Transversals

Our  next unit in geometry covered angle relationships formed through transversals. This is probably one of my most favorite topics in geometry. We started out talking about the two types of lines that don't intersect, parallel and skew. I open up talking about this because a lot of times students think that parallel lines are the only types of lines that do not intersect. True in 2D, but they often forget about 3D space.

 Then we talk about transversals. This is one of my favorite foldables ever. We talk about the look of a transversal line that cuts two parallel lines. I need to start watching my wording a little more than I do when it comes to this topic because my students forget that the line that cuts the parallel lines is called the transversal line. Anyways, we look at the transversal and about how it's cut into two different parts, interior and exterior. I had my students color the parts two different colors and label it. Next year I'm actually going to have them write that the exterior is outside the parallel lines and the interior is between the parallel lines.

 On the inside, we talk about the different types of angle relationships and where they are. I've found that color coding really helps.

After we talk about all of these angle relationships, we practice. I've done this a couple of ways. One way is that I've put painters tape on the floor and made a giant transversal and had pairs of students stand in spots that show the type of angle relationship I call out. They like this a lot. It gets them out of their seats and moving. Another activity I've done is where I'll put a picture on the board and they have to write the angle relationship on a white board and hold it up. That one is ok but I'm not a huge fan because it can be kind of boring. 

If you have any transversal activities that you like to use in your classroom, leave a comment below and let me know about it. I hope to get a digital copy of this foldable uploaded soon. Happy teaching!

Logic and Proofs

Logic and proofs...the most loathed favorite chapter! I love logic and I think my kids don't mind it too much. Proofs on the other hand...
My geometry teacher in high school didn't teach us anything about proofs, so when I went through college I struggled with proofs. I think that's because I wasn't exposed to it at all until then. Proofs can take a great deal of time to teach, so I try to balance it out the best I can. I teach my students about logic first and then will teach them the basic proof writing techniques and we'll do some basic proofs. Most of them are sure they're not going into any kind of field that requires math, but it's still good to show them because you just never know where their paths may go.

Logic

For logic, I start out by giving Rebus puzzles for them to think about for a while. They loved/hated these. They liked it when they understood the puzzle, but hated it when they couldn't figure it out. If you've never seen a Rebus puzzle before, here's an example of one.

The answer to this is first aid. Clever, huh? I love these puzzles.

Next year I hope to give them a few more logic puzzles and less Rebus puzzles.

We start out talking about what statements are. We discuss the hypothesis and conclusion of statements and talk about the fact that statements have a truth value. Then we talked about the ways you can change and combine statements by negations, conjunctions and disjunctions.

After this, we did a snowball activity. I love these! If you've never done one, here's how it works...

I had my students write a statement on a piece of paper. They then crumble it up and throw it in the middle of the room. When I say, they go grab a paper out of the middle and I'll tell them to find a partner. They have to then write the two statements, the negations, conjunction, and disjunction and give their truth values. After a few minutes, we crumble the papers back up and throw them back in the middle and go again with the same partner they had before. It doesn't matter if one of them gets the same statement they've had before because that could change the truth values depending on the other statements. We keep going a few times around until I feel like they get the hang of it pretty well.

Next we talked about conditional statements.

As we discuss conditional statements, we look at truth tables. I'm not going into detail about this because the only way to get truth tables is to practice them a bunch, which is what we did. We then talked about related conditionals.

For these lessons, I made a spinner and students had to spin twice to get two different statements. They then wrote the conditional and related conditionals for those two statements and gave the truth value.

This was a simple thing to make...paper plate, brad, and a homemade arrow out of cardstock. I think next year I'm going to have students make their own and they'll switch with another group so they statements are a lot more original and fun.

Next was deductive reasoning. Some people skip right over this, but I teach it anyways. I found an activity that goes along with understanding the laws of syllogism, detachment, and contrapositives on Teachers Pay Teachers here. I do the activity first, and then we put notes in our notebooks over the 3 different laws.

Proofs

Once we finish logic, we start talking about proofs. I start out by taking a step back into algebra and discussing algebraic proofs. I review the properties of numbers with students first and they fill out these reference cards and keep them in their notebooks. Then, we go over a bunch of different algebraic proofs. I found an activity on Teachers Pay Teachers that is was a great resource to practice. Unfortunately that resource is no longer available there. Basically, it was a proofs cut and paste activity. I feel like my students really understood proof writing by the time we got to geometric proofs. We did very similar stuff for geometric proofs.

Last year when I taught proofs I felt as if I took way too much time to teach it and they still weren't understanding it very well, and those were advanced kids. This year I didn't take a terribly long time and I think my students got the idea of it a lot better. Proofs are one of those topics that can be very difficult to teach. Hopefully this gives you an idea of where to start. I'm always looking for ways to improve teaching this topic, so if you have any ideas about what I can do to improve this use Contact Me above or comment below. Happy teaching!

Basic Geometry

This is the 2nd year I've taught Geometry. Last year I taught Honor's Geometry, so those students were EXTREMELY intelligent and got things pretty quickly. This year I had a mix of high and low kids, so it was a little bit of a challenge for me. I used a lot of the same things I did last year, and it worked well for the most part. There are some things I wish I would have taken more time with, especially in the beginning. Geometry is picky...if things are labeled correctly, it can change the entire picture. When we first start geometry, we go over all of the basic definitions in detail. We do Frayer model definitions for all of the basic terms and talk about what each of them are. Next year, I need to take more time doing this to really make sure they understand and can label/draw things appropriately. I found out in 2nd quarter that we still couldn't label a ray correctly, and that's kind of a problem.

Basic Geometry Definitions

This lesson takes a little bit of time just because it's a lot of writing and cutting out/gluing. However, I think it's good to talk about what each term is and show them examples and non-examples of what we're talking about. Next year, I plan on taking a little more time with actually drawing/labeling things so they can learn to do it right at the beginning.

The next lesson we did was about distance and midpoint. I gave students the formulas to write in their notebooks and we did an activity to practice. For the activity, I made a copy of the school map and drew a coordinate plane on it. I had students map out their schedules for the day. They then had to find the distance and midpoints between each of their classes during the day. We acted like birds and "flew" over the walls so we didn't have to worry about going through walls and all that. This project took a couple of days, but they got a lot of practice with the distance and midpoint formulas. One thing I learned from doing this is that my kids didn't remember that squaring a negative number results in a positive number, so I had some issues with the distance formula. Overall, I think this was a good activity.

Distance and Midpoint

(This is not the best pic of the map, but you get the idea. I put a point in each room for them to use as reference for that room. So my room has a point of (-1,7).) You can find a copy of the map project outline here.

I wish I would have taken pics of what the students' work looked like. They did a good job with this and really took their time on it. 

Our next lesson was over basic angle relationships, another integral part of geometry. First, we defined what angles are and how they are made, which seems pretty obvious knowledge but you would be surprised. We then talked about how to name angles, which you can see in this foldable.

Angles and Angle Relationships 

Next, we defined the basic angle relationships: angle bisector, congruent angles, right angles, acute/obtuse angles, vertical angles, complimentary angles, supplementary angles, adjacent angles, linear pair, and perpendicular angles. The first sheet is something I made. The second is a foldable I found for free on Teachers Pay Teachers here. It worked for what I needed it to. I think next year I'll tweak it a little and add linear pair and perpendicular angles to it just so everything fits in one foldable. Since there are so many different angle relationships, I broke this into a 2-day lesson.

We then practiced naming different types of angles from a PowerPoint I made. It just has a pic of an angle relationship and they told me what kind of relationship it was. You can do this several different ways...4 corners activity, white board activity, SMART response, quiz, whatever you like really.

The last basic geometry lesson we did was over 2-D and 3-D shapes. They learn about this in middle school, but as I've learned you can't ever assume they remember it. We went over the formulas for the 2-D shapes and practiced using them.

2-D and 3-D Shapes

(The one I gave students is blank. They had to fill in all of this information. Here's a copy of them both: blank, filled in.)

For 3-D shapes, I decided to do a little more than just give them the formulas and we practice and move on. I like doing projects, so I figured why not do one for this? I assigned each student a 3-D shape and had them present the following: the net, the shape, the number of edges and vertices, the volume formula, the surface area formula, and examples of how to use each.

Here's a link to the project.
Since the net and shape had to be tangible, I made a mobile out of them and hung them in my room. Next year, I'm going to make this a requirement when presenting their project. While they presented, the rest of the students were given this sheet and had to copy down the information being presented to them.

Here's the link to this page.

Here are the mobiles that I made from their work.

I liked this project a lot, but it took a little too much time to do. It will definitely be like a 2-day project next year. I'm also going to require them to get their information approved before presenting. Thankfully it only happened once, but one of the formulas presented was wrong which caused some issues but nothing too major.

If this is the first time you're visiting my blog and you're curious as to how my notebooks work, follow the links below and you can see how my notebooks are set up!
ISN Set-Ups 2015-2016
ISN Set-Ups

I hope you find some use in your classes from these ideas. Feel free to leave comments about how these lessons went for you or if you have any suggestions I'd love to hear them. Happy teaching!

Bazinga: Another Easy Review Game

We're coming upon the end of the school year, which means finals! I've had this game ever since I've started teaching and it's one of my favorites to use. It can be used for any type of class, not just math. The kids love it because it's not one of those games where the smartest group wins (though they have the best shot). I found this on Pinterest during my first year of teaching, but it didn't link to any instructions, so I kind of made this up based off of what I saw in the picture. I call it Bazinga (I've heard others call it ZAP, but I like Bazinga better).

To make the board, I bought a piece of foam board. I got the pockets from Mardel (they don't sell this particular pocket anymore, but they sell many others that are cute). I hot glued the pockets onto the board and printed out the pocket numbers, discards, and Bazinga onto lime green cardstock. I just hot cut that stuff out and hot glued it on the board also. Once the board is together, then you just create the cards. I have 31 cards, but you can have more or less. I wouldn't go less than 27 so you can have 3 in each pocket. On the cards, I wrote many different things that I thought would make the game interesting. Here are some ideas:

• Add 1 or more points to your score
• Take 1 or more points from your score
• Take points from the winning team's score and add to the losing team's score
• Winning team does 10 second dance
• Losing team does 10 second dance (they HATE these cards...if they don't do the dance, I take all of their points, and all group members must stand up and dance before I start timing)

Of course, the Bazinga card is in the mix. It doubles that team's score, so they are always trying to find the Bazinga card.

So this is how we play...students will get in groups and come up with some group name. I'll write the names on the board so the score is kept up there. They'll pick numbers and whoever is closest gets to go first. I'll write a question on the SMART Board and they get to answer. The other groups must work out the question at the same time. I sometimes give time limits, depending on what we're reviewing. If that group gets the question right, they get a point and get to draw a card and do whatever that card says. If they get it wrong, the question goes to the next group. If they get it right, they get the point and the card. If not, it keeps going until someone gets it right. (If I feel that no one will get it right, I'll go over that question with the class and no one gets the point. This doesn't happen too often.) After the correct answer is given, a new question will go to the next group and continue like that until we either run out of cards or the bell rings.

My students love this game and they get pretty competitive with it. It's another quick review game that I don't have to put much effort into, which is why I love it. I pull out the board and get some questions together from the text or worksheets and we get going. Easy as that! I hope that your students like this game as much as mine do. Happy reviewing!

Notebook Set-Ups 2015-2016

This year I set up my notebooks pretty similar to last year's with some minor changes. For the covers, students used cardstock and a pre-made class label. They had to put 5 numbers that represented them. After they were finished, I covered them with some clear plastic covers I found at Five Below. It was kind of like laminating/contact paper in one, but much easier to work with and thicker. I had bought it hoping to make a cabinet dry erase when I discovered they were actually clear. That was a happy mistake because they made excellent notebook covers. Here are what mine look like. I used all of the same numbers about me for each. I wasn't feeling too inspired that day I guess.

 

We all set up our notebooks just like mine. I do this for a couple of reasons:

1. If they miss a day, they can get caught up pretty easily from anyone that was there.

2. It makes it a lot easier to grade since there's is supposed to look like mine.

3. It teaches them organization.

4. They actually use them to help on their homework/open note tests since they're more organized.

On the inside front cover we put our notebook rules. We go over them and discuss how their notebook will work. Since this was their first year with me, it took them a little while to get used to how we take notes. I don't think the teacher before me required it. After a while, they quit asking "what page does this go on" and "do we have to write this down" because they knew the answers to those questions.

 

On the first page is our Table of Contents. We do this together every day so all of them look the same. We do this so they can reference to something quickly instead of flipping through all of their pages to find something.

On the next few pages is the vocabulary section, which I call "Words Worth Knowing" or WWK. I kind of got a little lazy with this part, unfortunately, and we didn't have nearly as many words as we probably should have. There's always next year...

After that is the syllabus.

Then we start our notes for that class.

On the last page we have the iPocket. This is where we put papers/foldables that we didn't get a chance to glue into our notebook yet or we're still working on.

And on the back cover is the common types of math mistakes. I go over this with them at the beginning of the year, hoping they would be more proactive and fix their own mistakes instead of hearing "I don't know what I did wrong" or simply "I don't get it." Alas, that was not the case.

So here is our math notebooks this year. I'll be posting foldables and activities soon from each class. If you would like any types of resources, use the contact me button on the right hand side and I'll be happy to send you what I have! Happy teaching!