Two-Column Proofs and Logical Reasoning

The second unit in Geometry for me is Logical Reasoning. I do three things: 

  1. Inductive and Deductive Reasoning
  2. Conditional Statements
  3. Two-Column Proofs

Monty Python

I have fun teaching inductive and deductive reasoning. I usually start the lesson by having students watch a YouTube clip of Monty Python and the Holy Grail. It’s a pretty hilarious demonstration of how drawing conclusions based on patterns can lead you to the wrong conclusion. This would be a great place to talk about stereotyping if you would like to go a little deeper into how people base information sometimes from the media or gossip. This lesson has 12 task cards to practice reasoning and knowing the difference between the two types. 

Conditional statements is also fun to teach. I love it when kids say that it doesn’t seem like we are learning math. We discuss where the hypothesis and conclusions are in the conditional statement so the students can write the converse, inverse and contrapositive. We also discuss counterexamples and biconditionals. This lesson has some hands-on activities where students create if/then statements and the related statements and tape them into their journals. 


The last part of this unit is spent on two-column proofs. This usually happens for me in October, sometimes earlier but close enough that I can show them a silly Halloween proof that I created. I made this up a long time ago after watching “It’s the Great Pumpkin, Charlie Brown.”  It’s got all the elements of a real proof. I’ve used this as a bulletin board in past years. Feel free to use this in your classroom.geometric-proofs-b

One thing that is in this lesson that helps my students is a set of matching cards. Students will match the property or definition with its name. I do this as a collaborative activity. Students enjoy this and it helps them to have some tools to use going into writing proofs. This is a beginning proof lesson. I only practice two-column proofs. In lessons that follow this one, I introduce the other types of proofs like paragraph and flowchart proofs. 

If you are teaching online, no problem. I’m in the process of making these lessons more online friendly. Teachers Pay Teachers has a new tool that can take a PDF and transform it into an interactive worksheet. Look for the “Use as a Digital Activity” button on products that are available for this. You as a teacher can modify it as you see fit then assign it to your students. 

I love this part of Geometry. It’s different from the norm in math. It’s always a fun time of year. If you’d like to use my lessons, then the best way to get them and save a little money is to purchase the Unit 2 Bundle

Good Luck and I hope you have a successful year!

Geometry – Transformations Hands-On Activity

I am excited after going through a transformations activity that I have created. I’m gonna have to say, it’s pretty good! (Just saying…)

The first thing I do is show my students a Mario Brothers Transformation PowerPoint that I created this year. It’s a free download on my TpT site. So FUN! I tell the students to number from 1 to 4 in their journal and then I go through the PowerPoint to see if they can name the different transformations. I want to know what they remember from middle school.mario-transformations

Next I have the students jot down a few notes and then I begin the hands-on part. I use patty paper and wikki stix. Every student was engaged, asking questions and YES….LEARNING! I show them pictures of me working on the transformations which is very helpful. I don’t have to stop and do it in front of them…pictures are worth a thousand words! The pictures are provide in the product and I think you will find them very useful.


What are wikki stix you ask? I think they are just thread or string that has been dipped into wax which means they will stick to things. I use them as my lines of symmetry as well as a tool for rotations as seen below:



If you haven’t done transformations this year, I hope you will check out my Transformations Activity. Included is a note page, pages for each type of transformation, a quiz, keys and pictures. You will have a great time working through this with your students. Let me know what you think! Hope to hear from you soon.

You Have TI-Nspires…Now What?

TI-Nspires are amazing calculators. There are so many features, don’t try to learn them all at once. First of all, get the teacher software! I can’t live without it. In my district, even the students have the software available on their laptops. It’s wonderful.

How do you get started? The first thing I learned was go to the HOME SCREEN and choose NEW DOCUMENT. If there is a screen that asks if you want to save, say no. Now choose what you want to do. If you are learning, you will only choose graph or calculator. This is what I still choose most of the time!

new-doc-screen  choice-screen

The calculator screen is easy to use. If you are looking for something specific it is probably here: (see below) I used this button to type in a cube root as seen in the next pic.

special-characters  calculator-screen

Let’s say you now want to graph something. You have a choice. Start completely over and go to the home button and go through the same steps explained above, or add a page to your document. Let’s add a page. Simply click CTRL (blue button) +Page (doc button below home.)

add-a-page   graphing-1

Choose Graph! Now you can type an equation. The x button is one of the white alphabet buttons at the bottom of the calculator. Hit enter when you are ready to graph. To graph a second equation, click the tab button and type in a new graph… or to change the first equation, after clicking tab, up arrow to the original equation. If you know this much, you are ready to use the calculator. The only other things that are nice to know at this stage is that ctrl t will pull up a table (and ctrl t will take the table off).


AND the menu button has many things that will help you. I suggest clicking the menu button and checking it out! I use #4 and #6 daily. #6 is where intersections and zeros are and #4 of course helps you change the window settings like on the 84+.


My goal was to help you get started. If you will start using these features and become very familiar with the calculator, you will discover new things on your own. Your students will also help you discover things. The main thing is to get started! Don’t let those calculators just sit. They are really awesome and helpful!

Seating Charts – Are They Really Necessary?

Do you want your students to be focused? Do you want to keep your students on their toes? Are your students not performing as expected? Seating charts might the answer!

On the first day of school, I put the students in alphabetical order and keep them there for the first six weeks. This helps me learn names quickly. It also helps me learn who not to sit together in the next seating chart. In the first six weeks you will also learn who is quiet, who is loud, who can’t see very well, who is unorganized, who needs special help…the list goes on. My second six weeks has started and I will concentrate on partner work this six weeks. I have my desks in rows still but now I have 8 rows with


4 seats. Yes it’s crowded. I pair students up like this:


If I have an extra student, then he/she will pair up with the group in front or behind. When pairing students, I used my first 6 weeks grades. I tried to put a low with a high. I also have a few students with special needs, so I strategically placed them. I have one student that brings a huge backpack everyday. I put him on the far left, so he has plenty of room to spread out. Anyone that failed the first six weeks, is now right by my desk or at least in the front row so I can keep an eye on them.

It really bothers me when the desks don’t stay where I put them, so I put tape on the floor and the front person knows that at the end of class to make sure that’s where their desk goes and the whole row will follow suit.

Is this time consuming? Only on the front end. It is worth it though. I also like to label each row as an “A” or “B”. I will say things like, “A, you will tell your partner what the definition of perpendicular is and B you will tell your partner what parallel is.” I try as often as possible to have them speak the language of my class to each other.

Seating makes a difference. If students know you don’t care where they sit, it becomes a free for all. I’ve become a control freak over the years but it is only because I’ve been the teacher that let’s their students sit where they want, listen to their ipods, bring in food and so forth and guess what? It turned out to be horrible. My students were too comfortable and not ready to learn. I’ve changed and I’ve seen a big change in how my students perform. You will too when you gain control.