## Monday, July 29, 2013

### #Made4Math - Chair Pockets for ISN Supplies

This will be my first #Made4Math Monday post!  Yay!

As I plan to start Interactive Notebooks this year, I needed a good way to manage the tape, scissors, colored pencils, etc.  I don't have the best set-up (no tables) for the cute little table buckets of supplies that I've seen, so I tried to think of something else I could do.  I thought of chair pockets.  I have my desks in groups of 3 and I thought one pocket per group would be best, so I decided to set out to make some.

I have a sewing machine and basic sewing skills.  I like sewing because I see it as problem solving!  I don't like following patterns, but I do like trying to figure it out.  I was busting my brain, but then (once again) I remembered that this is the age of the internet, so I found some blogs that shared how to make chair pockets:

I set out to measuring my chairs:
 To make sure the pocket would fit the chair
 To make sure I didn't make it too long (silly, probably, but hey, why not?)
And then there was a lot of trial and error...but I now have one I can share, so here we go!

Through my trial and error, I determined I needed to start with fabric that was 19'' x 26''.  So here is my fabric.  Two pieces laid right sides together.  (Do you like my beautiful thrift store fabric :)

I pinned the two pieces together.  Here you can tell that there are two pieces!

Then I started sewing.  The blog recommended three sides, then turn the correct way, but I always do 3 1/2, because I think it makes it easier to finish the fourth side if it has already been started.

This is about where I stopped, so from where the machine is to the end of this side will remain un-sewn, the rest is stitched together.
Turning it right-side out it looks like this.  The edges need ironing at this point, so get to it!
Now it's time to work on the part that still needs sewn.  I start were I left off and tuck in, ironing as I go.  The ironing hold it well, but use a few pins just in case.
It should look like this now:
Sew it all the way across to close.  I think closer to the edge is better because you will make sure the thread grabs those edges you turned in.  Also important to go all the way across the edge so that your seam doesn't awkwardly stop half-way across.
I even sewed across the other short end to have consistency.  Here it is now.
You are almost done!  Time to fold.  I wanted around 7'' for the chair, so I folded it, ironed it, and pinned it down.
Then flip it upside down and fold up the other end to wherever you want your pocket to go.  My cat tried to help, but you can still see that my folded part is now down.
Fold, iron, and pin again.  I guess I didn't get a picture... But then you just sew along the "long" sides at one go.  At one point the pocket will be in the front, the next it will be in the back.  If you have it pinned it should work out OK.  Here's mine
Now I'm moving to the part where the pocket is on the backside.
And once you do that on both sides you are finished!  Ta-da! (This is in my house, NOT my classroom...)
I wanted to show you a picture of it in my classroom, since that is what I will be using them for.  Here is a pic of the pocket in use.  I sewed additional seams along the pocket so that I could organize my supplies better from left to right I have:  colored pencils; scissors and scratch paper notepads; tape and glue; whiteboard markers and erasers.  In the basket under the desk is a textbook and a little whiteboard.  Not sure if'I'll do that for sure, but it's an option.

That's all there is too it.  Now I just have to make 7 more!

-Kathryn

## Sunday, July 28, 2013

### Liebster Award

I was nominated for the Liebster Award a while back by Scott from planting-ideas.  But that was the day I left for vacation, so I didn't really have time to do anything about it.  Now I'm finally getting around to accepting my award :)  However, there are some "rules" attached to it!

Here they are:
• Link back to the blog that nominated me (yup I already did that :)
• Nominate 5-11 blogs with fewer than 200 followers
• Share 11 random facts about yourself
• Create 11 questions for your nominees
• Contact your nominees and let them know you nominated them
Because I'm me, I will be doing those things in exactly that order. Step 1 is done :)

Nominate 5-11 blogs with fewer than 200 followers (these come in no particular order):

1. Garnett Hillman at When There's a Fork in the Road...Grab a Spoon!
Garnett is my SBG guru.  She has given me a lot of practical suggestions in my process of implementing SBG.
2. Matt Owen at Just Tell Me the Answer
Matt and I have had many Algebra 1 conversations via twitter.  Enjoy having someone to help me process all of the standards.
3. Jessie Hester at Mrs. Hester's Classroom
Love all the ISN ideas from her blog.  I learned so much from her top 5 post!
4. Kelly O'Shea at Physics! Blog!
Whiteboarding.  Enough said! (Barely made the under 200 followers cut off!)
5. Jessica Hardy at Tweetching Math
One of my new twitter friends!  Hopefully she will have a #made4math post on her blog soon!
6. Robin Matthews at Romanthio
Another new tweep.  Love all the work she put into sharing her SBG journey on her blog.
Honorable Mention (she has over 200 followers...):  Sarah Hagan at Math Equals Love
Confession:  I read Sarah's entire blog in one night because I just couldn't stop.  (Hope that doesn't come off as creepy!)  Great ISN ideas!

1.  Is there anything you wish you could teach, but don't get the chance to?
I love teaching Algebra that is definitely my #1 passion.  But I also would like to teach economics and computer science, however I'm not certified (at this time) to do that.

2.  Did any teachers when you were in school particularly challenge you, and how did they do it?
I felt very obligated to be successful in my economics course.  I had an out-of-school connection with my teacher and at one point he told me that I understood a lot more about the world than a lot of people my age.  Knowing that he thought highly of me only made me want to work harder for him.  (And I loved the applicability of mathematics in economics.) So in short--relationships!

3.  Do you worry about continued employment from year to year?
After my first year of teaching my position was cut.  But at my new school I do not worry about it.

4.  What do you think is the greatest impediment to people becoming or staying teachers?
I think it's too different things. I don't see much impediment to becoming a teacher, but I know a lot of people who choose not to stay a teacher.  I feel as though this is because of the overload of work.  It's a lot to manage a classroom; effectively plan a scope and sequence (for up to 7 different courses); deal with paperwork, technology, students, parents, and administrators; plan lessons that will effectively hook students and help them learn; assess students appropriately; and all the other things that didn't pop into my head instantly.  So many stressful things makes for a lot of stress.

5.  If you could have your own child in one of the bloggers who you follow's class next year, who would it be?
Well, I don't have any children, so I don't think I can reasonably answer this question.  I would guess it sort of depends on the child's personality.

6.  If you could take your class next year on a field trip, where would you take them and why?
Probably somewhere to learn about the wind turbines.  I just think they are so awesome and so full of math, but I don't really know anything about them...

7.  If you're in the middle of a lesson which is bombing, what do you do?
I look at my students and I say.  OK, by the end of class, I need you guys to learn this.  Any ideas?  What can I do that will make that happen?  What can you do that will make that happen? (I honestly did that once and it was OK.)

8.  In the past year, approximately how many hours of (real life) professional development have you done?  approx. how many hours of virtual PD?
I had at least 16 full days of real life PD in the last year, and we have almost weekly 1/2 days of PD...so we'll say around 200 hours.  Virtually, I couldn't even start to count.  The MTBoS is pretty much my life.

9.  Are you a member of the national association relating to your subject matter (ie, NCTM)? If so, why. It not, why not?
I am a member of NCTM because I get journal, etc. that give me teaching ideas.  Also discounts on books.

10.  What is the opinion of your co-workers (about you and what you do) in your department at school?
I don't know, because I'm not them, but I suppose they think I'm OK and that I'll get better with more experience.  Somethings I say/do are good, but others need work :)

11.  If you were made superintendent of your district for a day what would you change about how things are currently done?
Please, please, please don't make me superintendent!  Way different role than what I want.  Not even sure what all the superintendent has control over.  My classroom is enough responsibility for me!

Share 11 random facts about yourself:
1. I've known since 11th grade that I wanted to teach mathematics.
2. I traveled to Africa twice.  Once to Ethiopia and once to Malawi.
3. I have 7 brothers and sisters.  Don't expect me to remember your birthdays because I have enough trouble remembering theirs :)
4. My favorite TV show is Bones.
5. My husband and I have been camping in Maine, Montana, Iowa, and Colorado
6. I student taught in Chicago in a high school with almost 3,000 students.  Then my first year teaching I taught at a high school with about 100 students.  (Big change!)
7. I would prefer to have school year-round with longer breaks throughout the year.
8. One of my education professors told me to make sure to learn something new every year.  I take that to heart.  This year I tried horseback riding for the first time!
9. I moved this summer so that instead of having an hour drive I have a seven minute walk.
10. My husband got my a kitty for Christmas and I love her to death.  She is very spoiled!
11. My mom got a smart phone before me.

Create 11 questions for your nominees:
1. What made you decide to start a blog?
2. What do you feel like the purpose of your blog is?
3. How did you choose the title of your blog?
4. Would you rather...have 1000 people read each post and none comment or 10 people read each post and all comment?
5. What is the greatest benefit you have found from reading blogs?
6. When did you know you wanted to become a teacher?
7. If you had to pick another career what would you choose?
8. What is the best teaching advice you have ever heard?
9. Is there anything you wish you could teach, but don't get the chance to?
10. Share a favorite classroom memory, either from when you were a student or a teacher.
11. What do you feel is your greatest accomplishment as a teacher?
Contact your nominees and let them know you nominated them
Well, I guess that's up to me to do once I post this blog!

-Kathryn

## Saturday, July 27, 2013

### Unit 2 LTs (draft)

I have been working on my Unit 2 Standards.  Please remember that my big unit breakdowns are coming from Appendix A (this is because of my school's curriculum and the project I've been apart of).  The second unit from Appendix A is GIANT.  Over twenty standards.  That is difficult to manage, thankfully I had did some breaking-down of it this past year as I taught it, so I had a bit of a foundation.  I have changed a lot though, so without further ado...

UNIT 2:  LINEAR AND EXPONENTIAL RELATIONSHIPS

Standards Addressed Throughout:  F.BF.1, F.IF.4, F.IF.6, F.IF.9, F.LE.5

Section 2.1:  Functions in General
2.1A:  I can find the domain and range of a relation (in any form).
2.1B:  I can determine and justify if a relation (in any form) is a function.
2.1C:  I can use function notation to describe, evaluate, and graph a function (in any form).

Section 2.2:  Linear Functions
2.2A:  I can determine and justify if a function (in any form) is linear.
2.2B:  I can find the slope and y-intercept given a linear function (in any form).
2.2C:  I can graph a linear function (in any form).
2.2D:  I can define an explicit function to model a given situation.
2.2E:  I can interpret the meaning of the slope and y-intercept of a function used to model a situation.

Section 2.3:  Systems of Equations
2.3A:  I can state whether or not given values for the variables represent a solution to a system of equations.
2.3B:  I can estimate a solution to a system of equations graphically.
2.3C:  I can identify a solution to a system of equations numerically.
2.3D:  I can solve a system of equations algebraically.

Section 2.4:  Exponential Functions
Standards Addressed:  F.IF.9, F.BF.3, F.LE.1, F.LE.3
2.4A:  I can determine and justify if a function (in any form) is exponential.
2.4B:  I can find the base and y-intercept given an exponential function (in any form).
2.4C:  I can graph an exponential function (in any form).
2.4D:  I can define an explicit function to model a given situation.
2.4E:  I can interpret the meaning of the base and y-intercept of a function used to model a situation.

Section 2.5:  Sequences
2.5A:  I can identify if a sequence is arithmetic, geometric, or neither.
2.5B:  I can define an arithmetic sequence (in any form) recursively and explicitly.
2.5C:  I can define a geometric sequence (in any form) recursively and explicitly.
2.5D:  I can explain why a sequence is a function.

2.6A:  I can find powers and roots.

2.6B:  I can translate between exponential and radical expressions.
2.6C:  I can simplify exponential and radical expressions using the properties of exponents.

A few of my thoughts:
• I want my students to understand that a function has multiple representations, and I want them to be comfortable moving from one representation to the next.  This is why I put "in any form" in so many of the learning targets.  I think it's obnoxious, so I think I will take it out...but for now I need it to remind myself of that crucial important concept.
• I think Section 2.6 actually fits better before Unit 4 (when quadratics are introduced).  For Unit 2 all I need is the definition of an exponent, negative exponent property, and the zero exponent property to go along with exponential functions.  I don't think it's worth doing all properties that far ahead of when they can be used in context.  So I will likely break slightly from the recommendations of Appendix A and place this with Unit 4.
• [Edit 7/28]  There is nothing specific in here about comparing linear and exponential functions, but we do it as we explore exponential functions, and also with sequences.  That's one of the reasons why I chose to not integrate sequences into the other sections.  We will discuss similarities and differences, and I will ask students to compare on assessment (we have "advanced" questions so I can ask an extension of a LT fairly).  Does that make it OK that I don't have it as a specific LT?  I just feel like there are SOO many...
PLEASE, PLEASE, PLEASE give me feedback.  Either by commenting here or by tweeting me (@kathrynfreed).  I want feedback from you no matter what you think.  Making decisions like this for my classroom is a little terrifying for me, so your feedback helps me know what I need to change to make this the best I can for my students.

-Kathryn

## Sunday, July 14, 2013

### Teacher Binder

Here is a quick look at the cover of my teacher binder.  I will finish this post later, but I wanted to get a picture out there and our internet is too slow for me to tweet the pic.
 Perfectly Purple Teacher Book Cover :)
Thanks to @mathtastrophe for the post on using Colourlovers to get the design! Read her post here.

## Saturday, July 13, 2013

### Unit 1 LTs (draft)

This is a follow-up to this previous post on Unit 1.

I (finally) have my first draft of Unit 1 LTs ready to share.  I am very eager for feedback, as I want these to be as good as they possibly can!

Section 1.1:  Reasoning Precisely with Quantities
Standards Addressed:  N.Q.1, N.Q.2, N.Q.3, A.CED.3
1.1A:  I can choose appropriate units and interpret units for a given situation.
1.1B:  I can determine an appropriate level of accuracy required for a given situation.
1.1C:  I can use dimensional analysis to convert units in the context of a problem.

Section 1.2:  Reasoning Precisely with Equations
Standards AddressedA.SSE.1, A.CED.1, A.CED.2, A.CED.3, A.CED.4, A.REI.1, A.REI.3
1.2A:  I can create equations and inequalities and use them to solve problems (1 and 2 variable).
1.2B:  I can graph equations and choose an appropriate scale.
1.2C:  I can solve an equation/formula for a specified variable.

Please, please, please give me any feedback you can! (I'm pretty much begging you.)  Whether you think I dominated unit 1 (probably not) or think I totally screwed things up (much more likely), I want to hear your feedback so that I can improve them before the school year starts!

You can comment below or tweet me (@kathrynfreed) to give me your thoughts!  Thanks!

-Kathryn

### Reflection on "Fair Isn't Always Equal"

I just finished reading "Fair Isn't Always Equal" by Rick Wormeli, and was encouraged by @druinok to blog on my reflections before moving on to another book on my list.  So here is my attempt and doing that.

Section 1:  Differentiation and Mastery
The first part of this section was an argument for differentiation.  As I have already been convinced of its impact on learning, it was not a game-changer for me.  However I did really benefit from the multiple attempts to define and clarify differentiation.  Here is a statement from p.4:  "Differentiated instruction does not mean we make learning easier for students.  Instead, it provides the appropriate challenge that enables students to thrive."  This is a good clarification.  We are not making it easier,  but rather providing students with the skills they need to embrace the challenges we give them.

The second part of the section was dedicated to sharing the importance of knowing whether or not a student has demonstrated mastery.  This really pushed me to understand how important it is to ask good questions both in class and on assessments.

Section 2:  Assessment
If I hadn't already been convinced of the usefulness of re-assessment prior to reading this, it might have been a turning point.  What was good for me was the argument for pre-assessments.  I did not do those often this past year, and even when I did, I rarely got around to actually looking at them and using them to the extent I should have.  I want to be able to give each student three types of feedback at the end of each semester (1.) mastery level, (2.) growth, and (3.) behavior.  Prior to reading this I had planned on doing (1.) and (3.), but through reading this and a Twitter chat with Garnet Hillman, I decided that giving feedback on growth was also important, for the student and for me.

But that isn't the only reason I find a pre-assessment valuable.  Being able to give the student something that shows them where they need to go to achieve mastery is also huge.  And I am totally pumped that a pre-assessment can do both of these.  I plan on giving students their pre-assessments back and referring to them throughout the remainder of the unit.  It can be used for formative assessment opportunities!  Students could write a letter to themselves on how to correct a mistake they made the first time the took the assessment (after some learning had happened).

For me, this was the most valuable part of the book (at this time).  Because my brain continues to overflow with ways that the pre-assessment can be valuable (and I hope to have one written for each unit by the end of the summer...I better get to work)!

Also this section was full of ideas on types of assessments, both formative and summative.  Ideas on differentiating assessments, tips for writing good questions, and general assessment ideas.  This will be a place to refer to as I continue planning throughout the year.

First and foremost, I appreciate the distinction made between assessing and grading.  Much too often those two get muddled because grades are based on assessments (and at times other things).

A lot of the grading recommendations I have already adopted and/or do not have control over.  We use a 4-point generic rubric to score in my district.  I love it, but I wish we could use something other than numbers to provide feedback so that students would see it as feedback rather than a score!  Also I have been developing my own layout for my gradebook.  My students will have the same in their ISNs for them to track their progress with each learning target.

I appreciate this reminder when considering grades.  I always remember it with assessment, but perhaps not always with grades:  "We're out for students' success, not just to document their deficiencies." (p. 114)  Keep that in mind when determining grades.

I also appreciated the chapter on conditions for redoing work.  I often feel as though I should ALWAYS allow students to redo work for full credit.  Now I still believe this is ideal, however it was good to be reminded that this is for the benefit of learning, and if it is not done within that perspective, then it is perhaps better to not allow it.  I usually allow re-dos for up to two weeks, but I rarely helped students plan for how to be successful in managing this, so I appreciated the idea of creating a calendar for students to help them be more successful on re-assessments.  I also plan on adding that all re-assessments are done at teacher discretion.  This is a nice reminder for me that I don't always have to be superwoman and manage everything.  Sometimes it is just not possible.

Section 4:  Implementation and the Big Picture
The final section was dedicated to ways of implementing changes in assessment in your district.  This felt like something useful for an administrator or a teacher in a leadership position.  That's not me, but I am glad to know all of those resources are there if I ever need them when talking with a colleague.  The most important piece for me was to remember that even small movements forward are positive things to celebrate. Sometimes I get to caught up in working toward the ideal that I feel I have failed when I don't reach it.  I have to keep in mind that it is a journey to get there and all those little steps forward are moments to celebrate.

Well, I think that is one of my first attempts at a book reflection.  Thanks to @druinok for nudging me to do this.  I'm grateful to have my thoughts in one place!

-Kathryn

## Friday, July 12, 2013

### Organization Container

After seeing this organizer on Leslies's blog, I knew I needed one. Well, I finally made it to Home Depot and got mine! Here it is right out of the package:
And so with the dimensions from this blog I made my own labels and printed them. The file is here if you want it.

I decided I wanted green and black so I copied them onto green paper and began cutting
And cutting
And then I got to tape (I used double sided tape like Leslie recommended.  It worked both for attaching the papers together and for attaching them to the drawers.)
And voila!  Here it is!

My favorite parts:
• It matches the new paint in my room perfectly!
• I feel super organized now!

Advice:  If you are going to cut them down (like I did with the big green ones) orient them at the bottom of the table cell so you don't have to cut so much (silly me)!

## Wednesday, July 10, 2013

I have found that little pieces of scratch paper can be extremely useful throughout a day of teaching mathematics.  I always have SOOO much scratch paper and I could NEVER use it all (even though I use it whenever I can) so I found another way of using it.

I had seen something that made me think this was possible and just didn't know how to make it work.  Then I remembered that this was the age of the internet, so I found some blogs of people who had done it (http://www.chicaandjo.com/2008/10/22/make-your-own-custom-notepads/ http://www.instructables.com/id/Duct-Tape-Tear-Away-Scratch-Pad/ and many others) and set out to try it myself.

I started with scratch paper and headed to the paper cutter!  I wanted to use 1/4 of a piece of paper, so I started cutting...
 Starting Point

 In Progress

 Cut Paper
Then with my stacks of cut paper, I headed back to my classroom where I found binder clips and rubber cement.  I decided not to use anything as backing because I knew my students would go through these notepads quickly!
 Everything I Need
At this point I made little stacks of paper and tried to get one edge as flat as I could.
 Make an edge flat...
I then used binder clips to hold the paper together.
 Clip
And I used the rubber cement to glue!
 Glue

 Ta-da!
I carefully put a clip on the glued end without touching the fresh glue.  This helps to make sure there is pressure in the middle of the notepad too.
 One more clip

Now I have perfect little notepads that I can use in many ways throughout my lessons!

I usually glue them 3-5 times before calling it good, but it only takes a little bit of time in between to dry.

## Monday, July 8, 2013

### ISN Set Up

So I couldn't help but start my ISN because I have so many awesome ideas rolling around in my head that I NEEDED to try them out.

Here is what I'm starting with:
 My ISN!
You can already see a few things I'm definitely going to do.  First, use a rubber band to help hold it all together.  I'm guessing my idea for that first came from here.  But, I stapled it to the back instead.  It didn't take a fancy stapler or anything and it seems a little easier than the hole punch, at least to me.
 Staple :)
Also I want use tabs for each section so that students can find things faster.  I got this idea from Mrs. Hester here.  Since I'm at home I worked with what I had available, so this tab is made from masking tape, but I will likely do something similar to what Mrs. Hester did.

When you open it up I'll probably just do a basic info page.  Name, Algebra, Period or something.  I am the type of person who never (ever) uses the first page of a notebook, so I couldn't think of anything better to put here.  If you have ideas, please let me know!
I also wanted to put my syllabus in my ISN and after reading about it here, I wanted to do a tri-fold brochure type syllabus too.  But it's going to be a challenge for me to fit my syllabus on that little of paper...so we'll see how it goes.  Anyway the back side of the first sheet is reserved for the syllabus.
 Syllabus (and yes that's my foot...I'm not a great photographer...)
If I do a table of contents I would do it next, but I'm not sure I want one if I have tabs...I have a space in each section I could add page numbers (see below), so I'm still undecided...

Then the first section:
 Title Page
And a pocket behind it for all the papers from that section...Quizzes, Test, In Progress papers... I first heard about the pocket here, but I think they are pretty common.  I don't want mine super stuffed, so I figured one per unit will help with organization.
 POCKET!
The next page is what I ended up attaching the tab to.  I was going to attach it to the pocket, but it felt flimsy when I put papers in my pocket.  On this page of each section we will tape/glue in a paper that lists learning targets and students can record their scores. I got this idea from Jonathan here, but changed it a little to meet my needs.  As an FYI, I am planning on have a page in my gradebook for each student (yikes!) and I will just tape one in for each student, too. (Interactive Teacher Gradebook :)
 Tab and Records for Section
Here is the file:
https://www.dropbox.com/s/ofjb69pmqnxlubu/Section%201.1%20Records.docx [does not currently work]
(I've seen some people with their dropbox files embedded...please teach me!)
Oh, also I might have them put page numbers here so that it is a table of contents for the section.

 View of open notebook
After that we would start on the first learning target.  I know that ISN is usually input on right output on left, but that seems really backwards to me...why not start on the left and work toward the right.  Also what if someone write big and wants more space?  I am probably going to let them move to the back page of the right side.  (I'm not going to be OCD about everyone being on the same page...I hope!)  But I suppose if someone could prove to me that it would help my students learn better to do it the other way then I could probably switch. (That means leave comments or tweet me if you think it's totally wrong that I want to do notes/foldable/graphic organizer/input on the left and practice/reflection/activity/output on the right.)
 Section 1
Well, that's all I have for now.  That's mostly just the big, basic structure of it, but the way my brain works I have to figure that out before I can figure out the rest!

## Wednesday, July 3, 2013

The final books from my summer reading list arrived.  Can you guess that assessment is a HUGE focus of mine right now?  I was never really challenged to think about it too much before this past year and now I just love reading, learning, and thinking about assessment.  So excited for the good changes I'll be able to make next year due to these awesome resources!

Here they are:
• Classroom Assessment for Student Learning (2nd Edition) by Chappuis, Stiggins, Chappuis, and Arter (Copyright 2012 by Pearson Education, Inc.)
This is the book (well the first edition I think) that teachers at my school used to guide them toward SBG.  They studied it as part of PD for several years (all before I started there), so I figured I should pick it up and start working through it.  I read bits and pieces here and there over the school year, but haven't done much with it since summer started.
• Embedded Formative Assessment by Dylan Wiliam (Copyright 2011 by Solution Tree Press).
I heard about this book first by reading tweets about #efamath.  I was so frustrated that I didn't know what efa stood for that I looked it up and then really wanted it since I've been doing a lot of reading, learning, and thinking about assessment, but felt really lacking on formative assessment info.  I just got it today, so I have not yet started, but plan on lurking at #efamath chat tonight :)
• Fair Isn't Always Equal by Rick Wormeli (Copyright 2006 by Rick Wormeli).
Rick Wormeli is the second name I heard associated with SBG (after Stiggins since our school was reading the previous book).  I think I got the idea to read this from #sbgchat, and after watching some of his videos, I knew I needed to buy it.  I got it sometime during second semester and got through the first few chapters before the end of school.  I would say I'm about halfway through at this point.  (When Nathan Wear visited our Algebra Project he recommended this book and I felt super awesome because I had already been reading it!)
• How to Grade for Learning (3rd Edition) by Ken O'Connor (Copyright 2009 by Corwin).
This is the book that we were required to have for our Algebra Project.  Lots of good examples and recommendations of where to find other good examples in here.  Not as dense of a reading as Wormeli, but I also feel like the goal is to pursuade you to do SBG and I'm already pursuayed.  In that way I feel like it is a little less beneficial for me.  But if you are like, "Still not sure why I would do that" then it would be the perfect read for you.
• Understanding by Design (2nd Edition) by Grant Wiggins and Jay McTighe (Copyright 2005 by ASCD).
I was given only standards when I started this year, and feel really unprepared to begin developing serious curriculum.  This UbD concept makes a lot of sense to me, but what I've learned through the grapevine wasn't enough, so I bought the book.  This is the other that just arrived today, so haven't started it yet, but hoping it will spur on some of the places I feel lacking with the curriculum writing.  (If I just had manageable units I could really get to work, but trying to put the standards into manageable units is hard.)
Wow, sorry!  I thought this would be a shorter post, but I still wrote a lot.  Enjoy!

Leave a comment if it works--been having some issues lately :(--otherwise you can tweet me @kathrynfreed  I would love to hear what you are reading and/or what you think of the books I'm reading!

--Kathryn

## Monday, July 1, 2013

### Units for Algebra 1

I had SBG and Learning Targets forced on me (and I don't mean that in a bad way) this past year.  The school I started at had been working to implement these for somewhere around 5 years (not exactly sure since I wasn't there).  And the teacher that left didn't leave anything for me.  So I fumbled around a lot at the beginning of the year trying to figure out what other teachers did, why they did that, what the benefits were, and how to apply it to my classroom.  What I ended up with are some poorly organized units with learning targets that are OK.  One of my goals this summer is to create some more solid units (with assessable learning targets) that are organized, teachable, and centered around the standards.

Our district's guideline for core math classes is Appendix A [pdf].  (I really don't want to get into an argument over whether this is a good choice or not.  I was not at the district when the choice was made, therefore I have little say.  Also I don't hate it.)  This means that the standards Appendix A suggests for Algebra 1 are the standards I have to teach, and I need to make sure my students demonstrate them to the level that Appendix A recommends.

I do not have to teach the Appendix A units, but it seems like a good place to start.  However Appendix A units are big, so I wanted to break them down into sections/modules/something smaller and more manageable.  What makes sense to me is to group certain standards together and create learning targets from there.  However I have kind of hit a wall trying to do this.  I've been working with Unit 1 and trying to break it into 2 or 3 sections/modules/whatever, but I am hesitant as to what is best.

The goal of Unit 1 is to continue students' work with linear equations and increase fluency/adaptability.  Students should already be able to solve linear equations and some simple systems.  Students analyze the process of solving and practice moving between forms of an equation (summarized from the Appendix A document).  To me, Appendix A is an opportunity for students to apply and play with linear equations and expressions.

Here are the recommended standards:

• N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
• N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
• N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
• A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
• A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
• A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
• A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s lawV = IR to highlight resistance R.
• A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
• A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

(Sorry for the list--please don't stop reading! I think you need this to tell if my grouping makes sense.  I'll try to not blabber much more.)

Group 1:  N.Q.1, 2, 3/A.CED.3
Mostly focused on precisely modeling and appropriately using units to assist with this.  (More "simple" modeling situations.)  Could get into expression vs. equation as that is an important distinction, but a lot of modeling situations could be solved either way.

Group 2:  A.CED.1, 2, 3, 4/A.SSE.1/A.REI.1, 3
Focused both on modeling and on the "pure" algebra.  Would get into more "complex" modeling situations where restraints on domain/range may come into play.

I have also thought of breaking a few from Group 2 to form
Group 3:  A.CED.4/A.REI.1, 3
This would allow a section focused on the algebra outside of modeling (not always, but a little bit more). Not sure if I want this or not...

Ok, so what do you think?  Two groups or three?  What are the pros and cons of each?  Would you do it a completely different way?  I am not an expert, so please tell me what you think.  I need something to help me continue moving forward in my planning for next year.  Thanks!