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

Practice Structures

So, Sarah Carter and I chatted on twitter some about practice structures, and she totally beat me to blogging about it.  Read her post here.  She also calls for you to submit the practice structures you use.

My goal is to generate a reasonable list of practice structures that will be efficient for me to use and also beneficial for my students.  Ones that make them think, move around, and engage in their learning.  Efficiency is an issue because I don't want to always spend 15 minutes explaining a new structure.  There are lots of options out there and if I'm always doing new things then the focus comes away from the learning.  Here is my list so far, and I'm going to explain how I have/plan to use them and what the benefits I see are.  I'm also interested in how these can be incorporated into student notebooks.

Card Sort:  I most often do this individually where each student gets the whole set and sorts and glues into his/her notebook.  I like that it is a sorting activity, so good for organizing the learning in the brain.  I like that it goes well into the notebook.  I don't like that students don't have to explain.  One idea on making this better is to have them do the sort as a group and pick a few each to put into their notebooks with an explanation.  Which gives fewer, but more meaningful, examples in their notebooks.

A few times this past year I made a whole class card sort where students each got one card and had to find their match.  If the class had an uneven number then I would leave one out on a table and one person would match the table.  As they match up they come check with me.  Sometimes I time them and they compete class period to class period.  Fun, but each student does not see all matches.

Quiz-Quiz-Trade:  I'm not really sure I do this correctly for it's given name...but I give each student a problem, have them work it out.  Then after a set time I make everyone partner up, work their partner's problem (which becomes their problem), and talk through it together.  (Maybe I could call it "Do-Trade-Do-Talk"; DTDT for short.)  Then after a set time, new partners, repeat.  There might be some benefit to having a student keep the same problem as "theirs" the whole time, but I'm not sure yet.  Good practice.  We often do 4-8 problems when we use this structure.

I have a handout (pictured below) that they use and keep in their notebook pocket for the unit.  This means that the students probably don't look at it ever again, but I feel like this past year my students were better at that, so perhaps I can help my students develop that better.  I would suspect it would be easy to get students to put this in their notebooks as well.

Stations:  I have 6 table groups set up in my classroom, so I usually do 6 stations.  Students rotate based on my timer from group to group.  I usually post answers on the back of the next station so students can check their work themselves.  I don't always have great participation in stations, but it might be because I haven't found a good way for students to record their work.  Sometimes it's just on whiteboards, so maybe they think it's less important?

I have had some thoughts of making stations a more challenging structure - more than just rinse-repeat practice problems.  This would make it more important for students to work together as a group, hopefully getting better involvement.

Jigsaw:  I have only done this a few times, and I think it was all last year.  But I use this as a way to jump-start a class discussion where I want students to "notice" and "wonder" about a new idea.  Each table group would be given a problem or group of problems to complete and present to the class, afterwards as a class we discuss patterns and try to draw a conclusion.  It would be possible to have discussion questions for groups of students as well, but I generally facilitate the discussion as a class.  Perhaps a well-written "talking points" could follow the sharing part and precede the group discussion.  I want to use this more in the future as it seems to be a good use of class time.

Posted Problems:  I tape problems up to my walls and students do whichever they want in whatever order.  I usually post answers for them to check as they are working.  This gives them movement and the option of working alone or with a partner.  Also works pretty easily in their notebooks.

Scavenger Hunt:  This is where problems AND answers are posted throughout the room.  Students work a problem, then find the answer (to the one they just did) attached to the next problem they are to work.  It is self checking (AWESOME), students can start anywhere because it just does a big loop, and makes kids move.  A lot like "posted problems", but a little more work to set up and get students to understand the structure. Since I usually post answers so matter, I'm not sure the benefit of one over the other.

Coloring Page Worksheet:  Like a worksheet, but includes a picture to be colored as the problems are worked.  Answers are placed in spaces in the picture and when students get an answer to one of the problems they find that space in the picture and color it.  It is very calming for students to color, however I often have some students who just color and some students who just do the math.  The students in the former group are the ones I'm concerned about.  However, I feel it beats just a regular worksheet, which I use sometimes, too.

Add Em Up:  I'm sure I learned about this from Elizabeth at TMC14 during our morning session, but she has blogged about a complex number placemat activity here.  I've done this once or twice and I need to do more of it.  I just don't have a good answer to "What if I have a group of three?"  Also it's a lot of paper to give each group all the placemats to do their work.  Often I use whiteboards, so I could probably make that work better.

If you haven't done it before, students work problems in their group in "rounds" and they are told what the sum of each of their results will be.  In that way it is self checking.  Each student does their individual work in the corner of a "placemat" which gets them focused together as a group.  If their sum doesn't work out from the beginning then they have to check each others' work.

The Mistake Game:  I found this from Kelly.  She actually has several posts on this structure, but here is The Guide.  Simplified, groups of students present solutions to problems that include at least one mistake.  If they accidentally include more mistakes it is better.  The audience has to find the mistakes.  This is more engaging for the students.  Read her post for more details.

I have done this with my freshmen and my upper classmen.  It works really well with my older students, however I don't think it's ever worked well with my freshmen.  I'm not sure why.  Maybe I need to persist and do it more often?  I try to get all students to ask questions and present, but some are really hesitant and expect the other students to find all the mistakes for them :(  What usually happens is it ends up taking FOREVER to find the mistake and then a student blurts it out instead of asking a question.  Or the same student finds mistakes in 12 out of 15 problems.

I really, really, really like this, but I need to find a way to make it work better in my Algebra classes.

Open Middle Style:  This is where #mtbos is compiling problems of this nature.  These problems require a lot more thinking and tinkering with the mathematics than regular practice problems.  I would like to provide students with at least one problem like this for each learning target we have.  (Maybe these types of problems would work well as stations...hmm...) Sarah has posted some she has created here and here, and I have a few I might share as I work through my functions unit.  However, there are a lot on the open middle site I linked above, so check them out!

So those are the practice structures I use/have used/want to use.  Some of them I want to use every unit (card sort, quiz-quiz-trade, stations, jigsaw, add em up, open middle) and some of them I'm not sure I want to use at all (scavenger hunt, coloring page, mistake game), but now I have a starting point as I work through my units.

Please let me know your thoughts on any of these practice structures!  Ones that are great, ones you don't like because..., ones I'm missing here that I should definitely include, etc.  I would like to know so that I can use the best ones for my students.

-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

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

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

[Unit Overview] Polynomials

This is very old and thus is going to be mostly pictures since I already have them updated :)

Finding the Degree and Naming Polynomials:

We actually filled this in as much as we could and discussed why we couldn't really have a constant trinomial...

Adding and Subtracting Polynomials:  I wrote up some notes and passed around papers to groups so that they could put what they wanted into their notebooks.  There were also some practice problems and answers.

Then here is what my notebook pages looked like:

Multiplying Polynomials:  I demonstrated two methods for them to choose from.

This is my go-to style for practice problems

Factoring Polynomials:  We defined factor of a trinomial and did a few examples.  Prior to the examples we completed an exploration activity with multiplying polynomials finding b and c and then making observations.  I've done it twice now and it's pretty structured, but I think it's better than me just stating the pattern for them.

Well, that's my quick post that should have been completed in March or April :)  Enjoy!
-Kathryn

Checklists: Why I'm Excited to Try Them!

This morning I saw Steph Reilly's post about Checklists and Error Analysis.  Both are genius ideas (please, go read and I'm grateful to her for posting them.  I think checklists are going to be a life-saver for me...and here's why.

I don't grade homework or notebooks.  I don't have time and I don't want to put so much emphasis on homework that students want to copy.  (I wrote a lot more about homework here.)  However, I had a lot of trouble getting students to do the work required to get the learning.

Because of that I chose a unit and planned to have students do an Agenda assignment in preparation for the test.  I gave them an "agenda" with lots of options for tasks to complete.  (By the way, creating the agenda was a LOT of work for me.) They got to choose which ones to do in order to earn x points.  They had class time to work, but were expected to complete some if it out of class.  They had to have it completed BEFORE they could take the test.  This was pretty unsuccessful.  Students hated the agenda, to put it nicely.

I've been debating all summer how to hold students accountable for doing the work, but I knew that agendas probably weren't going to work.  There is something similar I'd heard of called "menus", but I'm not really sure they would be any better.  So I had a problem with no solution, and that is one of the reasons I was so excited to read Steph's post.

Here are the things I like about the checklist:

• Can be built as we go, so I don't have to plan everything out ahead of time
• Can include whatever I want, even notebook pages
• It won't overwhelm students at the beginning because it will be empty
• It will give students things to work on if they finish something else early
• It will remind students of things that we have done that they have forgotten about

Anyway, I liked the idea so much that I am fairly certain it is the solution to many of my problems.  I wanted to link the assignments to specific learning targets, so I added a column that Steph didn't have in hers.  I also typed up some instructions, but didn't want to have to include them on the actual checklist, so I think I will make them notebook friendly and tape them in the front of our notebooks with our syllabus, bellwork schedule, and classroom expectations.

Since I made the documents, I'm going to go ahead and call them my #Made4Math Monday, but I totally stole it from Steph as stated above, so please read her post!

My instructions document

My Unit 0A Checklist as shown above

Note:  These files will open in google drive and you will have to download them to edit them in Microsoft word.

-Kathryn

#alg1chat Master Topic List

I wanted to share tonight the Master Topic List we began creating for #alg1chat.  If there is something you are required to teach in your Algebra 1 class that you feel is not included on this document, please add it!  It's very disorganized right now, but we'll get it organized at some point :)

Master Topic List

-Kathryn

#MTBoS30
13/30

Foundational Standards

At our last Tiered Algebra day, we spent an entire morning choosing foundational standards for Algebra 1 (specifically looking through the Appendix A standards that were identified for Algebra 1).  We wanted to be make sure to state that we are not choosing Power Standards.  Common Core specifically clarifies that all standards are equally important.  In our core instruction, we need to be teaching all standards.  
However, we felt it might be helpful to identify some standards that were critical to the learning of other standards.  We wanted our foundational standards to be ones that:

• would help students learn other Algebra standards

• would be necessary for life

• might help bridge between 8th grade math and Algebra

An example is that if students have trouble solving linear equations, it is likely that they would have trouble solving systems of equations, quadratic equations, etc.  In that way, solving linear equations is a foundational standard.

After much discussion we came up with the following foundational standards/groups of standards:

EQUATIONS/INEQUALITIES
A.CED.1:  Create equations and inequalities in one variable and use them to solve problems.
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.CED.4:  Rearrange formulas to highlight quantities of interest, using the same reasoning as in solving equations.

SLOPE
F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

POLYNOMIAL OPERATIONS
A.APR.1: Understand that polynomials for a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

MEANING OF A GRAPH
F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graph of the equation y = f(x).

A.REI.10:  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

INTERPRET PARTS OF AN EXPRESSION

A.SSE.1:  Interpret expressions that represent a quantity in terms of its context.  Interpret parts of an expression, such as terms, factors, and coefficients.  Interpret complicated expressions by viewing one or more of their parts as a single entity.

EXPONENTS AND RADICALS

N.RN.2:  Rewrite expressions involving radicals and rational exponents using the properties of exponents.

USE UNITS

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.

It was a morning of long debates, so I would easily say that almost all of us would argue to change something about what we came up with...overall what to you think?  Is there something you would add or remove?

-Kathryn

#MTBoS30

8/30

Solving One-Variable Linear Equations

Confession:  I taught an entire semester of Algebra 1 without spending time solving linear equations. 

Why?  Because I knew my students had seen a lot of it in 8th grade, and I also knew that they were all at different places and ready for different challenges.  I also knew that they had forgotten some of what they had learned and a little reminder might take them a lot further.  All of this is hard to address in a class of 20+ students.

However, I knew it was something I needed to address at the start of this semester so that we could solve systems and eventually some quadratics.  I gave a pretest, but it was evident that not a lot was immediately recall-able for them.  So I spent a few days focusing on solving 2-step equations.  Here are a few reasons why I chose to start with 2-step equations:

• I can say they can all be solved in 2-steps, which helps the students process what they need to do
• I can address issues like "Ah, there's a fraction!" (but it really just means division) and I can even throw in some parenthesis
• I can challenge all students with things like -t + 10.2 = -23.1 (the negative variable is really tricky the first few times they see it)
• It is not out of the reach of most students (I do have a few students who still struggle to solve one-step...but those are students who did not take 8th grade math in my district last year.)
• It is enough to bring back a lot of what they learned about solving equations

I have one Algebra class that is a little bit quicker than the others, so I got to move away from 2-step equations with them on Friday.  I couldn't decide exactly how to do it, because there are SO MANY ways to solve different equations.  I really just want to ensure they are aware of the various options they have and give them some practice at choosing what to use in what scenarios.  I don't want to say:  "always distribute" or "put the variable terms on the left and the constants on the right" or anything that shows that there is only one way to solve.  I want problem solvers, not procedure followers.

Anyway, here is what I ended up doing.  I just gave them 4 "challenge" equations to solve.  And for the most part, they worked HARD for 30 minutes to work out solutions.  Here are the equations:

• 2(-1x + 6) = 22
• 2x + 2 = 32 + 5x
• 3 - 2x + 6x = 15
• 5x - 7 = 2(x + 1)

I put the four equations on the board and said "I challenge you to use the resources available in this room to find the solutions (and perhaps a solution method) to these equations today."  We discussed what resources were available and then they got to work.  The review we had done with 2-steps was enough for several students to remember even how to move variable terms to the other side.

There were a few students who "tried" and then gave up and didn't accomplish much at all, but I would say at least 85% of my students worked hard during the time I gave them.  I was SO PROUD of them.  I just wanted to brag a little about my students, because it was everything I hoped it would be.  

We will continue to work with advanced linear equations on Monday and Tuesday to get them more fluent at being aware of the strategies that are available and choosing an appropriate one.  Perhaps with some whiteboarding...

-Kathryn

Linear Functions

We jumped into linear functions this week.  Here are some of the things we did (and by some I mean pretty much my entire week of lessons).

What does it mean to be linear?
I really wanted to emphasize the various representations of linearity, so that students could see how they all work together.  So I started with this foldable to define linear.  I gave them the algebraic and graphic definitions, but we used those to come up with what it means to be linear in a table.

I did this by giving them each a graph of a linear function, with four points marked on it.  (Here are the graphs I used.)  Then I had them in groups of two create a table on the board for their graph.  I was hoping this would help students with the concept that a line is made up of points as we have been struggling with that idea.  Once we were done with that we made lots and lots of observations about the tables.  This took a LONG time.  I let them notice anything, so it took a while to get away from "they all have a 0/1/-2" type of statements into noticing the various patterns that were there.

But eventually we came up with "x and y both change by constant amounts".  I was very happy because in every class students recognized that they could choose any of the tables on the board as an example.  And students were willing to try to think of non-examples.  So each student got to make that part their own.  I know that is the purpose of things like this, but we don't get there often enough.  It was nice to get that far with this.

Here is the inside.  (And here is a link to the foldable.)

I created a card sort as a way to help them practice telling if something is linear.  I really wanted to get at the fact that linear is a word that describes a group of functions.  So something must be a function before it can be linear.  So we sorted between "Not a Function", "Function-Linear", and "Function-Nonlinear".  It was a lot harder for them than I thought it would be, but eventually we began to get the hang of it.  They still struggle with messing up whether VLT is for function or linear...but one step at a time.

As you can see, instead of gluing the cards in, we recorded the answers in our notebooks.  I hope that students will try to sort the cards on their own as a way to review.

Thoughts:

• My card sort is not perfect.  Two of my tables are non-functions for the same reason, that was a typo...I want to fix that.
• Also didn't really mean to have the equation x=2 in there because we didn't discuss what makes an equation a function...but it did lead to a decent conversation.  I think I would prefer to replace the card with a linear function that is not in slope-intercept form.
• One class got into a really good discussion about whether or not y=(1/3)x was linear or not.  Even when b=0 was thrown out as an idea, one student was still adamant that it needed to be written down for it to be in slope-intercept form.  I kept the conversation going for a while and then moved on without giving up who was correct.  While I was talking a student looked to the student sitting next to him and asked, "so is it linear or not?".  Aren't I mean?  The next day I eventually showed them the graph and they all agreed that it was linear.  I also explained that mathematicians tend toward laziness and prefer not to write something if it is unnecessary.
• I went hard-core with colors in my notes, but students didn't in theirs.  That is something I need to work on being more intentional about.

Finding slope and y-intercept

To begin our discussion of slope and y-intercept, I had students write "what I know..." and "what I want to know..." on the board.  Here is one example:

We used this to jump start our graphic organizer for notes.  Starting with what they already knew, but still getting it into the notes was a win-win.  They got to feel smart for knowing it and I got them all to put it into their notes anyway, especially since not all students knew it.  Here is what we came up with.

I don't think they've seen the slope formula, and I really wanted to share that with them for the Numeric part, but they thought smarter than me and were ready with ideas by the time we got their.  They remembered finding the change in y and x when deciding if the table was linear or not, and figured that would work!  It is really quite brilliant, and I feel lame because I didn't think of it first, but by the time I made it to the end of the day I had abandoned the slope formula.  I want to work back to it for tables that don't have a constant change in x, but still might be linear...we'll see if I can manage that :)

Then we practiced finding slope and y-intercept with a boring worksheet.  But it was quick and worked as a check to see where students were at.  I used my name cards to call students for answers at the end of class.

Thoughts:

• I really wish I could have just had them create their own graphic organizer for this, but I'm not sure I could have been clear enough for them to understand the expectations
• Once again I went hard-core with color and they did not (but look how cute it is!)
• The worksheet was boring, but didn't take too much time.  I think that's OK, because I just needed enough for them to get back into things.  I would have done things slightly differently if this was the first time they had been introduced to slope-intercept form.

Unit 5 LTs (draft)

Well, here I am again, asking your advice on my learning targets!  But the difference today is that this is the last time :)  Here you go!

UNIT 5:  QUADRATIC FUNCTIONS AND MODELING

Section 5.1:  Graphing and Interpreting Quadratic Functions

                Standards Addressed:  F.IF.4, F.IF.5, F.IF.6, F.IF.7, F.IF.8, F.BF.1

5.1A:  I can find the intercepts and extrema for a quadratic function (in any form).

5.1B:  I can graph a quadratic function using the intercepts and extrema.

5.1C:  I can interpret the meaning of intercepts and extrema of a function used to model a situation.

5.1D:  I can calculate and interpret the meaning of the slope between two points of a function used to model a situation.

Section 5.2:  Comparing Functions

                Standards Addressed:  N.RN.3, F.IF.9, F.BF.3, F.BF.4, F.LE.3

5.2A:  I can compare properties of two functions (in any form).

5.2B:  I can describe and identify translations that determine function families.

5.2C:  I can find inverses of linear functions (in any form).

Thoughts/Notes

• All but three of the standards in this unit were addressed previously in unit 2.  In this unit they are to be extended to quadratics.
• I kind of would like to throw 5.1D in with 5.1A and C, but I couldn't get the wording right and so then I questioned whether it actually fit or not.  Thoughts?
• I honestly feel like this was the easiest unit...maybe that's because I'm to the point where I'm not as worried about perfection as I was at the beginning...?  Maybe that means this unit is awful...?

Once again, I ask for your feedback.  I want to know what needs to happen to make these awesome for my students.  I appreciate you taking the time to read these!  Thanks, and once again remember...ALL DONE!

-Kathryn

Unit 4 LTs (draft)

I still have a million thoughts whirling around in my head about Unit 3 based off of comments and twitter conversations, but onto Unit 4 I must go!

UNIT 4:  EXPRESSIONS AND EQUATIONS

Section 4.1:  Polynomial Operations and Modeling

                Standards Addressed:  A.SSE.1, A.APR.1, A.CED.1, A.CED.2

4.1A:  I can add and subtract polynomials.

4.1B:  I can multiply polynomials.

4.1C:  I can create equations to model situations and use them to solve problems in the context of the situation.

Section 4.2:  Zeros of Quadratics Algebraically

                Standards Addressed:  A.SSE.2, A.SSE.3, A.CED.4, A.REI.4, A.REI.7

4.2A:  I can find zeros of quadratic functions by taking the square root.

4.2B:  I can find zeros of quadratic functions by factoring.

4.2C:  I can find zeros of quadratic functions by completing the square.

4.2D:  I can find zeros of quadratic functions by using the quadratic formula.

4.2E:  I can solve an equation/formula for a specified variable.

Thoughts/Notes:

• Do I really need 4.2A?  I'm looking at A.REI.4b, which says students solve by inspection, taking square roots, completing the square, the quadratic formula, and factoring.  Well, that's a lot, so I feel like it needs more than one LT, but not 5!  And to me if you solve by CTS you are taking a square root...would basic square root equations build up to CTS?  I would prefer 4 LTs to 5 in that section...thoughts?
• I'm a little confused about how I can fully meet A.SSE.3 and A.CED.2 which both have graphing components when most of the graphing standards aren't until Unit 5 (F.IF.7, F.BF.3, and many others).  We will likely do all our graphs by plotting points or using technology for Unit 4. 
• Last year when we found zeros of quadratic functions we did algebraically, numerically, and graphically all together.  I'm a little sad that they are split up here.  :(  I like drawing all the connections, but it will have to wait to Unit 5.

Please give feedback by commenting below or tweeting me (@kathrynfreed).  I really appreciate how much everyone has helped me so far with processing these.  Every time I think my brain is over-capacity with thoughts on standards and learning targets somebody will make a comment that gets me thinking again!

For those of you who have been walking through this entire journey with me, there is only one unit left!  Hang in there!

-Kathryn

Unit 3 LTs (draft)

I promised Unit 3 LTs by the end of the week, and I think I made it on time :)  There's nothing like cutting it close.  I had hoped to have units 4 and 5 done by this time as well, but we'll just have to see where I can get.

Here they are.  More thoughts at the bottom!

UNIT 3:  DESCRIPTIVE STATISTICS

Section 3.1:  One-Variable Statistics

                Standards Addressed:  S.ID.1, S.ID.2, S.ID.3

3.1A:  I can create plots (dot, box, histogram) to represent data.

3.1B:  I can find and interpret the mean, median, IQR, and standard deviation.

3.1C:  I can compare the shape, spread, and center of data sets using the mean, median, IQR, and standard deviation.

Section 3.2:  Two-Variable Categorical Data

                Standards Addressed:  S.ID.5

3.2A:  I can create a two-way frequency table for categorical data with two categories.

3.2B:  I can find and interpret relative frequencies (joint, marginal, and conditional) in the context of the data.

Section 3.3:  Two-Variable Quantitative Data

                Standards Addressed:  S.ID.6, S.ID.7, S.ID.8, S.ID.9

3.3A:  I can represent data with a scatter plot.

3.3B:  I can find a line of best fit and use it to solve problems in the context of the data.

3.3C:  I can interpret the meaning of the slope and the intercepts.

3.3D:  I can find and analyze the meaning of the residuals and the correlation coefficient.

3.3E:  I can make inferences about correlation and causation.

Thoughts/Notes:

• It makes sense to me to study 1-variable statistics separately, so I'm mostly OK with the organization of 3.1.  We did get a quite decent twitter conversation on whether or not students should be required to calculate standard deviation by hand.  Any further comments on that are welcome.  Thank you to those who already participated and gave me ideas.
• I had planned on doing all two-variable statistics as one section, but there is a lot there!  And it seems weird to me to have 1 standard on categorical data when the rest are on quantitative data.  Hard for me to make that fit well.  There is so much with the quantitative data though that I couldn't combine them.  I hate having 5 LTs in one section (it feels so big) but I feel like I still haven't done the standards justice.  Also I think Section 3.2 being so short will provide an opportunity for a different structure of class.  Maybe we will do a project assessment instead of a test

Please, please, please leave your thoughts in the comments or tweet me (@kathrynfreed) Like I have said with every other unit, I really truly want to make these the best goals I can for my students.  I appreciate all of your feedback whether praising my awesome-ness (not usually) or giving me advice for improvement (usually), I really like how you guys can always make me think more--even when I think my brain is dead!  Thanks for that!

-Kathryn