Math = Love: May 2013

Friday, May 31, 2013

Algebra 2 Conic Sections Foldables

The tornado in Broken Arrow yesterday hit about a mile from my family's business.  I ended up in the storm cellar at my parents' house for the second time this month.  I've always hated tornadoes, but this one hit way too close for comfort. 

Yesterday, I wrote about the amazing experience my Algebra 2 students and I had using Cindy Johnson's Conic Cards.  Here's the proof.  Instead of giving my Algebra 2 students a final exam, I challenged them to complete three interactive notebook pages over three topics we had studied this year.  I was pleasantly surprised to see tons of projects about conic sections! 

While working on these projects, my students asked me where the conic cards were so they could use them as a reference.  This is a testament to just how comfortable they feel using the conic cards.  Even though they hadn't used them in several weeks, students still knew exactly where they could find each piece of information that they needed.  And, I'm pretty sure hyperbolas were their least favorite conic section because only one student submitted a project over hyperbolas.   
Again, remember that these are student projects.  If you decide to use any of these with your classes, be on the lookout for small and large errors! 

Circles Foldable - Outside

Circles Foldable - Inside

Ellipse Foldable - Outside

Ellipse Foldable - Inside

Ellipse Interactive Notebook Page - Outside of Foldable

Ellipse Interactive Notebook Page - Inside of Foldable

Parabolas Interactive Notebook Page - Outside of Foldable  (Notice - they accidentally flip-flopped their foldables when they glued them down.)

Parabolas Interactive Notebook Page - Inside of Foldables

Ellipse Interactive Notebook Page

Circles Foldable - Outside  (The inside did not photograph well, so I am not posting it.)

Parabola Interactive Notebook Page - Outside of Foldable

Parabola Interactive Notebook Page - Inside of Foldable

Parabolas Interactive Notebook Page - Outside of Foldables

Parabola Interactive Notebook Page - Inside of Foldables

Circles Foldable - Outside

Circles Foldable - Inside

Hyperbolas Foldable - Outside
Hyperbolas Foldable - Inside

Circles Foldable - Outside

Circles Foldable - Inside

Parabolas Interactive Notebook Page - Outside

Parabolas Interactive Notebook Page - Inside

Parabolas Interactive Notebook Page - Inside

Circles Interactive Notebook Page - Outside

Circles Interactive Notebook Page - Inside

Circle Interactive Notebook Page - Outside

Circle Interactive Notebook Page - Inside

Parabolas Interactive Notebook Page - Outside

Parabolas Interactive Notebook Page - Inside

Thursday, May 30, 2013

Conic Card Diary

This post has been setting in my drafts since early April.  I finally got around to finishing it today.  If you teach Algebra 2 and you haven't heard of Conic Cards, I want you to stop what you are doing right now and send Cindy Johnson an e-mail right now.  Cindy Johnson is a National Board Certified Teacher.  Her e-mail is johnsoncindy2002 at yahoo dot com.  You can also check out her blog at Conic Card Lady.

The conic cards include ten equations, ten graphs, and ten descriptions of each type of conic section for the students to match.  Formula cards are also included.  There are 9 different decks that allow students to practice matching different equations, graphs, and descriptions each day.  When you e-mail Cindy, she will send you the cards to print, worksheets for each day, and copies of tests and projects she has successfully used in her own classroom. 

If you're thinking that these conic cards can't possibly be that great, lots of other bloggers have already written about their love for conic cards.      

Conic Cards
Honestly, I was dreading teaching this unit.  When I took Algebra 2, I remember struggling with conic sections more than any other topic we studied.  There were so many formulas to remember, that it was quite overwhelming. 

The Preparation Process

Lots of Cutting and Laminating!

Day 1: Parabolas
If this was a one-day activity, I would call it a failure.  But, it's only day one of a learning process.  My students obviously don't know how to follow directions.  I thought that asking students to remove the cards with only one word on them was as clear as possible.  I also thought that asking them to remove the cards that didn't have a number, letter, or symbol in the top left hand corner was clear.  Wrong. 

My students really wanted me to let them use their graphing calculators.  All year, we've used our graphing calculators.  So, it was hard for them to understand why I was asking them to identify parabolas without the calculator. 

They didn't pay as much attention to the formula cards as I would have liked.  But, I have to keep reminding myself this is Day 1.  They will start to see the patterns.  They will start to look for the patterns. 

Day 2: Parabolas and Circles
Conic cards are great.  Conic cards held together with a rubber band are less great.  I don't know what it is about a rubber band, but my students can't seem to stop playing with them.  Let's just say that tomorrow, my students will find that their conic cards are stored in freezer bags instead of held together by a rubber band. 

Some of my students really stepped it up today.  They started looking for patterns in the formulas of the parabolas and circles.  I had a couple of students ask a really great question about determining the vertex of a parabola.  They had one equation of a horizontal parabola and one equation of a vertical parabola.  We had a great conversation about how the location of h and k in the equation depends on what variable the equation has been solved for. 

It wasn't a perfect lesson, though.  One student who was absent on Day 1 wanted nothing to do with the conic cards.  She refused to participate.  She refused to work with her partner.  She even refused to scoot her desk next to her partners.  Instead of asking questions, she just wanted to talk to the boys sitting behind her and play with the rubber band off her deck of conic cards.  She ended up actually walking out of my classroom without permission.  Some other students stepped in and helped her partner, and that was really great to see. 

The Day 2 activities did not entirely fill our 50-minute period.  But, I'm kind of glad.  The early finishers really stepped up today and helped the other students.  Those who had discovered patterns and created tricks of their own started just going around the room and helping others.  And, they weren't giving answers.  They were actually explaining and helping each other.  I consider that major progress.          

Day 3: Parabolas, Circles, and Ellipses
The students noticed today that the rubber bands were gone.  They were sad.  I wasn't.  The girl who stormed out of class yesterday acted like she didn't want to participate today either.  I let her and her partner work individually.  I don't know if that was a good decision or not.  I mean, it worked out, but was I rewarding her for acting out?  Since I had three students working individually today, I ended up doing a lot more explaining than on the previous days.  I like the group work aspect of this.  It encourages mathematical conversation.  Still, many of my students refuse to talk to their partner.  Or, one partner tends to dominate the sorting process.  I saw students stepping up and helping other students today which was exciting.  And, I loved seeing my students' reactions as I checked their answers.  If the first trio of cards was correctly matched, they would utter a quiet "Yes!"  With each successive trio, their exclamations became louder and more excited.  Excitement in Algebra 2?  Yes, it's possible.  But, I have to say I haven't had enough of it in my Algebra 2 class this year. 

I took for granted that my students would know that an ellipse was oval-shaped. 

One group of boys even went ahead and matched the hyperbolas even though that wasn't part of today's lesson.  I didn't stop them, though.  I'm still not sure how to best manage my class time during this unit.  The matching does not take my students the full 50-minute class period.  Even after doing two EOI prep questions as bellwork, the students still complete the matching and finish their homework with more time to spare than I'm comfortable with.  I want my students to be working from bell to bell.  Maybe I'll try to sneak in more EOI review at the beginning tomorrow.  I know my students are going to love me!   

Day 4: Parabolas, Circles, and Ellipses
I think my students are finally getting the hang of the card-sorting process.  When I hand out the cards, they simply start sorting the cards into groups.  They're doing really well with parabolas and circles.  Ellipses are still tough for them, though.  Some of my students have figured it out, but most just cross their fingers and guess which ellipse cards go together.  Tomorrow, I think we're going to spend some time graphing ellipses on the smart board and discussing what role each number and variable in the equation plays. 

Day 5: Parabolas, Circles, and Ellipses
So, after graphing some ellipses together as a class, my students did a much better job today of matching their ellipses.  My students are really anxious to start the hyperbolas.  Every day, they come in and ask if we're going to do hyperbolas yet.  A lot of students have been gone lately for various school activities, and that makes me nervous.  I told them that they would need to come in before school, after school, or at lunch to work on matching up the cards from the days they were gone, but they don't seem too concerned.  Next year, I think I don't think I want to save conic sections for the very end.  This whole unit is feeling a little more rushed than I would like. 

Day 6: Parabolas, Circles, Ellipses, and Hyperbolas
Today was my students' first experience with hyperbolas.  They whizzed through their matching of the parabolas, circles, and ellipses.  Then, everybody seemed to raise their hand at once wanting help with the hyperbolas.  Since I don't have the ability to clone myself, I told them to look at their formula cards for help and to discuss ideas with their partner.  Then, I slowly worked my way around the room.  I think I'm going to have to do the same thing with hyperbolas as I did with ellipses.  I need to walk my students through the process of graphing a hyperbola tomorrow.  If I was teaching a Pre-AP Algebra 2 class, this direct instruction may not have been necessary.  But, my school only has one Algebra 2 class.  My class is made up of students of all levels.  Next year, I think I will design interactive notebook pages that we will complete together as a class before jumping into the card-sorting.  This will give my students something to reference when I am not immediately available to answer their questions.

Day 7: Parabolas, Circles, Ellipses, and Hyperbolas
Half of my class was gone today.  Students are still frustrated over hyperbolas.  So, today I decided that we would get out our interactive notebooks and write a summary of each conic section.  This too a lot more time than I expected, but I think it was worth it.  I'm pretty sure I saw a few light bulbs come on. 

One of my students raised his hand to ask a question.  "How can I be good at this when I haven't understood anything else all year long?"  These cards work.  These cards show students that they are capable of doing algebra.  And, that student did pass his Algebra 2 EOI exam.  He may have struggled with the concepts more than his fellow students, but he definitely learned a lot this year.  I'm proud of him and all the hard work he put in even when it didn't come easily to him. 

Day 8: TEST Day!
Yesterday, I told my students they were going to be having a test.  They weren't excited.  But, when I told them that their test was to simply match up all the conic cards, they didn't seem to have a problem with that. 

I just got finished grading the tests, and each group scored at least a 90%.  I would call conic cards a definite success.  Now that I fully understand how the cards work, I'm looking forward to teaching conic sections next year.  I'll be making a few tweaks, and I look forward to sharing those with you next year! 

Wednesday, May 29, 2013

Common Core Flipbooks

As soon as I saw this post by Algebrainiac, I knew I had to make my own common core flipbooks.  Oklahoma is one of the many states to adopt the CCSS.  We still have one more year of our old standards, but we are supposed to be starting the transition process.  I'll be honest.  As a first-year teacher, I did very little with common core.  I read a lot about it, but my main focus was getting my students ready for their end-of-instruction exams which are required for graduation.  And, those exams are not common core aligned. 

Next year, I have plans to do better.  I want to make a conscious effort to incorporate as many of the mathematical practices as possible.  I want to ask more rigorous questions.  And, I definitely want my students to ask more questions.  I'm going to be part of the Oklahoma Geometry and Algebra Project (OGAP) this summer, and I'm hoping to learn a ton more about what exactly common core will require in my classroom through that. 

Back to the flipbooks.  I printed the flipbooks off of this website.  Next year, I am going to be teaching Algebra 1 and Algebra 2.  So, I decided to print off one flipbook for each.  I didn't print off the entire thing, though.  That would be a bunch of pages!  Instead, I use our Oklahoma OC3 standards to figure out which common core standards belonged to each subject.  I followed Algebrainiac's advice and color-coded my booklets. 

I printed these off double-sided on letter size paper.  All the colors I used were 24 pound paper except one of the colors which was 20 pound paper, and I noticed it really did make a difference.    

To make these more durable and to make sure I could tell them apart, I printed off covers for each booklet on cardstock and ran them through my laminator.  This will protect the cute little tabs when I'm not using my flipbooks.  I love that these flipbooks put the standards, sample problems, common errors, and more all in the same place.  I can already see me using these a lot!   

My finished products:

Front Laminated Covers of my CCSS Flipbooks

Inside Pages of CCSS Flipbooks

Close-Up of the Inside

Tuesday, May 28, 2013

Math Lessons in the Making

This summer, I've been scouring thrift stores and yard sales for stuff.  Not just any kind of stuff, but the type of stuff that can make math come alive.  The only problem is that I don't know what that stuff is until I see it.  It started when I asked my mom to keep an eye out for Barbie dolls when she stopped by a certain thrift store.  I've read so much about the Barbie Bungee activity on other blogs.  I decided it is a must-do with my Algebra 1 students next year.  The only problem is, I didn't own any Barbies. 

I didn't stop at just buying Barbies.  I'm a very visual person, so here's pictures of my "stuff."  I already know how I'm going to incorporate some of it into my classroom, but I'm still waiting for inspiration on how to use others.  So, if you have any great ideas on how to use this stuff to help my students experience the power and beauty of math, please share!  And, are there any other unconventional teaching tools that you think every math teacher should have in their classroom?  

I picked up this Guess Who? Game at the thrift store.  I've got plans to repurpose it into a "Guess My Equation" game.  Instead of asking if the person is wearing a hat or glasses, one student will ask another, "Is your equation in point-slope form?"  "Does your equation have a positive slope?"   

My sister actually made these in her elementary art education class this semester.  I don't know what it is about these, but I just think "math" when I see them.  These will definitely be finding a place on my wall in my classroom.  Last year, I hung up some geometric string art that my sister had done, and it was a big hit. 

Oatmeal Cans.  I don't have plans for these *yet.*  If I was teaching geometry, these would definitely be making an appearance when we talked about the surface area of a cylinder.  But, I'm teaching algebra instead.  Hmm...

Aren't these the cutest little container tubes?  I don't know what they're from, but I picked 20 of them up at a moving sale for $2.00.  I'm planning on making some self-checking activities for my students to use as remediation or extra practice if they finish early.  And, I think these cute containers will work perfectly to keep these activities organized. 

Bingo Chips.  I bought red and yellow bingo chips last year to use to model adding and subtracting integers.  I'm excited to see if there are any other ways I can use bingo chips in my classroom. 

I picked up this Katamino game at a garage sale for $2.00.  It's brand new and still wrapped in the plastic.  I had my first experience with pentominoes in the second grade, and I've loved them ever since.  I plan on keeping this in my classroom for early-finishers or those crazy days where everybody is gone except two people. 

Playing Cards.  I've seen tons of math ideas using playing cards.  I can't wait to try out a few with my students!

Slinkies.  If these will successfully travel down the stairs at my school, I can see myself challenging my students to write a linear equation that models the height of the slinky at time t. 

These lovely ladies will be participating in our First Annual Barbie Bungee Competition. 

These men may also be participating in the bungee jumping festivities.  My dad told me that I needed to give the boys a more manly option.  I found these at a garage sale for 25 cents each. 

This isn't a math lesson, but I'm excited that I will have a trash can behind my desk next year.  Last year, my classroom only had one trash can, and it was as far away from my desk as possible.  I guess I could make this into a math problem by asking my students to estimate how much less distance I will cover in year if I don't have to walk across the room to throw something away. 

I couldn't resist picking up this light-up hula hoop for a dime.  This will definitely be making an appearance in my Algebra 1 class' unit on ratios and proportions.  Now, I just need to find a couple more hula hoops so I can make it into a group challenge. 

I found this bucket of 30 sets of Tangrams on Amazon for $9.00.  These will be used for early finishers.  Or maybe, I could plan a day of math Olympics where students compete to complete various math-related games. 

I saw a post on pinterest that said these foam rollers can be used as mini dry erase erasers if you take out the plastic part.  My students are in desperate need of new erasers for their dry erase boards, so I'm looking forward to trying these out to see if they work. 

My mom picked up this globe for my classroom.  I'm not quite sure what I'm going to do with this yet, but it will look pretty cool setting on top of my pi filing cabinet until I come up with an idea. 

Sunday, May 26, 2013

Algebra 2 Foldables Made By My Students

Earlier this month, I posted about the project I assigned my Algebra 1 and Algebra 2 students in lieu of a semester test.  Their assignment was to create 3 interactive notebook pages over 3 topics we studied this year.  I was really impressed with what they submitted.  Please note that these were all produced by my students, and there are several small mistakes sprinkled throughout them.  If I do this project again, I think I will have students submit a rough draft for me to review before they complete their final drafts. 
Many of my students chose to do their notebook pages over conic sections, but I'm saving those for a special post of their own.  I know that I was definitely inspired by seeing what my students were able to create, and I hope that others can find something of use here, too.     
Quadratic Formula Interactive Notebook Page

Under the Foldable on the Quadratic Formula Page

Real Number System Interactive Notebook page

Arithmetic Sequences Interactive Notebook Page

Imaginary Numbers Interactive Notebook Page

Inside of the Foldable on the Imaginary Numbers Page

Quadratic Formula Foldable

Inside of the Quadratic Formula Foldable

Function Operations Foldable - Front

Function Operations Foldable - First Set of Inner Flaps

Function Operations Foldable - Second Set of Inner Flaps

Function Operations Foldable - Example Problems

Arithmetic Sequences and Series Foldable and Interactive Notebook Page

Inside of Arithmetic Sequences/Series Foldable

Geometric Sequences and Series Foldable and Interactive Notebook Page

Inside of Geometric Sequences/Series Foldable

Quadratic Formula Interactive Notebook Page