Hands-On Math: Number Sense

$1.99
iPad
Levels:  I would say any student who needs to develop number sense would benefit.

I've been exploring a lot of apps lately, looking for just the right apps to share with other teachers and using my 3 nieces, Kdg, Grade 2, and Grade 8 to test them out on.  I have found many apps that allow students to practice what they already know but I've come to realize that there are few apps that actually teach number sense.

I am happy to say that this app tops my list!  On the left hand side, students will find a set of blocks sized 1-10 that they can easily change from 1-10 to 0.1-1 to 1/10 - 1.

The teacher can download a teacher guide pdf with instructions from the website or through the app on how to use the program or sample activities the students can try.

Students can use the program to explore addition, subtraction, fact families, multiplication, division, greater than, less than, equal to, the commutative property, comparing and ordering whole numbers.

By clicking on the calculator, students are provided with a randomly generated question.  They can use the program to solve the question.  If they enter the correct answer, they receive acknowledgement from the program verbally.  If the answer is incorrect "Try again" appears.

 

There's also a number line that can be turned on and off and converted to whole number, fraction or decimal format.

What a great program to use if you don't want to pull out all of the manipulatives for one or two students, if you don't actually have the manipulatives in your classroom due to budget cuts, or for students use at home or on the road or anywhere they happen to be when they want to practice!

I found this features list on the Ventura Education Systems website and stole it to include here.  Shhhh.  Don't tell!

Hands on Math:  Interactive Number Sense creates a virtual math playground where students explore, investigate and discover mathematical concepts.  When students are interacting with the Number Sense Playground colored number bars are used to represent whole numbers, fractions and decimals.  

• Using [this app] students can develop important mathematical concepts:  
• ordering and comparing whole numbers, decimals and fractions; 
• adding, subtracting, multiplying and dividing whole numbers, fractions and decimals;
• locating whole numbers, fractions or decimals on a number line.

Sound Effects:  Can be turned off.
Speech:  Can be turned off.

There's a slider bar titled Whole Number View Options.  You can set it so that the blocks show up individually, as a single block with the number written in the center or as a single block without a number.  This allows students to move from the concrete visual to a little more abstract.

Other than that, I didn't run into any kind of technical difficulties while running this app.

As one of my nieces would say "Two thumbs WAAAAAAAAY up" for this app!

The Review I added to the app:
I've been exploring a lot of apps lately, looking for just the right apps to share with other mathematics teachers and using my 3 nieces, Kdg, Grade 2, and Grade 8 to test them out on.  I have found many apps that allow students to practice what they already know but I've come to realize that there are few apps that actually teach number sense.  This app would be a great addition to the home and the classroom.  It's colorful, easy to use and I didn't have any technical glitches which is always a bonus!

This app allows students to explore number sense on their own or based on questions provided by the calculator.  No rods to lose!  This is an app that will remain on my ipad forever regardless of the ages of my nieces or the grades I am teaching.

Monkey Math

Monkey Math

$0.99
iPad, iPhone, iPod touch
Levels:  I would say Pre-school, Kindergarten and Grade 1.

I had a blast playing with this app on my iPad 2.

The fun monkey keeps you entertained while playing.  All instructions are spoken and written. They are repeated if you take too long to answer.

What happens if you make a mistake?  The monkey says "uh uh" and you try again.

What happens when you answer correctly?  Responses are repeated back.  For example, when completing a pattern, once you input the correct response it will tell you the basic pattern again.  If you added a missing number, it will read the full string of numbers.

After you get so many activities correct, you win an item for your aquarium.

Activities include:  Pop the biggest number; sets of 2; least # of item.   Fill in the missing number.  Connect the dots (numbers).  Find the shape with # sides. (Counts sides after you pick and says name of shape)   Addition time (shows qty of items as it's saying #). Subtraction time (shows qty of items and crosses off the subtraction).  Trace the #.  What comes next in the pattern.

Would I recommend this app?  Definitely!  It's well worth the $0.99.
My nieces say "Two Thumbs Up!" so I placed it in my Math Favorites folder on the iPad.

Music:  Can be turned off.
Sound:  Required for a few activities  unless students can read.  Most of the activities are pretty obvious, however.

I didn't run into any technical difficulties while running this app.

I found this features list on the Monkey Preschool website and stole it to include here.  Shhh.  Don't tell!

• 9 interactive games that teach kids about sequencing, patterning, counting, adding and subtracting.
  
• With very little interface, your child presses one button to immediately launch into uninterrupted play.
  
• Uses Knack™ Technology to instinctively adjust the challenge levels to each individual player.
  
• Irresistibly cute monkey guides the child through game play with animated celebrations for correct answers and gentle redirection for incorrect ones.
  
• Kids collect rewards in their ANIMATED AQUARIUM.
  
• Uninterrupted and unlimited play: game continues as long as the player desires.

The Review I added to the app:
What a fun and entertaining way to review math concepts!  I will definitely be recommending this to the K-2 teachers I will be working with.  I love that this app repeats back the responses for retention and prevents students from moving on until they have solved it correctly.  The aquarium is a cute addition.

IPads in the Classroom

I finally purchased an iPad 2.  I know...it's hard to believe it took me so long.  I felt I needed to justify it to myself, make sure that it was truly a head decision instead of just a heart decision.  I watched my coworkers at meetings and sessions taking notes.  I spoke with colleagues who shared fabulous work apps that they use.  I tried hard to slow myself down.  Then, I did my first travel day in my new job.  I met with one of the administrators in a school division in my CARC area.  We drove around to meet all of the math teachers in 6 schools.  I took pen and a book for notes.  During these meetings, I frantically took notes, detailing important information.  Now, if you've ever seen my handwriting, you'll know that when writing fast, you can barely read it and my hands cramp up!  So, finally, I gave in and purchased the iPad.  It was an exciting time! 

I purchased it while out shopping with my sister, heading straight over to her place afterwards.  I brought my laptop, knowing for now, I still needed a laptop with itunes to get started.  I lovingly removed it from its sexy package.  Carefully placed it inside the case w/keyboard I purchased.  Booted up iTunes and we were off and running.  Well.  Sort of.  After syncing it, that is. 

My nieces, who had been thrilled with my iphone and have several favorite games installed on it, were blown away by this big version!  Does it have Talking Tom Cat they wondered?  What other cool games would I add to it?  Be patient!  They are downloading as we speak.

The next day, I was off again to visit more schools in this same district.  Instead of totting around pencil and paper, trying to decipher my handwriting, I was happily typing away, keeping better notes that I knew I could read later.  The keyboard was a bit tricky as there's no right hand shift and the apostrophe and quotation marks are below instead of beside the ;. 

What else could be better?  A few days later, I was contacted by a principal asking for support in early numeracy in a K-4 school.  She wants to learn about iPad apps that she can use to help struggling math students!  Wow!  What perfect timing!!!  So, off I went, looking for apps.  Mainly, I focused on the free ones, knowing schools have limited budgets but I saw many that looked amazing and were cheap.  My problem was that I didn't want to spend the money to test them knowing some of them wouldn't be worthy of sharing.  What to do?  It was simple.  I sent them an email, introducing myself and my new role.  Explaining that I will be holding workshop sessions introducing iPad apps.  Would they be interested in providing me with their product for my review?  If they were worthy, I would tell other teachers about them and let them try them on my ipad.  I have received over 40 free samples so far and more keep coming in. And that's after only 2 work days. I haven't even come close to going through all the math apps in the app store, either.

I thought I would share my favorite apps in upcoming posts.  I'll also be adding them to my delicious account as well with the tag ipad_apps.  I'll also include tags that indicate a general curricular theme as well.

If you know of a great math app that I should check out or would like to give me a promo code for your own math app, just send me a quick email!

Teaching Math without Words

This video really made me think about the way we, as teachers, present our materials.  Looking back at my own teaching, I wonder how many students were overwhelmed by the number of words that were contained in my lessons, activities and assessments.

I can see using the games integrated into my classroom to introduce concepts.  I couldn't get a big enough feel for it based on the sample games I played.  However, I must agree that the games I experienced were very intuitive.

It would be interesting to see if and how people have implemented a similar approach within their classrooms.  What kind of activities do you use?  What pros and cons do you see?  Please, share even if it's not exactly as described in the video (which would be very difficult to do)!



You can find out more about their program on their website:  MIND Research Institute.

I saw this video on Great Maths Teaching Idea.   I had to request more information about the program and it's price because I couldn't find a ton on the internet.  I was a bit worried because I couldn't even put in a Canadian postal code.  (Got around that by placing it in the province section and adding 99999 for the zip code.  We'll see if it works.)

Open Ended Questions

At the end of June, I had the fortune to meet Marian Small while participating in High School Math Institute in Red Deer, AB.  I absolutely love her approach to Mathematics which focuses on creating open ended questions and parallel tasks.  Today, I'm going to focus on creating open ended questions.

I had a few samples of her open-ended questions from the session but wanted more so I went to her website in order to check out her other workshop presentations. (She uploads all over her presentations).  I received one of her books because I video taped my class for presentation as part of the High School Math Institute.  However, this book is tucked away at home so I was unable to use it today.

Today, I was busy creating a Junior High Math Pedagogy presentation so was looking for and creating questions for Grade 7-9. 

A little background on Marian Small's style...Create questions that allow for students to answer at their own level.  This means that the questions have to be specific enough for you to tell if they understand the big idea but general enough that everyone can complete it. 

Some examples:

• Original question:  3x + 5 = 11.  You might rework it to "An expression has a solution of 11 when p=2.  What are at least two possibilities for the expression?
• Original question:  A cylinder has a radius of 5 cm, height of 8 cm.  What is the volume?  You might rework it to be:  A cylinder has a volume of 200 cm squared.  What could the dimensions be?
• You put some counters in a bag.  You want the probability of choosing a red to be 0.4.  What might you put in the bag?

These are just a few samples of the questions I have added to my presentation.  I will add the final list once I am done my presentation.

My challenge to you:  Look at the curriculum you are working with.  Find one big idea you want to focus on.  Take a typical question and turn it into an open-ended question. 

I would love to see what you've done!  Share the grade level, original question and your new open-ended question below in the comments!

Also, if you know of any great websites where there's already a bunch of questions made, please feel free to share those links as well.

Math 11 Cohort

Today was a day well spent sharing the benefits of google calendar with a colleague and helping him set it up on his computer and iphones.  I don't know how I would survive without google calendar!

Don't worry.  That's not how I spent my entire day.  On Monday, September 26, I will be hosting a "Math 11 Cohort" Part 1 of 3.  I've never run a cohort before and I want it to be successful so I am carefully devising my agenda, gathering resources and prepping my presentation.  The question becomes "How much is too much?" to share on the first day?  I'm thinking of the following for an agenda...and I would appreciate constructive criticism on it.

9:00 - 9:15 Welcome, Introductions and Housekeeping  (The obvious stuff plus I will show them the moodle website where we will post all resources, etc).
9:15 - 10:00 Let's Get Philosophical (This will be an opportunity to explore the philosophy and pedagogy of the new program of studies as grade 11 math has a new curriculum this year)
10:00 - 10:15 Break
10:15 - 12:00 Dig in to Resources (I will share some activities and resources I have created and found.  We'll probably explore some activities done by Marian Small regarding assessment)
12:00 - 1:00 Lunch (probably shortened to end day earlier)
1:00 - 3:30 Getting down to business (They will divide themselves into course groups and begin creating resources)

So, have I packed too much information into one day?  Will they be overwhelmed?  What do you think?

Delicious

Today, I spent a fair amount of time creating a Delicious account (that part was quick) and then copying over all of my personal math links into the new carc_math account.  I didn't get everything done.  I made sure to go through each website to ensure that the link was still good and worthwhile.  This is a time consuming process!  Hopefully, people will find it useful as Delicious is a fabulous program for sharing websites!  I don't know what I would do with out it.  I would have lost so many websites over the years if I had relied on memory or computers.  I've switched to too many computers to have kept everything.

So, if anyone knows of any great websites that I should add to the account, feel free to post in the comment section, email me or send it through Delicious!

I also spent some time working on the new CARC Middle School Math Moodle.  Basically, I focused on the layout.  There is basically nothing for content.  It'll get there, though.  Eventually.

This post will be short today.  It's still cold in my office even though we turned up the heat and my fingers just aren't typing properly.

Summer is over...and a new year begins!

It's been a fast paced summer.  I visited my family in Manitoba, as I do every year, for three weeks.  My sister sold her house and moved to Red Deer so my husband and I took her 3 kids back with us a week early so they could pack.  Yesterday, I started my new job as CARC's Mathematics Teacher Facilitator.  All very exciting news!

In my role as CARC's Mathematics Teacher Facilitator, I will be working with K-12 mathematics teachers throughout Central Alberta.  I am excited but taking very deep breaths at the same time.  Today, I focused on two major concepts which I will be discussing in further blog posts.  At the end of each day, I'll post something that I've learned or created that I feel will help other math teachers out there.  Sometimes, it might be a "please help!" sent out to the universe.  Feel free to send back a response if you have something useful.


My main focus today was to search Geometer's Sketchpad for teacher friendly pre-made resources.  I will be offering a session in October to several teachers and would love to be able to provide them with tools they can walk away with, resource banks they can easily search, video or pdf tutorials for support and confidence to create their own.

I was provided with two CD's created by KeyPress focusing on Algebra and Conics.  I know the CD's are old but I was very disappointed that the files didn't include any instructions.  Now, I wonder if there was a manual that should have come with it that I didn't find but in this day and age, it should have been included as a pdf on the cd, right?

So, my journey will continue as I search for fabulous resources.  If you happen to know of anything that would help, please feel free to share those resources in the comments section!

Sandi
TechnoBabe

2 yak or not 2 yak...

I found a fabulous blog today by exzuberant who focuses on math in the classroom.  Many posts caught my eye and I'll be spending a lot of time going back and reading the ones I didn't have time for but I wanted to talk about the original one that jumped out at me.

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A short excerpt: 
Would you like 2 yaks or 3 yaks with that test?
I took a (small) risk last week and tried something different for our Year 8 Algebra test. I'm calling it the "2-Yak/3-Yak test". The idea in a nutshell: students choose the level of difficulty of the test.

Each section of the test provides questions grouped into level of difficulty indicated by the number of yaks. Students were required to do the 2-Yak column, and then for each section choose between the 1-Yak or the 3-Yak column. If students selected the 2-Yak/3-Yak combo, they would automatically get the marks for the 1-Yak questions. I suggested to students that if they wanted to do the 3-Yak questions but thought they might be too hard, to just do the 1-Yak/2-Yak, move on to the next section - and then at the end, if they had more time, go back and try some 3-Yak questions.

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I thought this was such an interesting concept!  Every student is required to attempt column 2 and then based on their skill level, attempt 1 or 3.

My only concern would be that some of my stronger students would attempt column 1 because they know that they'll get it right whereas column 3 might cause them to lose marks.

Exzuberant answers this question as follows:

It turned out to be quite easy to allocate automatic 1-Yak marks to students who didn't do that column. In most cases I gave them full marks - although if I saw the student didn't really understand the concept I docked a mark. But it was very clear there was no need for these students to do the 1-Yak questions

I ended up giving all students two scores: a Baseline score (1-Yak+2-Yak or 2x 2-Yak) and an Extension Score based on the number of correct 3-Yak questions. In my markbook, I recorded these in two columns - treating them as two different tests. For my final grading, I will weight them so students doing the 3-Yak question get the equivalent of 0.5 marks extra per 3-Yak question.

When you're focusing on Standards based grading, this system is a lot easier to work with.  I'm not exactly sure how I can transfer these marks to my own grading system.

Question to You:   If you were to try a test like this, how would you determine a final mark?

Virtual Calculators and programs to go with it...

When working with calculators, it's very difficult to show students exact steps unless they can see your screen.  I used to bring in a document camera and use that to project my calculator on the screen.  The only problem with this is the fact that I don't have the document camera stored in my room.  If I just need it for a minute, is it really worth all the effort to go get it?

So, what to do?  I explored the internet looking for a free downloadable virtual calculator.  It took some time but I finally found the Ti-83 Flash Debugger SDK program.  Once you download and install it, just follow these easy steps.

1. Open program.
2. File==>New
3. Select either of the first two choices.
4. Press F5 OR Debug==>Go.
5. Don't close this screen.  Just minimize it.
6. When done, just close the entire program.  Don't save.

Pros:
This calculator works just like a real Ti-83.  Keep in mind that every time you start the program, it reverts to the original mode which means you have to change from Radians to Degrees if needed.

Cons:
If it sits unused on the screen too long, it turns off.
Requires a couple steps to open every time.

Too Small
Now, some people have commented that it is quite hard to see the buttons.  However, if you have Smart Notebook installed, you can use the magnifier found listed under "other SMART tools".  Selecting the red box/grey box button (second from the right) seems to work the best.

Disappears When You Click On Something Else
I use this program in conjunction with Smart Notebook.  Of course, when you click back on the notebook, the calculator disappears in behind.  Sometimes this can be a real pain.  I know that I could resize the screen so both would show at the same time but sometimes I want the notebook large as well.  Again, I spent some time and looked for a program that would keep both on the screen at the same time.  This time, I found a program called DeskPins, a free download.  When you run the program, you can pin the calculator to the screen so that it always stays on top.  Perfect!

Now, I am completely happy with the way this program runs.

Get 'em to think the second they step foot in the door

Part of my new role as CARC's Mathematics Teacher Facilitator is creating and locating resources for teachers to use in their classroom.  I will be focusing on different units of study for different grades, sifting through online resources, collecting and sharing those resources.  If at any point in time, I put an all call out to my readers, please, please, PLEASE share what you have created or found!  It won't be for my benefit alone.  Many people will benefit!  Don't even worry about the date of the post.  I don't care if you find a post 2 years after it's written.  Share anyways!

Ok.  Enough of a spiel.  On to today's thought.

I want my students thinking mathematically from the second they step in the door until they are out my door and beyond the classroom.  Let's start small and work with "stepping in the door." 

Last year while I was prepping for Math 10C, I was introduced to two Alberta teachers who were teaching Math 10C and posting all of their resources online as part of a project.  One of the first things that caught my attention was an activity that Bonnie Layton posted.  It is one that I quickly adopted in my classroom.  Although it takes a bit of time to prep, it is something I can use year after year, especially if I laminate the cards.

The Reasoning:
Let me give you a bit of my reasoning first.  I find that students tend to sit with the same people every day.  Sometimes this is a good thing.  Other times it can be detrimental.  However, I believe that it's imperative that students learn to work with many different types of people.  We will not always have the opportunity to work with our best friends, right?  So, I needed an activity that would force students to work with different people each day and engage their math brain at the same time.  This fit the bill perfectly.

How it works:
When students walk into my classroom, they reach into a little basket and pull out a card.  That card will help them find their partner for that class.  That is the key.  Students are only paired up for one class.  Everybody can work with someone for 84 minutes and survive.

On that card, students will find information that will help them figure out who their partner is.  For example:  one card might say (x^2)(x^3) and the other card might say (x^7)/(x^2).  Both students would have to figure out their answer of x^5, find each other and come to me to check their answer.  Each card has a number.  For example, if (x^2)(x^3) had 3 and (x^7)/(x^2) had 10, they would say "3 and 10".  I would check my answer key (which I just wrote on the outside of the envelope that I stored each set in.  If it said 3, 10 then I could tell them they were correct.  If not, I would just say "nope" and send them on their way.  In the beginning, I didn't have an answer key and would have to figure each answer out every time.  Pretty easy when it's simple exponent laws but get more complicated and talk about a lot of wasted time.

What I Would Change:
I've considered making a Smart Notebook file that would allow them to check their answers themselves. There's two main reasons why I haven't done that yet. 

1. When students find their partners, there's an activity displayed on the SmartBoard for them to get started on right away with their partner.  There'd be a lot of flipping back and forth while students checked their answers and worked on the question.  Could get very annoying.
2. I like having the students check with me.  I know right away if there's misunderstandings and can offer feedback as needed.

What I Still Need To Do:

1. I still need to attach all of the curricular outcomes to the pairing activities I have already created.  I made these activities for Pure Math 20.  Since the curriculum is changing next year, I thought it was silly to waste my time assigning it to the old curriculum but I didn't have time to focus on the new one yet.  I just made each set up after my lesson for the day.  This way it would be focused on the lesson from the previous class.
2. Finish making pairing activities for the lessons I didn't have time to do.

Where Can I Find These Resources?
I will be creating a moodle website for all the resources I find/create.  As soon as I have that created, I will post a link.  I have attached a sample one  so you can see what I'm talking about.  Students had to find someone with the matching leading coefficient or degree (depending on the statement on the card).

Degrees of a Polynomial

Where do WE go from here?
Create your own pairing activity and share!  Indicate Course name and outcomes covered so we can adapt as necessary.  Share a link in the comments.  Can't wait to see what you share.  Remember, it doesn't matter if you see this post 2 years from now.  Share anyways!

Times Have Changed...

I started this blog last fall as part of my PLP group.  As you can see, I haven't updated it in forever.  However, I have made it a new goal in my life to update this every few days from now on.  Why the change of heart, you may ask?  A couple of reasons.  One is that several people have told me it's important for more women to share their voice and their message.  I believe that's true.  For many years, I have allowed my voice to remain a whisper but no longer will I hide.  I'm throwing myself at the mercy of whomever chooses to immerse themselves in my thoughts.

However, there is a second reason.  Several weeks ago, it was strongly suggested that I apply for CARC's Mathematics Teacher Facilitator position.  Nervously, I did so and anxiously awaited a response to my application.  It finally arrived with the news that I would have to prepare a presentation for my interview to occur in just a few days.  Wow!  I was so excited but absolutely terrified at the same time!  What format would I use?  They mentioned PowerPoint in the email.  I considered it.  I know PowerPoint inside and out.  It wouldn't be much of a challenge.  All I'd have to think about was my content.  I started gathering information that I wanted to share.  Found photos that I had already taken.  Told my students I was preparing for a presentation focusing on me as a math teacher and they agreed to be videoed and photographed.  I decided to use Prezi, although I hadn't used it before so I spent my time inputting the information while I was learning the program.  I sat down with my Vice-Principal the night before the interview (only 1 day after finding out about the interview) and shared my beginning presentation with him.  He made suggestions.  I made changes.  I went home and put the changes in effect but still felt something was missing.  So the next day, I gave each of my students in my math class a piece of paper and asked them to finish the sentence..."One thing Mrs. Berg does well is..."  The comments they wrote down almost made me cry.  I was truly honored!  I also spoke with a teacher, telling her the same story.  (I wasn't advertising that I was applying for the position yet).  She wrote up a fabulous quote as well.  So at lunch time, you could find me hunched over my computer entering these comments and fine tuning the presentation.  No pressure.  Interview wasn't until 4:30.  Oh wait.  They moved it up till 3:00 or as soon as I could get there.  Yikes!  Good thing I had a prep last block!  Race home.  Change.  Race off to the interview.  Darn.  Forgot that road didn't go all the way through.  Back track a couple of times until I got myself on the right road.  Whew!  I made it there shortly after 3.

I think the interview goes ok but I'm definitely nervous.  The next day, I get home after work and my husband tells me that someone has been trying to call me.  They had tried me at work but I was gone.  They tried me on my cell but there was no answer.  (I don't get reception in my classroom).  She announces to him that she has done her due diligence and now I have to call her.  To me, this means that I did not get it.  She leaves her home number as she is leaving work.  I call.  Machine picks up.  Leave a message.  I call 45 minutes later.  Husband answers.  She's not home yet.  I call 30 minutes later.  Still note home.  I'm dying here!  I ask him to give her my cell number...just in case.  We're going out to dinner.  I don't know if it's a congratulatory dinner or a consolation one.  Can't let go of my cell phone.  Dinner's over but no phone call.  Now I am very sad.  It's obvious.  I didn't get it or she would have called me back.  We arrive home and are just unlocking the door when I hear the phone ringing inside.  I pretty much shove my poor husband out of the way to race up the stairs and answer it.  It's her!  My saviour!  She's about to put me out of my misery.  But guess what!  I GOT IT!!!  I'm so excited that I can barely contain myself.  First, I tell my husband.  Then I call my mom.  Then I call my principal and vice-principal but the stinkers tell me they knew first thing that morning!  Aw man!

So, as of August 22, 2011, I will working for CARC as the Mathematics Teacher Facilitator.  It's a one year position possibly leading into two years.  I am thrilled to have the opportunity to work with teachers focusing on math.

Now, how does this lead to me returning to my blog?  This blog will follow my journey within this position.  I'm not sure what my topics will focus on...basically whatever comes to mind that day:  a response to a reading I have done, sharing a lesson or activity I have created or found, a request for ideas, wherever my journey takes me.

I hope that you will join me on this journey.

Below is the prezi that I used in my interview.  Maybe one day I'll get around to adding a voiceover. 

Sandi Berg: Excellent Candidate for Mathematics Teacher Facilitator on Prezi

Oh yeah.  I almost forgot.  When I told my math students that I wouldn't be returning next year because of this position, they got very suspicious.  "Is THAT what those quotes were for?"  "If we had known that, we would have lied and said you were a mean and horrible teacher who never helps us!"  They're so sweet!  I got a similar reaction from the teacher who did the quote for me as well. 

I'm really going to miss teaching those students next year.  I'll miss working with my staff too.  That is the ONLY sad thing about this new position.

Our journeys in life may lead us away from those we care about but they also lead us toward a horizon where a beautiful sunrise awaits.