Domain & Range from a Graph

My students have never had such accuracy in identifying domain and range from a graph.

Thanks to this little unsuspecting guy.

I blindfolded him and gave him eyes on the sides of his head.

And then he took a stroll across the x-axis to find to find domain.

Now the x-values that are included in the domain can be determined by stating the x-values where our little friend can "see" the graph.

Can he see it here? No.

What about here? No.

What is the smallest x-value where he can see the graph?  -9

Can he see it here? Yes

What is the largest x-value where he can see the graph? 9

So the domain is [-9, 9]

To find range, he strolls up the y-axis.

For a function that doesn't have endpoints, we talked about what the function looks like beyond the plane that is shown. Students really didn't have trouble with this.

All this silliness is the result of desperation.

For the first time ever, I am teaching two levels of Algebra 2. I am finding that some of my "standard" explanations aren't working with the "not advanced" group.

So then I'm all "Okay, that didn't work. Here, let me grab this toy bug from my closet." And stuff like this happens.

What if My Students Use Programming to CHEAT?

One question comes up as I've recently dipped my toes into programming on calculators with my students . . . You teach your students to program, but what if they start programming formulas into their calculators?

I've been thinking about this question, and playing out a few scenarios in my head . . .

1. Don't teach students to program. Maintaining ignorance is a good way to keep students from doing things you don't want them to do.

2. Teach them to program, but make sure they don't use it for cheating. Reset calculators before every test. This is a good way to make sure students don't spend too much time on any programs.

3. Let them program away. What might happen? Student who learns about the quadratic formula might think about programming it into her calculator. Later on, student encounters an equation, recognizes it is quadratic, correctly identifies a, b, and c and then executes a program she has coded herself to solve the quadratic.

I think I can live with option 3.

In fact, I'm over here smiling.

Why I Blog

Chiming in a little late, but I wanted to share my journey into blogging . . .

I still remember the day when I discovered math teacher blogs. I had been teaching for maybe eight years and I was in a rut. I had gotten to the point where I pulled out the folder of unit whatever from last year and wash, rinse, repeat. I was doing an adequate job, but I was bored.

On THE day I was sitting at my computer and I wondered if there were any math teachers out there blogging about teaching math. I started to search. I found Kate’s blog and Sam’s and a few others. Their blogrolls lead me to others. I started reading and I could not get enough. I tried log war and row games and other stuff. I got creative inspiration and I started to enjoy teaching again. My learning of new things was no longer limited to a rare conference here or there or from conversations with my two colleagues.

I started to recognize that I was a pretty mediocre teacher, and I stopped being content with mediocrity.

It was less than a year later that I started a blog of my own. Initially, I felt that I had gained so much from others that I wanted to contribute something to the community. It didn’t take me long to realize that what I had to share was just a drop in the pool of resources out there, but some people seemed to find what I had shared to be helpful and that felt great. I also wrote about what was on my mind and I was able to solidify many of my thoughts about teaching and learning through thinking them out in writing.

The real hook for me came when I started receiving feedback from others who were reading. I found that even when I posted something that I thought was super amazing, someone would give me an idea to make it even better. I asked questions when I wasn’t sure where to go with a topic, and I got answers. I am so very thankful to those commenters who have made me a better teacher.

I have subscribed to Sam’s philosophy about blogging – it shouldn’t be a chore. But while I refuse to let blogging be stressful, it has provided me with some motivation to produce share-worthy moments in my classroom.

I still mess things up all the time. I still spend too much time talking at the front of the room. I still have so much to learn . . . but there is no question that I am a better teacher than the blog-less version of myself.

And I’m definitely having more fun.

Programming Part 3

Day 3, for documentation purposes . . . I now have so many questions swimming around in my head related to how & when I would use programming in the future. But that's another post.

For Day 3, students were introduced to loops. This was a little more difficult for all of us, but the students were still super interested in the process.

Chris gave us these programs to try:

1. Use a loop to write a program that prints all multiples of three from 3-42.

2. Primality testing: Write a program that lets the user input a number and then checks if it is prime.

3. Number of numbers divisible by 3: Write a program that will let the user input a number, and then the program searches for and counts the number of numbers up to that number that are divisible by 3.

4. Product of first n numbers: Write a program that will let the user input a number, and then it will find the value of the product of all the integers up to that number.

5.  Averaging test scores:  Write a program that asks the user how many test scores they want to average, and then prompts them for each test score and finds the average.

Harder ones:

6.  Reducing Radicals:  Write a program that can reduce a radical. For example, if the user enters 20, it should return the numbers 2 and 5, representing 2 root 5.

7.  Finding perfect numbers:  A perfect number is a number that is equal to the sum of its divisors, besides itself. Example:  6 = 1 + 2 + 3. The first 4 perfect numbers were known in antiquity. Write a program that can find all perfect numbers up to a number inputted by the user. You will most likely need nested loops.

These were tough! I did not get through the list of programs today (or past #3).

The activity is still a hit with students. They are seriously begging for more!

Tomorrow they are each going to present one of their original programs.

Programming Part 2

For Day 2 of my introductory adventures in programming, we (I mean Chris, the amazing student teacher) did this:

1. Introduce students to test and logic commands (2nd MATH). We practice writing logic statements and identifying if they were true or false.

2. Introduce students to "IF" statements. Together we wrote a program that asks the user to input an x and y coordinate, then identify its quadrant.

3. For homework, students worked on these:

*A program that asks the user for 2 numbers, and then displays the larger number.

*A program that asks the user for the center point and radius of a circle, as well as an additional point, and will display whether the point is inside the circle.

*A program that asks the user for A and B from a function in the form Ax^B, as well as an x-coordinate. It then displays the slope of the function at that point.

*A program that asks the user for the slope of 2 lines, and then displays if they are parallel, perpendicular, or neither.

*A program that takes in a number from the user and displays whether it is even or odd. (Hint:  use fPart command).

Day 2 was just as much fun as Day 1! A few students have been enamored with the idea of a guessing game program where the computer generates a random value between 1 and 100 and coaches the user's guesses with "too high" or "too low" until the value is found. They've been working on it even though they don't have quite all the tools yet, and some of them are figuring it out.

Diving Into Programming!

This post is 100% inspired by Jasmine's TMC13 presentation-turned-blog-post. I thought it was a great idea from the beginning, but I honestly didn't take it very seriously for myself. I guess I just didn't think it would work for me. And I don't teach geometry. I passed Jasmine's post on to our geometry teacher and her student teacher. Chris (student teacher) got really excited about it. The more we talked, the more I started to see the potential for any of the classes I teach.

So, Chris and I decided to join forces and introduce our combined Calculus & Pre-Calculus classes to simple programming. I have almost zero knowledge about programming. So by "join forces", I really mean that he taught the class and I'm over here learning along with the students.

This was sort of a spur-of-the-moment interruption-to-your-regularly-scheduled-math-class-kind-of-activity. We have flexible schedules, so we decided to jump in and try it and I am so glad we did! I am feeling confident about doing this on my own in my other classes now.

I am sure this is all painfully simple to anyone who knows anything about programming, but it was mostly new to me. I wanted to document here for my future self. Maybe someone reading is like me and never thought you could do this sort of thing. You can! If you don't have a stellar student teacher to help you out like I did, just follow these steps.

Day 1 looked like this;

1. Distribute TI-83 calculators. Some kids had them already, we had enough for the rest to borrow.

2. Demonstrate the location of the PRGM button, the NEW tab, name a program, and locate all the commands within the program menu.

3. Demonstrate the ClrHome and Disp commands. Write a program to display the word "HELLO".



4.  Demonstrate the Input command. Show students how to store a value, calculate and display a result. Write a program to request someone's age and tell them how old they'll be in 20 years. (I did not like my number).



We also did a pythagorean theorem program together.

5. Send them home with some programs to try:

*Write a program that asks the user for the year they were born, and then displays approximately how many years old they are.

*Write a program that asks the user for 2 x-coordinates and 2 y-coordinates and then finds the distance between the points.

I cannot tell you how much fun this was for me, mostly because I got to learn along with my students. I saw several of them later in the day, and we couldn't put our calculators down. We had to stop and compare distance formula programs. We exchanged calculators and tested each other's programs. Students started coming up with their own ideas for programs and asking me to test them out.

It was a super fun day to be a teacher  student.

I am pumped for my next lesson!

Stay tuned for Day 2.

This Lesson Cost Me $1

Zero product property today, only the students don't know that yet.

For them, its a game-show-style guess-the-number game.

I want a fun prize for the winner, but all I can come up with is a couple of quarters. That will have to do.

Before class, I write a bunch of numbers on this board and cover them with index cards. I'll even give a hint about the first two.

The students are totally into it . . . 2! . . . 3! . . . 6! . . . 1! . . . 

Someone decides to try negatives . . .  -1! . . . -2! 

Finally, someone else tries 0.5. . . Fancy. But wrong.

I let this go on for a bit.

Then I break the bad news. Sorry guys. It was 6000 and 1/1000. Better luck in round 2.

And there are more guesses . . . 1! . . .  -1!  . . . 12!

Someone is on to me . . . "Guys, this could be ANYTHING!" 

So you give up? It was 58 and 1/58. Okay, on to round 3.

At this point I am expecting all hands to go up. In a perfect world, everyone would want to guess zero! Right? Wrong.

That's where I am surprised. One lonely hand goes up . . . Zero? He asks hesitantly. My first two examples raised enough skepticism that students are sure there must be a catch.

This isn't how it worked in my head but that is okay. I can adjust.

Is Tyler right? Can we know for sure that one of the numbers is zero? Discuss at your tables. 

I walk around and listen and most seem to be figuring it out. Someone suggests 5 and -5 but quickly realizes that won't work. For those who aren't convinced, I challenge them to come up with a number other than zero that will work.

We conclude that Tyler is right and move on to the final round.

Zero!!!

 Not exactly. I tricked you this time by using variables. But tell me what you know . . . 

"x minus 3 or x plus 2 equals zero". 

Yep. That is all.

P.S. Next time I am giving everyone a white board to write down their guesses for each round. I had a lot of participation, but definitely regret that I didn't get a response from every single student.

Homecoming Balloons

Me: Okay, the balloons are in my closet. Now, there are 50 pink and 50 silver but only 25 of the black. Remember that when you are planning out your rows.

 . . . later . . .

Decorating girl:  We decided to put the rest of the balloons on the floor.

Me:  Oh, I thought you were going to do three rows on the ceiling.

Decorating girl: Yeah, but there weren't enough black balloons to continue our pattern.

 . . . sigh . . .

Desmos Test Question

I am kind of excited about this (bonus) test question I used today . . .

My advanced algebra 2 students just finished studying a few of the basic parent functions and their transformations. Today, they took a test.

First there was a standard paper/pencil part of the test. Nothing unusual here.

Next, they picked up one of these cards containing the description of a parent function and a transformation.

The cards were color-coded according to difficulty level. Students were free to choose. Every card is different, so you won't be working on the same graph as your neighbor. Students were to pick up an iPad and use Desmos.com to create the function described.

Green Cards: Create a graph using a given parent function and animate one given transformation.  
Purple cards: Animate two given transformations.

When finished, students bring me the iPad. I check that the graph matches the description, stamp the card, and clear out the graphs for the next person.

I was really pleased with the results. Almost everyone was successful in creating their graph. I don't feel like this needs to be a bonus question next time. It might even become a regular part of test-taking in my classroom.

Now I am thinking about the possibilities. My head is already spinning with ways I can use this question format for other topics:

Quadratics/Polynomials: Create a function with given vertex or given zeroes. Can you keep the vertex in place while animating the zeroes? Can you keep one zero in place and animate the other(s)? Create a function with given end behavior.
Systems: Create a system with one solution, no solution, or infinite solutions. Create a system with a given solution.
Rational function: Create a function with given vertical and/or horizontal asymptotes. Animate one or both asymptotes.

P.S. If you are wondering what we did in class BEFORE this assessment, here is a quick summary:

1.  We spent several days sketching parent functions and transformations the old fashioned way, using paper and pencil. Students completed tables and plotted points, sketched graphs, looked for patterns, and generalized their discoveries.
2. Once students had mastered the basic functions and their transformations, I spent one class period introducing Desmos.com. I reserved our math department's shared iPad cart. I showed students how to enter equations, create sliders, and click play to ANIMATE (<3). They were as enamored as I was when I saw this a month ago at TMC13! Then I just let them play.
3. Finally, I started giving them a few challenges. Try to make an x^2 that moves vertically while stretching. Can you keep it from turning upside down? Can you restrict its movement to the second quadrant? Can you make it move horizontally along the line y = 2?

Four Friday Favorites

Four things made my day today:

First of all, my district switched things up by replacing my smart slate with an iPad. Now when I want to write on the board, I can see what I am writing. Nice. At the same time, writing has become more difficult because I am very particular about what writing should feel like. I NEED to have a precise writing tool, and I NEED to rest my hand on the surface while I am writing. Monday I went home feeling stressed about a lot of things (most are better now). Of all things, not being able to write comfortably was really irritating me. Plus I was first-day-of-first-full-week-of-school exhausted. And grumpy.

My husband loaned me this stylus, and I am a fan. It writes as smoothly as a pen, with all of the precision. I sketched some graphs in class today, and all the points landed right where I wanted them to land. It is expensive, but I am happy with it (so far anyway, it may be too soon to tell). I already owned its less expensive little brother, and that guy doesn't work well at all. They look the same, but the cheaper one skips constantly. I am hoping to continue a long and happy friendship with this new stylus. I gave hubby the other one. He's the best.

Then there is the issue of NEEDING to rest my hand on the iPad. I dug around my house and I found this glove with missing fingertips. It works perfectly. It protects my palm from the screen while keeping my fingers free to use the touch screen. I don't even care that I look like a dork wearing a glove in my classroom in August. Maybe I will buy one in every color and match them to my outfits. It will be the new math teacher vogue.

I really enjoyed this little ice breaker from Dan Meyer. I love that it combines mathematical thinking with a get-to-know-you element. I walked around the room and kids were asking each other how many siblings they had, how many pets they had . . . how often they brush their teeth. The only problem I had was when the number of students in a class was not divisible by four. I learned not to allow a group of three. It makes the task WAY too easy. I ended up making groups of 5 and adding an extra dot in the middle, which provided an interesting additional challenge. Then I started thinking about making a page with multiple configurations of dots. (Or have students place the dots themselves before they get the instructions?) So many options! Maybe next time . . .

Finally, I found these birthday stickers in the dollar spot at Target, and I have been handing them out on birthdays. A senior boy immediately put it on his shirt and today he told me how useful it was because,  "You WANT everyone to know its your birthday, but you don't want to go around telling them it's your birthday". That made me smile.

Happy Friday, everyone!

Highlights of TMC13 (finally)

So many people have done a wonderful job of re-capping the events of TMC13. I am pretty sure I have nothing original to say about the (most amazing) conference I've attended. EVER.

I decided to focus on the aspects of TMC13 that made the biggest impact. This is not even close to a comprehensive list of take-aways:

Rich Problems/Tasks:  It started with Max's presentation on noticing and wondering. The simplicity inspired me. Two powerful questions can bait our students to dig into problem solving. Glenn's session was the perfect follow-up. He showed us how to extend any problem by listing its attributes, changing one thing, and then see where it goes. Then we worked through a couple of tasks with Karim from Mathalicious. I can't wait to use these and others. These sessions all worked together to boost my confidence about implementing these types of problems in my classroom . . . This will be my main goal and focus for this next school year.

Interactive Notebooks:  I will admit to dragging my feet when it comes to INB's, but Megan's session won me over. I learned that I can modify much of what I already have, so my fear of starting from scratch was dispelled. I also learned that INBs are particularly affective in engaging lower-level students and helping them stay organized. I'll be incorporating these into my regular Algebra 2 class this year.

SBG: I might be the only math blogger who hasn't implemented standards based grading. I do not know why, because the philosophy totally aligns with what I believe about education. It was good to talk to people who are using SBG. They don't want to ever go back. It was good to hear that there are a hundred different flavors, not a right way or a wrong way. I figured out where to start. From there, I will make it work for me. I'll be incorporating SBG into my calculus class this year, but I suspect I will be expanding it to the others before long.

The People: Finally, a few words about the social aspect of TMC. Even though I have been blogging for a while, I have had a limited presence on twitter compared to most. I did not know many people going in. Add to that the fact that I am an introvert . . . I had some anxiety at first.

But I was determined, so I carried my introverted self down to the lobby where I folded paper and made plans for the evening. I went to karaoke expecting to stay for an hour, and ended up staying until closing time (and singing!). I had amazing meals with interesting people, and everywhere I went people could not have been nicer.

I decided not to name names because I will surely forget to mention someone. But I truly appreciate the generosity of those who gave me rides, brought me bagels, and included me in their plans . . . Thank you. I am thankful for every conversation, every walk from here to there, every meal, and every thoughtfully prepared session.

This tweet I sent from the airport sums it up pretty well:

Arrived excited and nervous. Leaving with new friends in the 'sphere. :) #TMC13
— Amy Gruen (@sqrt_1) July 28, 2013

I don't want to ever miss this again. And I am really going to TRY to spend more time on twitter for lots of reasons, but especially because all those faces now have really amazing people attached to them.

Zombies, Logs, Noticing, Wondering, Precalculus, and #TMC13

I attended the precalculus morning sessions at twitter math camp. Among other things, we made a list of topics that can typically be problematic when teaching precalculus. Then we each signed up to work on one of these topics and produce something useful.

I ended up working on logarithms with Summer (@mathdiva77) and her adorable southern drawl. I am not sure that she would appreciate the adorable adjective, but it's my blog.

We agreed that we both felt pretty comfortable with the procedural part of teaching logs, but we were missing some pizazz. We were missing a hook.

Our fearless leaders, Sam and David, had suggested that we start by trying to focus on our topic's big idea. We decided that logs, being the inverse of exponents, allow us to find an unknown exponent. Check.

So . . . How could we get our students wondering about exponents? We started talking about Max's session on noticing and wondering (one of my favorites!) and then Summer started talking about zombies because they're all the rage right now and we started getting super excited.

Zombies! We needed pictures of zombies! More importantly, we needed pictures of zombies multiplying exponentially. It took some effort to find some classroom appropriate, mild-looking zombies in groups of one, two, four, and eight. We pasted them onto a page in that order.

Then we typed the words "What do you notice?" and "What do you wonder?" at the top of the page and we were done. We basked in the glory of our creation. We envisioned our students noticing the number of zombies and wondering when there would be 1000 zombies, or when zombies would outnumber people. They would be putty in our hands. They would be begging us to tell them about this thing called a logarithm.

Next Sam said that it was time to share what we'd created. At this point I started to have doubts because, hey, did we seriously just paste four pictures into a word document and call that a project? The group offered some helpful suggestions, like attaching the pics to a timeline. We might let our students wonder about that, too, but we would ultimately have to provide that information in order for the questions to be answerable.

The more I think about it, being simple is kind of the beauty of it. Maybe it isn't that hard to bait students to ask the questions we want them to ask. Maybe the chasm between being teacher-centered and student-centered is much smaller than we think. Maybe all you have to do is start with a carefully selected picture, and then get out of the way.

We'll let you know how it goes. Stay tuned.

Unintentional Math Encounters of the Non-Mathy

If you are a math teacher, this has probably happened to you . . . Someone you know has come across a problem involving math and they ask you for the solution because, hey, a math teacher must know how to figure it out.

First, a little background story:

I grew up on a farm in Kansas. (So that's what me and Superman have in common.)

Over the years, my Dad's specialty has been modifying the equipment he uses to make it more efficient, user-friendly, and/or comfortable for the farmer. Several manufacturers have visited our family farm and utilized his ideas in their designs. I am proud of him, if you can tell.

On the fourth of July, after grilled hamburgers and before the small town fireworks show, my 73-year-old Dad pulled out a yellow notepad and sketched this:

He has been working on a piece of planting equipment, and he needed to know the length of x in order to form interior angles of 11 degrees and 6 degrees. It is a pretty simple right triangle trig calculation, but he didn't remember how to do it. I figured it out for him and we discussed the feasibility of my answer (x was smaller than he expected).

Since then I have been holding onto this sketch. It has me thinking about other times that I have been asked these types of questions . . . A former student building a garage with his Dad, another farmer calculating a complex feed ratio for her cow herd, and others.

It seems like these should be some of the best problems to put in front of our students because they are from non-mathematicians, unintentionally encountering math as a part of daily life. This, for lack of a better phrase, is "real life math".

I'll put this sketch in a folder and start collecting other questions as non-mathy people corner me for answers. But I am afraid my collection is not going to grow very quickly. And even if it did, the scenarios from the rural community in which I live are limited. I am always looking for ways to expand my students' perspectives.

I'd love to have help here. What math have your non-mathy friends asked you to solve?

Summer Work

I had a great summer work day with my colleagues this week. We worked on a plan of attack for the changes coming our way, and there are a lot of them. When I recently complained that "change everything" was on my summer list, I was only kind of kidding.

1. Incorporate MTSS. Our district has decided to implement multi-tiered systems of support in the area of math. This means that our most struggling students will have extra time to work on deficient pre-requisite skills. We have a plan for identifying these students and scheduling an extra period in the day for intervention.

2. New Courses. In addition to adding extra support at the lower levels, we also felt the need to do a better job challenging our advanced students. So, as a fairly small school (lower 300's for 9-12) that has traditionally offered only one track for math, we have decided to expand our course offerings to include a regular and an advanced course at each level. (There will be a regular Algebra 1 and an Advanced Algebra 1, etc.) We think this will be great for students . . . but it means that each of us will have at least one additional prep in order to incorporate all of these new classes.

3. New Textbooks. This year was the adoption of new math textbooks district-wide. I actually stopped using a textbook several years ago, so this isn't a huge deal for me. My colleagues are planning to follow their new textbooks, so they are stressed at the thought of starting from scratch. I am needing to make a lot of changes myself, due to #4 . . .

4. New Standards.  Common Core.

5. New Technology. We are fortunate to have some very current technology available in our district, but as new purchases roll in and old ones are removed and/or re-distributed, we are finding that our comfortable way of utilizing these devices is in need of a revamp. We spent a chunk of time figuring out the best way to meet each person's technology needs utilizing a laptop, iPad, apple TV, projector, and smart slate.

6.  New Teacher! In related news, we hired an additional math teacher to help make all this happen. We got to meet and hang out with him all day. He did not run screaming from the meeting, so that's a good thing. We have a challenging year ahead, but I am feeling a lot more confident that it will be a good one!

Summertime Blues

I am going to interrupt this blog's usual programming for a few moments of whining and complaining.

Then I will get over it.

So . . . I have been on summer break for more than a week already. Yay me!

But really. When the last bell rang on Friday the 17th of May, there was no skipping down the hallway. I did not hear the hallelujah chorus as I walked out the door. There were no celebratory cartwheels in the parking lot.

I am stressed out and overwhelmed . . . ABOUT NEXT YEAR!!!

I don't know why. . .

My summer list has only three things:

1.  Change everything.

2.  Rewrite curriculum from scratch.

3. Plan two new preps, for a total of five.

Ugh.

Have you ever had that back-to-school nightmare where you have a room full of students looking at you and you have no lesson plans? I had that dream. In May. . . a good three months from the start of the school year.

I will figure it out. I will find balance and I will enjoy summer with my family. I will also be productive. I will find the joy in the profession that I love. I will rise to the challenge and I will plan my little heart out. But right now, just for a little while, I kind of want to not be a teacher.

Best Last Days

In college, one of my professors told a room full of future teachers that our second-hardest day of school would be our first day . . . because we don't know our students. The hardest day? Our last . . . because we do know our students.

I realized that for all the time I spend agonizing over the perfect first day, I rarely put much thought into the perfect ending. I usually write my seniors a letter, but mostly I just pass out a final exam and wave good-bye and good luck as they sprint out of the building. I decided to be more thoughtful and intentional about the ending this year.

For calculus, I allowed some extra days throughout the semester for the students to research and create mathematical art. I was very excited about this, as I am a wanna-be artist myself.

On the next-to-last day, we set up an art gallery and invited the faculty to come view our finished products. Some of the students did the minimum, but a few of them created some beautiful pieces. 

"Can I keep that, please?", begs Mrs. Gruen shamelessly.

I cannot wait to hang these origami archimedean solids by my window!

The students all brought toppings and we had a taco bar lunch together between showings.

On the very last day I asked students to write letters to next year's calculus students. The letters were adorable, and insightful. I can't wait to share them with next year's class.

For physics (all the same students plus one extra), I scheduled the final exam so that we would have one day left afterwards.

I had a brief college advice session, sharing words of wisdom from someone who has been there (even though it was a long time ago). I talked about studying, advocating for yourself, communicating with teachers, and keeping your student loan total as small as possible. That stuff has to be paid back, people! If you sacrifice now by driving a reasonable car, working a part time job to pay the rent, and eating ramen instead of ordering so much pizza . . . . your future self will thank you. I promise.

And then there were presents!

For the girls, I made these necklaces featuring their college logo. I had a little help from Pinterest.

The boys got these clip boards with their college logo painted on the back. It is unusual to have them all going to the same school, but it happens to be my alma mater, so yay!

And finally, because it seemed like a very sophisticated thing to do, I brought glasses from home for a sparkling grape juice toast to their futures. There may have been a few tears.

My calculus and physics classes are usually small groups of all seniors. We become a little family during our year together. I start to feel like their Mom (or maybe a cool Aunt, because I like to pretend I am not old enough to be their mother). I teach them, cheer for them, advise them, and even get frustrated with them. But I still love them. And I will miss them.

Best wishes, class of 2013. You are going to love what comes next!

Plethora of Practice Possibilities

I wanted to help my students practice evaluating different trig ratios for special angles, so I made two sets of cards:

Set #1 is a set of answer cards. I made them out of craft foam so they would be sturdy and also look different from Set #2 which is just a set of small flashcards (problem on the front, answer on the back).

At the time, I had an idea about how I was going to use these . . . but then a bunch of other ideas came to mind. I am probably going to be changing the way that I teach this particular topic for next time (more focus on the conceptual understanding, less on the "trig hand"), but surely these scenarios could be adapted for other topics? Hence, I thought I would share:

Everything went in a bag, one for each table.

Modified flyswatter game:  The flyswatter game is oodles of fun. I thought it would be perfect for trig ratio practice. It was not. Students felt pressure to answer immediately, so they ended up slapping a random answer which was rarely correct. I also wanted to have more than two students answering any given question. For the modified version, students spread the answer cards out on their desk and point to the correct one as I ask questions.

Matching work mat: This is just a card with a bunch of problems, all with unique answers. Students can place their answer cards and move them around until they're all in the right place.

Flashcards:  Students quiz each other at their tables. The flash cards are also perfect for a Kagan Quiz, Quiz, Trade. Gotta love the photo-bombers in the back.

Group Quiz:  The answer cards are spread out on the table, and students have cards with four problems where each person at the table is responsible for a different one. Students can flip over a problem card at their table, and each person reaches for their corresponding answer card. I would choose problems that have similar answers, so that there is a chance of students reaching for the same answer card and being forced to talk it out.

Matching Flashcards to Answers: Students spread the answer cards out on the table and turn all the flashcards face up. They match the flashcards to the answers. The beautiful thing here is that it is super easy to self-check. Students just have to turn over the flashcards to see if they are right.

There's probably more . . . I also thought about the potential for making different sets for each table and then rotating them for multiple days of practice. But at the moment, I can't think of a topic that would require that much practice.