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

#TMC14 Things I Shared

Sarah Martin (@Sarah3Martin) and I met with the administrators from our school to share some of our highlights from #TMC14.  I figured I'd give an overview of the things I shared as it will be a good summary of TMC.

Talking Points (shared at TMC by Elizabeth)


Talking Points was the biggest take-away for me.  If you haven't already, please go here and print off the instructions and one of the talking points and find 2-3 other people and just DO IT!  I am so excited to try this in my classroom.  I love that talking points gives ALL students a voice and requires ALL students to listen to their peers.  This is something we need to teach to our students, and talking points is a great way to facilitate this.

Math Maintenance (shared at TMC by Kathryn @iisanumber)

Kathryn used Math Maintenance as bellwork, but I am seriously considering using it as homework this year.  It would help me to review older material with students regularly and to prepare them for what is coming in advance.  It might also help me prepare students for a re-assessment on an older learning target to ensure retention.

Here is Kathryn's post on Math Maintenance.

Desmos Lessons

I shared desmos.com and a little bit of what it can do as well as teacher.desmos.com.  Mostly I shared their vision for providing these things for free forever.  It isn't to the point yet where it can do everything I need, but the idea that there are people out there talented at creating this sort of thing for our students is awesome.  And I believe it really helped to demonstrate to my administrators what kind of people go to TMC.  It was a picture of how awesome our community was.

My Session

I shared a little with them about the session I led on intervention strategies.  I wanted them to know that I appreciate the opportunities they have given me, and that not all teachers get those opportunities, but those are signs of how we care for our students.

After hours productivity
One thing that makes TMC stand out from other conferences (not that I've been to a bunch of national math teacher conferences) was that the after hours talk was productive.  Outside of sessions it was always possible to find someone to discuss teaching math with you.  At breakfast, lunch, supper, and well into the night there was always a good conversation to be found.  And usually you had to choose which one you wanted to participate in the most, which was often a big challenge!

Sarah will be shared about Embodied Mathematics, plickers, Nix the Tricks, and Formative Assessment Strategies.

What was really cool about sharing with them was watching their attitudes change as they heard more about TMC.  They were willing to admit that "Twitter Math Camp" didn't sound like much more than a super-fun weekend with geeky people, but at the end they were astounded and excited by everything we had learned.  They were shocked by the wonderful community of math teachers that we have found and how that community can help us become better teachers.  I think each of them walked away with something that they were still pondering and wanting to share with others.  I call that a win!  (Even though they might still think we are strange for enjoying talking about teaching math every minute for 3 1/2 days!)

-Kathryn

Reflections on RtI

We spent a major part of our year studying RtI at my school, and we were asked to do a reflection.  I am sharing part of my reflection for my post today.

Identify next steps needed in your district or school to prepare for use of this approach.

                There are two things I would like to see done to help facilitate effective RtI at the high school.  One of them is a real effort to identify root causes.  As was emphasized in the webinars, when students are not being successful it is important to identify the root causes so that we can try to address those rather than the side effects of the root causes.  This can be a very challenging task, and likely we will not succeed every time.

                Currently I feel as though we often address behavior issues with academic interventions.  These attempts to intervene do not get at the root cause and therefore do not actually help solve the problem.  So even though it will be challenging to identify the root causes, and even more challenging to provide interventions, it gives more hope of success than what we currently have in place.

                The other thing I would like to see happen in order to facilitate effective RtI at the high school is implementing an enrichment/intervention period during our day.  I can see many ways of making this work, but all of them would be a challenge to set up and implement.  All staff would need to be involved to make it successful and all would need to be committed to making it valuable for students.  The enrichment opportunities would have to be things that students would be interested and willing to dig in to that are more than and outside of what they get in the classroom.  The intervention classes would have to be additional instruction for the students, not study hall.

                I believe implementation of these two things could have a drastic effect on the success of many students at our school.  They would both take a lot of work, but they would show that our focus is on the students and creating a system that supports them as learners.

What changes would you make if you could to help implement appropriate response to intervention?

-Kathryn

#MTBoS30

12/30

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

Coteaching--For Real!

At semester, when schedules were rearranged, I got a new opportunity.  We fiddled with a few things so that a special education teacher and I would be able to coteach an intervention class.  She has been involved in our project with the AEA, and as we were continuing to have conversations about how to help the students, it became evident that this was something we both thought would be good for the students.

It has allowed me to serve more students during the intervention time than I did previously; and with less stress.  We arranged it so that some of our lowest students are in the intervention class together.  We have 12 students and 2 teachers.  It is such an awesome opportunity for me (as a gen ed teacher) to have so few students at a time!

We had some conversation about how best to coteach, because it is not very common in our school or even in our area of the state.  But this teacher is also a reading teacher, so we thought it would work well to have her do vocabulary and then I can work on the content for each of our weekly units.  Here is a breakdown of what our week looks like:

THURSDAY:

• Opening Task:  fluency practice
• Vocabulary (as a class we make flashcards for our vocabulary words for the week)
• Very simple intro to the content

FRIDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

MONDAY

• Opening Task:  counting circle
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

TUESDAY

• Opening Task:  fluency practice
• Split Class:  Vocab and Content then switch so all students get both
• Finish content work
• Exit Ticket

WEDNESDAY

• Opening Task:  counting circle
• Vocab and Content assessment
• (every other week we progress monitor)

Most of the ideas for how to structure this came from the project with the AEA.  We just manipulated it to fit our situation best.  Let me know what you like or what you would change if it was you!

-Kathryn

Quizlet

I need to get back onto the blogging wagon, and I have been trying unsuccessfully.  So instead of blogging about something thoughtful, I'm just going to share something I learned about at our PD technology day on Monday:  quizlet.com

On this site you can create "sets" of flashcards and study them in many different ways.  Since I've been working at pushing vocabulary in my intervention class, I decided that this would be something to try with them.  Some of the reasons why I decided it was worth trying:  it has a math option for "language" and you can add pictures to the flashcards.  A set can be public, so a set I create my students can use to study.  Also there are apps available for both android and apple devices.

So I created a set for students for this week's vocabulary and had students create an account and join the class to practice for a while today.  We are a google apps school, so I had students use their google account to create a quizlet account.  Then I had them join my class so they could easily access my set, but you can share it by link like this:  Variables and Expressions Set.

What I like is that the students can do several things with the flashcards:

• use them as flashcards...front - back - front - back - etc
• "learn"...it gives definition; student types in word
• "speller"...it says word and gives definition; student types in word
• "test"...set up a test with x fill-in-the-blank questions, y matching, z multiple choice, and w true-false
• "scatter"...a matching game where students drag word and definition together; if it matches they disappear
• "race"...definitions move across the screen and student has to type in the word before it gets across; speed GRADUALLY increases

I think both of the last two will keep a rank of the students and that helps encourage some healthy competition.  I played first so they would try to beat me :)  (However when using the app it doesn't record their scores in comparison to the rest of the class.)

I can think of a lot of things this would be useful for, but you can figure it out too.  So far I'm using the free version, but a better version is available for $15/year or even better for $25/year.  

-Kathryn

Integer Work

I hadn't planned on doing much with integers and order of operations, because I really wanted to stick to the Common Core curriculum.  However, as things got going I began to see integer operations really hurting my Topics students.  So I decided I really did need to backtrack and do some work with integers.  Here are some of the things we've done so far:

Manipulatives:  We worked with little pieces to show addition of integers.  I made a set of these for each of my students and had them show things like (-5) + 2 and (-4) + 10.  I even encouraged them to show me two things that added to 5 or -1.  They thought that sounded hard, but once they tried they realized it was easier than they thought it would be.  One student even commented "That was easier that it sounded!"  Slowly this has lead to drawing + and - signs instead of actually using the pieces, which is just as valuable.  I think this aligns very well with what the students have seen from the 7th and 8th grade teachers as far as integer addition.

Integer War:  Thanks to Lisa's post, I decided to play Integer War with my students.  I created a file for them to use to keep track that I thought would help see their progress.  I even have a picture of my practicum teacher working with them.

When kids finished their first game instead of asking, "What do we do when we're done?" They were asking, "Can we play again?" And at the end of class in order to get them to clean up I had to say, "I will not write you a pass to second hour.  You must leave now."  I think this was the best thing for them ever.  I even had two students come in during homeroom later to play their 5th game to determine an overall winner.

(With an odd number of students, I got to play a game, too.  I could do this because my practicum teacher was walking from group to group ensuring that they were on track.  Lucky to have 2 teachers in the room!)

Grudge:  Sarah's post reminded me of Nathan's post about the most fabulous game ever.  I had played it once at the end of last year, but had forgotten about it over the summer.  I decided to play with my students.  They loved it!  And it allows for lots of different challenge questions that all kids try because they want to get someone back.   I did have to make a modification this year.  The kids were taking  FOREVER to choose who to erase an X from and get back to their seats, so I timed them and said that if they weren't back in their seats then I would erase an X from them.  This got them scampering back to their seats right away (even if they were out of Xs).

The kids have been asking to play again every day since.  I think that is a good sign.  I want to find a good balance of when to play and when not to, so I keep telling them I'm waiting for the perfect time.

That's mostly what we've done for now.  Next week we will add subtraction of integers and parenthesis!  We might play Integer War again with subtraction.  I think that would be good for them at some point, but we do need some more instruction and "basic" practice first.  I'm looking for good subtraction of integer lessons.  Throw any ideas my way :)

- Kathryn

Day 1 Lessons

Build up:

I had all summer to plan my first few days, but I just couldn't find the perfect thing.  At my school, all teachers are required to hand out the syllabus day 1, but I didn't want to spend the whole time reading it.  Last year I focused on procedures at the beginning, this year I wanted to focus more on relationships with my students and math.  I have heard from all my blog-reading that it is OK to save procedures for a few days.

So I set out to search for some good lessons.  While watching the #globalmath session My Favorites (you can view it here), I got lots of good ideas.  I knew right away that @misterpatterson 's Spaced Out sticky note lesson (you can find it an other lessons here) would be AMAZING for my intervention students.  It would address number sense and the usefulness of Algebraic thinking.  It is a perfect fit with my first unit as it also asks students to create an expression for a situation.  There were lots of other great ideas, so I followed links provided by @jreulbach to look at what other people have done on the first day. I ended up really enjoying the By the Numbers introduction that I found from @AmberDCaldwell here.  I thought I could tie it into the decorating ISNs I have seen.

So here's what I did:

For my topics/intervention classes, I modified Spaced Out to meet my student's needs a little bit better.  Here is a link to the document I used:  Spaced Out (modified by me) .  I gave a brief introduction to myself and the class and then had the students begin working.

Spaced Out (modified by me)

I really had to clarify the rule about the space on the ends being the same as the space in the middle.  It seemed a little hard for them to understand, but once they figured it out they started going.  No one was super excited about it, but when they got close and I told them they weren't being accurate enough, then they started to get that determination to succeed.  I only had 1 group (out of 4-5) in each period "pass" level one on the first day.  I made them write notes to themselves so that they would be ready to go on Friday.  For the most part on Thursday the only assistance I gave was checking their measurements and asking questions like:  What have you tried?  Why didn't it work?  Was it too much space or not enough?  What are you going to try next?

After watching my students working through levels 1 and 2 on Thursday and Friday, I wish I had added a level between 2 and 3 that was something like this:  A table is 300 cm long, how much space will be between the five sticky notes?  Hopefully that would push them toward think algebraically instead of just through guess and check.  We will finish it up on Monday.  I set them up at the end of the day on Friday with a hint about calculating the space rather than guess and check; I'm hoping that will get things moving a little more quickly on Monday.

In my Algebra classes I used a Mrs. Freed By the Numbers matching activity to introduce myself a little bit more.  Here is what they saw:

In their group they had to assign a number to each description.  After we finished I asked them to think of 5 numbers that describe them and share them with me.  That was their "exit ticket" on day one.  Hopefully on Monday we will turn their 5 numbers into the back of their ISNs :)

I did also introduce ISNs and give them their syllabus.  I showed them how it folds up so that we can tape it into their notebooks.  Looking forward to doing that with them on Monday when I set the deadline for having a composition book!

Thanks for reading about my first days!
-Kathryn

Presenting our Plan

We were asked to present our plan for implementing instruction at three levels at our Day 3 meeting.  Not sure why us or what part of it most people are interested in, but we met after school today to look over our plan again and discuss our presentation.

There are two main aspects of the plan:  assigning students and scheduling classes.  I will give some highlights of each below.

Assigning students to the Tier II and Tier III courses:

• Students who have addition math instruction as a requirement of their IEP will receive Tier III instruction
• Students will be identified for intervention (Tier II) using a variety of sources:  Algebra Aptitude Test, IA Assessments, Previous Course Grade, Teacher Recommendation.  We will likely choose a cut off for each of these and then flag students who are on the list for 3 of the 4 identifiers.  This may include IEP and non-IEP students.
• Our principal, the math team, the special education instructor, and AEA representatives will all participate in selection process
• Currently we have no official universal screen or progress monitoring in place

Scheduling, Planning, and Instructing Tier II and Tier III:

• We are on a 7-period day, with 51-minute class periods (and a 17 minute homeroom)
• As the Algebra teacher, I will give up all my non-Algebra classes next year (currently consisting of 2 periods each day) to provide tier II instruction.  So I will teach 4 periods of universal instruction and 2 periods of intervention.
• I have requested that the tier II classes be schedule at the beginning/end of the day so that all students in the class will have had same universal instruction
• My dropped courses will be taken on my the 2 other mathematics teachers we have by increasing enrollment in advanced classes and no longer offering Pre-Algebra
• Tier III will be given to students during their Guided Studies time.  It will mean of their 51 minutes of GS, 30 minutes each day will be Algebra instruction given by the Special Education instructor
• I will be planning (with the help of all my peers in this project) the universal, tier II, and tier III instruction
• We have requested 1 day each week to collaborate on the instruction for tier III students
• Students will receive elective credit for tier II and tier III algebra.  Will be unable to shift in and out of course as needed (not seen as a potential problem).
• We have a special education associate who will be able to facilitate instruction during universal, tier II, and/or tier III

Why?  I honestly think that is what some people want to know.  "Why are we willing to go to all these lengths to provide something like this?"  I would have to say because I can see that my students need it.  I have many students in Algebra currently that I desperately wish I could provide this opportunity to.  I see the need and I address as good as I can, but without the additional time and the smaller class sizes I cannot do all that is necessary.  

These are the ideas we are going to try to get across within our 10-minute time frame, as well as providing an opportunity for others to ask questions.  I hope this will help others find a way to make this successful in their schools as well.

Day 2

Our second meeting (also known as "Day 2") was packed full of thought-intensive analysis of multiple things. We started by discussing "Understanding by Design" lesson planning, where focus begins with the desired result.  There are 3 stages of this planning method:  the Desired Results, the Assessment Evidence, and the Learning Plan.  This process can be challenging because only after a long time looking at the standards and choosing an assessment method can the instruction planning actually begin.  As teachers it is hard to wait so long to plan instruction!

After discussing this method, we broke into groups and began unpacking various standards from Unit 1 of Algebra 1 as defined by Appendix A of the CCSS with this template to guide us.  This is really challenging!  At first we were supposed to base it off of our professional understanding of the standard (which is not always clear), and discuss our understandings.  Then we could look to some other documents, but there are few resources available from the authors of the CCSS to help us unpack them.  We spent all morning doing this!  It felt very unproductive to me for two reasons.  First, because we were working in groups with people we didn't know very well, and so it was hard to respectfully critique each others' ideas.  And secondly, because we did not define "understanding" and "knowledge" prior to getting started.  All in all a challenging morning for me.

We were actually supposed to do one more thing before lunch.  Choose one of the practice standards to focus on for the rest of the year--yikes!  I remember hearing someone say that the first four are the most important, so we chose to go with #1:  Make sense of problems and persevere in solving them.  Then we had the opportunity to change the rubric for it.  The rubric we were given was not structured the way I like to have rubrics structured, so I redesigned it with the help of my coworkers present at the meeting.

After lunch we created a proposal for how our district should implement Tier II of the instruction.  We had already had quite a few conversations with our principal and other math teachers in our district, so I felt as though the proposal was just formalizing all of those conversations.  The goal/plan is for me to teach only Algebra next year.  Four periods of Algebra (tier I) and two periods of Strategies (tier II), while a special education teacher would teach the students receiving tier III instruction during their guided studies time.  My hope is that I can have the "strategies" courses at the beginning/end of the day, so that the students have had the same instruction from the Algebra class.

Once we completed that, we discussed the benefits of standards based grading.  My district is already in the process of developing standards based grading, so we have an idea of what it is, what it might look like, the benefits, and the drawbacks.  However I still found this conversation to be very rewarding.  I jumped into standards based grading this year without all the background work that teachers in my district have done, so it was good for me to step back and remember why they chose to move in this direction.

The last thing we did is to split off as Algebra teachers (special education teachers did something else) and look through 7th and 8th grade standards that we might have to teach during the transition to the common core.  These are the standards that are necessary to meet the Algebra standards, and may not get mastered in 7th and 8th grade.  I think it was important to acknowledge that it is a transition to the common core, because at times I feel pushed to move my students over to it too quickly.  It is important to get there, but we also have to remember that we are in a transition time.

So when I left Day 2, my brain was working in many different directions, but I felt that all were beneficial for the future of our students and their mathematical learning.  I sometimes just wish that it didn't take so much work, but in the end it really does.  In which case it is important to remember the purpose--student learning!

Day 1

I attended day one of our Tiered Algebra 1 Action-Research Project.  We got an overview of the project including the components that will be involved:  Iowa Core Standards, Standards-Based Grading, and Tiered Instruction.

We spent a lot of time discussing the tiered instruction because that is the newest idea for most of us.  This is based off of RTI, or Response to Intervention, a method used to keep students performing at grade-level and provide assistance when they fall behind.  There is not much information published about implementing RTI at a high school level, especially for mathematics, so we took a look at the basic structure of the program.

We will provide three tiers of instruction.  The first is universal.  All students receive the first tier of instruction.  The second tier is for some students (10-20%) that for a lack of a better phrase are "chronic mathematics strugglers".  These students need to receive an additional 30 minutes of instruction everyday in small groups (7-10 students).  The third is for a few students (1-5%) who have IEP math goals, with additional mathematics instruction written into their IEPs.  These students will also receive an additional 30 minutes of instruction everyday in even smaller groups (1-3 students) with a special education instructor).

Oh to think of all the scheduling issues this creates!  Thankfully our math department had already been discussing the need for intervention and brainstorming ways to make it work.  All that brainstorming with this guidance for how best to help those students allowed us to see this not as an impossibility, but a challenge we would have to work around.