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.  This is the type that we will have available for in class use.   However, it is hard to find these sold individually because the people who buy these are usually Geometry teachers wanting a class set.  

Pretty Good

The Bow Compass is pretty good, but can be expensive.  This is why we won't have class sets of these.  In addition, parts get lost or broken easily and they require specialized lead (as seen in the image).  You need to be careful with these and their many parts.   You will find that most bow compasses come with a special case.  If you get one that doesn't have a case, make sure you have a sturdy pencil case to keep it safe.   They have a tendency to get broken in backpacks.

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.  One of the reasons why Ms. Hill hated her Geometry class was because she had to use this horrible thing to attempt constructions.   We honestly don't know why these are still on the market.  

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, 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 lazy 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.  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!  

Part 3:  Concept Review


The following are some concepts that you will be using throughout the year.  Linear concepts of Algebra show up a lot in the first semester, which is why it is part of the summer review.  In the second semester, quadratics and radicals will pop up and we'll review that mid-year.    


Be prepared for a quiz that first week back over these concepts.  We aren't making you do any practice problem over any of these.  If you want practice problems, check Khan Academy.  


Taking notes is required for rounding, but is optional for slope and linear equations.   Make sure to list your notes in the table of contents.


1.  Rounding -- MUST TAKE NOTES ON THIS

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 points on many tests, including final exams, because they ignored the information in this document!!!!!!!


2.  Dimensional Analysis -- MUST TAKE NOTES ON THIS

This is something that was taught by Kealing Science teachers before the pandemic days and it is a shame they don't teach it anymore.  This is something that will really help you in Physics and Chemistry.  We are making you learn it now because units will be a thing in Geometry.  Here are some notes and some REQUIRED problems


3.  Slope -- Notes Optional

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!!!!!  Geometry is a no calculator class so you are going to have to do these calculations by hand.


4.  Linear Equations -- Notes Optional

Be able to write equations for a line in point-slope and slope-intercept forms.  WITHOUT DESMOS!!!!!


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



Conditional Statements

"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.  An axiom is a property that we accept as true, like the commutative property.   We observe some more, create new definitions, and form conjectures.  A conjecture is a property that can be proven from your definitions and axioms.   Continue this cycle of observation, definition, conjecture, proof and we have an axiomatic system.   All of the Geometry you have learned and study so far was built on 3 definitions 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 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 the Geometry when we start class in August.   We just need you to know about conditional statements.   But, pay attention to the information below.  Be prepared because notes will be different in Geometry and NOT OPTIONAL.... like we are going to check often!



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 will want to find these quickly and easily in your notebook so you can reference them until you know them by heart.  Vocabulary, axioms, postulates, theorems and conjectures must be copied VERBATIM!  If it comes with a picture, DRAW IT!  Many of these will have conditions so 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!

Not only that,  all vocabulary should be prominent portions of your notebook... I mean boldly written and obvious.  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.  


A Special Note About Next Year

Next year, AISD middle and high schools will be on a 9-week grading cycle.    Each semester will consist of two 9-week grading periods.

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 20%.

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