My school uses PowerSchool and a grading scale which is required by the school board. I have spoken to both the vice principal and department chair and they are interested in Standards Based Grading, but they also seem hesitant to allow a single member of a department to deviate significantly from what other members of the department teaching the same class are doing with regard to grading. I've been told that I can make changes within the approved structure, but I cannot just throw it away.

Currently grades in the math department are calculated by using the following system:

20% final exam

40% Tests (and these are common assessments, given by all members of the department teaching a particular class)

20% quizzes (there is some wiggle-room here as these assessments are not necessarily common assessments)

10% homework

10% teacher's discretion (traditionally I've used this as a participation grade based upon warm-up compliance and general participation.)

The first 3 listed above are pretty much written in stone. These are the ones I really cannot change. With regard to the 40% test category, we already do give students the opportunity to reassess the complete test (which covers either half or full units).

The common assessment tests are how I will either show that my attempt to implement Standards Based Grading is having an effect or is not. I like the fact that these assessments will require retention from my students, which I see is a possible pitfall of most SBG systems I've encountered. I will need to take the "common assessments" we have created and cluster the questions in such a way that I can more easily evaluate student comprehension across the standards, but otherwise these tests will likely be the same as those given in other Algebra 2 classes in my school. Reassessment will be Standards based rather than whole assessment based as the department currently does things.

I will be modifying quizzes to be standard (or skills) based so that I can more easily determine where a student would need to reassess. This would allow me to reassess particular skills rather than reassess a complete quiz. Also, my students will be assessed more frequently than other students in Algebra 2. Students who will need to reassess will not receive a percentage grade, instead they will get strategies for reassessment. The 10% teacher discretion points will factor in here.

I want to add an additional kind of quiz as well. I want to implement what I am calling "Mastery Quizzes". These quizzes will be focused on skills from Algebra 1 (or previous semesters in Algebra 2) in which students should be computationally proficient. For the first trimester the "mastery quizzes" will focus on solving equations (probably 2 of them) and working with exponents(most likely 1). These quizzes will contain 10 questions, and students will have to perform at the 90-100% level in order to not have to reassess. In later trimesters these quizzes will include factoring, completing the square and other topics I have noticed that students struggle with when we reach later units (ie, rational expressions and conic sections). My teacher discretion 10% will factor in here as well.

Homework: Here's my thoughts on homework. I have basically been told homework needs to a component of my grade scale. So, I am leaving it as 10% (department policy) but I am grading each homework assignment as 1 point (which means first trimester should include approximately 35 - 40 points here). Another component of this 10% will be the Interactive Student Notebook. The ISN will be worth 100 points. Lastly, any student getting Mastery level on any standard (skill) will receive full credit (whether completed or not) on the homework related to that standard (skill). So, potentially it is possible for a student to receive full homework credit and not have completed a single homework assignment.

What does this look like? Good question. Here's a snapshot of my changes:

20% Final Exam

40% Tests (with reassessment on any major standard which is below proficient)

10% Homework (ISN and homework as described above)

30% for quizzes: Mastery Quizzes will only count toward the 10%. Standard (skills) assessments will count towards the 20% (department mandated) and the 10% as well.

My original thought were to make the quizzes worth a total of 40% and tests 30%, but it was pointed out to me that if what I am doing works then the 10% shift really wouldn't greatly affect the grades. Making such a shift, would potentially make comparing my scores with the scores of other classes teaching Algebra 2 difficult and such a shift would also require school board approval which might be difficult given that no one else has tried using such a grading system previously in my district.

## Sunday, July 28, 2013

## Saturday, July 27, 2013

### Twitter Math Camp 2013

Ok, I didn't get to go. Wish I could have, but it would have required more planning than I was able to pull off this year (and my wife had foot surgery 2 weeks ago and has been couch-ridden ever since).

I followed as best I could on twitter and by reading blogs, and now that it is over I can't wait to see what great kinds of collaboration have occurred and what kinds of ideas people have taken home with them. If you haven't seen the program list then (look here). Reading through this course list alone gave me ideas on ways to think about what I am trying to accomplish with my own students. It has also given me a list of things which I really want to see someone, preferably both a presenter and a observer, post a blog regarding.

I don't know much about GeoGebra, I've heard of it but that is about it. Looks like something I might want to learn more about. As I'm looking to use Interactive Notebooks, Megan Hayes-Golding's presentation would have been a great one. I saw David Wees name in the listing after Megan's presentation, and then saw him on twitter. Next thing I knew I had spent 2.5 hours reading his blog. Hedge, I'll drop and give you 20 if you share your presentation on your blog.

Even without being there I've been thinking, growing and planning. There is a whole bunch of us out here who didn't get the opportunity to go, but in a way impossible a few short years ago we were participating. We're teaching during an era where things are changing at an incredible pace. I'm not sure what changes will come to our profession in the next decade, I do know many of the people who will be helping to make and understand those changes

This post is dedicated to all the teachers who participated in Twitter Math Camp 2013, in person or from their own homes.

## Thursday, July 25, 2013

### Make-Over Monday ~ Postage

Dan Meyer's Make-Over Monday task for this week is about an example of a piecewise function. It relates to the cost of postage since 1995. The original problem gives the students a table, labeled with years and cost in $ (presumably per ounce) to ship a letter to a domestic destination. (I tried pasting the picture into the blog, but the scale was all wrong...so here's a link instead)

**http://blog.mrmeyer.com/wp-content/uploads/130715_4hi.jpg**

I submitted a suggestion on twitter on how to improve this question. First off by posing the question, without taking the fun of finding out the information from the students. I know that doing this would help avoid a pitfall my students seem to always fall into, how to deal with the independent variable. (should you look at 1995, 1999, 2001, 2002, etc

**OR**should you consider years since 1995?)

Secondly, I suggested that the students could also look at how costs for postage have changed in other countries (Canada, the European Union, or its member-states). Lastly, I suggested that the students could also look at how shipping costs using UPS and FedEx have changed in that same time-frame.

I think this question has another good extension which could be done. Looking at how the postage costs have changed (since 1995) could be compared to either the inflation rate (another piecewise function) OR the costs of various different products (during that same timeframe). The natural extension for each of these explorations would be to predict when the next price increase would occur, or how much that next increase would be.

Of course, the best case scenario would be if you could introduce the original problem (but not how the original problem was given) to the students and if

**were able to come up with the extension activities**

__they__

__out of their own curiosity__

__on their own.__## Thursday, July 18, 2013

### Sequences and Series Unit

For me, the sequence and series unit is the third unit we will cover this year in Algebra 2. I like this unit, because ideally students should be pretty comfortable with linear and exponential equations already (from Algebra 1). Because of this, my assumption last year was that I didn't need to spend much time reviewing explicit (or as I called them, "function"-al equations). This was a mistake, I figured out after the unit was done. I'm making changes to prevent the mistake and timing of figuring it out.

As I am going to be trying to create and use an interactive notebook system with the students in Algebra 2 this year, I figured it would be nice to create a set of cards which I could use with this unit. My thoughts progressed and as of now I am planning on using 3 different sets of cards, one of which is a set I made for Algebra 1 + 2 last year that only includes graphs.

One of the other sets will be one in which tables and equations are to be sorted by whether they are linear, exponential or other. In this way I can get the students looking at 3 of the different representations linear and exponential equations can have.

The last set includes finite and infinite sequences. There are 40 cards and most of them are arithmatic or geometric sequences. (I debated including some non-arithmatic, non-geometric sequences and decided that an other category is a good thing because it allows me to more easily differentiate the instruction for students who need a challenge). I figure this same set of cards can be used for series as well as sequences, with 2 dice used to identify the upper and lower values for summation.

I haven't actually written the interactive notebook pages to go along with these card activities, though I do have an idea about what they will likely look like. I am hoping to get to those pages sometime in the next 2 weeks, though.

sequence and series cards

Feel free to look at them, criticize them, use them. If you have suggestions, please let me know.

As I am going to be trying to create and use an interactive notebook system with the students in Algebra 2 this year, I figured it would be nice to create a set of cards which I could use with this unit. My thoughts progressed and as of now I am planning on using 3 different sets of cards, one of which is a set I made for Algebra 1 + 2 last year that only includes graphs.

One of the other sets will be one in which tables and equations are to be sorted by whether they are linear, exponential or other. In this way I can get the students looking at 3 of the different representations linear and exponential equations can have.

The last set includes finite and infinite sequences. There are 40 cards and most of them are arithmatic or geometric sequences. (I debated including some non-arithmatic, non-geometric sequences and decided that an other category is a good thing because it allows me to more easily differentiate the instruction for students who need a challenge). I figure this same set of cards can be used for series as well as sequences, with 2 dice used to identify the upper and lower values for summation.

I haven't actually written the interactive notebook pages to go along with these card activities, though I do have an idea about what they will likely look like. I am hoping to get to those pages sometime in the next 2 weeks, though.

sequence and series cards

Feel free to look at them, criticize them, use them. If you have suggestions, please let me know.

## Sunday, July 14, 2013

### How do they know how to do something we never show them...

Random thought...actually I was reading a blog on someone who I wish I knew better's site. Research in Practice - Ben Blum-Smith If you've not seen it, take a look. Just come back here when you're done.

............

I've seen some D. Ball videos. I was forced to watch the same one 4-5 times and the little kids are cute, but they're not high school students. My kids are a little more, um, real. I've taught from 5th grade right through 12th. Elementary school kids are much easier, molded. (I sometimes wonder why I moved up) She's still a master.

I live in Michigan, and though D. Ball is at Michigan State I still think she rocks, but my wife doesn't (really, just on general principle. If you lived in Mi you'd understand)

Its so frustrating being the only person, in most classes, asking the questions. Lets face it, at times we're like chess masters playing high-school neophytes. I hate this. I've once, in the past 5 years, had a student really surprise me, mathematically. If only we did a better job modelling having a good mathematical discussion, then maybe they would know what one looks like (and how much fun it can be).

Our choices are to model this behavior in some way... Or, hope that mathematical discussions will just spontaneously begin and allow us to be witnesses of it. (or you can become known as the weird math teacher with all the puppets and strange voices..)

I've done the "special-ed" co-teaching thing. Generally with a teacher who is also teaching history and another math class as well. I love the Special Education Dept at my school, so let me get that out into the open and honestly had I done things differently then I'd be one of them as well. That being said, they are either stretched too thin, pulled from the class or honestly ill-prepared and sadly the kids get an opinion about them that unfortunately is true.

I want a teacher, someone who the kids know is in the classroom to come by and visit. I want 5, maybe 10 minutes of their time. Just to come by and have a mathematical discussion. It doesn't need to be scripted out, the visiting teacher would get to choose the topic (and would pre-warn me...seriously, if I've got to talk about the economic theories of Malthus or something I want a little notice). I want

I've contemplated the idea of doing this virtually. Timezone issues make this problematic, though not necessarily too bad as I live in the Eastern Standard Zone. For teachers in the West, sorry it is not fair. (math teachers will get that, probably no one else). It does require two teachers willing to follow the same general curriculum timeline (hello CCSS... you've given us the same topics lets see what we do with it). Although in all honesty, it really doesn't. Better yet imagine Skyping with my class; as students in my class help you introduce Logarithms. In this way we first model the discussion, then we show students having the discussion with a teacher and perhaps, finally our kids could discuss mathematics with each other. Either IRL or virtually.

............

I've seen some D. Ball videos. I was forced to watch the same one 4-5 times and the little kids are cute, but they're not high school students. My kids are a little more, um, real. I've taught from 5th grade right through 12th. Elementary school kids are much easier, molded. (I sometimes wonder why I moved up) She's still a master.

I live in Michigan, and though D. Ball is at Michigan State I still think she rocks, but my wife doesn't (really, just on general principle. If you lived in Mi you'd understand)

**I'm calling this the "Case for Co-teaching"**Its so frustrating being the only person, in most classes, asking the questions. Lets face it, at times we're like chess masters playing high-school neophytes. I hate this. I've once, in the past 5 years, had a student really surprise me, mathematically. If only we did a better job modelling having a good mathematical discussion, then maybe they would know what one looks like (and how much fun it can be).

Our choices are to model this behavior in some way... Or, hope that mathematical discussions will just spontaneously begin and allow us to be witnesses of it. (or you can become known as the weird math teacher with all the puppets and strange voices..)

I've done the "special-ed" co-teaching thing. Generally with a teacher who is also teaching history and another math class as well. I love the Special Education Dept at my school, so let me get that out into the open and honestly had I done things differently then I'd be one of them as well. That being said, they are either stretched too thin, pulled from the class or honestly ill-prepared and sadly the kids get an opinion about them that unfortunately is true.

I want a teacher, someone who the kids know is in the classroom to come by and visit. I want 5, maybe 10 minutes of their time. Just to come by and have a mathematical discussion. It doesn't need to be scripted out, the visiting teacher would get to choose the topic (and would pre-warn me...seriously, if I've got to talk about the economic theories of Malthus or something I want a little notice). I want

__to model__a mathematical discussion. I want the students to see two people work their way through a problem involving mathematics. Imaging me coming to your class (for sake of argument, my part in any movies will be played by Johnny Depp as he is the teacher I most often get told I look like) and asking you to help me with proving Heron's formula the week before you start teaching proofs to Geometry students. (I promise I won't try and make you change all the "s"'s to "arrrrrrghs".)I've contemplated the idea of doing this virtually. Timezone issues make this problematic, though not necessarily too bad as I live in the Eastern Standard Zone. For teachers in the West, sorry it is not fair. (math teachers will get that, probably no one else). It does require two teachers willing to follow the same general curriculum timeline (hello CCSS... you've given us the same topics lets see what we do with it). Although in all honesty, it really doesn't. Better yet imagine Skyping with my class; as students in my class help you introduce Logarithms. In this way we first model the discussion, then we show students having the discussion with a teacher and perhaps, finally our kids could discuss mathematics with each other. Either IRL or virtually.

### Liebster Award

Wow, I got an email saying I was nominated for the Liebster award (actually, now in my comments I have been twice nominated).

So what does this mean? Well, first of all it means somebody out there is reading!! Secondly, it means my next blog post is all about the requirements of this award. Seems there are a bunch of questions and I have to go out and nominate a few blogs to receive the award as well.

So what does this mean? Well, first of all it means somebody out there is reading!! Secondly, it means my next blog post is all about the requirements of this award. Seems there are a bunch of questions and I have to go out and nominate a few blogs to receive the award as well.

__The "Rules" to Accept the Award__**:**

• Link back to the blog that nominated me

• Nominate 5-11 blogs with fewer than 200 followers

• Answer the questions posted for you by your nominator

• Share 11 random facts about yourself

• Create 11 questions for your nominees

• Contact your nominees and let them know you nominated them

Lessons With Coffee (Jameson Michelle) questions:

1.

**What made you start writing a blog?**
I've been reading blogs now for about 9 months. Last year the MTBoS had a challenge for new bloggers. I was hoping for one for this year and basically harassed Sam Shah one evening on twitter about when it would be and he challenged me to blog 3x a week for the summer.

2.

**What song do you most listen to when you are in need of a pick-me-up?**
Lately I would have to say Get Lucky by Daft Punk

3.

**Can you name a movie adaptation that was better than the book?**
No, I cannot

4.

**What children’s book describes the meaning of life best in your eyes? OR What book (children or adult) changed your life and why?**
I've always read so much and pieces of lots of books have helped shape my perspective. There's a mnemonic device in Piers Anthony's On a Pale Horse involving 5 lines which I frequently find my mind returning to when I am stuck on a problem that has probably influenced me as much as anything.

5.

**What obscure pieces of trivia are you most impressed with yourself for knowing?**
That there are 8 letters which can act as vowels in the English Language.

6.

**What are you thinking about doing for Open House this year?**
Stations. Having parents do an activity like their kids are doing and getting as many of them signed up on the grade program as possible in one of the stations

7.

**What are you thinking about doing for first day of school this year?**
I just blogged about this one. Feel free to go back up and read my last blog posting.

8.

**If you had to pick another career what would it be?**
Ombudsman. Plant propagator. Own my own restaurant.

9.

**Who is your celebrity crush?**
Christina Ricci (but not from Casper, like from Sleepy Hollow) Though I would totally like Nicholas Cage to play me in a movie.(not that he looks like me) My Math Crush is of course Fawn Nguyen

10.

**What is your favorite thing about your mate or best friend?**
She's very supportive.

11.

**What is one piece of advice you would give a new teacher?**
Find your own voice. Each day should be used as an opportunity to challenge your students and yourself.

Radical Robin's Questions:

**(from Flip Learn Share)**
1

**. What was your favorite subject in high school/college?**
In High School, my favorite class was Humanities. In college, it was Geometry (which is odd because I didn't like it at all in high school)

**2. Where is your favorite vacation spot?**

In winter it is visiting my family in Florida. In summer it is Little Compton, Rhode Island.

**3. What is your favorite book/movie or play?**

There are so many books: The Bible, Kafka's The Trial, On a Pale Horse, the Joy of Mathematics Series, too many to continue

**4. Why did you become a teacher?**

June, July, August. Just kidding. I had a math teacher in high school who came in one day and said "I've not gotten this far in the book in too many years. I've forgotten how to do these problems. We'll work out the first 20 and whomever gets the most correct gets to teach for the next 3 weeks" Lastly, I had a son young and the notion of being able to have a job which allowed me to be with him as much as I could was extremely appealing for a non-custodial father.

**5. Do you follow your textbook from start to finish?**

Heck, no. In fact the kids complain that I make them bring it from time to time because I so infrequently actually use it for other than homework.

**6. What is your favorite teaching resource?**

how about top 3: projector (sorry I remember chalk all too well), my Algeblocks and my gridded whiteboards

**7. What is/was your favorite lesson to teach?**

I've got a few. I do one on scientific notation which is filled with really crude humor and its a lesson in which I have 100% of students on task the entire time, we laugh almost the whole period and scores are always very good on the assessment. (But I would never do it with witnesses present) I do another one called "Is Mr. Hills Normal" relating to the distribution of heights and its another good one. I'm short and according to the math I end up within 1 standard deviation of the mean (Normal) every year! (at least when the whole class is included)

**8. What kind of music do you like?**

Everything. Name a style and I'll name 2-3 groups/artists I like.

**9. What is the funniest joke you know?**

I'm telling you, that Scientific notation lesson keeps 34 of us laughing and fooling around for 70+ minutes. That's the funniest thing I can think of.

**10. How did you choose the title of your blog?**

I wanted something for my twitter handle that combined my teaching and gardening interests. I kept the same name for my blog.

**11. If you could live anywhere in the world, where would it be?**

Somewhere where I could have 4 seasons, enough land to garden to my heart's content, a stream where I could fish. Close enough to civilization that a trip into town doesn't feel tedious. Far enough that I cannot see my neighbors.

**My 11 questions:**

1. Is there anything you wish you could teach, but don't get the chance to?

2. Did any teachers when you were in school particularly challenge you, and how did they do it?

3. Do you worry about continued employment from year to year?

4. What do you think is the greatest impediment to people becoming or staying teachers?

5. If you could have your own child in one of the bloggers who you follow's class next year, who would it be?

6. If you could take your class next year on a field trip, where would you take them and why?

7. If you're in the middle of a lesson which is bombing, what do you do?

8. In the past year, approximately how many hours of (real life) professional development have you done? approx. how many hours of virtual PD?

9. Are you a member of the national association relating to your subject matter (ie, NCTM)? If so, why. It not, why not?

10. What is the opinion of your co-workers (about you and what you do) in your department at school?

11. If you were made superintendent of your district for a day what would you change about how things are currently done?

**11 Random facts about me:**
1. I'm short. 5' 5.5"

2. I'm the oldest math teacher in my department at school and you'd never know it.

3. I've taught Science, History, Math, Grammar, Literature, Business and Sunday School.

4. Some people have gambling or drinking problems, I have a gardening problem.

5. I have a poem I recite before each quiz, test or final. The kids expect it and "remind" me when they think I've forgotten it.

6. I have 4 kids, an almost 20 year old boy, a 9 year old boy and 2 new children a 13 year old girl and a 10 year old girl.

7. I cook well, well enough that I've been told I make the best grilled cheese in the world. (and honestly that's not the extent of my ability, I swear).

8. I cannot eat cheese.

9. My desk is always messy... but I know where everything is

10. I never get as much one on one time with students as I would like.

11. I love it when ex-students come back to visit

**Blogs I'm nominating: (in no particular order)**

**1.**Kathryn at Restructuring Algebra

This Kathryn is a friend on twitter and she is giving a great perspective with regard to trying to apply CCSS standards to Algebra 1)

**2.**Kathryn at i is a number

This Kathryn is a new find for me, but I am very impressed with her energy and perspective on INB/ISN's

**3.**Andrew at Social Studies and More

Andrew is brand-new at blogging, but I follow him on twitter and he is well worth following)

**4.**Druin at Stat Teacher Blogspot

I really should know her real name, but @druinok is her Twitter handle. this one undoubtedly breaks the rule regarding less than 200 followers, but she definitely deserves a mention!

**5.**Jessica at Algebrainiac

Generous with her creations, been doing SBG for a while, down to earth and easy to talk to. Well worth a look!!

**6.**Amy at Teach Reflect Repeat

I love the fans! I really have got to find a way to use these in my INB/ISN this next year!

## Friday, July 12, 2013

### I want it, I need it, I've gotta - gotta have it

As I look at materials and make plans for next year, I have come to the conclusion that there is something else I want...

I want good questions. I want the kinds of questions which will make my students interested in figuring out why something is true. I want the kinds of questions which catch the class' attention and keep them thinking about math well after the bell has rung.

Here's my problem, though, I don't want to be the only person asking these questions. I want my students asking these questions. I want to end class at least once a week not even knowing the answer(s) to these questions myself.

They say in government that you subsidize what you want more of and tax what you want less of. I need to subsidize inquiry.

I am planning on introducing the creation and use of an interactive notebook in my Algebra 2 classes. I have been thinking about how to use the left-side of the notebook. I've asked friends on twitter (hello: @mgolding @algebraniac1 @druinok @reilly0141 I think those are the peeps with whom I discussed INB's on Tuesday). I also reviewed the Global Math Department recording from a couple weeks ago where INB's were discussed.

Formats for the left sides are pretty fluid, leaving the options very open. I know that I plan on having students reflect on topics in that section. I also want to encourage asking good questions there. I generally try to not pay off students with candy (erasers, etc) too often, but I want good questions and deep thought too much to not consider the use of bribery to get it.

I have started mapping out my first couple units in the INB (well, the right-hand sides). I will be reading, asking and thinking about how to utilize that left side. I'll share my thoughts once I reach a comfortable place with how I am envisioning that part of the notebook.

I want good questions. I want the kinds of questions which will make my students interested in figuring out why something is true. I want the kinds of questions which catch the class' attention and keep them thinking about math well after the bell has rung.

Here's my problem, though, I don't want to be the only person asking these questions. I want my students asking these questions. I want to end class at least once a week not even knowing the answer(s) to these questions myself.

They say in government that you subsidize what you want more of and tax what you want less of. I need to subsidize inquiry.

I am planning on introducing the creation and use of an interactive notebook in my Algebra 2 classes. I have been thinking about how to use the left-side of the notebook. I've asked friends on twitter (hello: @mgolding @algebraniac1 @druinok @reilly0141 I think those are the peeps with whom I discussed INB's on Tuesday). I also reviewed the Global Math Department recording from a couple weeks ago where INB's were discussed.

Formats for the left sides are pretty fluid, leaving the options very open. I know that I plan on having students reflect on topics in that section. I also want to encourage asking good questions there. I generally try to not pay off students with candy (erasers, etc) too often, but I want good questions and deep thought too much to not consider the use of bribery to get it.

I have started mapping out my first couple units in the INB (well, the right-hand sides). I will be reading, asking and thinking about how to utilize that left side. I'll share my thoughts once I reach a comfortable place with how I am envisioning that part of the notebook.

## Tuesday, July 9, 2013

### What should the first day of school look like?

**OR**....What should the first day of school NOT look like.

I promise I will not: read through the syllabus

I promise I will not: lecture on day 1, not even rules!

I promise not to waste any time assigning seats.

I promise I will not: give a written assessment of any kind, not even an evaluatory/prescriptive one

I promise to: DO MATH

I promise to: make the kids think

I promise to : DO MATH

I promise to: challenge the students in an engaging fashion with something they can find an entry into which may or may not tie into something they might see again in class.

I have a hint at what I'm teaching, my letter of guarantee of employment for next school year only said that I would be a math teacher at (XXX) High School. (my certifications potentially allow me to teach math or ELA at middle or high school). I did speak to an administrator who did say that as things were (at the time of the discussion) that it was likely I was teaching Algebra 2 and Statistics.

In my school, Algebra 2 can be a class Freshmen are placed into, and I know I had a couple classes last year (I also taught Alg2 then as well) that were primarily Freshmen. I, actually won't know who is in my classes until the weekend before the first day of classes.

I want to start off with an activity like 4-squares, as mentioned on Mary Dooms blog (July 1st, 2013). I will have my desks set up in pairs (33 kids per class, 15 pairs and 1 triple). I want the students trying and sharing with their partners and then discussing with the class. Then I want a meatier challenge. I'm currently leaning towards Matt Vaudrey's Mullet Lesson (The only lesson they'll remember). My goal isn't evaluation, its setting a tone of exploration and risk taking with the math (in a fun way). I've got to speak to a couple of my colleagues about having prepared measurement cards and being willing to have their class interrupted to give them out.

I have 73 minutes, so I'm thinking I can at least get through enough of the mullet lesson to make it interesting. I'll let the lesson spill into the next day just a little, even if only to get them writing about the thinking process. (besides, one of the two days we'll be getting books - sad when I barely use them except for homework).

What goals do other teachers have in their lessons for the first day of school? I remember only 1 such lesson from my high school years (too long ago...). This particular teacher came in, had us write on the first page of our notebooks 3 pieces of information: a date, a phone number and Peanut M&M's. (his birthday, his phone number and his favorite candy. He got bags and bags of them on that date. Maybe he was onto something...

## Sunday, July 7, 2013

### Pascal's Triangle, Binomial Expansion, Combinations

Looking at the probability unit (which in my classes will be the second unit we work on in the first trimester), I am trying to think of a way to show the parallels between binomial expansion, Pascal's triangle and combinations. In previous years much of this was just given to the students. (its only my second year teaching this and I took cues from what had been done before in many cases).

I'm considering a stations activity, but one in which groups are assigned to a station and work on it on a large sized whiteboard, and then without erasing a thing, they will be switched to another of the stations to see what has been done before and hopefully add to it. When completed, the groups will post their whiteboards (with 2 additional ones whose use will be apparent in time) for a gallery walk (which is when those two other boards should be completed)

I have individual sized whiteboards that I purchased a couple years back and last year we got the school to get us Home Depot boards which we had cut down to 2' x 4' size for group work.

I see one group, being given the pattern for Pascal's Triangle. (this should be a group of students who need a lower level introduction to the mathematics we will be doing). Two other groups will split up the combinations (evens one group, odds the other). Two other groups will work on binomial expansion of (x+y) with one group again doing evens and the other odds. Ideally, weaker students will get the chance to rotate from the Pascal's Triangle station to both of the other problems. Stronger students should be ok with only seeing Pascal's Triangle from in the Gallery walk.

I see the groups set up as 1. Pascal's Triangle (weaker), 2. Binomial expansion evens, 3. combinations odds, 4. binomial expansion odds, 5 combinations evens

Thoughts: I like the notion of being able to differentiate the work, with weaker students getting a view of all three procedures. I like that I'm not just showing them these things and doing a "taah-daah!" I like the idea of giving my strongest students the chance to practice distribution on a bigger problem, and have it not be busywork. I worry that I'll just get people putting (x+y)^4 = x^4 +y^4 . I'm thinking that showing the parallels for 7 rows should be sufficient and provide the students with enough practice of the skills I want. I have a germ of an idea about having students "see" the differences between permutations and combinations using differently colored beads. Maybe I can use something from that idea (which should come before this one) to flesh out the work being done by the combinations groups?

I have been trying to get the students to produce something personal to go along with these kinds of explorations (otherwise they don't remember the reason for the activity a week later) This is still something I haven't really done on this idea yet, though I'm sure I'll think of something or something will be suggested.

I'm considering a stations activity, but one in which groups are assigned to a station and work on it on a large sized whiteboard, and then without erasing a thing, they will be switched to another of the stations to see what has been done before and hopefully add to it. When completed, the groups will post their whiteboards (with 2 additional ones whose use will be apparent in time) for a gallery walk (which is when those two other boards should be completed)

I have individual sized whiteboards that I purchased a couple years back and last year we got the school to get us Home Depot boards which we had cut down to 2' x 4' size for group work.

I see one group, being given the pattern for Pascal's Triangle. (this should be a group of students who need a lower level introduction to the mathematics we will be doing). Two other groups will split up the combinations (evens one group, odds the other). Two other groups will work on binomial expansion of (x+y) with one group again doing evens and the other odds. Ideally, weaker students will get the chance to rotate from the Pascal's Triangle station to both of the other problems. Stronger students should be ok with only seeing Pascal's Triangle from in the Gallery walk.

I see the groups set up as 1. Pascal's Triangle (weaker), 2. Binomial expansion evens, 3. combinations odds, 4. binomial expansion odds, 5 combinations evens

Thoughts: I like the notion of being able to differentiate the work, with weaker students getting a view of all three procedures. I like that I'm not just showing them these things and doing a "taah-daah!" I like the idea of giving my strongest students the chance to practice distribution on a bigger problem, and have it not be busywork. I worry that I'll just get people putting (x+y)^4 = x^4 +y^4 . I'm thinking that showing the parallels for 7 rows should be sufficient and provide the students with enough practice of the skills I want. I have a germ of an idea about having students "see" the differences between permutations and combinations using differently colored beads. Maybe I can use something from that idea (which should come before this one) to flesh out the work being done by the combinations groups?

I have been trying to get the students to produce something personal to go along with these kinds of explorations (otherwise they don't remember the reason for the activity a week later) This is still something I haven't really done on this idea yet, though I'm sure I'll think of something or something will be suggested.

## Saturday, July 6, 2013

### Feeling terribly scattered...

I have made the decision that my next school year will be a lot like my previous couple, I will be making big changes... (the kids joke that if you have me again next year, things will be different)

I need to make the switch to a Standards Based Grading system. I know that this will allow me to more easily track where a student's deficiencies lie and hopefully inspire the students to work on specific topics on which they are struggling. I also am trying to build in a means of having students work for deeper understanding and for retention (and of topics, not the student). I will be doing this in a school where I will be the only teacher making this change, so besides having to prove the idea to my students I will also be under the watchful eyes of many others.

I need to start my class with a prescriptive assessment. We've done similar things before, but I am carefully creating a new test with certain topics in mind. My thought is that when I go to the Dr.'s that I fully expect him to run tests, make a diagnosis and then start a course of action to deal with my particular ailment(s). I certainly wouldn't want to b treated for diabetes, just because most of his patients need such treatment.

We are getting Ipads for the math department (due to a race to the top grant we were awarded by the state just before we ended our monitoring... We were a "failing" school, and managed to remove ourselves from the failing schools list... Sadly, as far as I'm aware, we're the only secondary school in the state to accomplish this). I'm sure the ipads will pose their own issues, and I do have some ideas on how to integrate them, but that will have to wait until I see if we get them immediately and how much influence we have on what apps are available to be put onto them.

I also am planning on starting to develop and use an interactive notebook system in my Algebra 2 classes. (well, the non-honors classes to start) We have our CCSS curriculum pretty much ready, I will just be creating the notebook around that format. This means the first topic my students will see in their notebooks will be Univariate Data Analysis.

To this end, I have started working on this first unit. Skipping the table of contents, grade analysis sheets, standards list (with A and B standards identified and written in student friendly language) and my expectations pages (most of which I have already created as well). My students will see a 4-door mean/median/mode/range foldable, 4 flap foldable on creating box and whisker plots, s sheet showing how to find standard deviation using a table, a page on finding measures of central tendency with the NSpire, a page on Normal Distribution and the Empirical Rule, a page on skew and z-scores. I've made homework assignments for many of these days, all with A and B problems (total of 4-6 per topic) My Normal Distribution and Empirical Rule page includes a QR link to an online Plinko simulator (this seems like a natural time to introduce the Ipads to the students). AFter these notebook days I have 2-3 data collection and analysis activities planned, one of which I know works well to discuss and illustrate Normal Distribution.

I have decided that practice with many of these topics in class will be done in pairs and/or with stations. I am half wondering if I should give a quiz to the students the day the NSpires are handed out, but before the calculator work so that I can assess how they find M/M/M/R and SD by hand, but as this is a B level standard, I don't know if its worthwhile.

I guess the questions I'm still wrestling with are: 1. how do you decide when to assess students on different standards? 2. Do you have students include practice in the interactive notebook? 3. Because its possible in my school for a student to have 3 different teachers, one each trimester, for the same course, how do I deal with students who only start to have me 2nd or 3rd trimester with regard to the INB? (I know that I will be relying heavily on the students who had me the previous trimester to help the newbies).

I snipped and~~stole~~ "borrowed" heavily for some of the other pages (and some are just very simplistic) but I'll share the Standard Deviation table page. If anyone wants to see more, just let me know.

standard deviation with tables

I need to make the switch to a Standards Based Grading system. I know that this will allow me to more easily track where a student's deficiencies lie and hopefully inspire the students to work on specific topics on which they are struggling. I also am trying to build in a means of having students work for deeper understanding and for retention (and of topics, not the student). I will be doing this in a school where I will be the only teacher making this change, so besides having to prove the idea to my students I will also be under the watchful eyes of many others.

I need to start my class with a prescriptive assessment. We've done similar things before, but I am carefully creating a new test with certain topics in mind. My thought is that when I go to the Dr.'s that I fully expect him to run tests, make a diagnosis and then start a course of action to deal with my particular ailment(s). I certainly wouldn't want to b treated for diabetes, just because most of his patients need such treatment.

We are getting Ipads for the math department (due to a race to the top grant we were awarded by the state just before we ended our monitoring... We were a "failing" school, and managed to remove ourselves from the failing schools list... Sadly, as far as I'm aware, we're the only secondary school in the state to accomplish this). I'm sure the ipads will pose their own issues, and I do have some ideas on how to integrate them, but that will have to wait until I see if we get them immediately and how much influence we have on what apps are available to be put onto them.

I also am planning on starting to develop and use an interactive notebook system in my Algebra 2 classes. (well, the non-honors classes to start) We have our CCSS curriculum pretty much ready, I will just be creating the notebook around that format. This means the first topic my students will see in their notebooks will be Univariate Data Analysis.

To this end, I have started working on this first unit. Skipping the table of contents, grade analysis sheets, standards list (with A and B standards identified and written in student friendly language) and my expectations pages (most of which I have already created as well). My students will see a 4-door mean/median/mode/range foldable, 4 flap foldable on creating box and whisker plots, s sheet showing how to find standard deviation using a table, a page on finding measures of central tendency with the NSpire, a page on Normal Distribution and the Empirical Rule, a page on skew and z-scores. I've made homework assignments for many of these days, all with A and B problems (total of 4-6 per topic) My Normal Distribution and Empirical Rule page includes a QR link to an online Plinko simulator (this seems like a natural time to introduce the Ipads to the students). AFter these notebook days I have 2-3 data collection and analysis activities planned, one of which I know works well to discuss and illustrate Normal Distribution.

I have decided that practice with many of these topics in class will be done in pairs and/or with stations. I am half wondering if I should give a quiz to the students the day the NSpires are handed out, but before the calculator work so that I can assess how they find M/M/M/R and SD by hand, but as this is a B level standard, I don't know if its worthwhile.

I guess the questions I'm still wrestling with are: 1. how do you decide when to assess students on different standards? 2. Do you have students include practice in the interactive notebook? 3. Because its possible in my school for a student to have 3 different teachers, one each trimester, for the same course, how do I deal with students who only start to have me 2nd or 3rd trimester with regard to the INB? (I know that I will be relying heavily on the students who had me the previous trimester to help the newbies).

I snipped and

standard deviation with tables

## Thursday, July 4, 2013

### I do exit tickets wrong

I've got a good reason, really...

My class periods are 73 minutes long. How long is your attention span? Right now my mind is wandering to those biweekly staff meetings, once a month the meeting is 75 minutes and I'm rarely 100% focused on what the meeting is about. Sure I start out well, I even have a notebook each year and keep track of what we do each meeting.

I try to keep this in mind when planning a lesson, I've even been known to make the kids do the wave, get up and stretch or just find some other reason for students to do something to break up the monotony. Because of this, my 73 minutes is frequently broken into thirds or at least half. Seems like a perfect time for an exit slip.

Since I've already planned the rest of the class, I don't feel as guilty leaving a topic which just isn't sticking to reconsider and try another time. This also gives me time to go through those exit slips and if I want look at the topic again before sending my students off to their other classes. Also, if I need them to practice some part of the lesson, I now have a better idea of what they're capable of doing and what will just frustrate them. (Or the time to access and prepare a flip for them to watch at home instead of or in addition to something written).

I made up 4 (or so) different kinds of exit slips and I made a couple hundred copies of each, so the students don't necessarily know what I'm going to ask. (I tried posting links at the bottom of the post).

I realize that it's not exactly an exit slip, but there are technological tools which can accomplish something similar. At school they're pushing using the NSpire Navigator system ( not entirely because of the great cost it took to get). Sorry, TI, but I'm not a fan of the NSpires for this, because unless the kids use them almost daily that logging-in and such always takes more time than I'm willing to trade off on something like this.

I also do "my favorite no" as an opening activity a couple days a week. I've found that my exit slips from the day before frequently guide me about what to ask and whose examples to be prepared to share. I first saw the my favorite no concept in a video online, and I'm sorry to say I do not know to whom to give credit...it wasn't me, but I'll describe how I use the concept for those who don't know about it.

As students enter the room, they see

It works well to look at material from the previous day, but I find that it really shines for me when I need to get them thinking about prior knowledge in order to reference those skills in the lesson I am giving that day. (I recall converting 1/7 to a decimal, without a calculator, the day we started polynomial long division).

I can't see any reason to start doing exit tickets correctly... at least not as I currently use them...

exit slip #1

Exit slip #2

Exit slip #3

exit slip #4

I think there are 2 more at work... I'll try to update at some point

My class periods are 73 minutes long. How long is your attention span? Right now my mind is wandering to those biweekly staff meetings, once a month the meeting is 75 minutes and I'm rarely 100% focused on what the meeting is about. Sure I start out well, I even have a notebook each year and keep track of what we do each meeting.

I try to keep this in mind when planning a lesson, I've even been known to make the kids do the wave, get up and stretch or just find some other reason for students to do something to break up the monotony. Because of this, my 73 minutes is frequently broken into thirds or at least half. Seems like a perfect time for an exit slip.

Since I've already planned the rest of the class, I don't feel as guilty leaving a topic which just isn't sticking to reconsider and try another time. This also gives me time to go through those exit slips and if I want look at the topic again before sending my students off to their other classes. Also, if I need them to practice some part of the lesson, I now have a better idea of what they're capable of doing and what will just frustrate them. (Or the time to access and prepare a flip for them to watch at home instead of or in addition to something written).

I made up 4 (or so) different kinds of exit slips and I made a couple hundred copies of each, so the students don't necessarily know what I'm going to ask. (I tried posting links at the bottom of the post).

I realize that it's not exactly an exit slip, but there are technological tools which can accomplish something similar. At school they're pushing using the NSpire Navigator system ( not entirely because of the great cost it took to get). Sorry, TI, but I'm not a fan of the NSpires for this, because unless the kids use them almost daily that logging-in and such always takes more time than I'm willing to trade off on something like this.

I also do "my favorite no" as an opening activity a couple days a week. I've found that my exit slips from the day before frequently guide me about what to ask and whose examples to be prepared to share. I first saw the my favorite no concept in a video online, and I'm sorry to say I do not know to whom to give credit...it wasn't me, but I'll describe how I use the concept for those who don't know about it.

As students enter the room, they see

**MFN**projected onto the board. (underneath it says, get an index card from the back holder and write one problem on the front and the other on the back, then by yourself try to solve the two problems). This gives me time to take attendance, walk around look at homework and speak to students, approx 3-6 mins. I do not have students add their names, unless I get lots of students doing nothing, in which case I have them add initials (though I see who is doing it and who isn't while walking about). I then collect the cards and sort through the 1st problem, picking out a card in which the problem was started well, but something went wrong. The class then gets to figure out what went wrong and suggest how that student could remember not to make the same mistake(s) again. While they're doing that I sort the second side to do the same thing with that side.It works well to look at material from the previous day, but I find that it really shines for me when I need to get them thinking about prior knowledge in order to reference those skills in the lesson I am giving that day. (I recall converting 1/7 to a decimal, without a calculator, the day we started polynomial long division).

I can't see any reason to start doing exit tickets correctly... at least not as I currently use them...

exit slip #1

Exit slip #2

Exit slip #3

exit slip #4

I think there are 2 more at work... I'll try to update at some point

## Monday, July 1, 2013

### how fair is it?

my next blog posting was going to be about why I thought one particular unit was difficult for my students last year and what I was planning on doing about it this year. I'm sure it will be coming soon, but instead....

I had a discussion with 2 other teachers in my school. I, as a general rule, this past year wrote most of the assessments. It primarily worked out that way because I was the one teaching the honors class, so I was reaching the material first. Then, as they caught up, we would review the assessments which I had created and looking at the honor's classes results on those assessments we would "agree" to modify them. I put the "agree" in quotations because it wasn't infrequent for items to be removed, made significantly easier (reduction in Depth of Knowledge) or otherwise significantly changed.

I'm not using my, limited, platform to complain about my co-workers. My thoughts are instead drawn to the comment of one of them and I want to stream of consciousness my thoughts about that comment.

The question had the students performing a task which they had not previously done in class. It was a question relating to probability - and I wish I had saved it to post it here, but when I copied my files at the end of the year onto my portable hard-drive the original was replaced by what was given to the students instead. (If I find it, I'll try to add it, but its not really necessary for the rest of the posting)

Is it appropriate for students to be asked

The math coach we had said that my question was "ambitious" but she refrained from commenting further when asked about the decision of the rest of the Algebra 2 teachers to remove the problem. It was pointed out that there were plenty of other kinds of questions which did more closely resemble the kinds of questions the students had previously seen in class which would also assess the same standard. It was further pointed out that this was a question which the honors kids had struggled with as well (I believe the percentage was about 30% had gotten it correct).

My feeling is that by only asking safe, expected kinds of problems we are limiting our students. It may be perceived as unfair, but I'd rather a spectacular attempt at a problem that was different than 10 perfectly executed examples which the students had seen, or themselves, done before. I also point out the argument I used with the other teachers before the problem was removed, - I'm sure the assessments coming down the pike will include many problems unfamiliar to my students and I want them to at least try.

I see both sides and while I feel justified in my position, I can recognize that as many of our students freeze or just write the dreaded IDK (why would they write "I Dumb Kid" on their papers anyway... I can assure you after I question a few of them each year and assure them that I seriously doubt it, they don't do it anymore in my class...lol...I also point out that they could just as easily have written IDT...I Didn't Try)

It was one thing when NY changed their standards and NY teachers felt pressured, or TX ratcheted up the testing, but now its all of us and I'd rather challenge my kids and drop the points for a question and hand out candy to the ones who succeed or fail spectacularly, rather than remove the difficult questions from the test. I want my students to know that on each test that there will be questions which they've never seen and know that something they've learned is appropriate to solving it. If individually they never have to work on something like this, then I can't imagine how they'll ever deal with the tests which are coming....

I had a discussion with 2 other teachers in my school. I, as a general rule, this past year wrote most of the assessments. It primarily worked out that way because I was the one teaching the honors class, so I was reaching the material first. Then, as they caught up, we would review the assessments which I had created and looking at the honor's classes results on those assessments we would "agree" to modify them. I put the "agree" in quotations because it wasn't infrequent for items to be removed, made significantly easier (reduction in Depth of Knowledge) or otherwise significantly changed.

I'm not using my, limited, platform to complain about my co-workers. My thoughts are instead drawn to the comment of one of them and I want to stream of consciousness my thoughts about that comment.

The question had the students performing a task which they had not previously done in class. It was a question relating to probability - and I wish I had saved it to post it here, but when I copied my files at the end of the year onto my portable hard-drive the original was replaced by what was given to the students instead. (If I find it, I'll try to add it, but its not really necessary for the rest of the posting)

Is it appropriate for students to be asked

*to perform a task or experiment uniquely different than something they've previously seen in class, but still within the scope of the curriculum?***on an assessment**The math coach we had said that my question was "ambitious" but she refrained from commenting further when asked about the decision of the rest of the Algebra 2 teachers to remove the problem. It was pointed out that there were plenty of other kinds of questions which did more closely resemble the kinds of questions the students had previously seen in class which would also assess the same standard. It was further pointed out that this was a question which the honors kids had struggled with as well (I believe the percentage was about 30% had gotten it correct).

My feeling is that by only asking safe, expected kinds of problems we are limiting our students. It may be perceived as unfair, but I'd rather a spectacular attempt at a problem that was different than 10 perfectly executed examples which the students had seen, or themselves, done before. I also point out the argument I used with the other teachers before the problem was removed, - I'm sure the assessments coming down the pike will include many problems unfamiliar to my students and I want them to at least try.

I see both sides and while I feel justified in my position, I can recognize that as many of our students freeze or just write the dreaded IDK (why would they write "I Dumb Kid" on their papers anyway... I can assure you after I question a few of them each year and assure them that I seriously doubt it, they don't do it anymore in my class...lol...I also point out that they could just as easily have written IDT...I Didn't Try)

It was one thing when NY changed their standards and NY teachers felt pressured, or TX ratcheted up the testing, but now its all of us and I'd rather challenge my kids and drop the points for a question and hand out candy to the ones who succeed or fail spectacularly, rather than remove the difficult questions from the test. I want my students to know that on each test that there will be questions which they've never seen and know that something they've learned is appropriate to solving it. If individually they never have to work on something like this, then I can't imagine how they'll ever deal with the tests which are coming....

Subscribe to:
Posts (Atom)