First Day Plans

First Day of School Plans with #SundayFunday

Numbers About Me:

For the past several years I have enjoyed doing a "Numbers about Me" activity with my students on the first day that then turns into the cover of their notebook.  I have refined it over time, but last year I made it into a card sort and I think I'll keep it like that this year.  I really enjoy starting the year with a card sort because it is something that I do often in class.

I start with 10 numbers and units that describe me, but I separate the numbers from the units.  They work as a table to try to match them up.  I want around table to table and check their work and tell them how many matches they have correct.  I DO NOT tell them which ones are correct.  This is the golden part of the activity.  I can draw it out as long as I want, or end it as quickly as I need.  I give them time to struggle and then reveal the answers.  My son was in my class last year and his group did not match up all of the numbers.

I then present the answers and give a mint to the students in the group with the most correct answers.  I then turn it to them to create 5 numbers and units that describe them.  They write it on a notecard and turn it in by the end of the day.  They must use a variety of numbers:  percentages, decimals, fractions, negatives, positives, integers, etc.  

Our first unit in Algebra is on numbers and units so this ties in really well.  The second day I usually ask them all to have their notebook and they decorate a cover page with their five numbers about them.  It's crazy, but it works!

I often do the card sort part with all my classes, but usually only Algebra does the follow-up part.  By the time my students are in Statistics or Discrete, I've usually taught them before, so fewer time spent on introductions is necessary.

Two Truths and a Lie:

Another thing I did last year that I really enjoyed was for my Discrete Math class after reading the syllabus we did a class version of two truths and a lie based off of the syllabus.  I had each student submit a notecard with two truths and a lie written down.  We went over each as a class and they used mini-whiteboards to give their answers.  I kept score on the board.  It fit well, because our first learning target for Discrete is about propositions, and that's what they had written for me already!

Syllabus Scavenger Hunt:

Another activity I've considered doing is chopping up the syllabus and posting it all over the room.  Have groups read a part and then answer one question about that section before they can move on to the next section.  I feel this would engage them better in the "reading the syllabus" process.  I plan to do this in Algebra and Statistics this year, but not on the first day (maybe the second).  

I have even considered breaking it up by the name of the course (7 sections for Algebra, 10 for Statistics) and they earn each letter by accurately answering the question.  Then they have to work to collect all the letters.  

A teacher move that seems obvious to me now, but I wouldn't have been aware of it my first several moves is that when the group comes to me for a question, I would ask it, give them time to discuss, and then use a random generator to select one of them to answer it for me.  If that student can't, then they'll have to try again with a different question!  (Meaning that I would need to have multiple questions for each section...)

Talking Points:

Another thing I introduce at the beginning of the year is Talking Points.  I use talking points throughout the year about weekly for bellwork.  I have some general ones and some unit-specific ones that I use throughout the year with my Algebra students.  However, one day at the beginning of the year (first week), I introduce talking points by having the students teach themselves.  This is all from Elizabeth (aka Cheesemonkeysf).  All of it.  Anything Talking Points is all her.

Quick Coherence:

One thing I want to try this year is this:  Quick Coherence

I tried it at a parenting seminar this summer and watched it help calm down a room of preteen boys, so seems like it's worth a try.  And in terms of creating a culture equitable to students who have experienced trauma, I think this is worthwhile.  Exactly how and when and how much is up for debate still, but likely to do a session at the beginning of each class on the first day!

I'm sure I'll be doing other things at the beginning of the year, but those are the biggies that allow me to flow through the first day of school and a little beyond.

-Kathryn

 If you want to read more #SundayFunday posts about First Day Plans, then check out I Speak Math after Sunday, Aug. 13!

Goals for Fall 2017

Goals with #SundayFunday

I am expecting to have four different preps this year.  I am used to having three, so this is causing me some anxiety.  However, I'm trying to stay calm and not allow my job to consume my life.  I'm having some problems balancing my passion for work with my personal life.  My children require a lot of work and attention and so I need my work to not invade that.

I'm hopeful that with #SundayFunday I can do all this and blog some more than I did the past year!  I'm excited to set some goals for this year.  But maybe I should just set goals for first semester because that seems more reasonable.  I also think three goals would be a good starting point.

1.  One performance assessment per unit in Algebra.  I want to assess students in multiple ways, and this is something that I've been working on over the past several years, and I'm close to meeting this goal, so it seems reasonable.  However it is also important to keep it as a goal so that things are in perspective.

2.  Topical use of my prep.  I discussed this on twitter with Shelli @druinok and Casey @cmmteach and there was a blog post by Krisanna at The Teal Paperclip.  I then sat down and looked at my schedule and designed a slide for my school planner.  You can find that slide in this document which contains all the printables I will use.

One of the reasons I want to have this as a one semester goal is that I could love it or hate it.  So if I try it for a semester, I should know!

3.  My new prep is Statistics.  So I want to make sure that it doesn't take over everything, but also that we do engaging activities.  So I guess my goal there is that I modify/create something once every section (3-5 chapters).  This could be ANYTHING - notes, activity, card sort, practice problems, journal, etc.  The other part of this goal is to then blog about it.  This will help me #pushsend and demonstrate my imperfections as a teacher.  I am not a superhero teacher, and I don't believe that teachers need to be superheros!

Thanks for Reading!
 - Kathryn

If you want to read more #sundayfunday posts about Goals, see Julie's collection at I Speak Math.

Checklist turned Tracking Sheet

At TMC16, I went to lunch with a group to discuss SBG and Interactive Notebooks.  We ended up mostly talking about SBG, which was great because I got a new idea!  Jessica Breur (@BreurBreur) shared how teachers at her school use tracking sheets for the students to reflect on how they are doing with each target and record scores the teacher has given them.  Then at the end of the unit the teacher collects and keeps them.  I asked her to share with me, and she kindly did!

While looking at all her resources and thinking through it all I was thinking about how it would make a lot of sense to combine this with my checklist, since most of the assignments are recorded there anyway.  Also students rarely keep their checklists after the unit is over, so it doesn't seem detrimental for me to keep them.  I would just need to add quizzes and tasks to the checklist when we do them, which wouldn't be too tricky and would be incentive for students to make those up right away when they miss them (bonus!).  So instead of using any of her wonderful resources, I worked on creating my own.

I needed to break up the spots for assignments based on learning target and provide a space for students to graph their scores for each assignment, so I have a sample that looks like this:

It has room for four assignments per learning target (3 learning targets on the front, zero or one or two on the back depending on unit), and a big miscellaneous section at the bottom of the back.  I figured I would use the miscellaneous section for assignments that related to multiple (or no) learning targets and overflow if I need more than four assignments for a given learning target.  Here is a picture of the back side:

I did an example of what I would write if there were five assignments for the first learning target.

Thoughts I still have:

• Will the stamp space be big enough for my stamps?  (I'm going to test it out tomorrow)
• I am concerned that I will end up needed more than four assignments often, making it pointless to separate it by learning target, but I need to fit three learning targets on the front when I have five learning targets in a unit.  I am especially concerned if I am adding quizzes, group tasks & reflections, and open middle type problems to this.
• I used to require students to have 80% of their checklist complete in order to take the test.  I could do it that same way, or I could say you can at most one missing from each section.  I want this to be a reflective tool, not just a punitive tool, but I also feel a need to hold them accountable.

What potential concerns do you see?  What things would you change?  Any ideas on my thoughts above?

-Kathryn

PS - I am on a blogging roll since TMC16, and I have a lot more ideas to come!

Writing in Math

At TMC I really felt pushed to have my students doing more reflection, which I had already been thinking about.  I want them to have "math journals" where they can reflect on what we're doing in class, their homework, and "I see math" entries.  I didn't go to Anna Blinstein's "Journaling and Writing in Mathematics" session, but maybe I should have.  There were a lot of sessions I wanted to go to, but didn't, so I've committed myself to look over their resources on the wiki.  I wanted to take some notes while looking over Anna's slides, so here they are.  Also here is a link to Anna's presentation.  It's way better than what I have here.

Initial Thoughts

• What do you value in your class?

Learning. I tell my students "we are here to learn" often. I also value my students. As people. I care about them and their personal growth.

• How will doing more writing help you achieve this?

I want to have my students keep a math journal so that they can reflect on lessons and share where "I see math"

• What concerns do you have about doing more writing with students?

I can't figure out if I want them to do it on paper or electronically and I can't figure out if/when I should read it. How I would find time for all of it and how it would be marked.

Reasons to Write in Math Class:

• metacognition/retention
• communication
• fun
• better assessment

Possible Prompts:

• Describe the mistake.
• Summarize today’s lesson in a few sentences.
• Which of these is correct? Explain how you can tell.
• What would be a good question someone could ask about this topic?
• What’s something that’s confusing to you right now?
• Pick one problem and explain what you did and why.
• Which homework problem was the hardest for you? Why?
• Would you use strategy A or B here? Why?
• What is going well in class for you? What is not working as well?
• How do you learn best? What can I do as a teacher to help you learn?
• What are your goals for this semester? How will you reach them?
• What’s one good thing that happened this week?
• What is something mathematical about which you want to learn more?
• Did your performance on the quiz surprise you - why or why not?

Note to Self: Differentiate (to self) whether you want journal for the day to be metacognitive/reflective or an opportunity to assess student learning. Prepare prompts in both categories and place in notebook to use. Have one selected for the lesson, but be willing to change it up.

Ways to get buy-in:

• share student work (with class, parents, admin, on classroom, twitter, blog, wall)
• respond to their writing
• Share purpose
• Give them interesting problems to write about
• use during assessments?
• Give feedback:
• short is OK
• coach on how to improve
• acknowledge progress
• ask students to reflect on their journaling
• short and frequent is most important!

Note to Self: If I decide to ask for formal write-ups, there is a structure outlined on the wiki

Assessing Journals:

• Two sentences: acknowledge something good, suggest improvement
• more detail
• clearer explanation
• connect math/writing
• better justification
• more precision
• more math vocab
• include examples
• extension
• look for connections to other content
• Scoring:
• Foundational: student reflection responds to some part of the prompt and generates some insight about self and/or math (this is a 2)
• Proficient: student reflection engages with the prompt; uses reflection to plan and reach goals (this is a 3)
• Exemplary: student reflection yields insights, connections, and specific areas of need; student reflects deeply as part of process beyond specific prompt (this is a 4)
• More scoring rubrics on wiki

Note to self: I could have students "redo" if they don't show foundational. Also, do I really want to score them? How would I connect to standards? SMP?

Thoughts Now:

• What would you change about your responses?

Still have same concerns

• Do you have any new ideas or concerns?

Lots of ideas on assessment, buy-in, questions to ask, and ways to give feedback

• What do you need to do in order to be able to include more writing in your classes?

I need to decide if/how to score, how to have them keep their journal (notebook or electronic), when to check, and some prompts to give. I also need to set up notes to myself about the structure in my notebook.

Where do I go from here?

• Ask Anna, Carmel, kristen about journaling on paper vs electronically
• Select some common prompts and organize into my notebook
• Determine goal frequency of journalling in class (twice a week?)
• Talk with Nicole about scoring or not (when we go back to school)
• When lesson planning: select prompt for lesson, timing, and method for increasing student buy-in

If I follow-through with this, you should be hearing more about journaling on this blog. Ideas, suggestions, comments, please leave them below or tweet me (@kathrynfreed). I'd love to continue this conversation, because I still have a long way to go with it.

-Kathryn

Algebra 1 Learning Targets and Reporting Standards

I've been working on my learning targets for this coming year and linking them to reporting standards.  My goal is that the learning targets will be somewhat evenly spread out among my eight reporting standards.  I'll present them unit by unit here, but first I should let you know what my codes for my reporting standards stand for.

NQ = Number and Quantity
SSE = Seeing Structure in Expressions
ER = Exponents and Radicals
CRE = Creating and Reasoning with Equations
IBF = Interpreting and Building Functions
LER = Linear and Exponential Relationships
SID = Statistical Interpretation of Data
SMP = Standards for Mathematical Practice

I've got 10 units set up for next year.  Hoping for five each semester, but I could also probably do four first semester and six second because we have more time second semester and starting out the year always goes slow.  I'm also hoping to give a performance task each unit, but I don't have them all the way planned out yet, so that's what you'll see at the bottom of each list of learning targets.

Numbers and Units

Functions

Linear Functions

Exponents and Radicals

Exponential Functions

Sequences

Polynomials

Quadratic Functions

Solving Equations

 Statistics

So this is the basic plan.  Questions, comments, concerns can be left below or by tweeting me (@kathrynfreed)

-Kathryn

Restructuring...Again

Well, I'm at it again...trying to figure out how to make my classroom and curriculum better for my students.  I like a lot of things about a lot of my units, but I found myself wondering if it would be more engaging and connected for students if I reordered some of the units.  SO...this is what I'm thinking:

Unit 1:  Numbers and Units
I am hoping to collaborate some on this with the science teacher.  We will teach unit conversions together.  It will be interesting as I have never done something like this before.

Unit 2:  Functions
This is the big change.  Instead of doing all the standards that are "close" to 8th grade standards first, and then starting functions second semester, I'm going to start with functions right away.  I want have a more "function" focus throughout the year.  I also really, really want my students to develop a lot of flexibility with their functional thinking, so hopefully having more time will help. (Some of the flexibility I want to see:  evaluating from equation, graph, table; understanding function notation and y= are similar; find average rate of change and tie it into slope; thinking about "characteristics" of a graph:  x/y-int; increasing/decreasing; extrema)

Unit 3:  Linear Functions
So after a broad introduction to functions, we will focus on various types of function on and off.  Linear is first!

Unit 4:  Exponents and Radicals
As a preface to Exponential Functions unit next, we will manipulate exponential and radical expressions (hopefully with and without variables).

Unit 5:  Exponential Functions
Back to another big function group.  Going to discuss the characteristics of an exponential function algebraically, graphically, and numerically.

Unit 6:  Sequences
Here we tie arithmetic sequences to linear functions and geometric sequences to exponential functions.  Hopefully my students can see the domain of each of these functions will be restricted to the natural numbers.  Also want to make sequences more challenging by including variables in the terms.

Unit 7:  Polynomial Operations
Adding, subtracting, multiplying, and factoring polynomials.  I LOVE polynomials.  I need to make sure my students see more than just quadratics here, but it's OK if it's my focus.

Unit 8:  Quadratic Functions
I have a lot of good things here, but it is not quite a cohesive unit yet.  Needs a little bit more work to develop into that.  Hopefully by not being THE LAST unit I will be able to be more cohesive.

Unit 9:  Statistics
Saving statistics for this point will allow application of the three types of functions we study.  We can do some fun regression for various functions.

Unit 10:  Solving Equations
This will include solving linear equations (which we will constantly review throughout the year, since it is 8th grade, too), quadratic equations, and systems.  I think I'm going to like that systems can involve quadratics :).  We might have to discuss why we don't solve exponential functions yet in Algebra 1.

Five units a semester seems doable, right?  Better than 12?  I think we did 8 this year.  I'm hoping some intentional unit-specific planning this summer will allow me to progress better throughout the year.

Let me know what you think!  Am I missing something big that won't work with this?  Have you tried it this way before?  How did it go?  I'll post learning targets and unit outlines later in the summer (hopefully)!  But probably not chronologically.

-Kathryn

Desmos Picture

My students in Algebra 1 are learning about functions, and we start with domain and range of relations.  Due to amazing #MTBoS resources, I had some excellent resources to integrate into a week long lesson, which started with pictionary thanks to +John Scammell (@scamdog) and his post here.

My one good thing, however, is about the performance assessment I assigned to students using +Desmos free online graphing calculator.  On our PD day at the beginning of the semester I attended a session by our curriculum director @montemunsinger about creating rubrics for performance assessments, so I used it to help set up this rubric based on my standard related to domain and range:

The assignment was to create a picture in Desmos with at least 10 relations.  In addition, students must restrict the domain for three relations and the range for three relations.  Then students complete a reflection where they explain one domain choice they made and one range choice they made.  The reflection is important to me because it is their opportunity to share what they learned, not just what they created via trial and error. Don't get me wrong, the trial and error aspect of Desmos is the only thing that makes this assignment at all possible for my students, but I want to make sure that through the trial and error process they are learning something.

So my #onegoodthing is watching my students create!  We worked on it off and on throughout almost the whole week.  Some students jumped right in and have created some awesome things, others wanted to copy a previous Desmos picture they saw, but could explain polar coordinates to me (shocker!) so I made them start over (aka not copy).  Some students needed a lot of guidance at first ("Try y=mx+b and substitute some things in for m and b until you get what you want.  Now what part of the line do you want for your picture?  How do we do that?") and then were able to take off and just ask me for help with troubleshooting when they made an error ("Why did my whole line just disappear when I did the domain?" *I check and see -7.5<=x<=-8*  "Remember to put the minimum on the left and the maximum on the right...").

Hopefully, I can get permission to post some pictures here, but let's just say I've seen Olaf, a Christmas tree w/star and presents, batman symbol, personal designs, etc.  My favorite part, however, is when the students learn about new types of relations.  "How do I make a circle?"  "How do I make an oval?"  "Can you help me make this rounded?" I don't usually get to share about circles and ellipses in Algebra 1, but we did this week!

-Kathryn

First Week Plans: Algebra 1

Here are my basic plans for Algebra 1.  I have four sections of this.  Mostly freshmen, but some older students as well.  However, I basically consider it a freshmen course and work hard to help my students feel welcomed to high school, learn the structures of our school, and help them stay organized for my class.

Monday 8/24

• Will be randomly assigned to a table as they come in.  I will meet them at the door, high five them, work on learning their names, and assign them to their table
• Numbers about me activity.  I want to blog about this after school starts, but since I haven't yet, I'll give a little guidance. 
• When they come in this paper will be at their tables:

• After everyone is in class and I have taken attendance and gotten settled, I will run through a powerpoint of the answers with pictures.  And I say something like "Clearly the numbers are important, but the units attached to those numbers are just as important." to tie it into our first unit on numbers and units.
• Then I give them this instruction:

• Depending on time I might have them share their 5 numbers with an elbow partner.
  Oh--and I need to change the instructions because they have to use a percent, fraction, decimal, or negative number.  Maybe two out of the five numbers have to be one of those.  We can't just be all positive integers :)
• Then we'll wrap up class.  The first day we usually only have 20-30 minutes with students, so I think this will get us through.  I will also say something like:  "Make sure to have a notebook tomorrow like this *I hold up mine*.  You will need one that you can use ONLY for this class and that you can use ALL YEAR LONG.  If you brought it today you may find your folder by that wall and leave it in there so you don't have to worry about it tomorrow."

Tuesday 8/25

• We will look at the syllabus...the plan is to glue it into our notebooks, but I just got an email from my principal that might change that plan--so we'll see.  I will not read it all, but students might look over it in groups or something and do a 3-2-1 reflection on it to be handed in.
• Talking Points Structure.  We will learn about talking points today!!! I'm so excited.  First we will talk about the structure, and glue that into our notebooks.  Then I want some sort of model of talking points, so I might see if some teachers/or my family will make a video with me of a few rounds of talking points.
• Talking about Talking Talking Points! Now the students get to try it for themselves--woohoo!  We will share out at the end.  Maybe we'll do a big circle to reflect on it.  For sure each group hands in their group reflection.
• Then they get to be crafty and turn their "5 numbers about me" into the back cover of their notebooks :)  Then if they leave them with me I will tape them on with my super awesome Duck Brand EZ Start Packing Tape.  It basically laminates the paper onto their cover.  One reason I like to do this (because reasons not to are price, class time, and my time) is because they have now invested a lot into this notebook which will make it more likely to last the whole year.

I just realized I could to syllabus, TP structure, and "numbers about me" as stations and then do the actual talking points at the end.  That might save me the mess of clean up at the end of each class, because the "numbers about me" stuff would be contained to one area...hmmm...things to think about.

Wednesday 8/26

• We will start the number line task I blogged about.  Starting with Part 1.  I'll probably allot 10 minutes.  So timer and go.
• Group Roles:  We will discuss group work structure and roles.  Gluing them into our notebooks.  I will have all the "recorders" meet to discuss their role (and ask me questions if they have them), etc.  Then they go back to their groups and share out:  "my job is to..."  I make sure to teach the resource managers how to ask a group question.
• Number line task:  Part 2.  And before the end of class they must complete the reflection, which is mostly about their roles.

Thursday 8/27

• Talking Points:  talking about group roles.  This gets them talking about group roles to remember what they learned yesterday about them.  Some of the statements are opinions and others are about the roles themselves. We will reflect individually, as groups, and as a whole class afterwards.
• Number Line Task:  Part 3.
• Exit Ticket:  reflection of task---not sure whether I will have them complete this now or later if their class hasn't finished part 3.

Friday 8/28

• Estimation 180.  They will glue the handout into the back of their notebooks.  We'll probably do two days to get the hang of it.  From this point forward Estimation 180 is our Friday bellwork.
• Expectations Foldable.  This goes into our notebook and it talks about expected behaviors for certain methods of learning we will be doing.  If I don't include the syllabus in their notebooks then I need to add to this page.  I will likely put it into the notebook as a whole class, but then read through it and reflect in groups.  Maybe have groups share out.  This is also the time where I will share about "I was...I should have been..." reflection form I have students complete when they are not following directions.
• Set up Unit 0.  We will set up our first unit in our notebook.  This includes a tab, table of contents, and pocket.  We might also try to put in some notes depending on how the number line task went.
• Homework:  show off your notebook.  I think at this point there will be enough stuff in the notebook that I want students to take it home and show it off.  I will create a form for them to have completed.  "I saw these things in the notebook...I have these questions...I would like to be contacted through this method..."

Thoughts:

• I want to set up google classroom sometime this week
• Want to look into "Class Messenger" one of the downfalls of google classroom is that it leaves parents out.  Might want to do class messenger.  If so, include information on the "homework" for parents to see.
• I really want to show the videos about How To Learn Math, either from the MOOC or from the "week of iMath" on youcubed.org
• I also want to do Music Cues, but I haven't sat down to look at it yet, so can't plan it into classes yet.
• Things I want to remember:
• Count down from 5 to get attention
• Two Nice Things
• High Fives
• Introduce "while you were out" in each period when first student is absent
• Write notes to students
• I'm sure there's more, but I'm out of thoughts for now!

Give me all your thoughts!  Tell me what parts you don't like or what parts need improvement--because I still have a week before school starts, so I can change it if I want to.

-Kathryn

First Week Plans: Algebra Topics

Well Andy (@rockychat3) was nice enough to share his entire year's worth of plans for his block Algebra course, and he said he was interested in hearing about mine.  So here it goes!  These are my plans for my Algebra Topics course, this is a course for students who have struggled some in math before.  They take this course IN ADDITION to Algebra 1 (which I also teach and will be posting plans for later).

Monday 8/24

• Randomly assign groups
• Noah's Ark:  I heard about this from Steph's post here.  This post is what made me want to do this with my class right away.  I am going to continue to remind myself to ask questions to make my students think.

Tuesday 8/25

• Continue Noah's Ark, debrief if groups finish.  I still need to think through some individual and group reflection questions.

Wednesday 8/26

• New random groups
• Stations:
• I have the SET cards and I will take a group and work with them to learn SET (I usually start by taking just one type of shading to simplify it.) We then use SET daily as warm up.  Students always share out SETs with reasoning.  I used the daily set puzzle online, which can be found here. 
• Another station will be the syllabus and I'll have students complete a 3-2-1 reflection as a group.  
• The third station will depend on whether or not I have an associate in my classroom.  I might have the students complete a dispositions survey on their chromebooks

Thursday 8/27

• Review SET
• Transition to Algebra:  Unit 1 Launch
  The transition to algebra curriculum can be found here.  My school purchased it.  I really like that it helps students develop conceptual understanding.  It takes time to work through the units, but developing conceptual understanding does take time.  I try to do the lesson from these units on Tuesdays and Thursdays because that gives me time to look at students' work and reflectively consider how to help them develop better understanding in the next lesson.

Friday 8/28

• New random groups (these will last for the whole next week)
• Review SET
• Problem Solving Task:  Finding One Half
  This task is a page of figures with part of it shaded.  Students look through and select the ones where half of the figure is shaded.  This looks for conceptual understanding of what half is.  Mostly I use it to get students used to sharing their reasoning.  I try to be really difficult and find a figure that's not "half" but that meets the rules that their explanation gave so that they have to learn to be more specific.

Once we get going throughout the year I try to structure the course to be Monday/Wednesday support for learning in Algebra.  This would be reteaching, fluency practice, mixed practice, review, or whatever the students need to help them be successful in Algebra.  Tuesday/Thursday I do lessons from Transition to Algebra, as I mentioned above.  Then I reserve Fridays for problem solving tasks, and sometimes these carry over onto Monday.  I like having this structure because I feel like my students know what to expect (which is good), but more importantly I don't get off track with one thing or another.  I'm held responsible for keeping the pace of the course moving along.

Hope that helps!

-Kathryn

Algebra 1 Units, Learning Targets, Pacing, and Reporting Standards

I finally got to spend some quality time in my classroom this afternoon.  It was just a couple hours, but I felt SO productive.  After cleaning my group whiteboards with WD40, I set out to rearranging units, learning targets, and a pacing calendar.

Before

After

[Sorry, the pictures are not that great.]

Reporting Standards

One of the things that is new for me this year is that my school is moving forward with standards based grading.  We have written "reporting standards" for one class (I chose Algebra 1), and students will receive a report card with those 4-8 standards on it for each class.  So I thought about which reporting standards connect with each unit, which I'll share below as well.

Here are the reporting standards:

• Organize numbers, quantities, and units to solve problems (NQ)
• Numbers and Units; Exponents and Radicals
• Rewrite expressions to solve problems (SSE)
• Expressions and Equations; Polynomials; Quadratic Equations; Quadratic Functions
• Rewrite and evaluate exponential and radical expressions (ER)
• Exponents and Radicals; Polynomials; Quadratic Equations
• Create equations and use them to solve problems (CRE)
• Expressions and Equations; Linear Functions; Exponential Functions
• Build and interpret functions in multiple forms (IBF)
• Functions; Sequences; Linear Functions; Exponential Functions; Quadratic Functions
• Identify and compare linear and exponential relationships (LER)
• Linear Functions; Exponential Functions; Sequences
• Organize and analyze categorical and quantitative data (SID)
• Linear Functions; Exponential Functions; Quadratic Functions
• Approach problem solving as a mathematician (SMP)
• ALL!

I'm sticking with my goal of integrating the statistics throughout multiple units, and I've written my learning targets in a way that I think will allow that to work well.  I will probably not test over statistics, but there will be various ways of assessing statistical analysis.

Units and Learning Targets

Unit 0:  Numbers and Units (08.24-09.11)

I can identify and justify number order and equivalencies.

I can simplify numerical expressions by following the order of operations.

I can convert units.

Unit 1:  Expressions and Equations (09.14-10.02)

I can identify and create equivalent algebraic expressions.

I can evaluate algebraic expressions for the given value(s) of the variable(s).

I can solve one-variable linear equations.

I can rearrange multi-variable linear equations for a given variable.

Unit 2:  Systems of Equations (10.05-10.30)

I can state whether or not give values for the variables represent a solution to a system of equations.

I can estimate a solution to a system graphically.

I can estimation a solution to a system numerically.

I can solve a system algebraically.

Unit 3:  Functions (11.02-11.20)

I can find the domain and range of a relation.

I can determine and justify if a relation is a function.

I can use function notation to describe, evaluate, and graph a function.*

Unit 4:  Linear Functions (11.23-12.17)

I can determine and justify if a function is linear.*

I can find the slope and y-intercept given a linear function.*

I can graph a linear function.*

I can define an explicit function to model a given situation.*

I can interpret the meaning of the slope and y-intercept of a function used to model a situation.*

Unit 5:  Exponential Functions (01.05-01.29)

I can determine and justify if a function is exponential.*

I can find the base and y-intercept given an exponential function.*

I can graph an exponential function.*

I can define an explicit function to model a given situation.*

I can interpret the meaning of the base and y-intercept of a function used to model a situation.*

Unit 6:  Sequences (02.01-02.12)

I can identify if a sequence is arithmetic, geometric, or neither.

I can describe a sequence recursively.

I can describe a sequence explicitly.

Unit 7:  Exponents and Radicals (02.15-03.04)

I can evaluate exponents and radicals.

I can simplify exponential expressions.

I can simplify radical expressions.

Unit 8:  Polynomial Operations (03.07-03.25)

I can identify the degree of a polynomial.

I can add and subtract polynomials.

I can multiply polynomials.

I can factor polynomials.

Unit 9:  Quadratic Equations (03.28-04.15)

I can solve a quadratic equation by factoring.

I can solve a quadratic equation by using the square root.

I can solve a quadratic equation by the quadratic formula.

I can determine which of the above methods is most effective for a given function.

Unit 10:  Quadratic Functions (04.18-05.13)

I can determine and justify if a function is quadratic.*

I can translate between standard, vertex, and factored form of a quadratic function.

I can find the zeros, vertex, and line of symmetry of a quadratic function.*

I can sketch a graph of a quadratic function.*

*Learning target includes statistical component

Notes:

• The dates are an approximate for pacing, so NO, I will not end every unit on a Friday
• I think I left a week open at the end of the year, which is good, because I didn't count holidays or long weekends when setting this out
• It will change; I'm sure; it always does
• Homework will be the same as last year
• I want to have finals at the end of each semester be 7 sections, one for each reporting standard
• I think this came out to 42 learning targets.  I heard once that 30 was what you should aim for...so I'm a little higher than that, but I guess paring it down is a goal for next year!

Well, that's a summary of my work from today!  I hope you can use it in some way!  If you have questions, please ask via comment here or twitter (@kathrynfreed), especially if you have an idea that can possibly make some part of this better.

-Kathryn

Brain Dump...Beginning of the Year

So I have a bunch of random thoughts about the beginning of the year bouncing around in my head, and I need to get them out because I won't be able to hash anything out for a few days and I don't want to forget them!

I've been thinking about my first day of school plans with my Algebra students, and although I still want to do the number line activity that I did last year (which I still need to blog about), I want to make a few changes and turn it into a longer task.  This way I will be able to use it as a pre-assessment of our first unit (Numbers and Operations) as well.  When I figure out what this is going to look like, I'll blog about it.  Promise.

So I think I'm going to go back to the "number about me" type of activity that I shared here.  But I'm thinking about making my information as 5-10 multiple choice questions, Kahoot style, or with Plickers, or something else since we'll have chromebooks (maybe pear deck?).  Then I'll have students submit their numbers as an exit ticket or an entrance ticket the next day.  This definitely helps me to build relationships from day one because I learn 5 things about my students THAT THEY CHOOSE TO SHARE.  And then we can turn this into the front or back of our ISNs :)  I found that when students had decorated the covers they treated them better throughout the year, which is really important since I want the same notebook to last all year.

I still need to send postcards home.  That needs to be #1 at this point.

I also really, really, really want to write students notes throughout the year.  I also want to call parents regularly throughout the year.  But those things take time and work, which I know will be really challenging once school starts.

Another thing I read about somewhere at some point this past year was sending students home with their notebooks and having their assignment be to show an adult at home.  I really want to do that within the first week with the syllabus and other things we will have in our notebook.  Then I can have a parent sign and return it or email me.  [I saw ____'s notebook.  He/she showed me these things:  I have these questions:  You can contact me these ways:  I prefer this method:  ]  This way I can collect phone numbers and email addresses as well, since sometimes they show up weird on PowerSchool when I try to look them up.  Then I was thinking that as the year goes on and I make parent/student contact I can record notes on the back of the paper.

Oh, and I want to be happy.  Ridiculously happy.  Every day.  This didn't happen last year, and I need to bring it back.  I love teaching.  I really do.  I need to ignore how frustrated I can get about all the work that is expected of us, and just be happy that I get to teach young souls about the awesomeness of math.  Ignore how annoying it is when I already have my plans made and the school changes the schedule.  Ignore that I hate it when other activities take my students out of class ALL. THE. TIME.  And just enjoy teaching.  Enjoy the students.  Focus on the good.

Well, I think that is the end of my brain dump for now.  I may have to add more later...

Update:  Also, musical cues, because no one wants to here me talk all the time.

-Kathryn

Units and Learning Targets 2014-2015

I often see a tweet from someone who is searching for learning targets for Algebra 1.  Two summers ago I worked hard to create learning targets and units based off of the common core standards my district has chosen for Algebra 1.  Those are posted on this blog, but I thought it might be valuable to share what I did this year, as it doesn't quite line up with what I shared before (planning and reality rarely align).

Unit 1:  Number and Operations

• I can perform operations with integers.
• I can identify and justify number equivalencies.
• I can order numbers.

Unit 2:  Expressions

• I can use the distributive property to rewrite expressions in equivalent forms.
• I can simplify expressions by combining like terms.
• I can evaluate expressions for the given value(s) of the variable(s).

Unit 3:  Equations

• I can solve linear equations.
• I can graph linear equations.
• I can solve a multi-variable linear equation for a given variable.

Unit 4:  Systems of Equations

• I can state whether or not given values for the variables represent a solution to a system of equations.
• I can estimate a solution to a system graphically.
• I can solve a system using substitution.
• I can solve a system using elimination.

Unit 5:  Sequences

• I can determine if a sequence is arithmetic, geometric, or neither.
• I can describe a sequence recursively.
• I can describe a sequence explicitly.

Unit 6:  Functions

• I can find the domain and range of a relation.
• I can determine and justify if a relation is a function.
• I can use function notation to describe, evaluate, and graph a function.

Unit 7:  Exponentials

• I can simplify and exponential expression.
• I can determine and justify if a function is exponential.
• I can find the base and y-intercept given an exponential function.
• I can graph an exponential function.

Unit 8:  Polynomial Operations

• I can identify the degree of a polynomial.
• I can add and subtract polynomials.
• I can multiply polynomials.
• I can factor polynomials.

Unit 9:  Quadratic Functions

• I can determine and justify if a function is quadratic.
• I can find the zeros of a quadratic function.
• I can sketch a graph of a quadratic function.
• I can find the line of symmetry and vertex of a quadratic function.

Unit 10:  Statistics

• I can organize and analyze bivariate data.

My (Brief) Reflection:

• Units 1 and 2 were boring for many of my students this year, but things I perceived my students the previous year to need.  Also things I think many students benefited from.  I would like to do some sort of pretest to see which students could benefit from what...but that will be complicated...
• I want to integrate statistics into my other units.  It gives a setting to apply the other learning that is "real-world" and then I won't save it until the end and end up not being able to do it.
• I need to focus somewhere on "rate of change" a little bit more...maybe since we didn't really do a linear functions unit this year that struggled.
• I would like to take time to compare these to the original learning targets I planned out and decide which I prefer for which units.

So here they are to borrow, steal, or edit!  Enjoy :)

-Kathryn

New Homework Structure

My current homework structure is based off of @iisanumber (Kathryn Belmonte)'s presentation last year at #TMC14.  Here is her write up on Math Maintenance.  I used it to create a structure for homework for my students.  Five problems, every night Monday through Thursday.  On Tuesday we discussed Monday night's problems as our warm up.  Here is a picture of what a week's worth of homework might look like:

Things that were going well:

• spiraling in the review, so things didn't get "old"
• consistent structure
• quick, approachable homework for my students

Things that weren't going so well:

• there was so very clear evidence of copying
• many low students were not completing it regularly

And then, recently at a training by my local Area Education Agency (@ghaea) they shared this document with us:  Teaching Strategies For Improving Algebra Knowledge in Middle and High School Students [large PDF].  This is a compilation of research surrounding teaching secondary mathematics by the Institute of Education Sciences.  My understanding is that they summarize and compile all the research out there to make conclusions in one place.  Making it more accessible to educators who do not have time or resources to find all the research that is out there.  Pretty great resource for us to be taking advantage of.  Unfortunately, there is not a whole ton of secondary mathematics education research out there, so even the recommendations they make based on the research have only minimal to moderate evidence to support them.  Sad day.

Their first recommendation is the one that caused me to change my Math Maintenance.  It is:  "Use solved problems to engage students in analyzing algebraic reasoning and strategies."  This can be done in many ways, one of which is to juxtapose a correctly solved problem with a similar problem for them to complete.  This forces students to look at a solved problem, think through the reasoning, and then apply it to a new (but similar) problem.

At our training we were asked to think through ways that we could apply this in our classroom, and math maintenance seemed like a good place to start.  Hopefully it will make it more accessible to all learners, while simultaneously making it more rigourous.   Here is an example of what it looks like now.

Students who have successfully completed Math Maintenance in the past have been telling me that it is now harder, and I think that is a big win.  They went from having to repeat the same thing over and over to having to actually think through what was happening in that type of problem.  Students who had problems completing Math Maintenance like to have one that is already completed to look off of.  I think that means this is a double win :)

Could you see yourself doing something like this in your classroom?

-Kathryn

Update 8/19/2015:  Now by popular demand, here is a folder where I uploaded all of my Math Maintenance assignments from the past year.  They are all dated based on last year.  I will not use these exact documents this year, but create it to cater to our current learning.  Also I didn't start the new structure until the spring, so most are according to the old structure.  And finally, these are the electronic versions, sometimes I write on documents before copying out for my students.

Function Notation Slider

After my immensely popular tweet of these pictures:

I figured I should blog about what we did for function notation in my class.  We made this slider for our notebooks.  The files can be found here.  They are 3/page and 6/page with dotted lines where you need to cut.  You will need to download into word for the files to be formatted correctly.  We glued the top and bottom of the pink one down, so that the brown can slide.  (Side note:  9th graders might need instruction and assistance with cutting the isolated slits on the brown one.)  On the right side of our notebooks we worked through each different input value and simplified as much as we could.

The next day we did a quiz-quiz-trade activity.  This helped students gain confidence.  After doing four problems quiz-quiz-trade style I gave them one to do individually and went around checking their work.  I did a quadratic to make sure they were simplifying exponents BEFORE multiplying.  If students didn't have it correct I could give them some quick feedback, they would fix it, and I would check it again.

There's more to what we did (and are still doing), but that's all I feel like blogging about now.  Thanks for all the encouragement via my tweet.  It was amazing to see the power of twitter in that another teacher (in another country) took the idea and improved it and used it THE VERY NEXT DAY!  My students all think I'm a super-star now and they are impressed that I had one idea of my own.  It reminded me of what a blessing it is to be part of the #MTBoS!

-Kathryn

New Steps I'm Taking to Improve Group Work

I'm working a lot harder on making group work work in my classroom this semester.  I implemented some changes first semester, and expected it to work for itself from there...uh, duh Kathryn, you can't just put things in place and expect them to run themselves.  So I've been more thoughtful about it this semester, and trying to patiently look for small improvements.  Since I rarely blog, I will discuss all changes I have made this year.

First Semester

Desks in Groups of 4:  I have tables, so I've pushed two together to make groups of four.  I had this on and off last year, but I haven't even considered changing it once this year.

Group Supply Tubs:  I organized supplies into group tubs.  Something I sort of had last year, but that didn't work very well.  I also was intentional about not putting too much stuff in at the beginning of the year.


Roles:  I wrote about my role cards before school started, but I expected a little prep and some pretty cards to be enough for students to "play their role" every time...that is not enough.

Talking Points:  We do talking points as a warm-up every Thursday.  This helps give every student a voice.

Then I'd also throw around the phrase "do this in your groups" a lot and feel frustrated that they really weren't.  So I have tried to be more thoughtful.

Second Semester

Role Explanations in Notebook:  I made a half-sheet explanation of all the roles for students to put into their ISNs.  This way they ALWAYS had access to them and I could hold them more accountable.

Group Tasks:  I have been a lot more intentional about groups tasks.  One scored group task every unit is my challenge for myself.  This is super structured, and involves a significant amount of prep.  An important thing I learned from Elizabeth and our morning session at #TMC14 is to put in checkpoints for groups to call me over and see how they are progressing.  This helps a lot.  I even carry around a roster so that I can mark off what checkpoint each student has completed.  Then when I'm prepping for day 2 of the task, I have an idea of where everyone is and who I should maybe guide right from the beginning.

At this point I haven't done any amazingly exploratory/discovery task, but I think that's OK.  I'm not super-teacher, so small steps is what it is going to take.  I've turned some things I did last year (that I liked) into tasks that I now like better.  I'm sure they will morph next year into things I like even better...oh the joys of teaching!

Here is my sequence task:  Instructions, Cut Outs

Here is my function task:  Instructions, Cut Outs, Recording Sheet

Acknowledging What I Like:  I've been intentionally looking for things that I like during the group work time so that I can praise those things.  This helps me and my students, because I see the good things rather than the bad, and they feel encouraged.  It also leads to improvement because others see what I like from a group and they can work to do it in their group.

I actually just had a thought while I was blogging this that I'm going to try Monday.  I'm going to use my whiteboard to give these acknowledgements.  It is semi-public in that the entire class can see (but not other classes), but I don't have to spend the last couple minutes of class giving shout outs that they might forget by the next day.  AND other groups can IMMEDIATELY implement changes to get acknowledged as well.  I could even start with a few things on the board that I'm looking for and then write up the table number when I see that group doing it.

Group Reflections:  Every day we do any group work task work, I have them complete a quick reflection.  I'm sure I stole the questions from Elizabeth (bottom of this post) and just modified it a bit. It's just a quarter sheet, so I make a ton of copies and have them ready.  My hope is that by regularly trying to give a compliment to someone for playing their role they will become more familiar with the responsibilities of each role.  I might modify the reflection next task to involve something the individual did as well as something another person did.  Try to slowly increase the expectation that EVERYONE is playing their role.

Here is a link to what I've been giving (4 to a page).  And here is what I created for next time (2 to a page).

That's where I'm at with group work right now.  I'm proud of the changes I've made, but also disappointed that we're not farther along.  I have been realizing this year how long real change takes.  And it is a little disheartening because I'm starting to understand that it's going to take more than just me to make real change for our students.  We really need every teacher on board to make real change for students.

Let me know if you see something big (or small) that I'm missing that would make group work more valuable for my students.  I know that it is not ideal at this point, but I'm working on getting better.

-Kathryn

[Unit Overview] Exponents and Radicals

Here is a brief overview of the unit I just finished on exponents and radicals.  Because of time, I did not do everything as thoroughly as I would have liked to.  However, I feel the structure is something that I can hold onto and build on for next year.

Evaluating Exponents and Radicals:

I got the idea for this structure from Sarah Hagan at mathequalslove.blogspot.com.  Here is her post on Radical Radicals.  I liked this idea so much that I decided to apply it to exponentials as well, even though my students knew more of the vocabulary that goes along with them.

Front

Back

Front

Back

We still struggled with knowing what the word evaluate means.  That is something I hope to work on a lot more at the beginning of next year:  vocabulary like evaluate, simplify, solve, expression, equation, etc.

My File

Properties of Exponents/Simplifying Exponential Expressions:

I got the structure for this lesson from Lizzy-Sensei at dontpanictheansweris42.blogspot.com.  Here is her post on Exponent Rules.  I loved the structure of it, but I didn't want to print an entire page for each student for each rule...so I changed it to a half-page structure.  I also noticed that my students would fill out the table, but then stop without answering the questions.  That was frustrating to me, and I don't know how to make it better for next time.  Also by the time we made it through all the properties the students were really bored of that structure of the lesson.

However I do know that I would plan on formatting it just a little bit better for my notebooks next year.  Also need a box around where we actually put the rule, because when I had them look back in their notes for the rule, they didn't know where it was.  I'm also thinking about reorganizing the columns in the zero and negative exponent property ones because students kept thinking that the rule should connect the first and the last column, rather that the ones that showed the zero or negative exponent.

Also students struggled to put what they had learned into practice.  It seems that they needed much more practice as they went.

My File [Reformatted as a Book]

Translating between Exponentials and Radicals:

I did an intro to try to help show WHY this is true, but I don't think it was very good.  This is something I really want to think through developing a good discovery-type lesson for my students next year.  For this learning target we put the rules into our notebooks and then I had a matching activity for them to do.  I asked them to write down their matches on the bottom of the page.

Simplifying Radical Expressions:

We added, multiplied, and simplified radicals.  We did adding multiplied, added, and then simplified to show that we could add things we didn't know we could add.

Notes

Practice

Notes

Practice

Adding Notes/Practice

Multiplying Notes/Practice

Simplify Cards

I knew that was a lot in a few short days, and I had just read Kathryn Belmonte's post on Coloring Relay, so I made my students a coloring sheet with the answers written in.  I allowed them to work individually telling them that they could color in one section once they had completed the problem that had that answer...yes some students mostly colored and didn't do a lot of math.  But it was Friday and I wasn't feeling great, so it was a compromise I was willing to make.

This is not my favorite unit.  I think it is a lot of stuff to put into one unit.  But really it is only a couple standards, so it is hard for me to balance that.  It has taken me a long time to share this because I'm not very proud of this unit.  However, I put a lot of work into it.  I created and modified everything.  It was a lot of work, but hopefully now that I have things to this point I can make it better for next year.

-Kathryn

Note:  All files must be downloaded in Microsoft Word to get correct formatting.

#MTBoS30

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