step into my classroom: pre-algebra at ECA, quarter four

Seventh graders have been doing quite a bit of work with ratios, proportions, and other applications of fractions. To wrap up the unit, they used a scale drawing process to create a "king size" candy wrapper. After drawing a 1-centimeter grid over the original wrapper, they set up and solved proportions to determine the dimensions of their drawing. Then they drew a larger grid according to their calculations. From there it was a simple matter of filling in the boxes and adding color. The students LOVED this project, and now we have some pretty cool posters hanging in our classroom!

I don't know about you but all these candy wrappers are making me crave sweets!!

step into my classroom: pre-algebra at ECA, quarter three

My pre-algebra classes have been moving along at a steady pace since Christmas break. In an attempt to solidify some concepts for them during third quarter I relied on several projects to give them a chance to spread their wings and apply the skills they've been learning.

The eighth graders began quarter three with a rather complex unit on geometry and measurement. We relearned the names of the geometric solids, then learned how to find the surface area and volume of each. For some this was a very challenging chapter, as not every student is strong in visual-spatial skills. I had them build each figure out of paper to help them make the connection between a flat, two-dimensional shape and a three-dimensional shape.

Upon finishing that unit they completed a fun project in which they were the owners of an ice cream cone factory and had to make some decisions about what kind of cones to produce and sell. They were given a set of figures to work with and then had to use the formulas for volume and lateral surface area to investigate the affect height and diameter have on the end results. Finally, they had to design the ultimate ice cream cone and explain, mathematically, why it was the ideal cone. Some chose their cones based on volume and how much ice cream it could hold, while others tried to choose a surface area that would facilitate the perfect "cream-to-crunch" ratio. They summarized their work and conclusions in poster format and added some fun color and drawings to give it some flair. Who says math has to be all numbers?

The next unit took us in a totally opposite direction - data and probability! Another chapter that came easier for some, but was more challenging for those who struggle with critical thinking. After learning all the ins and outs of data collection, sample types, and bias, the 8th graders were set loose on the student population of ECA to conduct a survey. They had to write two unbiased questions, one that would require a categorical reply and one for numerical. They had to explain how they would randomly select 30 students from our 1-12 school. Some just put all the name in a hat while others did a stratified approach - either separating them by gender, grade level, or "school level" (elementary, middle, and high). After choosing the appropriate data displays they had to analyze their results and determine whether they had accurately represented the entire population. They also had to make some suggestions as to why the results turned out the way they did - and I was quite impressed with some of their ideas. One student's question was, "How many siblings do you have?" and she made the observation that many of her randomly selected participants were actually siblings with each other, which skewed her results significantly.

Finally, we did a fun probability activity on St. Patrick's Day - partly as an excuse for me to give them candy and partly as a chance for them to once again demonstrate and solidify the concepts we'd been studying. The students were given a random mixture of Skittles and M&M's, and after taking inventory of their candies they had to determine the probability of various events.

We had just learned how to find the probability of disjoint, overlapping, and complementary events. So, they had to write three examples of each, then find the probability of each example they'd written. The next day, they corrected their own work by presenting their problems for the rest of the class to solve.

Overall, third quarter was a challenging, but engaging time for the eighth graders. Hopefully something from this quarter with stick with them!

thankful thursday

This week I'm thankful for:

Good days with my 8th grade pre-algebra class. I've written about them a lot lately because they have been my most challenging class to teach. The majority of first quarter I felt like a total failure, but lately things have been looking up. Their attitudes have been improving and they have even said things like, "This is fun!" and "Whoa, this is so easy!" in the last week. Tomorrow is their first quiz of the new chapter, and I am very hopeful that it will go well for everyone...

EasyJet. Without it, I would not be able to travel to Germany so cheaply to spend Thanksgiving and Christmas with my "family." 

Rest days. As I mentioned in this week's Hello Monday post, I started doing Les Mills BodyCombat again. I'm currently following their recommended schedule for two rest days a week. So after three consecutive days of intense workouts, my shoulders are sore enough to make holding my hairdryer uncomfortable, and every time I sit down I feel the burn in my quads. There's something wrong with the fact that I am more sore after three workouts than I ever was after running a half marathon! I've even been taking the elevator because I just can't bear climbing the stairs up to the third floor! I know it's a good thing and my body will thank me for it later, but for now I am thankful that today, Thursday, is a rest day.

Chocolate croissants. I have a love/hate relationship with these bad boys and they have become part of my daily routine. The best ones are obviously in Germany, but I have found a suitable alternative (albeit not fresh) at the local Día (our grocery store). During second period each day I have gotten into the habit of pouring a cup of coffee and enjoying a chocolate croissant while I grade or read. My mouth loves them. My waistline hates them. So good and yet so, so bad.

What are you thankful for this week?

step into my classroom: pre-algebra at ECA, quarter one

In attempting to clean out my phone, I found a bunch of pictures of math projects. This made me realize that I never wrote a quarter one update on my Pre-Algebra classes! Better late than never, right?

Our Pre-Algebra course spans two years - seventh graders take Pre-Algebra A and eighth graders take Pre-Algebra B (unless they test out and move up to Algebra 1). This means I am teaching out of the same textbook for two different classes, but seventh graders are starting at the beginning and eighth graders are starting halfway through.

Seventh graders began with the basics: rules of integers, one-step equations, and basic graphing. Within the last week have begun to learn how to work with multi-step equations and will soon move on to multi-step inequalities, too! For their Chapter 1 project, students had to graph a given set of coordinates that, if graphed accurately, formed the outline for a shield. Students then had to design a coat of arms to represent themselves.

I really enjoyed seeing what symbols and colors they chose to represent themselves. Many identified with various countries and cultures by using flags, national colors, and symbols. Some revealed more about their families, their heritage, and some even gave a nod to their hobbies and passions by incorporating their favorite fútbol team colors. 

I asked the students to explain to the class their choice of symbols, and the most touching came from Alex, who told us that he chose gold to represent the cross because of how special Jesus is to him. In case you can't read his shield, it says "Live for Jesus."

The eighth graders spent the first quarter reviewing and learning linear equations: solving, graphing, and writing them. I found an awesome project on TeachersPayTeachers that incorporated all of these skills plus art, and it was a great chance for the students to relax a bit after a hard chapter. For this project, students had to select a country flag with at least two lines and at least one diagonal. Then they drew the flag design on a coordinate plane and used two points on the line to identify the line's slope. From there they were able to calculate an equation for each line on the graph. Some students chose flags that they knew would be very easy, while others went for a challenge. While I am proud of ALL their work, I was particularly impressed with the students who chose Canada and Australia. The more lines a flag contained, the more math a student had to do! 

By now we are almost halfway through the second quarter. Things are getting harder, and in response to that some students are thriving and others are sinking. My eighth grade class has been on my mind constantly. Please be in prayer - that my struggling students would find success in my class, and that I would have the patience and grace to know how best to teach them.

coffee cupdate: con leche, por favor

If we were to sit down for a cup of coffee, I'd have a lot to tell you.

I probably wouldn't know where to begin, because it has been so long since our last Cupdate. Carefully I would wrap my fingers around my mug and apologize for not doing my part to stay in touch.

You would probably ask me about my new students, and I would share little details about each one: how passionately Alex sings along when Hillsong's Relentless comes on during math practice time; how loudly my science class announces the arrival of Hump Day each Wednesday; how persistently Collin questions me, demanding answers far beyond my meager understanding of science; how Dafne and Elizabeth are attached at the hip; how adorable Jonathan's British accent is... I would shake my head in disbelief wonder aloud how it's possible to care so deeply for students I have only just met.

I might tell you how discouraging my first quarter of pre-algebra was with the eighth graders, but how many of them have turned over a new leaf in this first week of quarter two. I'd tell you with a huge grin how exciting it was to give out FIVE solid B's on last week's quiz, and how thrilled they were to have earned such grades!

Maybe I would share with you some of the inner struggle I have been battling each day here in Spain. I'd confess that while I am determined to be fully present and committed to my students and my role here at ECA, not a day goes by that I do not think of, miss, or pine away for my "old life" at BFA. You would most likely assure me that this is a normal part of transition and yet, I would still feel guilty for missing Germany so much. Together we might ponder how I ended up here--the way God has worked so clearly to orchestrate my timely arrival--and dream of what He will do during this year.

I might also share with you how, on accident, I have discovered the perfect café con leche at a small coffee shop in the neighborhood near my church in Madrid. You would be jealous when I tell you that this deliciousness is available for a mere fifty cents! At this point, I would simply wink and tell you that it's time for you to visit Spain so that I can treat you to one.

What would you share with me?

worth it

Last week I asked my 8th grade pre-algebra students to write me a note stating the areas in which they still felt weak in preparation for their retake of our chapter test. I thought if they could pinpoint their own weak spots, it would guide their study sessions. One student wrote the following:

Dear Ms. Bertschi,
First I want to thank you for helping us with a great mood. And we all love you very much. The only problem I have is finding f(x) equations. I would still need some more practice. Thank you for all your work.

* * * * *

I have struggled with this class from the beginning. Over the last several weeks I have agonized over their failed quizzes, taught and retaught over and over again, and desperately prayed that something would stick. I have told them every day that I believe in them. I have wracked my brain for new ways to explain the concepts, scoured Pinterest and TeachersPayTeachers for hands-on activities, bribed them with candy, showed them videos, had them teach each other ... and when they took the first chapter test I couldn't help but wonder if the last two months had been in vain. It's hard not to feel like a total failure when only one student scored higher than a C and several scored actual Fs.

Despondent, I asked myself if this struggle was really worth.

So when I read that note scrawled in typical middle school boy font, I was reminded that yes, it's worth it. All the late nights, early mornings, extra planning and brainpower that I have poured into trying to reach these struggling students is totally worth it. If only for one student to recognize his value and know that someone believes in him, for one student to see how much his teacher loves him and the lengths she is willing to go to see him succeed, for one student to build his confidence... absolutely, completely, 100% worth it.

technorama mama!

On Friday I had the privilege of traveling two hours into Switzerland with some high school students and staff for a field trip. We went to Technorama, an incredible hands-on science museum. I can't even begin to describe how awesome this place was - literally every single display had instructions telling you what to do or try, with explanations of the science behind it. I was worried that I wouldn't understand anything because it would all be in German, but at each display they also had cards with several languages including French, English, and Italian so everything made sense! It was also really fun to explore all of the exhibits with many of my former middle schoolers!

thankful thursday

Today I'm thankful for:

• Bright sunshine and warm spring air streaming through my windows at 6:00 am this morning
• Eighth graders who greet me with enthusiasm and bring a smile to my face
• Spontaneous theological discussions in the middle of science class
• Seeing my math students grasp and apply a concept
• The chance to visit an amazing science museum in Switzerland tomorrow
• The privilege of singing in the mass choir at The Great Hallelujah this weekend

The Course Evaluation [disclaimer: long post ahead]

At the end of each semester, BFA encourages us teachers to spend time in reflection. This comes in the form of a slew of evaluation forms: personal evaluations, supervisor evaluations, general evaluations of everything from administration to teacher resources... Check. Check. Check. The list goes on and on. But nothing compares to the one that strikes fear into the heart of every teacher: the Course Evaluation.

pi pie

On Monday morning I found a little surprise on my desk.