3 Dimensional Graphing

I teach Algebra 2 and one of the topics I find hard to teach is 3 dimensional graphs.  Partly because I am not artistic and so I can't really draw them myself.  And partly because I haven't found a way to help students "see" the third dimension on a two dimension surface.  

My classes have no problems with the Algebra...solving the equations with substitution and elimination is a piece of cake for them.  But ask them to plot the point (2, 3, -4) and they can't do it.  I've tried putting pencils together to show the octants, I've tried putting pencils through paper for dimension.  Not go.  Some students can see it right away, but others never see it.  I found a great website:  http://technology.cpm.org/general/3dgraph/ that does 3-dimensional graphing (see image).  Fortunately, we are a 1-1 school with airMacs and the students also have access to a program called Grapher.  This has helped a few of them get a much better visualization of the equations.

So this year I am trying something new.  I am having my classes create a diorama of a 3-dimensional coordinate system.  I've never done this before and I wasn't able to find anything like it on the internet.  Which makes me even more excited to see what my students create as they will be the first I see ever!

I was mean though....I gave the project over Christmas break.  I figured they would have some down time to put it together.  And maybe some extra boxes and paper left over from the holiday.  :)  I can't wait to see that they do!  I'll post pictures in the new year!

Here is the link to TPT if you are interested in trying it out yourself:  3-dimensional diorama project. 

Merry Christmas.

NCTM - Philadelphia 2016

I cannot believe it is finally here!  It seemed to take forever to get here!  So what am I so excited about....I am speaking at NCTM in Philadelphia on Wednesday!  My coworkers and I are lucky enough to be here and Nora Oswald and I were even more lucky to be picked to speak.  We are beyond excited, can you tell? 

Tomorrow will be all about me learning new things and supporting Nora.  She presents tomorrow on Gaming in an Algebra 1 classroom.  Check her out at 3:15 tomorrow if you are at NCTM!

I go on Wednesday.  Check out the write up from the program book.  I feel so professional now!   The room I am in is set up with tables for 120 people....and I only made 75 packets.     Hopefully I will need that many!   

Here are my packets for tomorrow....just in case you want to look them over!  :) 

Don't forget to wish me luck!

Business Math - Comfort Card INB Page

Not only do I teach Algebra 2, I also teach Business math.  In my business math class, one of my class philosophies is that I allow my students to use comfort cards on their tests.  Other teachers would call them cheat sheets but I call them comfort cards, because the students make them for their comfort during a test.  They are allowed to put anything they want on the card:  definitions, examples, formulas, etc.  The only restriction is that the card is 3.5 x 5in.  So it's not a large amount of space but you would be surprised at how tiny some of my students can write!  :)  My reasoning is that in the business world, we have the time and access to look up formulas and other needed information if we forget something.  Some students love them, but other students chose not to use them.   I also prefer them to open notebook tests as the creating of the card itself forces the students to study by looking over the material for the important items.  (And they just think I'm being nice!)

And in the spirit of INB pages...I had students create a pocket page for the back of our notebook for students to keep their comfort cards in.  This way they always have them to use on every test, especially the midterm and final exam.  I am going to have them write the most commonly used formulas on the pockets themselves for extra space and decorative purposes. 

Algebra 1 Word Problems Graphic Organizer

Do they every get word problems??  Today I was teaching word problems to my Honors Algebra 2 class.  They always hate word problems, even if they are only Algebra 1 word problems.  ;)

For most students the worst part about word problems is breaking them down.  They don't know where to start.  I've tried several different organizers and methods for helping with and have yet to find a way that I really like....until today!   Today, I went to my go to teaching aid - the Frayer Model.  I use it a lot in my classes.  From defining words to organizing examples, I use it a lot.  (I sometimes think my student's interactive notebooks will only be filled with them someday. )

In the past, I had used an extensive organizer for word problems, but frankly, it was just too many steps.  So I looked at it and narrowed it down to 5 parts, which would then fit on my Frayer model design.   Here is the end result:

If you like, feel free to use it.  Here is a PDF file for you to have:
Suzanne's Foldables

Did you ever lose your wallet?

On Saturday, I had my car broken into and my purse, with my wallet in it, stolen.  If this has ever happened to you, you know the frustration and heartbreak this is causing.  If it hasn't, please let me just say this....don't leave your wallet or purse in your car where anyone can see it.  Trust me on this.

Whoever did this broke into three cars, breaking four windows in the process.  It was at 10:30 in the morning and we were all about 100 feet from our cars.  They were fast and quiet.  I still can't believe no one heard or saw anything.  It was broad daylight and people were milling about at a softball game.  I was only there 10 minutes probably when they did it.

I am very fortunate that I lost nothing of personal value that can't be replaced.  I lost my favorite purse and my favorite wallet but I can replace them.  It may be awhile until I find another "favorite" but ultimately, they are just things.  I don't carry pictures with me and I did not have any jewelry or personal items in my purse.  Frankly, stealing my stuff is more of a hassle to me than a benefit to the thief.  They got very little cash and I was able to cancel everything before they even had time to look through my wallet. 

I was hoping that someone would find the purses and wallets laying somewhere, minus the cash, but that we would get our id's, etc back.  But almost a week has gone past and I no longer have hope for this.  And so my nightmare of changing accounts, replacing id's, and dealing with all the little details has begun in earnest.  Every day a new little annoyance occurs that I have to deal with.   And from what I hear, my journey is just beginning.  I remember reading once, that you should take a picture of the cards, front and back that are in your wallet.  I really wish I had done this.  I'm still not sure if I missed one. 

So why am I blogging this?  Mostly as a PSA.  I want everyone to take their purses and wallets with them when they leave their vehicle.  Or at least lock them in your trunk where no one can see them.  If they can't see anything they will move on.  There were over 50 cars in the parking lot and only 3 of us were broken into because we were the only ones with visible items.   And know what you have in your purse and wallet.
 

Protect yourself.

Act Fast: 7 Things to Do When Your Wallet Is Missing

Starting the year healthy

Recently, my 12 year old son Matty was diagnosed with high cholesterol.  I know it may seem strange and unusual for a doctor to even check a person of that age but it is now recommended to check children who have parents or family history of high cholesterol.  And unfortunately, my children qualify.  Although it is not so high as to require medication, it is high enough to warrant a change of diet for him.   So far, Matty is doing amazing with the changes!  He reads every label, eats Cheerios for breakfast almost every day, and has decreased the number of eggs he eats in a week.  But let us not forget....this is hereditary.

My husband has high cholesterol and my results are usually borderline.  As I have three children, I was happy only one result came back high, but because it is genetic, we are trying to change our FAMILY diet.  Shouldn't we all be eating healthier anyway?   Our family is great with staying active.  All three kids do more than one sport, and Mike and I are fairly active, given our age and time constraints.  :)  But food?  We are not as diligent.  Although we like to eat healthy, we are not great meal planners.  We don't always leave ourselves time to cook a full meal every night.  So we eat alot of quick, boxed meals or take-out.  All of which are now no-nos.

Now I don't know about you but the fall is the busiest time of year for my family.  School starts for 4 of us and we have to get used to a whole new routine!  Between work, school and sports our time at home is REALLY limited.  Healthy meals just don't happen that often.  We tend to eat out or on the go, which means ALOT of hotdogs and mac n cheese (BIG NO-NOs!)   So this year, instead of just preparing my lesson plans for the new school year, I also decided to plan my meals! 

Somewhere I had seen an ad for a website that had recipes for 31 healthy crockpot meals for the freezer.  (Click HERE).   I printed the recipes and grocery list last fall and have been wanting to make them but felt overwhelmed at the idea.  It seemed like a lot of prep work and planning and one really long day. A whole year went by and I did not do it.  When I saw the idea again last week, I couldn't resist sharing the idea on Facebook and asking if anyone wanted to do it with me.  I figured prepping and cooking with a friend would be much more enjoyable.   I was filled with dread and elation when my friend Erica said she wanted to do it too!  Without giving either of us time to change our mind, we chose Monday, August 15th to do it.  This gave us about 5 days to plan and shop.  Someone had shared with us a link for a website with only 20 meals but we decided "Go Big or Go Home."  So we stuck with the 31 meals and I cannot say it was a bad choice. I REALLY like looking in my freezer and seeing 31 meals...done!  

It got real on Saturday, when I started to pull together the spices on the grocery list.  I was up and bored so I did it just to get started and the next thing I knew Erica and I were going through the grocery list via text together.   We figured out what we needed to buy and what we could share.  Note....two people will go through one bottle of cumin and curry seasoning and ALOT of honey.  The grocery list does not really prepare you for this.  :)

Now I think we could have done our pre-planning a little better but we did GREAT for throwing it together so quickly.   One thing I would do differently is preparing my bags ahead of time.  Erica had hers all numbered and ready to go, but I didn't.  So I had to take some time at her house to label my bags.  Labeling your bags is SOOO important!  So make sure to do it ahead of time! Also, make sure you have all of the equipment you need to do the prep work.  And try to have two of everything so you can both work at the same time. 

I don't know what the easiest way to split the work would be, but we decided to work on one recipe at a time, each taking different ingredients and filling each others bags from the supplies.  This way only one person was cutting meat or onions at a time, and we hoped it would help prevent contamination of foods by doing that.  This is what worked for us.  You will figure out your own method by recipe #5. LOL!  We prepped for over 8 hours together.  We finished 27 bags of meals and had to stop at 11pm.  (Note to self:  start earlier in the day next time. )   I ran out of meats because I ended up doubling a few recipes as we were going as I have a larger family.  So at recipe 27, I called it quits for the day and I finished on Tuesday. 


Having finally completed this task, I still think this is a lot of prep work and planning.  And one VERY long day of putting together the meals.  But would I do it again?  Absolutely!  Not only did I have fun with a great friend but I walked away with 31 HEALTHY meals, all ready for the new school year.   I already know the recipes that I would use again and there are a few that I will probably tweek next time.  Some recipes will need to be doubled to feed my family of 5.  But I can positively say this.....Once they are gone, I will do it again.  Of that I have no doubt!


P.S.....I think this will have saved me quite a bit of money but I won't know that until after the one month is up!  :)

Properties of Exponents....will they EVER get it?

Even though I teach Algebra 2, I seem to spend a crazy amount of time on Properties of Exponents Rules.  When I say I taught it three times this school year, I am not exaggerating!   This latest time is to help review my students for they all important state tests that they have to take in two weeks.  Although I positively HATE state standardized tests, they are an evil we must deal with.  

Since I had already used two other foldables for properties of exponents and I was now in need of a new one, I did what many of us do....I searched pinterest!  :)  And I found this really cool one at Dividing by Zero.  I love the way it looks.  And it was really easy to  use.  However, my students did not find it so easy to make.  :)   The weaving of the paper might have been a little too much for some of the boys.  LOL!  I got reminded several times that this was math class and not arts and crafts.

I love the different colored papers you can use in this foldable.  I made a sheet for students to cut out of the rules and definitions and had them match them together before gluing them down.  Hoping a little hands-on will help make the rules stick! 

Because I had to glue the foldable into my notebook, I lost the use of one column for the back. I purposefully chose the "smaller" rules for the back so I didn't need as much space but I am already planning to adapt this foldable for next year to add a tab on the end that can be glued down and both sides will have 4 rows and columns.  I just haven't figured out if I can keep the paper weaving too!

(Notice my note to myself for the website I scored the idea from?  :)  )

I am hoping that the 3rd time is the charm!  

I text my students. Do you?

Having taught as an online math teacher for over 9 years, I have learned that texting is the much preferred way for my students to communicate.  They do not want to talk to me but they don't mind texting.  This way they can communicate with me while at a sporting event, or their job.   Frankly, I have learned to like texting as well.  It is not as instantaneous as talking but it gets the job done. 

What is weird is that in the 9 years I have been teaching online I have never given my cell phone number to my students that I teach face to face.  Part of it is that I see them daily so they don't really need it.  And the other part is I don't really trust them not to prank me.  :)   I am in constant war with myself over this. 

But I think I have found my happy solution!  Remind 101.  I LOVE IT! 

This website allows me to send out mass class announcements to my students and their parents.  You can use it to "Remind" everyone of an upcoming test, end of marking period, project due date, whatever!   Best of all.... it allows them to respond to me as well.  I have the settings set to text me to my phone so I get a notification immediately and then can respond by text as well.  And if I don't want to have texts sent to my phone, I can turn them off as well.  I love that if they have a question at 6:00pm they can ask me.  And if I have the time and availability, I can answer.  

But my best use of remind was when I took my class to Hersheypark on Friday.  Instead of having students have to find me at 12:30 to check in, the teachers took a selfie and sent it out as an announcement to the students that it was time to check in.  The students had been told to take a group selfie in front of the ride they were at and tell me their names and location.  It was great!  And my principal loved the pictures I forwarded to him of the kids as well.  Here is the selfie the teachers took to start the check-in!

 

Kahoot! Have you tried it?

 
My department was lucky enough to spend part of our last professional development day at Lehighton Area High School having a meet and greet with their math teachers.  It was amazing!  Math teachers from two different schools getting together to talk about their subject.  Professional development does not get better than that!

We talked about Common Core and Keystone exams; we talked about curriculum for various courses and we talked about formative assessment.    The last was the most interesting to me.   I am big on using whiteboard in my class but I am always looking for something to change it up.  And since our school has gone 1-1 with Apple Air Macs, the push to use more computer-based assessments has increased.

My friend Terri is a teacher in the LASD and while we were talking she showed me the online website Kahoot.  It is an online formative assessment tool for students.  It is multiple choice based so a great help in preparing students for those standardized tests!  It reminds me of an online-based clicker tool.  I immediately liked it and couldn't wait to use it in my class. 

To begin you need to go to GetKahoot.com and sign up for a free account.  Using it is easy after that.  They have over 7million public kahoots that you can play with your class or even copy and edit to personalize for your own class.  Or you can just create your own from scratch.  You can even insert images if you'd like.  I have created my own and I have borrowed some.   I duplicated one just for keystone exam review and it has the questions from the SAS portal.  Why recreate my own?  :)

I have used it several times in my class and I like the ease of use.  What I like about it.....
My students LOVE IT.  They love competing with each other and yet they are quick to praise each other.    They laugh at their wrong answers and groan at difficult ones.  

What don't I love?  With clickers you can see how each student did and get a report on them.  With kahoot, you don't get individual reports.  Just a bar graph at the end of each question on how many got them right/wrong.  And this disappears VERY quickly.   You also can't stop the quiz to discuss a question if you don't have it on the manual option.   So I often screen capture the questions with my MAC so I can review the ones they get wrong afterwards. 

All that said, I do like it as a quick, different type of formative assessment.  I can't use it everyday as it takes a bit of time, but I am working on once or twice a week to help review materials.

Try it!  You won't be sorry!

Field Trips

I teach math but sometimes it is nice to just do something out of the ordinary.  I was lucky enough last week to be a chaperone on a trip to NYC with my school's Spanish Club.  Now I don't speak Spanish (I only remember how to count in Spanish.  Sorry, Senor!)  But I did have a great time!  The food, the city, the culture, and the kids were just amazing! 

My group had 7 students, 4 of whom I was fortunate enough to have taught at some point.  And I was lucky enough that they wanted to explore.  As this was my first trip to the city, I was excited to see everything we could squeeze in!  The highlight of our trip though was visiting GMA.  We got up and went to stand out front at 5:30am.  Thank heavens for Starbucks!  We were invited backstage to listen to the band the Lumineers and even made it on screen, although you really have to squint to see us in the corner of the TV.  :)   After the band played, Ginger Zee came over and took pictures with us.  She is absolutely the sweetest person! 

Other highlights:  touring Times Square, Central Park, and a ballet.  We ate amazing food, and had many laughs.  What a great perk to my job! 

NCTM - Philly!

I'm so excited! I was accepted to present at NCTM in Philadephia, October 31 - November 2!  My topic is using the Frayer Model to help increase Algebra and Geometry understanding.  It is just a burst session but what a great way to start!   

I love my Frayer Model!  I use it ALOT in my Algebra 2 classes and I think I would use it daily if I taught Geometry!  This has transformed the way I introduce new topics to my classes and how I explain vocabulary.  It is such a simple graphic organizer but can be used in so many different ways! 

 Look back to my post on Introducing Quadratics for a specific example.  Click HERE.

Intro to ThisGraphing Quadratics Foldable

I have a few favorite designs for foldables.  I love a door foldable and I love a tabbed foldable.   Both of these are just great ways to organize multiple pieces of information about one topic.   For my foldable on graphing quadratics, I used a 3-door foldable, but had the doors fold down.  I left a little area at the top for a title, so that they don't fold the paper directly in half.  By this time of the school year, my students are so used to my foldables, I don't even have to tell them what to do!  :)
 

I use this foldable in conjunction with my Frayer model for quadratics.  It usually take 2 days to cover this with my regular class of Algebra 2 but I can do it in one day with my CPAlgebra 2.   This is just the overview and then I do an additional day for graphing using the intercept/vertex methods.  Next year I want to add in a lesson on teachers.desmos.com to help support the graphing portion.  I will probably do it as a review for this year though.  If I do, I'll blog it.  :)

In the picture below, I define parabola as the shape of a quadratic but when I taught it, I didn't like it and changed it to the graph of a quadratic....which do you think is preferable? 

Intro to Quadratics - frayer style

For me, my entire notebook is becoming all about the Frayer model.  I absolutely love it!   I find it is the best way to explain what things are because you can compare them to what they aren't.  I might have a slight addiction to them but that is just because they are just so darned easy to use!

So using one to explain Quadratic equations was easy for me to do.   What a great way to show examples of equations and graphs, and non-examples.  And it even helped start the students thinking about the similarities of the quadratic equation and the absolute value function!  The minute I drew it as a non-example, they started asking questions.  Don't you love when that happens?  :)

Exponent rules Grudge Game

Exponent rules.....teaching them is another necessary evil.    I LOVE solving problems with exponent rules!  They are like a puzzle to me.  But my students hate them. They don't "get" them, they say they don't know where to start.   And now I have a structured study hall, where I help the students with their classwork...and the students in there hate them too!  Every year students come to me in Algebra 2 and they don't remember the rules.  But we use them so much in Algebra 2 that they really need to learn them.  I figure it is like learning the grammar rules for writing.  Something you need to know in order to do the next thing.   So in the spirit of "if it isn't working, change it", I decided to change up my teaching. 

So this year when I taught exponent rules to my classes, I used the Grudge game to introduce them, adapted from Nathan Kraft's Blogpost.  Click HERE to see his original post.  I did this on Day 1 and I absolutely loved it!  The kids were engaged and competitive and they did great!  They even showed they remembered some exponent rules from Algebra 1.   I usually don't like games in my classroom but this one was fantastic!   All the kids participated.  I did bribe them a bit with candy, but hey, you gotta do what works right?  End of day 1 was FANTASTIC!    This is going to be great!

Here is the PowerPoint (Dropbox) I used to play the game.  Feel free to change it.  But at least it gives you a place to start.  :)    The image to the right shows the rules I used to help me remember how to play it for future use.  I love this game so much, I can't wait to try it again.  :)




So continuing with the need for a change,  I also changed the exponent foldable I usually use to a book of exponents, modeled after Sarah Hagan's from Math = Love.   I liked the way she laid it out and hoped that it would work better than then one I used last year.  Although I love the book, and the layout, I'm not entirely sure it was better than the one I used previously.   My students still struggle with the rules and the test they took showed they still have gaps of understanding. (I gave the test before Christmas so my post is a little out of date. ;)  )






So back to the drawing board for next year and for reassessing.  But I am keeping the game.  I think that was the perfect introduction to exponent rules for Algebra 2.  However,  I need to rethink the rest of it.

Feel free to share your success with exponent rules with me and others!  :)

Factoring a >1....

Factoring a > 1......is there really any easy way to teach this???   I rank it with long division....a necessary topic to teach in Algebra 2, but no real easy way to teach it.  :)

In previous years, I taught the guess and check method.  That is the same way I was taught in high school and it works.  But teaching it is so painful.  Some students get it right away....others never get it.   In the past, once I taught factor by grouping, I would go back and reteach factoring a > 1 using factor by grouping and would seem to get a few more students factoring this way.  

This year I decided to try something different and I taught my students the box method using a factor T.   I gave this graphic organizer to them to get them started.  I provided a link to dropbox below if you would like to download it for free.

In this method students multiply the "a" and "c" parts of the trinomial, find the factors, and look for the pair that makes the "b".  Then they place the terms in the box, using this design:

They then find the GCF of each row/column and voila....they have two binomials! It is easy enough to do and most of the students understood it.   I picked this method because it works every time but as I didn't teach the guess and check method first, my students did not appreciate the efficiency of this method.   It also makes finding a prime trinomial easier as well.

Here is an example I wrote out....I tried to write it out in steps but I did not write out explanations...on a student paper you would only need a box and a factor T.

My reflection:  Next time I will teach guess and check first as it is still the method I prefer first and then teach the box method as an alternate.   I'm also not sold on whether it is better than teaching to factor using the grouping method.   Which way do you prefer?



Get the file HERE for the factor box.

Hopeful Participant of the 2016 #MTBoS Blogging Initiative

I, Suzanne Milkowich, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the January Blogging Initiation hosted by Explore MTBoS.

You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!

 (Copied from Her Mathness....Wendy Menard)

This said.....writing is my weakness.   So let's just hope for the best!  :)