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

#5things To Welcome Next Year's 9th Gradersl

I LOVE meeting my future students!  I do a lot of things to help them feel welcomed and to try to provide a smooth transition to high school.

1.  Attend Their Math Class
I'm grateful that my principal will hire a 1/2 day sub so that I can attend their math classes one day and give them the Algebra Probe our district uses as a pretest.  I get to meet them, talk to them about high school, Algebra, and then assess them on what they can do.  All this happens in their 8th grade math class, which they are already comfortable in!  Hooray!

2.  Attend 8th Grade Parent Meeting
My district holds an 8th grade parent meeting in the spring for parents and students to attend.  I attend this meeting too, so I get to see the students and their parents again :)  I also work with other core and elective 9th grade teachers to have a supply list available to students and parents that night.

3.  Learn Their Names--FAST
I work by tail end off to learn their names as soon as I can.  I actually work on this all year.  Whenever I encounter 8th graders at school or in the community I ask other people their names and I try to figure out their connections to my current 9th graders.  Who is friends with whom...who is siblings with whom...etc.  It helps a lot.  Then when I go into their math class, I call them all by name and they are SHOCKED.  One class this year was so surprised that they asked me to go around the room saying everyone's name, and they clapped when I finished :)

4.  Tell Them I'm Excited
I always emphasize with them how excited I am to have them next year.  I share my excitement and ask them what they are looking forward to and what they are nervous about.  Some students shared about being worried they would embarrass themselves, so I shared something embarrassing I had done before--they all got to laugh at me :)

5.  Mail Them a Postcard
OK--I've never actually done this before, but I really want to!  I want to send a postcard home to each of my future students this summer.  A few weeks before school starts just send them a quick note letting them know that I'm excited for them to come to high school!  Then I can add a special note to kids I haven't met, kids who are in my homeroom, or kids I've encountered for other reasons.

-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.

How I Used Plickers

I just started using Plickers in one of my classes.  I learned about them at #TMC14, and if you don't know what I'm talking about go here to find out about them.

Note:  this is my reflection of my use in the classroom; nothing more

Set-up:  I printed the free plickers, size "normal" and copied onto colored paper, laminated, and wrote each student's name on the back in sharpie.  I had my students use the plickers for one question on Monday and one question on Tuesday, just to see how they would work.  Then I planned to use them multiple times on Wednesday.

Class:  I was doing this in my intervention class, which has 8 students enrolled.  I wanted to try plickers in my smaller, more flexible class before full-out implementing into my large core classes.

We have been studying domain and range, so I prepared seven graphs, each with 4 options for domain and range, trying to include common errors as possible options.  I also created some beginning questions about domain and range, just to get us started.

Implementation:  I showed the graphs and the options using my document camera and the students pulled chairs around the screen.  I did not show the plickers "Live View" because I was showing everything they needed through the doc camera.  I gave them 30 seconds to think then asked them to hold up their answers and I scanned with my iPad.

The app gives immediate feedback as to who was right and who was wrong, and which wrong answer they selected.  I can use that to base our follow-up conversation before we move on to the next question.

Reflection Thoughts:

• The kids LOVED it.  They asked to do it everyday and for the most part they were engaged the whole time.
• At the end of the lesson I gave the a graph and had them give the domain and range WITHOUT options.  They were more successful than they would have been before the lesson, but not as successful as I would have hoped.
• The app seems slow, but I have to remember that it is faster than if I had to read and judge them all.
• If they are covering up any part of the QR Code it will not read their answer.
• I'm not ready to implement in a full class, because it would be harder to keep everyone engaged.
• I can't think of a better way to help students learn about domain and range in a way that will engage them and simplify it to make it more accessible to all students from the beginning.
• I'm planning on doing something similar in the future with other concepts.

How have you tried plickers?  What did you like?  What does it take to make a good plicker lesson?

-Kathryn

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

Talking Points in my Classroom

After my Group Work Working Group morning session, I knew for sure that I wanted to try Talking Points in my classroom.  After a lengthy twitter conversation I was convinced that I didn't need to do it day 1, but that day 2 or day 3 was okay.  We ended up starting with talking points on day 3.

Here are the instructions I gave to my students:

I basically took what Elizabeth shared here (see printable student instruction sheet), and modified it to be only one side.  If you would like my file it is available here (titled structure overview).

We read through this as a class and then I passed out talking about talking and started my timer.  As I walked around I tried to remember that I should NOT be intervening unless they were having trouble with the structure.  Here were my observations:

• I did not observe any group ALL DAY doing 3 rounds per statement
• Most groups did not do rounds
• Many did first round without becauses and then went back and said why after hearing from everyone
• Many were not taking turns
• Many students took more than one "turn" per "round" (not really turns or rounds the way students were doing it)
• Saw dialogue between two students while two were silent (groups of 4)

I pretty much felt like a failure.  I'm really not sure why it my students could get the structure from the handout, but I had to do a lot of intervening.  I tried to wait until the end of a round to really get insight into what the group was doing in order to push them the right direction.  I looked for things groups were doing correctly, too.  And all the way at the end of talking points I shared with the whole class the good things I saw each group doing.  (ie. "I saw table 4 reading the statement out loud.  Thanks table 4!")

I had a thought or two about never doing talking points again, but instead I knew I just needed to push it harder and help students focus better.  I came back the next day ready for more talking points and a little more prepared for how to support my students.  I gave the whole class one structural issue to focus on:  say your becauses, and then went around looking for that as well as the other things.  The next time we did talking points I focused on take turns in rounds.  Then finally three rounds per talking point.  Each time I reminded them of the previous expectations, but added one new thing.  This worked really well for me to focus on the good things that students were doing.

We have done talking points four times now, and my students are starting to get it figured out.  I still have some things to work on with them such as:

• some groups were doing all statements round 1, then all statements round 2, then all statements round 3
• most students do not interact much with each others thoughts unless they are "commenting"
• still see "popcorn" conversation rather than turns dictated by rounds
• a few groups think round 2 can go as long as they want, giving each student more than 1 turn in round 2
• Sometimes I hear a student asking "Do you still think ____?" which I do not like
• A few groups are still not tallying responses during round 3...I'm not exactly sure if they're just writing down their opinion, or if they are voting

So far I have done talking about talking, talking about listening, talking about questions, and talking about roles.  I have mine formatted a little differently than Elizabeth, just because my brain works differently than hers :)  I also always copy the self assessment to the back side and have groups do that together.

All of my files are in a google folder that you can access here.  If you download the file it will open in word.  Also there are many shared talking points available here.

Did anyone else experience my struggle with talking points?  If so, what have you done?  If not, how did you set your students up for success?

-Kathryn