## Thursday, September 7, 2017

### Week 2: Days 3 - 7

On the first day of week 2 I passed out graph paper composition notebooks to 8th grade students to use for their classwork and homework. Students need reminders to use the front and back of every page and don't leave any blank space while still keeping it organized. I passed out CPM toolkits for my 7th graders to use. The notebooks could even be a task:

Name tents were a big hit again this year. It's great to have a back and forth written conversation with students willing to engage with you. Reveals a lot about what's important to them, if they are willing to reveal it.
After passing out the notebooks, students worked on figures 1, 4, 5, and 100 of a tile pattern. It created a great opportunity for students to see the figure number in the pattern and describe it's growth using academic language like row, column, horizontal, vertical, etc.

On Tuesday, I had a short Google slides discussing entering the classroom procedure, grades, Teacher Creed (from iunderstand.com), rules, and then they continued on the second tile pattern for the lesson.

Wednesday was a short day, but I managed to check homework and do the algebra walk outside. Great introduction to x axis, y axis, origin, quadrants, lines, reading graphs left to right, increasing or decreasing, steep or flat, etc.
On Thursday students completed input output tables for inputs -6 to 6. This created a chance for students to see patterns, ask each other for help, and then share the results. We also did choral response once people described the pattern. We also reviewed homework problem 1-7 before that which has students reading 3 different x-y graphs about cars A and B in regards to weight vs cruising speed and more.

On Friday we used technology and a game to create a need for academic language after feeling frustration. I paused, related it all back to the algebra walk with interactive notes, and then they spent the last 10-15 minutes playing the game armed with better questions and vocabulary.

This year I teach 4 sections of grade 8 and one grade 7. The focus for 7th graders was a lesson on "Guess my Number" where I highlighted two primary strategies: guessing and checking and working backwards by using inverse operations. Students learned and used each others ideas. On Thursday, and Monday of next week students investigated the height of a million penny tower. As you can see some of the initial predictions were wayyyy off, but gave a chance for students to reflect.

I used Google Drive to take photos of student work to highlight different methods. Some used their table and saw that 1 centimeter was 7 pennies, 2 cm was 14, etc. They reasoned 100 pennies must be 100 / 7 or 14.2 pennies, and then could scale 100 up to a million by multiplying by 10,000 to 100 and 14.2. The other method, that was more precise, was this student below dividing a million by 7:
Instead of Estimation 180, the 7th graders are doing Which One Doesn't Belong. After 20 days of these, I am going to switch to 20 days of number talks with students recording new methods they didn't previously know, in hopes of using new strategies later.

A theme of some mathographies students wrote, and it's my job to turn it around:
I will be doing my first mystery student activity using student mathographies next friday before the first assessment.

8th graders will be assessed on skills 1, 2, and 3, which are diamond problems (integers & fractions), coordinate plane identifying, plotting points, knowing quadrants, and calculating percent error.

7th graders will be assessed on finding mean and median, converting between fractions, decimals & percents, and finding area and perimeter of rectangles, triangles, and a trapezoid.

## Sunday, August 27, 2017

### Week 1: Days 1 & 2

I started day 1 as I suggested in my NCTM blog post #1 linked on my resume linked above. Students lined up, and I introduced myself and had them tell me their name or nickname and how to pronounce it. They then grabbed a playing card from a deck of Aces through 8's and an estimation recording sheet and searched out their seat. I am discussing with other teachers how to do my VRG or visible random grouping. At a bare minimum, I want to switch seats every chapter, like I've always done, but randomly. This would allow for an easier seating chart for a substitute and an opportunity for students to reflect on their team at the end of the chapter. Henri and others suggest switching every 2 weeks, which sounds nice, and is not too often. Alas, the research from Peter says that the best and most effective method is random groups, every single day. How would it work though when a substitute came in? As you may tell, I haven't had good experiences with how my students have acted with substitutes or what subs have allowed students to do.

Instead of jumping straight into my height, I figured I would go a different direction and have students estimate my age.
About 95% of students overestimated my age and I told them it takes a lot to offend me. As you can see from the bottom left of the tweet image above, I honored all responses for my age, after giving them my birth date.

The most common method was students adding 16 to 1984 to get to 2000, and then adding 17 to get to the current year 2017. Then most students who did that added 16 and 17. So, many thought I was 33. I waited, and a couple students reasoned I am not 33 YET, because it's not my birthday yet. On september 4th I'll be 33.

I asked for alternative methods, and students mentioned the subtraction algorithm of 2017 minus 1984.

I then passed out the name tents that offer 5 days of feedback. I've blogged about this before, if you've never heard of it, google Sara Vanderwerf name tent. It's a game changer and most of #MTBoS (math teachers on twitter) are doing it with great results.

Then we read the Chapter 1 intro and had students find the 3 other people in the class that had the matching graph. They glued it on and some started their stories.

With 2 minutes to go, I had students write a comment or question and then collected their name tents at the door.

On Day 2 I had students estimate my height. This time 95% of students underestimated my height. I measured myself at my daughter's doctors appointment and I'm 6'0.5" with shoes on, so I said I'm 6'.

I joked with students that they all think I'm really old and short, when in fact, I'm young, for a teacher, and taller than average people.

Then students finished their graph stories, and then did the 4 coordinate graphing. I'll post photos of these next week. They turned out great. I also have a TA 5th period who is hanging them for me around the room, in preparation for back to school night.

I then found out that Staples was doing their graph paper composition books for a buck each, for the first 30. I got a deal and got all 130 for a buck each.

## Saturday, June 10, 2017

### 2016-2017 School Year Student Testimonials, Surveys, Final Results, & reflections @classroomchef

Like with any communication with parents, it's always a good idea to start with the positives. So, the first artifact from this year I'd like to share was the one letter I got from a student during teacher appreciation week:

At the end of the year, it has been a tradition for our 8th grade teachers to give students class time to write a letter of appreciation to a teacher on campus. Unfortunately, one teacher who had 3 sections of 8th graders did not give the assignment, so this year's amount of letters was at an all time low. These letters I believe are important to me because it gives me insights into what was memorable, what I should continue doing, and what I should try to improve upon.

This student liked my sense of humor, and says he learned motivation from me. I wonder how I did that?

I saw a massive improvement in this student after requesting to join my math support class.

I saw a steady improvement from this student after also joining my math support. The most valuable part is I was her favorite teacher because I never gave up on teaching her. Aw!

This student felt engaged in my class. They clearly like Desmos activities because that's the main way I use the Chromebooks.

This student had a great work ethic already. In his letter though, he mentions how I care whether or not students understand the material.

This student liked sharing their ideas and learning in groups and feels he hasn't forgotten the material. And I was entertaining and amusing. That's cool.

So, instead of having a full period written final, I took the written final, anticipated common mistakes, and created a Google form with 36 multiple choice questions. Some had 3 choices, most had 4 choices. Once turning on the quiz option, you can create the answer key and basically students can view their results right after they submit their form.

My last question was this open response. Now the Classroom Chefs might call this a teacher report card, but this is a bare bones version since it's just this prompt, and unfortunately I gave it at the end of the year instead of the middle where I could have taken some more action.

me gusto mucho estar en esta clase aqui aprendi muchas cosas nuevas. aprendi un poco rapido pero todavia me ase falta un mas practica. todas las clases me parecieron divertidas (3)
In my opinion, this year went by quick and was a good learning experience. Some parts of this class that I liked was when we were able to choose seats, use chromebooks, and doing some fun activities such as the Algebra Walk. But, most of the activities were very boring and would be better if you added some wazzah to it :D (2)
This year in math i feel like it was harder than last year. And it was harder on me because i always struggled with math. Math is my least favorite subject so i didn't really have any favorite moments. (2)
Mr Joyce's teaching
My favorite part of the class is when we had to do basic equations with our group because equations are something that doesn't puzzle me. On the other hand my least favorite parts were either sitting next to some dude that goofs off or doing graphs because when a large scatterplot has to be made, I often times get my eyes hurt trying to plot the tiny dots from a huge scatterplot.
I liked this year in math class, since I felt like I did well. My favorite parts of the class were the mini-projects or group projects. My least favorite part was the homework (lol).
Easy, because I did most of them in Japan. I liked Wheel Project because I never did that before and it was fun. I didn't like powers like 5^3, because I don't really like calculating on paper. I like geometry better.
It was the best year of math i've had. Favorite parts were working in tables and least favorite parts were tests.
This year in math, it wasn't too hard for me it wasn't too easy for me. My favorite parts of this class was working with different people, my least favorite parts were doing assessments.
This year was the best year of math from all of middle school. My last two math teachers would shout a lot sometimes when you got an answer wrong but in this class I was never afraid of raising my hand and getting an answer wrong. My favorite part was when we did the water bottle flip project. My least favorite part was that we changed seats so often because if you really liked your seat and your table, it would change in like a week.
My favorite parts of class this year were whenever I really understood what I was learning. My least favorite parts were when I was confused on what we were learning.
This year of math further strengthened my math skills. I like the fact that we get to do the estimation warm ups, those are pretty fun, sometimes, I also like working in teams, which I usually hate to do. My least favorite part is testing since I lost most of my scores on it.
My favorite parts of the class were learning new skills in algebra and extending my knowledge in math. My least favorite parts were taking the assessments.
I liked solving whether or not equations had one solution, no solution, or infinite solutions. I also enjoyed finding the measurements of missing angles and finding the hypotenuse using the pythagorean theorem.
My favorite part of class was being able to work with people in the class I don't talk to outside of class. My least favorite part was taking quizzes because they are stressful even if they're easy.
This math year went well. My favorite parts of class was when we did mystery students and the fun activities we did. My least favorite part was the homework and the tests.
In math, some of my favorite parts were the illustrations, demonstrations, and test retakes. On the other hand, my least favorite part was the fast pace of learning a lot of new skills and new concepts in such a short amount of time.
My favorite parts of class was when we did activities on the chromebooks with friends.
my least favorite part was working in groups
My favorite parts of math class was the morning warm-up. The least favorite part about this years math class was that I had to work with people that I didn't know.
I really liked this math class because it taught me a lot of new things that I could learn and improve and carry on to high school. My favorite parts of the class is learning the pythagorean theorem. My least favorite part of the class was when we had to learn the line of best fit, because I had trouble finding out where the y intercept was.
Math this year in the beginning was easy. Then it got harder and harder and now its back to easy. My favorite parts of class was when we do the warmups and projects. My least favorite were the quizzes we had to take every Friday.
My least favorite parts were taking a test every Friday and working in groups, and having homework every night.
My favorite parts of the class is when the tables work together, and also the mystery student. My least favorite was the test and when we went to the back of the class and wrote see if we got the same answer as the table groups.
doing problems that had the algebra equations and graphs ARE THE WORST!!!!!
The beginning of the year was easier than what we learned just now. For example the negative and positive tiles are now easier for me and i don't really understand how to find what the cube root is in between. Like i wasn't sure how to solve the second to last problem.
My favorite parts of class where when we worked as a class. My least favorite parts where the math tests.
some tests were hard but working in groups was fun and the estimations were fun
My favorite part was when we could go outside, my least favorite was when we had to work alone on a problem.
Math this year for me was cool beacuse we did fish bowl which was fun and when the kids wen to sojurn we did water bottle flipping.But least favorite part was math is i struggle, as u can probs tell alrady so I do my best and work hard bu totherwise it was a cool year.
I don't really know.
Surprisingly my favorite parts of class were when we took tests and my least favorite parts of class were the estimations before the lessons.
I think this math year for me started slow but i caught on later throughout the year. My favorite part of this year was how we got to interact with different people in table groups even though it really isn't my thing, but i got used to it. I didn't really have a least favorite part this year. So overall this year was pretty good.
My favorite part of the class was finding volume of cones and using PythagoreanTheorem. My least favorite part of the class was graphing.
problems like the fishtank were fun and estimation. Least favorite had to be always changing seats.
Favorite parts were doing work independent work; Least favorite - working in groups.
I enjoyed doing hands-on activities to help visualize and understand the concepts more clearly. The table groups were also helpful, however, in some groups, it would be difficult to work together.
The Functions
My favorite part of class is learning new types of math.
Class was better in the beginning of the year than the end
This year in math was okay, some of the group projects were fun although i liked the chapters based on finding area and volumes and my least favorite parts were learning about the slopes and graphing.
My Favorite part was the group activities and my least favorite was silent work.
my favorite part was doing the estimation sheets, but not the graphing estimation, that was pretty bad also i liked when we did mystery student, that was fun. My least favorite part was taking weekly test even though they really were not that bad, i just needed something to say that was my least favorite because for the most part did not have any problems with this class
My favorite parts in class were doing group projects. I don't have a least favorite part in class
My favorite part of this class is when we learned the Pythagorean Theorem. My least favorite is when we were learning about graphing.
Favorite parts were hands on activities, least favorite part were the tests every Friday
favourite parts were pythagorean theorem. least favourite were how tests reflect so heavily on my grade
My favorite parts of class was learning things through projects and the group work. My least favorite parts were learning about y=mx+b for a long period of time as it got repetitive and i wanted to learn something else, but I see why we did it so much since some students didn't fully understand it.
Most of this class was boring, the only time it wasnt my least favorite part was when we didn't do work.
i had my ups and downs with it but that was my fault i thougth i had it under control but i dropped my grades. when we got new seats. when we changed seats and i liked my table.
doing class projects, i do not have a least favorite part
My favorite parts of class were the group projects my least favorite part of class was taking notes.
This year of math was very enjoyable, though there were constant distractions, and though my last of math class showed that I knew nothing, i was able to prove the contrary. My favorite parts of class were always the creative and new ways most lessons were. To be honest, There wasn't really a least favorite part of class because this is my favorite class. I enjoyed learning here more than ever. it is all thanks to the amazing math teacher I was able to have.
my favorite part was when we started the cones and cylinder
Although i was arrived in the middle of the school , my math went nicely, at first i used to have some difficulties in solving the problems with friends but now i learn many things here with the help of my friends and teacher .I always try to do my best in the class.My favourite part of the class is working with friends in the class, misri students, discussing about the problems about math.
My favorite part was doing triangles because i really understand it and knew alot about it from last year. My least favorite part was square rots because i didn't like to have to show all my work.
My favorite parts of class this year was when we switched seats every week because then I could work with more people and get to know new friends. My least favorite part of class this year was when we got yelled at.
This math year went great because this was the best math class and teacher I have had in the three years I was in Taylor Middle School. My favorite part of class was the estimation sheet we did in the start of class. There were no least favorite parts in my opinion
this math year went ok not the best not the worst the favorite part of class was everyone having a good time (even though we talked to much)my least favorite parts were when you yelled at us but whatever. hope you have a good summer and a great next year-
I loved this class even though we got yelled at alot i had a lot of fun with my friends and doing math because math is my favorite subject
i liked doing the mystery students. i did not like how we did an assessment every week but it helped.
My favorite part in class was being able to work in table groups and get help from other students when I was having a hard time on a question. I also really liked the way Mr. Joyce teaches because i got to learn a lot from him this year in math. My least favorite part was changing seats every week because sometimes my table would be very helpful and i would like to stay with them for a longer period of time. In other cases I would get put in a table that never does their work.
Class was interesting, i didn't have a favorite or least favorite part about it though.
it was okay i got to excell in the math skill. what was my least favorite parts was waking up
Favorite: Discussing the classwork/homework problems in class Least Favorite: Test every week
This year in math was better than 6th and seventh grade. I feel that I learned a lot more here than I ever did back in those two years. My favorite parts of class was when we calculated the surface area of cylinders and cones, integers, and transforming the triangles on the coordinate plane. Your teaching style is already great, but remember to pay attention to the quieter kids in class; they might need some more help than other students.
my least favorite was when mr.joyce yells. i liked getting to choose our seats for one chapter.
my favorite parts of class is when we do anything a kinda artistic and my least favorite parts is when u touch the tv screen and that we have a test every friday
Mr Jioce tuaght me alot and i think he is a good teacher.
My favorite part of this class is when I understood what we were doing and my least favorite part was not understanding the work
I think towards the end of the year i gotten better with math than the beginning of the year. My favorite part was when we did the spiral (a^2 +b^2=c^2). My least favorite was learning the volume of a cone or cylinder.
i came into this class recently but i have learned a lot here. i like how we all do the work with thw whole table
This year math was good. I understood it more. I liked working with table groups.
My favorite parts of class is when we use interactive tools to help us understand with what we're learning. My least favorite part is when people don't cooperate with you, causing you to do all the work.
my favorite part in class was when we did group projects and my least favorite part was that we rarely got to choose who we wanted to work with on a project.
tbh, I really didn't like this class. Like, at all.
My favorite parts of class were working on the group projects and my least favorite parts were the weekly assessments.
i liked changing groups often, and i learned a lot this year. i didnt like to take a test every week
The mystery student was fun because I got to learn new things that I didn't know about other people. I guess not getting my work done was not that efficient but it can always get better.
My favorite part of class was changing the dates when Mr. Joyce would forget too. Also taking off that piece of tape on his shirt that extremely bothered me. My least favorite parts were probably when Mr. Joyce would write down our group discussions and review to the class because I have the problem of blurting out things I shouldn't be saying and no one needs to hear that. Other than that math was pretty lit and shoutout to Mr. Joyce for actually making it through the school year without going insane with his fifth period class (thanks to me, duh).
Favorite parts was working with the tiles, it's because it was the easiest.
The year was good other than the part where our class would not stop talking when we were supposed to. I do not feel that we gave the respect to the teacher that he deserved. Mr. Joyce did a great job at teaching all the concepts and gave us all the tools and the right environment to work in. My Favorite part of this years math class was the mystery student when we got to learn what we had in common with the rest of the class.
i think the math class went good but i wish i understood math a little more
my favorite imporart had to be actually understanding the math, my least favorite as you know imas the yelling yeah it was a great year mr.joyce
My favorite parts was the classroom activities. My least favorite was homework.

I discussed some of the students responses with my colleagues, and the last section I discussed with my 5th period. Many students mentioned they didn't like it when I yelled. I observed that there period was the only one that complained about that. It was the lowest performing, most off topic class, and had the biggest spread between really high and really low. I also had a smaller variety of participation in the class because of this, and I really worked on my wait time a lot all year with this class.

At one point in the year, a student reminded me I threw a pencil at the wall, which scared her. I admitted that I took it too far that time, and was trying to get through to them by being dramatic. She said this scared her. I admitted I was wrong and apologized I went too far that time.

Even on the last week of school I was reviewing student results to Marbleslides: Lines while it was paused and students were talking when I was talking. I calmly said, this is a scenario where I yelled earlier in the year. And I'm not yelling right now, just pointing it out so you know.

Overall, students didn't like changing their seats weekly, even though many would ask are we changing seats today on Mondays.

It hurt seeing a student say they didn't like anything about the class at all, when struggling all year. I even would make a point to come talk to her on an individual basis in group work to build up her contributions and ideas.

Students really liked the Wheel of Theodorus project with pythagorean theorem, it was mentioned multiple times. Students who did the homework, liked the short discussion about it each day after the warmup. Many students grew to enjoy group work, and some still are against it. It's a work in progress.

Anyway, I'm looking forward to a great summer of reading, playing with my daughter, and with some math toys with my mom, daughter, and cousins.

## Thursday, June 8, 2017

### 2017 Summer of Math Box #tmwyk

I have ordered tiling turtles and a book of Christopher Danielson's, and recall other teachers subscribing to his Summer of Math last year. Then he sent out this tweet.

Prior to the box coming, a postcard came with a beautiful photo. My 1 year old daughter Everly loved the tiling pentagons! Check out the video:

Some alternating. I love the contrast of the shades of wood.

Then Everly looked at pictures from a book of her great grandma's 90th birthday party.

And back to playing with pentagons, throwing, picking them up, banging them together.
Each of the 3 months will come with 1 of 3 types of tiling hexagons. Here are the 12 setup to tile I think.

Making a hexagon with pentagons.

And this tweet from Mr. Stadel set off a cool domino effect of sharing of designs online:

## Friday, June 2, 2017

### Wheel of Theodorus Year 3

As a final project to practice using the Pythagorean theorem in an artsy way, I introduced students to the Wheel of Theodorus. I originally learned about it from Yummy Math.

This year, I showed students examples from last year's students, which I believe motivated more students.

The rubric is pretty basic. You get a 4, or A, for meeting all requirements: a minimum of 6 calculations for hypotenuses, labeling all hypotenuses I for irrational and R for rational, and making it colorful and creative based on what it reminds you of.

One of the biggest talking points is properly showing all steps accurately, as well as what happens when you square a square root. For example: squaring the square root of 2 equals 2. Another way to view it is you can square the radicand, 2, to get 4. The square root of 4, is 2.

Some didn't finish it or turn it in, some put some effort in, but the ones that put a lot of effort in are obvious. I selected a few, took photos, cropped them, and showed all the classes the next day. Many students appreciated the opportunity to have an artsy project (and I love it because it's still mathy).

I noticed students had trouble drawing the 1 inch perpendicular legs for the new leg of the next triangle. One tip was using the corner of your ruler to make sure it was 90 degrees. Next year I might print and cut out the card stock 1 inch by 1 inch squares suggested by Yummy Math to assist in this process.

Here are the ones that stood out as creative, thought provoking, and full of effort:

This makes me thirsty and ready for summer.

This looks like some really cool stained glass windows.

Apparently this is a Sponge Bob character. I wouldn't know, I've never watched it.

This one is titled "Moana"

## Monday, May 8, 2017

### 3rd @desmos print and student products

Today concluded the first of two days with our local librarian Debbie who brought in her 3D printer today. It is called an Ultimaker 2 Go. She started by showing the objects she had printed off of thingiverse as well as a model of herself using some sort of XBox 3D camera? We also passed around the sample from my previous blog post of my daughter's name plate "Everly."

Then I hooked up her laptop to the classroom display so she could introduce students to the history of 3D printing to it's many uses from decorating food, creating space parts, prosthetics, hearing aids, and much much more.

As students listened, they had a chance to ask questions after 15 minutes. Only 1 student asked a question. They were surprised that it would be free at the library. I think the hour time investment of orientation is not appealing to them.

Students were given time to continue working on their graphs. Students who had finished were following the steps in my slides to prep it for printing. In essence, it's changing all the equations to the color black, turning off the grids and axes and turning on the projector mode. Then export as a .png, convert it to .svg, import that file to Tinkercad, add a prism or cylinder as a plate, and turn the name into a hole. One student, Chloe, went through this whole process.

Three students prepared their graphs and emailed them to me, and I added them to the Padlet wall.

While students worked we printed out the name plate for my niece Callan. It came out on gray filament. I was able to pass it out with 15 minutes left in the class. Students thought it would be hot but it had already cooled off. The extruder on the machine though gets up to 200 degrees Celsius, which is almost 400 degrees Fahrenheit. A student pointed out that that's how hot an oven must get, which I agreed. It is kind of like baking something at high heat.

Then we started Chloe's printing. One obstacle we faced was her creating a Tinkercad account. Debbie suggested I look into whether there is a teacher account so students can login using that.

What I like about Chloe's is that she used a cylinder as the name plate background. Debbie shrunk it to cut down on the print time. What I love is that one of my students gets to see how math and their own work results in a real artifact from my math class. What a feeling. I personally remember that feeling from my woodshop and ceramics classes in middle and high school respectively. I do remember making a Factor Book in 8th grade Algebra with a Southpark theme but that's a different kind of artifact!

Here are my 5th period students getting a final look at the printer before class let out:

## Sunday, May 7, 2017

### Number Tic-Tac-Toe by @mburnsmath

It all began with a tweet by Marilyn Burns a few days ago...

I figured I would introduce it to my 7th and 8th grade math support for students who had finished their homework. I left the directions on the board. Students enjoyed it immensely! So much so, that other students who were still working on their homework stopped and joined in. This class can be hard to motivate at times so to see them want a play a math game was great.

Students liked that they could beat me at the game sometimes. I was really impressed with some of the strategies they were using. We will definitely return to it.

In 6th grade math support, we focused solely on the game. I left the directions on the board and had students practice with their table partner. They asked if they could use their partner's numbers to make three in a row, and I said yes. Also, some were caught repeating numbers so they had to restart.

I played a student and saw that there was a 9 in the middle. They knew they couldn't but anything less than 6 because than I could put a small number and win. So, they put a 7, pushing the sum over 16. I was very impressed.

I then printed out a 16 team elimination bracket by googling for it and randomly put the students names in the columns, making sure their first round game would be against someone different than their practice partner.

During the practice I could talk strategy and give suggestions, but once the bracket started I couldn't to be fair to both players. Students got ultra competitive! I mean, these are kids that have been disenchanted by math for a long time and they were loving this game. I couldn't believe the spark it provided for students. On Monday we have a semifinal match to finish to decide who plays against Faby for the championship (to win a confiscated ring pop...!)

So, thank you so much Marilyn Burns for inspiring my math support students to have fun with a really cool math game.

Here are the rules from the tweet:

UPDATE: