Triangles, Congruency and Proofs Oh My!

There are few words that a teacher can utter in a Geometry class that inspire fear students at just the mention of the word.  The big ones are of course, test, quiz, exam and maybe "you have to write a paper".  In my class, however, these words compete with one more - proofs.  Literally, as soon as I mention the word I get
hit with a tidal wave of sound and complaints that all have one common theme - they hate proofs even though they have never written one yet. 

So this year, I set out on a mission to teach my students how to write proofs without the fear. I planned out what I thought was the best way to introduce them and how I thought I could transition them to writing Geometric proofs.  My game plan started out with a discussion on logic and how to try to communicate what you thought to be true with a logically sound argument.  Given that they are high school students I knew that I need to started it out a little fun so I shared with them my favorite logic, but not logic, but logic movie clip! The Battle of Wits from the Princess Bride.  The students had a blast watching it and it spawned an awesome discussion on logic, arguments, and how to support your point.

Cut, Match and Paste

From there my game plan moved us on to the most non-threatening version of proofs that I could think of - Algebraic Proofs!  By the time students reach Geometry they have taken (at least in my district) two years of Algebra and therefore can solve pretty well a multi-step linear equation.  After teaching Algebraic Proofs I have my students do a cut, match and paste group activity.  I have designed the activity to be easily differentiated depending on student level and needs.  Different levels include asking students to fill-in missing pieces, cut apart scrambled proofs and reassemble them or to write the entire proof from scratch provided only the given and the prove statement. With my class, the majority did the cut and paste aspect as I am trying to focus on hands-on activities this year.  This really helped to focus the students how to support each statement with a reason.

Cut, Match and Paste

The next step in my game plan revolved around Methods of Proving Triangles Congruent.  These types of proofs have a "formula" to them more than any other type of Geometric Proof and therefore are the easiest starting place.  I spent a couple of days teaching the students about the five main methods (SSS, SAS, ASA, AAS and HL) and what they look like.  Once I felt that they had a foundational knowledge, I again put them in groups and had them do a second cut, paste and match activity on those methods.  The students are given the five main headings plus "more than one method" and 24 sets of triangles.  They need to identify the methods being used, plus draw conclusions about vertical angles and shared sides to deduce other methods as well. The discussion that the groups had during this activity was wonderful, full of mathematical facts and had all of the students engaged and learning! 

Missing Reasons

I felt that my students were close to being able to write proofs and feel confident about it, but I wanted to take one more lesser step along the way so I gave them a set of proofs that had all of the statements, but were missing the reasons.  I prepared two versions of this activity.  The first has all of the reasons (plus a couple of extra) in a box at the bottom of each proof.  This is designed to help the students who need to see the possibilities.  I also created a version without the "reason box" for those more advanced students.  My students really enjoyed doing this and I found that some students choose to do the activity without the reason box!

Proof Practice

The last step on our journey through proofs was to write the entire thing without anything besides the given, diagram and prove statement.  I was much less nervous about doing this than I had been in past years because I felt that my students were really prepared and had the foundational knowledge to be successful!  The best part, when I handed it out, the only complaints I got were the normal
"I don't want homework" versus the "I hate proofs, proofs are hard, this stinks".  When I graded it, the majority of the proofs were correct and well written!  I count this as win! :) 

Our next step...Geometric Proofs on Segments and Angle Addition.  Hopefully, this journey will help that task to be much less painful than previous years!

How To Assess Student Comphrehension and Have Fun at the Same Time!

As a secondary math teacher I am always on a quest to find ways to not only assess my students' knowledge but to also engage them as I do it.  I have researched various techniques looking for ones that encourage collaboration, assess knowledge and allow students to communicate mathematically.  The incorporation of these activities helps me to shift my room from the more traditional teacher center to one that is more student centered.

Right Triangles Vocabulary Matching

The first technique that I use addresses the variety of new vocabulary that arrives in Geometry and helps students to connect the pieces that go along with those terms including the definition, diagrams and ways to label the diagrams.  I have created a series of vocabulary matching activities for various units including triangles and congruency, right triangles and trigonometry, quadrilaterals, beginning concepts and circles.  Each activity includes a set of teacher instructions, a student answer sheet, cards for the term, definition, diagram and label (when applicable).  The activities encourage students to work collaboratively and are also great for use in station activities!

Beginning Concepts Bingo

The second technique, Bingo Games, also address not only vocabulary but also the ability to hear a definition or description out loud and make the connection to the terms/concepts.  These are also great fun!  I have made them for various units including triangles and congruency, right triangles and trigonometry, quadrilaterals, beginning concepts and circles.  Each Bingo game includes two sets of 32 cards - one with the term and one with diagrams, two different teacher call sheets and the cover squares as well.

Task Card Bundle

The third technique that I use is task cards.  Task cards allow students to focus in on just one problem at a time and can be written at different questioning levels which allows for differentiation and for students to work at their level of understanding.  They also allow you to identify where students may be having difficulty without the students feeling overwhelmed.  I currently have five sets of tasks cards that can be purchased individually or in a money saving bundle.  I have many more sets planned!  

Geometry Riddle Bundle

The last technique that I use is riddle worksheets.  Riddle worksheets are worksheets that have the students working through a puzzle as they solve problems.  Riddle worksheets are usually 15 - 18 questions where each answer corresponds to a letter in the answer to the riddle.  I love them so much that I currently have 22 riddle worksheets covering the major topics in Geometry and 7 for Algebra!  The Geometry riddle worksheets can be purchased individually in a money saving bundle. 

I am investigating new techniques as well including formative assessment, group projects and station activities!  I will share them with you a future post so stay tuned! 

Guest Seller - Featuring HistoryGal!

History has never been my strong suit, especially memorizing dates, what happened when, to whom, how, why and a thousand other facts that surround a specific event.  However, as a high school teacher, I inevitably get asked History (and English, Science...) questions because students assume we know it all - why else would be teachers right?

HistoryGal on TPT

Given that History was not my strong suit, I was thrilled when another seller on the forums suggested that we pair up with someone who doesn't teach our same content area so that we could not only help each other out but also learn something about another seller too!  I have the pleasure of being paired up with HistoryGal for the next couple of weeks and I have learned so much already!

Her store features a wide variety of topics including the ancient and semi-modern worlds.  Her products are a wide variety of activities, supplements and interactive lessons meant to engage the students and make history relevant instead of just a recitation of facts!

One product that caught my attention immediately (partially because I love the Greek Gods) was her Greek Gods Bundle.  It an amazing product that includes a Greek Gods Scavenger hunt (with or without QR codes), a Bingo Game, Printable Greek Gods and an editable quiz!

It pairs beautifully with her Ancient Greece Activity Bundle that includes  six different activities such as a Television show activity and Pictionary (and what student doesn't love to get up, draw and laugh while doing so?)

Financial Literacy

I would also like to highlight one more of her products before I end this.  She has a fantastic product called "Financial Literacy Unit: Things Students Should Know Before They Graduate"  It is designed for use in an economics or financial literacy class but I can see myself using it in my math classes as well.  How to survive

financially in the world is a skill that all high school needs and one that I don't feel they are being adequately prepared for!  This product really addresses those needs and gives students a financial knowledge foundation to help to get them started down the right path!

I highly encourage you to check out her store!  You will be so glad you did!

A Plan to Keep Your New "School" Year Resolutions

Soon, or perhaps already, a new school year will begin.  With the start of a new school year, we all make "resolutions" about what we will do different, what we will change, new ideas that we will implement and how we hope our year will go.  Unfortunately, unless you have a plan, like the New Year Resolutions we make on January 1st, these will quickly go to the wayside, discarded and wasted.  So this year, I am going into the year not only with resolutions but also a plan as to how to implement them! 

Resolution One:  Establish a classroom environment that encourages classroom discussions.

Getting to Know You

Why?:  One of the biggest challenges I encounter at the secondary level is that students don't want to participate in the classroom discussions because they don't want to be wrong!  In order to combat this I need to first help students to feel that is a) safe to talk, b) safe to disagree and c) safe to be wrong. 
Plan:  My plan is two-fold.  First we are going to establish together a set of classroom discussion expectations and consequences.  By creating them together, the students feel that their voice is being heard AND they start participating in the discussion without even knowing it!  The second part of my plan involves getting to know my students and having them get to know each other.  I purchased a fantastic resource (Getting To Know You - 3 activities to help you get to know a new class) from Stacey Lloyd on TeachersPayTeachers that includes three different getting to know you activities. One is a one page page that the students fill-out on themselves, the second is a reflection on the previous year and the third is a peer interview!  Perfect for starting a new year off showing the students that you truly do care about them!

Discussion Starters

Resolution Two:  Once I get the students to participate in discussion I want to take those discussions to the
next level.
Why?:  My experiences have shown that the better a student can communicate mathematically, the better their understanding and retention of mathematical concepts.
Plan:  I searched and searched and finally found a set of question starters that I think will work well.  I printed them on cardstock, laminated them and put them on an O-ring so that I can have them with during class.  I will also go through the questions starters ahead of time and tag a few key ones that will fit the lesson of the day well.  The cards are called "Discussion Starters for Math Problem Solving: Questions for Critical Thinking" and are written by Angela Watson on TeachersPayTeachers

Resolution Three:  I want to help my students to feel more comfortable asking questions and expressing what they don't understand.
Why?:  When students hold questions in, they hit a roadblock and miss future information because they

Signs and Headers

cannot get over it.
Plan:  In addition to small group, one-on-one and other personalized questioning methods I am going to establish an exit-wall.  It will be a place where students can place sticky notes expressing what questions they still have and what they have understood really well.  I saw the idea in a set of headers (Signs and Headers for the Secondary Classroom) that I purchased off of TeachersPayTeachers Store Room 213 .  The headers have all different types included such as months, days of the week, signs to post on the door if you are out of the room and the set-up for the exit wall!  This way students can sign their sticky notes or put them up anonymously!  


Resolution Four:  I want do more than just present lessons, I want to get the students exploring, talking and working together too.

Task Card Bundle

Why?:  The more responsibility a student takes for their own learning, the more successful they are.
Plan:  I am going to implement task cards.  Task cards allow students to work on a single problem at a time and really focus on one main concept without feeling overwhelmed.  (See my post here for more in-depth discussion about task cards). I have written five sets for the first unit of Geometry that hit upon all of the main topics covered in that unit.  I will implement them in multiple ways including small groups, as exit cards and as part of a station activity.  I have all five sets available in money-saving bundle here.  



With a plan in place, I hope to be more successful!  I hope you've also gotten some ideas and some products to help you to be successful as well!  Good luck in your new school year!

TPT Boost Sale - Only a few hours to go!

Today is the last Back To School Sale for the school year!  I hope everyone is able to stock up and save!  Anything and Everything in my store is 20% off and TPT kicks in another 10% to raise your total savings to 28%!!!!  I have back to school secondary binders, word wall posters, task cards and notes to start off your first unit of Geometry!  So stock up and save! :)

Thank you to Glitter Meets Glue Designs for the awesome graphic!!!

New Blog Design - Thank You, Thank You Kristy

I am debuting my brand new blog design today!  I must first give the greatest thanks and credit to Kristy of KristyBear Designs.  She took what could only have been the most ambiguous request/description ("something in black, gray and purple, that is secondary, geometric and not cutesy") and created exactly that I had in my brain, only better!  She was a dream to work with and I would highly recommend her to anyone who is looking to get a professional blog designed!

You can visit her TeachersPayTeachers store as well if you are in need of digital papers, clipart and more! 

Warm-Ups/Bellwork/Bellringers - The What, How and Why!

Basic Concepts Bellwork

Picture this:  The bell rings to start another class period, your last student or two tries to sneak as you shut the door so as to not be late and as you turn to greet your class you are met with a wall of noise.  You spend the next five minutes trying to quiet the class down while you take attendance, check-in homework or do other start of class tasks.  Once you are done, you waste another few minutes trying to get the class engaged and on task to start a new lesson, review or to take an assessment.  Suddenly it's 10-15 minutes into class and you have accomplished nothing...  This was a situation I dealt with often my first year - until I found a fantastic solution that is!

Circles Bellwork

My solution gets the students started when they walk in and engages them from the moment the bell rings.  My solution allows me to review previous concepts, preview upcoming topics, assess prior knowledge and direct where my lessons need to go.  They go by many names including Warm-ups, Bell-work, Bell-ringers, entrance cards.  They are nothing new having been around for as long as I can remember.  For those of you who are knew to them, however, I want to fill you in my lifesaver!

Right Triangles Bellwork

What they are:  A set of usually 2 - 5 problems that students work on during the first 5 - 10 minutes of class.  The problems can be solving, writing, explaining or illustrating depending on your topic area.  They are designed to be done individually or sometimes with the assistance of
a partner or notes.  I use them often to review what was on the previous nights assignment to make sure students are ready to move on the next topic. 

Answer Sheet

How to use them:  There many ways to implement them.  Way one:  You can project the problems on the board and give students a weekly recording sheet.  This allows you to save paper.  You can save time by walking around while they are working to stamp it as complete but only collect it once a week to put it in the grade book.  Way two:  You can print the problems on half sheets of paper and have students pick them up on their way in.  Students can hand them in immediately or compile a packet and turn them in once a week. 

Surface Area and Volume Bellwork

Why use them:  Besides the benefit of reviewing previous topics, bell-work can also help students to structure their questions.  Since the number problems is limited, it focus on doing them right.  Bell-work can be used to zero on skill deficiencies or a hole in the learning from the previous day.  Bell-ringers also structure your class from the beginning bell so that students get in to a routine and it lowers the incidences of off-task behaviors.

Quadrilaterals Bellwork

While warm-ups might not be for everyone, I have found nothing but benefits from implementing them!  In addition to the bell-work/bell-ringers/warm-ups pictured in this post I also have Area, Transformations and a money saving bundle!  Each set includes each day on its own page for projection, an answer sheet, an annotated answer key and the student problems double printed on half sheets of paper for handout!