evidence from fallible experimentation, but it is built on infallible logic."

Simon Singh

Fermat’s Last Theorem

One of the real reasons we study Euclidean Geometry is to learn how to problem solve and build the capacity to reason though logic in the process.  Yes, you will learn all sorts of attributes and properties of shapes, but those are the vehicles we use to develop your capacity to reason mathematically.   What we are really doing is demonstrating how to  build something called an axiomatic system. 

We will start off with some simple definitions.  We make some observations and form axioms (aka postulates).  An axiom is a property that we accept as true, like the commutative property of addition.   We observe some more, create new definitions, and form conjectures.  A conjecture is a property that can be proven from your definitions, axioms and previously proven conjectures.   Continue this cycle of observation, definition, conjecture, proof and we have an axiomatic system.   

All of the Geometry you have learned and studied so far was built on 3 undefinable terms and 13 axioms.  These were first presented in a cohesive and logical form by a Greek mathematician named Euclid in 300 BCE.  This is why the Geometry you will study is called Euclidean Geometry.

But, before we dive into and start building Euclidean Geometry, you need to learn a little bit about logic, specifically the conditional statement.

A conditional statement has a "hypothesis" and a "conclusion" and is often presented in an "if - then" format.  For example, "If it rains, Ms. Hill will not water her garden" is a conditional statement.  Axioms and Conjectures will be presented as conditional statements throughout Geometry.  

 

Your Task 


Is That All?

Yes.  We'll actually build Euclidean Geometry when we start class in August.   We just need you to know about conditional statements and a few properties needed for proof.   But, pay attention to the information below.  

You are warned!  The notes done as homework will be different in Geometry and NEVER OPTIONAL.... like we are going to physically check and grade your notes daily!   

If you don't have the notes, you will get a zero for that daily grade that will permanently be a zero, no make-up.    There are consequences when you don't meet your obligations as a student of this course.

Please note, we won't allow you to watch the video during class time.   You will have an activity that you must participate in for grade.    So, be responsible, watch your videos and take your notes before class.  



A Note About Taking Notes In Geometry

Geometry is filled with new, and very precise, vocabulary, axioms, postulates, theorems and conjectures that you will need to learn thoroughly.   You can't just "understand the concept" or "get the gist of it."

Many of the definitions and conjectures will have precise conditions.  Missing words can be disastrous.  Copy them exactly!!!!!!

Example:  True or False, two lines that never intersect are parallel.

False, the lines must be coplanar.  See, one word!

Vocabulary, axioms, postulates, theorems and conjectures must be copied VERBATIM!  If it comes with a picture, DRAW IT!  We will be looking for these during daily note checks!

Not only that,  all vocabulary and conjectures should be prominent portions of your notebook... I mean boldly written and obvious.  You will want to find these quickly and easily in your notebook so you can reference them until you know them by heart.   Use a different color, use a bolder marker, use a highlighter, something to set these apart.



Draw and Label


Get ready for this!  There are some problems that you will not be able to solve without a properly labeled drawing.  A lot of times the work that you will need to show will be your labeled diagram.  Here are some reminders:



If you are terrible at drawing (like Ms. Hill)  and are worried about it, consider investing in a Geometry template like the one in the link.  You want one with a variety of shapes and multiple triangle/quadrilateral types so you can use it all year.   Most of these templates will also have ellipses (ovals) and a variety of polygons that look squashed.  These are for drawing figures in 3D like prisms, cones, pyramids and cylinders.   We will have a class set of these for you to use during class, but you cannot borrow these or take them home.  


A Reminder About High School Credit 

Our Geometry course is considered "advanced" and for the purposes of GPA will be weighted on a five-point scale.  

During each grading period, you will be given 2 progress reports:  one at 3-weeks, the other at 6-weeks.

Semester averages will use the percentages to 40%, 40%, 20% , with the grade earned in each 9-week period constituting 40% of the average, and the semester exam/project 20%.

Speaking of Semester Exams... Ms. Hill's #1 suggestion for studying for Geometry finals is create flash cards.  There are a ton of vocabulary and conjectures in the Fall Semester that you have to know verbatim.   In the spring, there are TONS of formulas.  

Your grade in Geometry will be recorded onto your high school transcript.  

There is no EOC for Geometry.  During STAAR testing season, you will take your grade level Math STAAR.  

If things don't go well, you can drop Geometry for credit.  Since there is no EOC, the drop deadline is the end of the 5th week of the final quarter, so mid-April.   We'll send out letters when that date approaches.