# Logic Story Books

Students tend to struggle with symbolic logic.  It’s hard for them to see the order of the logical statements and the reasons behind it. They want to use the inverse or converse to prove something because it’s there. I feel like it’s hard for them to visualize why they can’t do it with symbols until they see why it doesn’t work elsewhere.

We had some time after a quiz on a long block day (85-minute class), and I decided to let their creative side show.

I asked the students to create a children’s book using logic statements.

• They needed at least 10 statements
• Create a story with fluidity by using the transitive property, contrapositive, and conditional of the statement at least once ( & identify when they used what)
• I gave the students the story “If you give a Mouse a Cookie” as an example

This really helped especially with creative transitive statements. For some reason, they seem to struggle with identifying transitive statements when creating proofs.

I let students decide how they wanted to create the story. Some students created theirs on paper while others created it on power point, pages, or google docs. I wanted everyone to see the other stories, however, class time didn’t allow that.

I decided to utilize the wiki feature on Haiku, and I set up a wiki assignment where every student uploaded their story. For homework, student’s had to comment on at least 4 other stories from any of the three geometry classes. This has the same effect as a gallery walk with post-it notes, but it’s now archived on their Haiku. This was a fun activity that didn’t take up too much time. Students really enjoyed creating stories!

# Create a Picture: Exploring Vocab and Geogebra

I love projects. From my observations last year, students seemed to get a lot out of applying their knowledge instead of taking a formal written assessment. After learning basic geometry vocabulary and briefly playing around with Geogebra for constructions, I created an art project for students to show me what they know.

• 15 words is a lot (agreed)
• Some students said they would have liked it better if they didn’t have to use GeoGebra. Part of the assignment is learning the software, so that part is staying for next year.
• Most students said that creating their pictures and having to write about what they did using the vocabulary really helped them visualize the vocab and apply it, instead of just memorizing

I also gave a quiz on the vocab after this project. Although this way a graded project, it was used as a way to enhance their learning, not just assess it. Below are some of the amazing projects I received. My students are so creative!!!  I also had my students do a gallery walk (each received 4 sticky notes but they asked for more) when the project was due. This gave them a chance to see other people in their classes work and made everyone feel good about their work 🙂

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# #ElonEd Chats Storify

We’ve had some great chats! #ElonEd Chats are open to all educators!

When?

Every other Sunday @ 8:30 PM Est.

Here are all of the archived chats in Storify if you missed them!

# Week 1: Creating a Culture of Math Discussions and Debates

Starting my second year of teaching.Thankfully, I had one prep that didn’t change, Geometry! I’m finally out of the “holding my head up right above the water so I don’t drown” year and am finally truly changing and analyzing my classes. This year I decided to have two main goals.

1. I want my students to speak and debate mathematically
2. I want my students to write mathematically

For this post, I’m going to focus on goal #1.  In my first week back, I created more mathematical discussion than I had the entire previous year.

At Twitter Math Camp this summer, I went to a morning session with Mattie Baker and Chris Luzniak  about creating a culture of mathematical discussion and debate. One of the many ways to do this was to set up a classroom environment is which students use the format

My claim is____________. My warrant is _____________  to express and justify their ideas.

I started using this format on the first day of class. I started asking fun questions like “what’s your favorite movie?” “where’s your favorite vacation spot” and some “would you rather” questions. This was a great way to help students become comfortable with the format, get comfortable with each other, and helped me learn their names very quickly. We continued with these same type of questions on day two.

Next, I started asking more mathematical questions, specifically for vocab that they were supposed to look up the night before for homework. I called on two or three students per vocab word to hear their opinions. If there was a controversial word, I asked more students for their thoughts.   This was a great way to go over and discuss vocab in an interactive way. I could also see what misconceptions they had of certain words.

Then I used this to explore a topic that we hadn’t really focused on yet. For homework, I had students look up the definition of congruent and equal and compare them. When they submitted their responses I could tell that there were misconceptions. Students also didn’t know when to use equal versus congruent.  I decided to start the class with some claims and warrants. The entire class became involved in the discussion on where = or congruent belongs and WHY it belongs there.

I have also used this to discuss a topic that we learned the day before. Chris had a great activity debating if the best method of finding distance  is the Pythagorean theorem or the distance formula (depending on the information given). I let students work through the three distance problems but also provide a claim and warrant for why they chose that method. At the end of class, we shared our claim and warrants as a class.

I’ve really enjoyed implementing claim and warrants into my class so far. I can’t wait to try (and blog) once I try other things from this session!

# Simplifying Rational Expressions: Mafia Edition

When simplifying rational expressions, students always seem to want to simplify TOO much (and incorrectly) !! Below are a few common”over simplifications” that I’ve seen.

This is where #lifelessonswithFinney kicked in. We started talking about the Mafia. Yes, the Mafia. Not only were we talking about the Mafia, but we were talking about killing off family members of the Mafia.

The polynomial is our numerator is a family. The Mafia Family. The denominator is our hitman.

I asked my students what they thought would happen if they tried to kill only one member but not the rest of the family.

“We’d be in trouble!!!! They’d come after us!!!!!!!!!”

Exactly. So we if we want to kill off one member of the family then we have to kill them all! This is the only way that you’d make it out alive! If you can’t kill them all then it is fully simplified. Killing doesn’t mean you have to get rid of it completely. However, you must “hit” every member of the family.

# Making Percents Real : Apple Edu

I just finished my first week of teaching Algebra 2 ever. On one of the first days, I wanted to dive in and do math, but I didn’t want to intimidate my students so early in the year. Julie Reulbach gave me the great idea of reviewing percents by looking at Apple Computers.

I handed out the sheet I created with no other instructions or introduction than they could work with a partner to figure out the answers.

The worksheet I created explored the 13-inch MacBook Pro. First, I had students find the tax  on the computer and then justify how they found it.

Next, we looked at the price of the 13-inch MacBook Pro compared to the price of the same computer from the Apple Education Store. Students had to find the percent discount.

Third, students had to apply that percent discount to the cost of the 15 inch Macbook Pro to figure out what education price would be.

This is where the conversation became interesting. After everyone was finished, I revealed the actual education price of the Macbook. They were outraged!!! The price was about \$100 more than they calculated it should be!!!

This then prompted the question “Do you think this happens for every Apple Product?”

Each group then picked an Apple product. We looked at Macbook Air, Ipads,  and Imacs (I have a class of 8 students).

Students picked what size they first wanted to look at and then found the percent discount from the original price to the education price. Once they found the percent decrease they wrote their percent on the board. They then looked up a different size of the same product to see if they discount remained the same!

This lead into a discussion about which product receives the biggest discount and why. Also what we thought affected the discount, and how sales aren’t always as straightforward as they seem.

This was a fun, easy, and real-world lesson that helped students review percents without sitting through a review lesson or by doing practice problems.

We did go over the worksheet to address any class misconceptions before we broke out to look up different products.  Originally, many students found the percent tax by finding the tax and then adding it to the original. This was a great opportunity to introduce original(1+percent) which they see for growth and decay later in the chapter.

# What Makes Twitter Math Camp so Special? Let Me Tell You…

What makes Twitter Math Camp so special? You’re going to a conference that’s referred to as a camp? Wouldn’t more official conferences give you more PD? You’re going to a conference about twitter? One year ago, when Julie Reulbach first told me about TMC, I had no idea what I was getting myself into. Although I had been on Twitter for professional purposes I had NO idea how many math teachers were on Twitter. I definitely didn’t know about #MTBoS.

Over the past year, I started blogging and connecting with other teachers via twitter and started to realize what Julie was talking about. I started making connections with educators who lived all around the world that had the same passions as me. I was tweeting with teachers who were influential in the math education world, but also teachers who were just starting out like me.

I was a little nervous heading all the way to Minnesota to meet a bunch of people who I’ve only interacted with on Twitter. I’ve been hearing about Twitter Math Camp, and I had extremely high expectations. I was afraid that TMC wouldn’t live up to the hype. Let me tell you… it exceeded all of my expectations.

Now, what made TMC different from other math conferences?

AMAZING Sessions

The teachers who attend TMC are teachers who are innovative and extremely involved and committed to changing math education. They are evangelists. All of the presenters are part of the community of #MTBoS. Their presentations are interactive and provide teachers with information and content that they can bring back to apply directly into their teaching.

TMC teachers were also given the opportunity to have a Pre-Conference with Desmos. New features of this amazing calculator are presented to these teachers. These teachers don’t only love new features but love to share what they’ve found.

The Schedule

TMC is organized in a way that allows teachers to truly take the most out of the conference

• 9:00- 9:30 Morning Opening and My Favorites: My favorites is a time for teachers who did not want to do an hour long session/found something cool to share a chance to share with the entire TMC community for 5-10 minutes. My favorites were accepted through out the week and open to ANYONE at the conference.
• 9:30 – 11:30 Morning Sessions: On the morning of the first day, you got to choose a morning session that you would attend every morning for three days. I chose “Talk Less, Smile More” Given by Mattie and Chris Luz  (Blog post to come). This 6-hour session inspired me to change the entire design and culture of my classroom. This session provided me enough time to truly learn about debating math in my classroom.   We were also able to work on things to implement into our classes during this session. I loved having a focus for three days.
• 11:30 – 1:00 pm: Lunch: During lunch, we look over restaurants, and talked casually about our morning sessions. This is also a chance to catch up with people who we’ve only interacted with on Twitter.
• 1:00- 1:30: AGAIN My Favorites: GIVING MORE TEACHERS A CHANCE TO PRESENT.
• 1:30- 2:30: Keynote Speaker: Daily motivational presentations that left educators in tears by the end. Have you ever been to a conference where you felt so inspired you cried?
• 2:45- 3:45: Afternoon Sessions: There were about 12 sessions to choose from every day. These sessions were pre-approved before the conference.
• 4:00-5:00: Flex Sessions: Flex sessions were an extremely cool idea. During the week many people found a common interest and they wanted to know more about it. Flex sessions were a chance for people who were not approved for the afternoon sessions to present. Anyone could present during the Flex sessions.

THREE whole days of Math!

Although the conference technically ended at 5:00 the learning and bonding didn’t stop. At dinner, drinks, 12 am in our rooms the conversations never stopped. There was never an “end” to the conference. Oh, and I did I mention we all stayed in dorm rooms together? I probably only slept about 5 hours a night…

The Community.

I honestly don’t know how to describe how amazing the community is at TMC. Everyone is extremely welcoming and willing and eager to share any resources and advice with you. I ‘ve never been to a place where it was perfectly normal to go and stand next to a group of people you’ve never met (or idolized) and they welcome you in with open arms to the conversation. I felt that I was connected with plenty of teachers on Twitter, but now I have an even wider network. I know that I can talk to any of the presenters even though the conference is over.

This conference focuses on building relationships and support within the math community. We all went out to dinner together one night where we took up half the restaurant. We also had a Trivia Night ( my team won btw ) where we broke out in song between every round.

We even created a TMC song where we choreographed dances, wrote lyrics, and played instruments (and Desmos Graphs) to represent our few days at this amazing conference. Truly a camp experience

I’ve learned so much at this conference about teaching, math, and myself. The more I learn; I realize that I know nothing. TMC is a conference where the learning never stops. You don’t dread being in sessions and you feel connected to the speaker. I’m part of a community where I can constantly learn and grow.

See everyone again on July 27-30 in Atlanta. Until then I’ll see you on Twitter. 🙂

# Day 0: #DESCON16.

As if going to my first Twitter Math Camp wasn’t enough, I also got to attend an entire day of Desmos! I just finished my first year of teaching and Desmos has been a staple in all of my classes. To the say the least, I was VERY excited.

The day started with breakfast and a video message from Eli from Germany. Then the Desmos team started showing us some awesome new Desmos Graph features and a Desmos Potluck. One of the  newest features makes Desmos accessibility for blind and low-vision studends. Pressing command F5 turns on the sound narrator which will allow Desmos to audibly describe your graph. You can also HEAR what your graph sounds like! During a session, a group of teachers worked together to create a graphical representation of “Mary had a Little Lamb” https://www.desmos.com/calculator/xdz17jn1rw SO COOL. This new feature is not only amazing for the low-vision students, but also opens up so many opportunities for interdisciplinary projects in Desmos!

During the day, we broke into groups and participated in a Desmos Graph scavenger hunt. During this scavenger hunt, I learned about another great Desmos feature http://learn.desmos.com/. This site provides interactive instructional activities on how to use different features on Desmos. I definitely had fun playing around with polar graphing!

Lunch time! (thanks  Desmos!).

Then we got to hear from our first keynote speaking.  Sara VanDerWerf. She was encouraging us to be “evangelists”!

Now for the best part: The Desmos team introduced two new features to the activity builder.

• Bundles: Desmos has taken a bunch of activities and “bundled” them into topics. These bundles are not only a bunch of content similar activities bundled together. The bundles also provides  key understandings and  suggest the order in which the activities should be played! This is an example of a Functions Bundle.

• Create your own cardsorts and marbleslides:  HALLELUJAH!   They now let you make your own marbleslides and card sorts! No more laminating, cutting, missing cards to do card sorting in class! It’s amazing! I made my first one on sorting different types of quadratic  equations.  We also created a collection of our card sorts! To activate the feature, just click on your name in the top right, then go to labs, and enable them.

After a day of Desmos fun, the Desmos team then took us out for Happy Hour!!!  Thanks Dan, Christopher, Michael and the whole Desmos crew for a great day! And Obviously, we had to take a selfie with Dan Meyer!

# New Idea for Checking Homework: Math Journals

As the year is coming to an end, I’ve started thinking about how I want to organize next year. I am really trying to include more writing into my geometry curriculum.

I have decided that I am going to create a math journal for my students for each chapter. This journal will include:

• Pre-assessment Essential Questions
• Notesheets
• Homework
• Blank note sheets
• End of chapter Essential Questions

During the chapter, I plan to check homework a few times a week. If students didn’t do their homework, I plan to mark the homework in red pen. If students didn’t do certain problems, I plan to circle the problem in red pen. This is the only recording I will do for homework the entire chapter.

At the end of the chapter, I plan to collect every math journal. Students must turn in a complete math journal. The homework that they did not do/finish must also be completed.

My idea is that  when I scroll through their math journals, I can easily see if they missed  a homework by looking for red-pen. If there is no red pen, they receive full credit for homework. If I see red-pen, but the problems were completed at a later date, they will receive a small deduction from their homework. If they did not complete the problems they missed, they will have a larger deduction taken from their chapter homework grade.

My idea is that this will encourage students to do their homework and make them accountable for doing homework they missed.  It also helps that all of their work will in one place.

Collecting the journals will also give me a chance to how my students have grown from the beginning to the end of the chapter. Looking at the pre-and post essential questions will help me easily see this growth.

The journal will also help keep my students organized. I’ve already started putting my first two unit journals together. A lot of my notes are done their PearDeck, but this journal gives me a chance to put in some guided notes and space for my students who like to take notes by hand.

I decided to break up the journals by chapter, so I’m not stuck with certain material all year. I just have to make the lessons for the unit a week before.

I’m looking for feedback, suggestions for this journaling and homework idea.  Has anyone tried math journals before? Do you think grading homework will be effective? All feedback is welcome 🙂

# Volume of 3D Shapes with Play-Doh and Water

I love when my students are engaged and visually learning.  After Julie Reulbach told me about how she used Play-doh to create 3D shapes with her students, I decided to try it out. I had students work in groups of two to create 3D shapes.

Supplies per group:

• One fun-sized Play-doh
• Ruler
• Plastic knife

Students were given the following instructions

1. Create a square prism
2.  Using your ruler, cut your shape into 1 cm pieces. Cut it away that all of your pieces are the same shape. Specify that you can only cut once to make the shape.
3. Next, we discussed finding the area of one piece and then multiplying it by the number of pieces to find the volume. They realized that the number of pieces their prism was cut into was the “height”.

We repeated this with a triangular prism and cylinder. Students came up with the formula that volume= area base*height.

Next, I had students create a cone and asked them to cut it into identical shapes. They realized they couldn’t. I wish that I had 3D solids at this point in class (I got some later), but I did the next best think by showing them a video.

I first started out by asking if they thought a cone could relate to any of the other shapes we’ve talked about. A cylinder quickly became the winner because they both of circular bases. I then asked how much bigger did they think the cylinder was compared to the cone. After taking classroom bets we watched a video using corn kernels from a cylinder to fill up 3 cones. This helped us derive the equation for the volume of a cone.  We did this same thing for finding the formula for a pyramid.

This play-doh activity really helped my students visualize the formulas and understand that the height of the pyramid didn’t always go from top to bottom. We described the height as the direction we’d slice the shape to create congruent shapes.

The next day, I did have 3D solids and set of stations around the room.

Station 1: Cone and Cylinders

Station 2: Triangular and Square Pyramids and their prisms.

Stations 3: Octagonal Pyramid and Octagonal Prism.

Station 4: Half Sphere and Cylinder

For stations 1-3, I had students first find the volume of the shapes algebraically. They then fill up the shapes with water and measured the volume of the water using graduated cylinders. They loved seeing their math match up (close enough). This also gave us a chance to talk about percent error (spilling water).

For station 3, I first had them fill up the half sphere with water and measured the water with the graduated cylinder. Next, they had to figure out how many half spheres it took to fill up their cylinder. The cylinder was the same height of the half sphere.

It was then up to the students to derive the formula for a half sphere, then a full sphere. The hardest part for them was making the connection that the height was also the radius.

I loved these water stations. Students got to visualize the formulas for the second time, they got to practice finding volume, and they got to derive the formula for a sphere.

After class, I asked my students if they would have liked doing the water activity on the first day. They told me they liked doing the water later in the lesson because they had a day to let the play-doh formulas sink in and they could reaffirm what they knew and discovered something new.