Monday, August 1, 2016

Algebra 1-2: Day 1

"Before anything else, preparation is the key to success" - Alexander Graham Bell
First Week of Lunches

It's the first week of my fifth year of teaching and for the fifth year in a row I will be teaching Algebra 1-2. At this point, I've written and rewritten the curriculum for Algebra 1-2 in an effort to align to the AzCCRs (Arizona's version of the Common Core Standards). This year, I will be rewriting my curriculum again to integrate our new textbook:
but also to continue making strides towards involving more problem solving and more student-led learning. Through this blog, I'm hoping to provide myself an avenue for daily reflections on my day-to-day teaching, even if that lesson is a boring straight-forward lecture. 

Here was the plan for Day 1:
(15 min): Attendance, Seating Chart, Schedule Checking, Three Things and a Goal
(15 min): Syllabus and Schedule
(5 min): One Thing...
(20 min): The $5.00 Problem

I share five slides on Day 1 to keep myself on track

Slide 1: Find Your Desk. As students enter the classroom I am required to stand by my door so I use this time to distribute half a playing card to each student. They then must find the desk with the other half. Every desk in my classroom is identifiable by card (set in groups by number). Throughout the year I am able to call on students randomly (eventually I will switch to Popsicle sticks with their names),pair them by color (reds pair up), or ask for a presentation from each group by suit (hearts present your group's work).

Slide 2: Three Important Things and One Goal. On this slide I list my name, my nickname, three facts about me, and this year I added the goal of having a 70% passing rate (Ds or better) for first semester which would be a 10% improvement from last year. I then asked students to write their own important facts and a goal on an index card that I left on their desks.

Results from 1st hour: 
  1. Pass C/D - 10 students
  2. Get an A/B - 10 students
  3. Learn more than previous years/Improve in Algebra - 5 students
  4.  Be less shy - 1 student
  5. Pay attention more - 1 student

Results from 4th hour:
  1. Get an A/B - 10 students
  2. Pass C/D - 9 students
  3. Understand Algebra / Ask for help - 5 students
  4. Learn more / Improve - 3 studnets
  5. Stay focused - 1 student
  6. Turn in work on time - 1 student

Slide 3: Syllabus - write your questions on the back of your index card

Slide 4: My daily schedule. I used this slide to introduce MathLab to my students. MathLab is our instructional support class for Algebra 1-2 and this will be my first year teaching it. The idea behind mathlab is to have smaller classes (8-12 students) to focus on building the pre-requisite skills and provide one-on-one support to students predicted to be unsuccessful in Algebra 1-2 in the hopes that they will benefit from the additional time. This class counts as an elective credit and not a math credit and is funded through Title 1 support services. During this week, all students will be required to take a state-provided test ranging from basic word problems through basic arithmetic with integers, decimals and fractions without a calculator. Students who score below a 70% are qualified to enter MathLab. My goal is to also identify students who want to be in an extra math support class based on their previous experiences in middle school. From the data I've studied in the past, and that I plan to evaluate again this year, about 1/3 of the incoming Freshman do not pass any of their middle school math classes prior to enrolling in Algebra 1-2 Freshman year.

Slide 5: One thing I can do to help you succeed. At this point I ask each student to grab a sticky note from their table and write down one thing that I can do as a teacher to help them be successful in class. On this slide I include my promise to update grades every three days so that the online grade book is a reliable way for them to keep themselves on track.

After 1st Period
Results: I made a rookie mistake and suggested things like talking slowly, using a lot of examples, etc and so of course that was the most common response in my first hour :(
  1. Help me when I'm stuck / Work one-on-one / Walk around to answer questions 12 students
  2. Use lots of examples / Show different methods 10 students
  3. Explain things in depth - 8 students
  4. Speak slowly - 5 students
  5. Provide reviews or review time - 5 students
  6. Challenge me to work harder - 2 students
  7. Be patient - 1 student
  8. Be fun -  1 student
  9. Write slowly - 1 student
  10. Help me learn in the best way for me - 1 student

Exit Ticket / Closing Problem

This summer I took a problem solving course for my Master's and have been thoroughly inspired to start integrating the techniques I learned into my classroom. This has to start by including tasks that help build problem solving abilities and give students the opportunity to reflect and grow as mathematical thinkers. To encourage this I knew I wanted a problem from Day 1 and that I didn't want more than a week to go by before I gave another thought-provoking task. That means the dead-time on Day 1 (since I can't start the first lesson due to the scheduling and attendance issues) was the perfect opportunity to input our first rich task... The $5.00 Problem. 

On an entire sheet of paper (with lots of space). I asked students to determine how to create exactly $5.00 using exactly 100 coins that can only be Quarters, Dimes, or Pennies. I encouraged them to write down all of their thoughts and as questions popped up I added encouragement to write down solutions that didn't work and to use those to try and build solutions that do work. The catch? There is no possible way to create exactly $5.00 using exactly 100 coins and I'm curious to see how many students catch on to that and how many students find a "closest" solution before stopping. 

Results from 1st hour: One student finished early twice, one from a miscalculation and once from using 128 coins instead of exactly 100. Many students suggested answers to be checked, but all of the answers were missing one of the two conditions. Questions popped up like, "Why can't we use nickels?" (A question I'm going to turn around on them tomorrow!), "Do we have to use all three coin types?", "Is this even possible?!"

Results from 4th hour: 

$5.00 Problem Follow Up:
I want to start a discussion tomorrow about one key aspect of problem solving: Identifying and understanding the conditions and variables since many students were able to find "solutions" that didn't meet both conditions. I also want to ask students reflection questions along the lines of problem posing such as, "What would have made this problem easier?" "Was it important to exclude nickels?" "Did you try 100 pennies or 100 quarters? Why or why not?" "What if... ?" and ask them to alter the conditions to change the problem. I haven't fleshed out exactly what this reflection will look like, but I will share it tomorrow after the lesson. Many students took a systematic approach, and very few students modeled visually. If I find any students who take different processes I'm hoping to share these examples on the document camera to talk about different approaches to the same problem (and why that's a good thing). 

Once we've had a chance to discuss the good and bad of the $5.00 problem I want students to complete a problem solving attitudes survey... but I'll save discussion of that for tomorrow's lesson!

Sunday, January 24, 2016

Analyzing M&Ms

Statistics is hands down my favorite unit of all time in either Algebra class. It's the one unit where I feel like you can't not let students make connections and problem solve on their own. So in Statistics for Algebra 2 I always introduce distributions, normal curves, and standard deviation the same way every year: with the M&M lab.

Here's how it works. I give every student a bag of fun size M&Ms and ask them to 1. Predict how many M&Ms the bag has, how many M&Ms the bag shouldn't have, and how many of each color they should have. 2. Record how many of each color in their bag as well as the bags of their group members. 3. Record the number of M&Ms in every bag for our class. Now, at this point the students work through creating a histogram, a probability distribution, calculating mean, and reading through various vocabulary in action. 

But what's really important is what I'm doing and not doing. As the groups work together I'm not answering questions directly, instead encouraging them to help each other and seek the answers from their group members. I'm also recording any questions that casually come up as the students count and record data. And lastly, I'm recording results from the M&M bags for the lesson follow up and the introduction to standard deviation and normalizing data. 

I'm impressed with the questions my students asked, and I'm excited to encourage them to follow up and investigate the results. Here's a picture I took of my board as I added as I recorded the questions.

These are the actually questions my student s asked, just worded nicely to fit on the screen. Because I collected all of the data myself from each group I'm going to use it to follow up and answer some of these questions. Students will learn normal curves and see what the distributions for the bags and each color look like. Then I might bring in a normal bag and a big bag to see how they compare. We might also connect this back to probability to answer some other  questions like, "what percent of bags will only have 4 of the 6 colors?". I'm interested to see where this takes us.

Saturday, January 23, 2016

Permutations and Survivor Season 8

My husband and I enjoy lounging around our living room with our 10 month old son while reruns of old Survivor seasons play in the background. Although we aren't fans of the drama and politics we both really enjoy watching the challenges (yes, we've seen every episode of Ninja Warrior). Before I continue I feel obligated to warn you of potential spoilers for a season that ended many years ago...

I'm watching Season 8: All Stars Episode 10 when the castaways are prompted to "Drop Their Buffs". To set the stage I'm going to provide a quick synopsis of the season so far. There are currently two tribes Mogo Mogo and Chapira. Chapira has 6 members while Mogo Mogo has 4. At this point in the game Survivor almost always forces a switch up (usually the merging of the two tribes). So, each of the 10 participants are asked to draw buffs from a jar because instead of a merge the two teams are going to be redistributed evenly, potentially "mixing up" the game. Imagine every ones surprise when every member of the previous Mogo Mogo tribe are end up together on the "new" Chapira tribe. I look at my husband as my jaw drops and exclaim, "What're the odds of that happening?!" And realize I've got the perfect hook for my students for permutations and combinations.

Now for some classroom background: My Honors Algebra 3-4 students are working at a brutal pace to include all of the material in Algebra 3-4 as well as all of the material in Pre Calculus (this is how we get our students into Calculus before they graduate). This is my first year teaching Honors Algebra 3-4 and although I'm keeping my eye on the state standards and doing my best to align I'm really just following the scope and sequence as it's been done for the past two decades with only a few changes (like the addition of ONE WEEK of Statistics to satisfy common core). That means I had 60 minutes and potentially one homework assignment to teach my students how to find probabilities using Permutations and Combinations. Surprise surprise, the students didn't get it and averaged a 50% for that learning target. What's a teacher to do? Assign practice and offer a retake of course! Unfortunately, I've seen this episode one day too late so now the question is, do I show this to my students for fun? Use it as a test question? Or file it away for next year? 

The plan: show students a clip of the tribe "swap" and then provide the prompt (which hopefully some of them are already thinking) "What are the chances of all four members staying together?"

Work through the problem in groups and collect questions/ideas/suggestions to share out. Two connections I want the students to make and will be listening for: the fifth member of the tribe can be any one member from the opposing group. (Which increases the possible combinations by a factor of 6) and 2. The four members could have ended up on either tribe (which doubles the possible combinations).

The solution as I've interpreted the problem: 2*4C4*6C1/10C5 = 4.8%

Of course I had to pause the show to crunch these numbers immediately on paper. After hearing the result my husband concluded: "Proof that the show is rigged!" But is it? Or is this just how random works? I wonder if my students will think the same.

About Me

This is my 4th year teaching Algebra 1, Algebra 2, and AP Computer Science A. This is my first year as the Algebra 1 PLC leader for my school as well as my third year as Algebra 1 representative in district collaborations (we call the cadre). I'm in pursuit of a Masters in Math Education and have previously completed a BA in Mathematics as well as a BAE in Secondary Education: Mathematics.