Reflections

I do not do Geometry often, which is a shame because it's so much fun! I have the opportunity to show a lesson tomorrow on reflections over lines in a plane.

When I think of reflections, the first thing I think of is a mirror. When you look in a mirror, you look at your reflection, which is an exact replica of yourself a certain distance away just in the opposite orientation. It's the same in a geometric reflection! A figure and its reflected image are equidistant from the line of reflection and they are orientated in flipped positions.

The key aspect of reflections is the equal distance of the original figure and the image figure to the line of reflection. Vanity mirrors also preserve this distance. A fun thing to think about is this image:

Why do passenger side mirrors make objects farther away? What must be different about the mirror?

Anyway, the students are going to investigate what happens when we reflect a figure over different lines such as the x-axis, y-axis, line y = x and line y = -x. Hopefully, they observe the respective patterns. To help, I have created some transparency squares:

I made these from transparent sheets like the ones my teachers used with overhead projectors in middle school and high school. I put decorative tape around the edges to avoid cutting fingers!!! So, using dry erase markers, students will draw the line of reflection and the figure; after, they can flip the whole transparency, match up the line of reflection, and see the reflected image. Students will then record the image points and observe how the coordinate values change.

We will investigate other techniques, like using a grid, for other vertical and horizontal lines in the plane. The challenge problem for the students will be to see if they can reflect a figure over a line in the form y = mx + b. We will discuss how the slopes relate between the line of reflection and segments created between original points and reflected points. If I had infinite time (if only), I would show students how to reflect over any line in 2D space using constructions.

To review the day's lesson, students will use the following online applets to check their understanding:

Graph Reflected Image

Find the Coordinates

Anyone interested in the constructions can check out these YouTube videos. I found them very helpful!

Constructing a Line of Reflection:

Reflecting a Figure Over a Line in Space:

Here's to many more Geometry lessons in my future!

Miss Schuck

Pi Day

March 14 is an exciting day for math teachers everywhere. The date's abbreviation, 3.14, is the number pi rounded to two decimal places. It is the perfect day to raise awareness of the sheer significance of this irrational number. To sum it up, I love this picture:

During my student teaching, I was in an 8th grade classroom during Pi Day and it happened to be my last day at that placement. So, we had a little party and I decided to read this book to the class.

This book series is really meant for elementary students, but I think the students really appreciated that nostalgia of being read to as younger kids. I decided to do the same thing for my high school students - I think they appreciated my funny voices and side commentary.

I also printed out a bunch of blank pi coloring sheets and let the students relax by decorating their own pi. My students work really hard in Algebra 2, Calc 1, and Calc 2, so I can spare a day where they can take a break. My classroom is already chock full of craft supplies, so it was easy to set up.

As you can see, I had my own pi project. I hole punched some colored paper and was determined to fill up the whole pi by gluing each dot individually. Whew. It turned out great and this still hangs in my room:

This year, my classes are a little swamped with how our breaks fell and the new Common Core Algebra 2 curriculum, so I couldn't waste a whole period on pi day activities. Instead, I baked for my students. I really wanted to make mini chocolate pudding pies, but I couldn't find any mini graham cracker pie crusts. So, I improvised - I bought plastic shot glasses at Shop Rite and decided to make Pi(e) Dessert Shots. Bear with me.

I got these graham cracker crumbs and combined them together with some butter. I filled the bottom of the shot glass with the crumb mixture. Then, I made the chocolate pudding  - I add milk to my pudding for a creamier taste. I filled the rest of each shot glass with chocolate pudding and let them cool in the fridge. I used one box of the crumbs and I think 6 boxes of pudding. I packed all 120 pie shots in aluminum tins and carried them to school. During each class, I passed out the pie shots with spoons and went around topping each with whipped cream - I used up two cans of Reddi Wip. My students and fellow faculty members loved them. It was the perfect amount of sweet.

The stickers I again found off Pinterest. I bought the labels at a nearby Staples and printed them on my home inkjet printer. You will need a Teachers Pay Teachers account to download the FREE sticker template. Thank you so much fellow math teacher, Jennifer, for these cute stickers! My fellow math teachers wore them with pride and they accented my dessert shots well.

I look forward to many more fabulous Pi Days!

Miss Schuck

Super Bowl 50

Against all odds, the Denver Broncos took on the Carolina Panthers in Super Bowl 50. As you know, my favorite quarterback of all time played for Denver, and, as it turns out, the teacher I share my room with is a big Carolina fan. It was on and I started it.

Yes, I drew this by hand on my homework board! No, I don't think I could ever draw it again. It's a Super Bowl miracle! Anyway, Mr. Ferguson couldn't let me show him and his team up.

So, it started out small. Mr. Ferguson made his own Panther paper chain. I decorated my table in orange and blue. Then, I went to the dollar store. 

And I made a wreath based on this Pinterest idea! For a total of $3, I bought the Styrofoam ring, a blue rectangle table cloth, and an orange rectangle table cloth. I cut the table cloth into about 18 inch strips (though they could have been shorter) and double tied them around the ring in alternating pattern. Once I covered the whole ring, I cut the ends down and fluffed them up. I added a bow from Michael's and a little name plate. For $3, I thought it was a great way to one-up Mr. Ferguson in our classroom.

But then, Mr. Ferguson copied by wreath idea, covered his door in a Panthers claw mark, and made an end zone. So, I obviously had to make an end zone. Mine was made from painters tape, which wouldn't ruin the floor. Mr. Ferguson out cardboard down before the duct tape in an attempt to protect the floor as well. We got permission from the maintenance guys too before we did anything!

And from then on, the competition grew fierce all during Super Bowl week. The students loved walking in everyday and seeing what was added.

My mom helped me with these pennants.  I cut them out of felt and then she sewed them with her sewing machine. They came out great. Thanks Mom!

I may have went overboard. I covered my seat cushions in make-shift orange and blue cases, and I drew on our classroom windows with window markers. It was well worth it though when the Broncos came out on top and WON SUPER BOWL 50! I was beyond excited and glad that Peyton Manning could go out on top.

I celebrated with a victory selfie and got to keep up all my stuff for the whole week after. Even though his team lost, I bet Mr. Ferguson can agree that it was a great time decorating our classroom and celebrating Super Bowl! :D

Miss Schuck 

The Most Wonderful Time of the Year

One of the best aspects of working in a private Catholic school is the ability to celebrate and decorate for Christmas! The previous teacher left me her Christmas tree, so all I had to do was buy a few ornaments and decorations. I set up the tree by my wicker furniture.

Most of the ornaments were gifts made by students and other teachers. The little ceramic present was also a gift from a student. I found the letters to Santa mailbox at Home Depot of all places! It gave me a great idea for some extra credit projects during the month of December.

I created my own Advent Calendar! Now, typically advent calendars are filled with little treats or pictures for children to open each day as they count down to Christmas. Well, I modified mine to to fit the needs of my math classroom. Most days were just silly jokes or YouTube videos to watch. One day we made origami Christmas trees - it's really easy! My favorite day was when I hid a picture of a pickle in the classroom and told students the first one to find it won a prize; though most of my students got up and frantically looked around the room, it was the quiet ones that usually found it just patiently glancing around the room. Go figure.

So, for 6 of the days, I put in tasks for students to complete to gain a total of six bonus points. No matter the task, students had to format it into a letter to Santa and place it in my box to receive full credit. What Christmas fun!

Task 1 - Write two haiku poems, one about our current topic in math and one about the holiday season. For the math poem, students had to incorporate a vocabulary word from the current units. I heard a lot about polynomials, derivatives, and areas between curves! 

Task 2 - Two mathematical puzzles. One can be found here, and students had to find two DIFFERENT solutions. The other had to do with the 12 days of Christmas. I wanted my students to mathematically show the total number of gifts one would receive from their true love if they were literally given all the things listed on each day. Yay Christmas math!

Task 3 - Draw and color a Christmas scene. I really wanted to reach all student talents with these tasks, so instead of an academic task like the first two, I went with something artistic for this task. Students had to draw, not trace, a holiday scene and color it for the bonus point. I kept some of the really pretty ones.

Task 4 - This was a Wikipedia Scavenger Hunt. I gave students a Wiki page to start on, like the Christmas stocking, and a page to end on, like the Aztecs, and asked them to find the linking page between them. It's not easy. Can you find the page that links these two together? Good luck!

Task 5 - For this tasks I had students create their own memes. They could not use images from the internet. They had to use pictures of each other, teachers, the school, or themselves and make a meme. Some were pretty funny and are still hanging on my classroom walls.

Task 6 - For this last task, I asked students to actually write a letter to Santa. They had to ask for three things - something for themselves, something for someone else, and something for the world.

I was charmed by some of  the things my students wrote. I am proud they took the assignment so seriously and asked for some wonderful things, especially for other people. It made the whole advent calendar worth it.

My students really enjoyed these extra holiday activities we did each day as we got closer to Christmas break. As a final send off, I had an in class hot chocolate bar. Yum!

I welcome any new ideas to get my students excited about coming to math class!

Merry Christmas!

Miss Schuck

Combing Like Terms Uno

This year I am taking on Algebra 2 Common Core! Much like the rest of the state, I have no idea what to expect. But, I did have an idea that I needed to know the algebra skills of my incoming students. My first unit was a hodgepodge of Algebra 1 Common Core topics. I really liked the introduction/review topics in the Common Core Algebra II textbook written by Kirk Weiler at eMathInstruction. Through this textbook, we reviewed algebraic properties, linear equations, basic exponents, multiplying polynomials, and algebraic expressions.

I am constantly on Pinterest, and so I thought I could find some review activities that would make the transition back to school and math class a little easier. And, I wanted my students to love coming to class! Through Pinterest, I found a link to Tara Maynard's blog and her Like Terms Uno activity. 

I wanted to take her idea and make it my own. So, I bought two packs of index cards from the dollar store and cut them all in half. I think I had about 50 cards to a deck. I have thirty students in my first period class, so I needed at least six decks to have groups of five. I kept the basic colors - red, blue, green, and yellow. I also kept Reverse, Skip, Draw Two, and Wild cards as per the original game. However, instead of numbers, each card had a term - constant, x, x^2, x^2y, y, y^2, xy^2 - all with different integer coefficients (both positive and negative). Part of a deck is shown below. I must have written UNO over 300 times!

To play, students are dealt 5-7 cards depending on the group size. Flip the card at the top of the deck and let the game begin! Let the students decide who goes first or use who's birthday is the closest or something along those lines. During each turn, students either put down a similar color or like term to the top card. If they have neither, they can use a wild card or pick from the deck until they can put a card down. When a student gets down to one card, they must yell, "UNO!", as per the rules of the game or they cannot win. If the deck is out before the came ends, students can reshuffle the discard pile minus the top card and keep playing. The first student to get rid of all his or her cards is the winner and has the right to brag!

Some students liked the game and others couldn't have cared less. I found it successful enough to hear student's exclaim phrases like, "You can't play that because x^2y and xy^2 are not like terms," or ask each other questions like "Does the negative matter?" I think it lead to great group discussions as well as forced students to check each other and make sure the rules were being followed. Students can be very competitive and that makes for great activities! If I make new decks, I think I would include fraction coefficients and maybe an added rule where if a student places on like term on another, they must write down the sum of the combined terms.

Please feel free to ask any questions and be sure to check out the sites and blogs I linked to on this post. There's a lot of great math ed out there, so please keep writing!

Miss Schuck

Homecoming 2015

At the end of August about a week before school was starting, my vice principal asked if I wanted to be the moderator of Student Government. I thought, why not?

What she failed to tell me was that Homecoming weekend was two weeks away and I had to plan Pep Rally, the Powder Puff game, and the Homecoming dance. Yikes.

Before I could do anything, I needed a student government. So I had to hold elections pretty soon after school started. Luckily, there are only four homerooms in each grade, so over the course of a few days, I had candidates campaign in their classes homerooms giving speeches and making flyers. By the end of week one, I had ballots from each homeroom and student representatives for each class. Whew.

Fortunately, I had a lot of help from the past moderator and a parent helper. I would not have been able to get everything done without them.

Pep Rally

The biggest headache of pep rally was the class t-shirts. The first big decision of the student government was class colors so that we could order t-shirts. Seniors wanted a white-out, so the juniors had to counteract with a black-out. Sophomores I believe chose blue and freshmen settled for green. The t-shirts could also feature a phrase or saying, which led to more arguing and a longer after school meeting for me. Once everything was decided, I got to pass off the details to the parent helper, who created and collected order forms from all the students and laid out the cash to buy and expedite ship all the shirts. I couldn't be more thankful. Of course, random students complained to me about the shirt colors and sayings, even though it wasn't me at all. Note to self here, Schuck: Plan shirts in May-June so we don't have to rush next year.

Then I had to get everything in order for the actual pep rally. I had to find student MC's, a student to be our mascot, the Eagle (pictured above), and volleyball teams. Homecoming pep rally features a volleyball battle between freshmen, sophomores, juniors, and seniors. I had to create sign-ups outside my door for players AND coaches, which could only be girls on the volleyball team. I had to find faculty volunteers to referee the game and ask the athletic director for a list of all fall sports athletes to be announced at the rally. I am sorry if I am rambling on about this. I think I am just writing this all down so I remember for next year!

The day of pep rally, I had to take my last period class to the gym and call down the varsity volleyball team to set up. Luckily, the volleyball players knew how to set up the court and score keeping section. Whew. I had to get all the sound equipment together, which was, of course, not all together. The mics were with the Mass stuff from the previous day and the speaker was hidden in the drama club closet. I had a student DJ hook up his iPad with the wireless speaker to get some music as students walked in. The cheerleaders started the rally off with a cheer, we introduced all the teams, and the classes played volleyball. Seniors were victorious. Of course.

Powder Puff Game

That night following pep rally was the girl's Powder Puff game because girls can play football too! I had to have sign-up for those teams and coaches as well, where coaches were boys from the football team. The girls got to play on the football field and the athletic director opened up the food shack, so it was a fun afternoon for students to just hang out at school. I had to find different MCs for this game and yours truly was the referee (pictured above). Two students refereed with me and they were pretty biased to the senior girls. We played a few games of 6-8 minutes each. As you can imagine, senior were victorious yet again. This was probably my favorite part of the whole weekend.

Homecoming Football Game

This wasn't my responsibility! I had a great time at the game cheering on the Eagles (pictured above)!

Homecoming Dance

Note to self: Again, we need to plan for this at the end of last year to cut down on all the rushing around; everything also has to be put in one place so it doesn't get lost/misplaced like this year.

I didn't have a student government to choose a theme yet, so I picked it. It was the "Shut Up and Dance with Me" Homecoming with a neon/80's theme. My parent helper did a great job of finding decorations like tulle, lights, lanterns, and glow sticks. My biggest job was finding a DJ in a pinch. I called a few local companies and told them my dilemma. DJ Joey B in Middletown, NY gave me the best deal at $400 for 3 hours of music and lights. The students thought it was the best DJ in recent years. Success. Thanks, Joey B!

A lot of other parents volunteered to bring snacks/water, chaperon, and help with set-up/clean-up. We worked all afternoon to make our gym look like a hopping club and we were there long after all the students have left. They all have my undying gratitude. There were glow sticks everywhere and the students had fun collecting and wearing them. With all the running around, I forgot to get a picture of all the decor, but it did look something like this:

http://gmp.garymusickproductions.com/bermuda

I wanted to set up a photo area in our courtyard and I thought a life-size Polaroid cut-out would go with the theme. For $10 at Home Depot, I used 3/4 in PVC pipes and connectors to make a standing frame. The guy at Home Depot cut them to size for free, just so you know! The art teacher had some long white banner paper that I glued to the poles and cut out a hole. Now, the Polaroid had to have a back drop, so I took a black sheet I bought at WalMart and had a blast throwing neon paint onto it. With a black light behind it, my photo booth looked great! My wonderful boyfriend helped me a lot during this week and weekend, so he's pictured with the final product (also pictured above).

http://www.weddingbee.com/2010/08/23/build-your-own-photo-booth/

The students had a blast at the dance and I know many took "selfies" in the Polaroid. There are a few photos of students and me in the booth - I need to find them! At the dance, I mainly focused on Homecoming King and Queen voting; I had other faculty check students in and monitor the dance floor. Tickets for the dance were $5, which were sold by my student government members and myself during lunch periods. We made enough to cover all the expenses and we had money left over for new events. Woo hoo! 

I am thinking of a Ms. and Mr. BC pageant to crown a pair of students who truly embody our school and its ideals. I'll let you know how that goes. In the meantime, here's a final picture of me from the end of the Homecoming dance and weekend:

Miss Schuck

Bulletin Boards 2015-2016

One of my favorite things to do at the beginning of each school year is plan my bulletin boards! I have two in my classroom. Last year I was a little overzealous and changed them every month or so.

The first week of school, my students spent solving brain teasers and logic puzzles. At the end of the week we compiled a list of problem solving strategies they could use not only for fun problems, but for math problems too! So, I figured I would incorporate one of my favorite fall past-times - FOOTBALL! As you know from the last post, I am a big Peyton Manning fan and hence a big Denver fan. Not pictured is my shrine to Manning on the left-hand side. I added pics from every game that I got offline and kept track of the team’s record. The footballs describe the steps on how to attack a problem and the jerseys are all the problem solving strategies my students came up with. The play in the middle is something I came up with and the defensive line in my Calc 1 class helped me fix it - my defense has 12 players! Oops. 

So, in a private Catholic high school, we can celebrate Christmas openly! So, I knew my next bulletin board had to have a Christmas theme. My Alg 2/Trig students were in the midst of their quadratics unit and thus, Solving Quadra la la la tics was born. There's the factor tree, the quadratic formula Rudolf, and, my favorite, the gingerbread men completing the square of their gingerbread house. It was a great reference for my students before the holidays! 

My next two boards focused on the holidays following midterms. First, I made a Valentine's themed board, complete with how math is love, how to spell LOVE and make a heart on the graphing calculator, and math pick-up lines that were appropriate for high school students in a Catholic school...

For St. Patty's Day, I researched lucky numbers around the world in an attempt to combine math and social studies. 

This. This was my pride and joy last year. We focused on trig the last part of the year and so I wanted to help my students out with this reference board. With the unit circle, special right triangles, trig identities, and degree to radian conversion, I covered the basic stuff everyone should know about trig. I did a beach theme since it was such a rough winter - everyone anxiously awaited the warm weather! 

To round out the year, I made a board about test prep for upcoming Regents and finals. At our school, every student has an iPad, so I incorporated that into my board. Each app is a test prep strategy! 

This year, I had to move to the next classroom over and share with another math teacher, Mr. Ferguson, who mainly teaches geometry. I didn't want to over step my boundaries and change bulletin boards as frequently as I did last year. I was also limited to one of the two boards. So, I needed something that would be helpful all year. Both my Algebra 2 Common Core and Calculus students need to know their parent functions, so Function World was born. Featured is the Square Root Express, Parabola Pirate Ship, Absolute Value Food Court, Natural Log Flume, Exponential Slide, and the dueling Sine and Cosine coasters. Love it. 

As you can see, Mr. Ferguson was so impressed with my board that he asked me to make one for him. Students in geometry need to grasp transformations like dilations, rotations, and reflections, so I came up with Transformation Station as a good pair with Function World - need to get their somehow! Can you pick out all the transformations in the picture? ;) So, I am not going all out in the bulletin board department this year, but I may change Function World into the Trig Top Circus. We'll see.

Miss Schuck