Category Archives: Algebra 2

Frustration with Class Attendance #junechallenge 1

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I have had so many thoughts running through my mind the past 2 weeks – wanting to put them down, yet trying to get through the final days of school.

I struggle with Algebra 2.  It is frustrating to me – SOOOOO much stuff jammed into one course.  I feel there is simply not enough time to really develop true understanding of many concepts.  I try to pick big ideas – focus on enduring skills –  from our curriculum that best suits our students in Room 123 and search for strategies that will best meet their needs, helping to move them forward.

As I look at these students at the beginning of the school year, three are meeting college readiness.  Several fall within the 10-15 ACT score range and majority in the 15-20 range.  Majority are down on math, do not enjoy it and feel there is “only one way to get THE right answer.”

I recall one particular day in class – a student stating, if you don’t get what the teacher said, they move on without you and you’re stuck, set up to fail.  This.makes.me.sad.

Our goal: to make it accessible, less painful, allow students room to think on their own, discuss their claims / strategies, test one another’s suggestions and move their thinking forward.

 

 

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A look at 3 years of EOC results shows improving results.  Is it enough?  Not sure, I’ll need to look at our district projections.

The 4th year is hypothetical – 20% of  students missed the next achievement level by 1 question.  1 question.  This is frustrating to have several that close to moving up another step, yet barely miss the mark.  Yet, we’ll celebrate their growth anyway!

I am concerned about this though because I experienced a high level of frustration the last quarter of school.  Added to weeks of snow days, no spring break to make up some time, it seemed our class attendance was the worst in recent years.  In the last 9 weeks prior to EOC testing, there were 33 days instructional time was interrupted – either by scheduling presentations, other state testing, benchmark testing, college visits, competitions, field trips, field trips.  The day prior to EOC testing, there were eight students on a reward trip.

Don’t get me wrong – student life and involvement is imperative – some of these activities are the only reason a few students even make an effort to be at school.  I would never want to take away these opportunities – they deserve the best.  However, I feel that our instructional time is valid, important and needs to be protected in a sense.

I am not a worksheet kind of person.  So much of what we do in Room 123 is hands-on, small groups and class discussions.  Its impossible to capture those same learning experiences when you’re not there. Trying to continue in-depth discussions and learning tasks was merely impossible.   There was no continuity with 7 students out one day and 6 out the next with a different 8 students out on a third day.    I failed because I gave up.

What if I had kept pushing through?  Maybe those  students would have reached their next level.

I’m not trying to whine – I’m looking for strategies – how others handle these same frustrations.  This summer, I intend to find or outline a resource, update an old class blog – something to provide for those students who are absent for whatever reason.  I’ve tried Edmodo (its okay), Class blog (very few students utilized it).  What about evernote?  One Drive notebooks?

So, how do you handle it when a students asks “What did we do?  What did I miss yesterday?”  How do you fill-in  for in class learning tasks for your absent students?

 

 

Combining Polynomials

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This is like something that others have done often.  Maybe I have even used something similar at times in the past, but today a group of students had a big a-ha moment.

We have reviewed the basic polynomial operations and like robots they can do it well for the most part.

The last 10 minutes of class, I popped the graphs
f(x)=x+2 and g(x)=2x-1 on the board.
I pointed out specific points, asking for their sum and recorded on the board.

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2+-1
1+3
3+4
8+8…
This graph only shows part of our discussion.

Next, I graphed a purple function f(x)+g(x).

“Holy shoot” was exactly what a student said. Yep, they edited the version just for me.  But there were several ah’s and oh’s. 

Thanks to Desmos…they could see the math they’d been doing on paper.

We combined f(x)+g(x) on paper to get 3x+1.  I graphed it and they were amazed it hit our points.

I know this isn’t so amazing for many, but the look on my students faces today…they got it.

I am looking forward to more…

Musical Chairs #eduread

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Thanks to #eduread chat last night with @druinok and @algebrasfriend – a simple, no prep idea to get students out of their seats…Musical Chairs… something @druinok shared she had done in some of her classes last week. 

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Today, after a mini quiz, we had less than 15 minutes left.  Students picked up a worksheet (given a scenario, they were asked to match a graph).  I chimed up some good ol’ Bluegrass from The Boxcars and Dan Tyminski.  Basically they wandered around the room, music stopped and they grabbed a seat, paired up with someone and discussed scenario #1. 

When everyone had a response marked, I started the music up again.  They smiled as they mixed around the room – some grumbled at my music choice.  Music stopped, they grabbed a chair, paired with a new person and discussed #2.  There were disagreements-(yeah!)-some nice math talk going on.  We continued right up until the end of class.

After lunch, the next class came in asking if they would get to play musical chairs, too. Cha-ching.

Thanks to my #mtbos peeps for adding a bit of joy to my classroom today!

#made4math Monday: Learning Target Quiz Cards

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Last year I wanted a file for each course, with sample questions addressing the learning targets to use as either an intervention or for retake quizzes.

Different suggestions were made in a discussion on Twitter regarding organization, offering different levels of questions.  This morning, I am trying to plan out my format.

Here is what I have come up with so far:

Supplies:

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Standards/Learning Targets
Index Cards
Index Card Dividers (Tina suggested coupon organizers for built in dividers)
Markers/Pens

I chose a standard.  Labeled my divider and thought it might be handy to write out the actual standard.  (Yes, this could be done with printed labels).

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I am using level colors that coordinate with our Discovery Ed. Benchmarking system.
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  L1-red, is the very minimal; L2-yellow, shows more understanding;

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L3-green, is where I want to get everyone (this set came from Illustrative Mathematics Project); L4-blue, are open questions for this example anyway…may need to change this later.

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I am including answers on the back for guick-check.

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These are a quick, rough sketch…trying to iron out my goal, how I want to use them.

My idea is to have a coupon/photo organizer for each unit I teach.  Use actual learning targets from our unit organizer in order to move Algebra 2 closer to SBG.

Suggestions for improvments or your own experiences are welcomed!

Inverse Functions #MTBoS30 Post 20

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This week we wrapped up our school year with 2 final teacher work days.  One day our department had some time to reflect onmour year.  One of our big issue is the immense amount Kentucky requires in Algebra 2.  Its nearly impossible to ‘cover’ it all, much less allow struggling math students time to process and develop a slight understanding.

I, personally, don’t worry with getting it all in.  I attempt to make the students’ time worthwhile and hopefully they leave with some deeper understanding about concepts rather than a list of procedures only 30% may be able to recall at any given time.

Anyway, we attempted to pick out 10 Big Rocks for our focus next year..the non-negotiables in a sense and that is where we will begin.  Sure we will have the “extras” ready should we achieve at a faster pace than expected.  But the goal is to truly develop reasoning and conceptual understanding of our Big Rocks.

While looking over the outline, there were a couple of things I remember thinking we needed to ensure we focused on during our functions unit.  1) composition of functions, not just in equation form, but to make sure we look at them numerically in a table of values and graphically as well. 2) a different approach to finding inverse functions.

It was Sam’s post that made me wonder if this way would make more sense for our students.
Looking at “x” think about and list order of operations.  Then, in reverse, list inverse operations and apply to x to get the inverse function.

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Inverse operations and inverse order.
Is this a strategy others use as well?  A couple of colleagues seemed to really like this.
Wondering what situations it may not work…or at least reasons I shouldn’t use this approach.  Is there anything that follows this would cause issues for my students?

Algebra 2… Outline #MTBoS 30 Post 7

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I teach Algebra 2.  At times, it feels so contrived and meaningless.  I wish I could infuse some magical potion that would ignite my students thinking.

Wondering if anyone begins with Probability and Statistics?  Sequences/Series?

It seems we could develop some strength in students numeracy with different types of  probabilities… those unions and intersections of sets.  Would this possibly help when reading reviewing compound inequalities/seep over when teaching systems?

As for stats…just some good old data collection early in the year…to model those common functions, giving students a concrete visual for a connection like Wiggie Growth when we begin exponentials.

And patterns.  Who doesn’t love exploring patterns?  Students can recognize them, describe them, continue them.  Why not begin the year with units that are both fun and challenging?  It seems these end up at the end with no real time to play and enjoy.

Just wondering if anyone’s curriculum begins this way? Or at least outside the traditional one?

Gallery Walk #ppschat Challenge

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A common theme in many chapters of Powerful Problem Solving is Gallery Walks. Several techniques are offered throughout the book, but the common goal is to allow students to view their classmates’ approaches to problems.

One of my faults with online book chats is lack of follow-through. I can sometimes use an extra nudge of accountability. There are often so many great ideas and strategies in the books we are chatting that I get overwhelmed and not sure where to begin. Advice: pick 1 thing. Try it. Reflect. Revise. Try it again.

So here is my attempt at a gallery walk. I simply cut apart a pre-assessment for a Formative Assessment Lesson and each pair of students taped it to a large sticky note, discussed and responded. I was confident in many of the questions, but my goal was to identify the few some students were still struggling to understand completely, mostly questions involving transformations.

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1. The large majority are fine with creating a possible equation, given the x-intercepts.

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2. Initially these students tried -6, -4 and 2 as their intercepts. I asked them to graph their equation then reread the instructions. Oh. They had read write an equation, looked at the graph for possible intercepts and failed to read the y-intercept of (0, -6). One quickly stated the connection between y-intercept and factored terms and was able to adjust their response with ease. I believe it happens often to see a graph skim question and think we know what we’re supposed to do, only to realize skimming sometimes results in miseed information.

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3. Within the lesson, many students quickly realized when a factor was squared it resulted in a “double root” and the graph would not actually pass through the x-axis at that point.

The 4 transformations seemed to causes the most disagreements. These were the ones we discussed folowing our gallery walk. However, it was during the gallery walk most students were able to adjust their thinking.

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4.i. Listening to students as they were at the poster helped me realize there was not a solid understanding of the reflection across x-axis and maybe we needed to revisit. Possibly, they are confusing with across y-axis?

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ii. A few students disagreed initially, but the convo I overheard was addressing that changing the x-intercepts was not sufficient, they looked at the graphs, then said, the functions needs to be decreasing at the begiining, that’s why you have negative coefficient.

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iii. Horizontal translations always seem to trick students up. One disagreement actually stated ‘they subtracted and did not add.” Of course, we definitely followed up with this one.

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iv. This pair of students argued over which one was right. The expaned version or factored form. Simple, graph the new equations and compare to see which one translates the original up 3 units.

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A1 & A2 I believe they’ve got this one.

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B1 & B2 some confusion here due to the extra vertical line in the graphic. This student was also interchanging graph & equation in their statement.

I thought the gallery walk was a good task to overview some common misconceotions. It was not intimidating, students were able to communicate their ideas, compare their own thinking to others. I truly tried to stand back and listen. They were on task, checking each other’s work. Each station allowed them to focus on one idea at a time. They were talking math. Most misconceptions were addressed through their discussions or written comments.

Having a moment to debrief the following day highlighted the big ideas students had addressed the previously and reinforced the corrections they had made. This was so much more valuable than me standing in front of the room telling them which mistakes to watch for. Their quick reflection writes revealed majority have a better ability to transform the functions, which was my initial goal for the gallery walk. A few still have minor misgivings that can be handled on an individual basis.

Number Talks 12 x 13

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I was cleaning up some files this evening and ran across these snapshots from a Number Talk in class a while back. 

Are all of them the most efficient?  For me, no.  However, if it made sense to that student at that particular moment, then it was most efficient for them.  I appreciate the various ways they consider “building” the product.

  I wanted to see their thinking on 2 digit multiplication to link back our unit on polynomial operations.

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Yes, they all had a calculator available, but my question was, how do you know?  As I learned from Steve Leinwand, “Convince me.”

Complex Numbers and Speed Dating

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About 3 years ago, I ran across this post from Kate Nowak called Speed Dating.  I have used it or a version many times.  Students do love it and often laugh about going home and telling their parents they speed dated in math class today!

She suggested placing desks so students are facing one another like this:

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I used 2 colors of markers (one purple, one blue).  Each card contained one problem involving arithmetic, simplyfing complex number expressions, conjugates, graphing in complex plane and finding the modulus. I used the other color marker to create a parallel set of problems.   Each student in one row received a problem from the blue set and the other row from purples.  This enabled every student to experience at least one of each type probelm.

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Students solved their problem, I confirmed or asked questions to clarify their work.  They became the expert of that problem.  Every person they “dated” would solve their problem.  As Kate’s post mentioned, you can easily assign problems to specific students to differentiate levels if needed.

Pairs would exchange cards, working the given problem.  The expert would check the other’s work, confirming or asking questions to help them correct any mistakes.  They would get their problem card back.  Front row rotates to next person.  Repeat.  By the end of the round, each student has practiced a variety of problems with immediate feedback as needed.

Exit slips revealed mistakes due to not paying attention to a given operation; a few need reminders of i^2 becoming -1 as one more step to simplify further; several still not comfortable with using conjugate to simplify rational expression of complex numbers.  Students enjoy working with others, an opportunity to be out of their seats.  Its a chance for them to ask questions of their peers in a smaller setting as opposed to whole-class.

Here is another idea…the Placemat Activity @cheesemonkeysf  incorporated to practice arithmetic with complex numbers.  Its amazing how quickly one forgets great little spins to use in the classroom.  Thank goodness for the open sharing of MTBoS to remind me!

INB Unit Organizer

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I wanted to create a unit organizer than encompassed several aspects but would also be narrowed to one page, fiting in to the INB.  Here’s a list of what I wanted:

vocabulary
unit overview/schedule
learning targets
record of assignments
track their own assessments/learning
place to record questions/big ideas
opportunity for end of unit reflection

Here is what I arrived at for a first attempt, copied front to back and folded in half, this is the order students will see the booklet. 

The vocabulary pre-assess was a great tool.  I saw this idea over at Math = Love earlier in the summer.  It went so well. It only took students a couple of minutes to self-assess their vocabulary knowledge.  As I walked around, I was able to see several terms had 3s & 4s.  We compiled a list of our 1s & 2s words.  I explained, as they learned a word or gained better understanding, they should go back and put a +.  Before the end of class, students were asking if they could go ahead and update their chart.

If possible, maybe completemthis part a day before beginning a unit, in order to make needed adjustments based on student responses.

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I included the correlated CCSS # for each target.  Eventually, these may be beneficial when looking online for a resource on a specific standard.

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I am not fully satisfied with this chart yet. Assignments made for specific targets can be listed, a note if completed (stamp) and place to monitor their assessment for each.  A second line has been included in case RTI/enrichment is needed.

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Finally, the back side has a place to record reflection.  Ideally, I would have them complete the reflection at least 2 days prior to unit assessment, allowing to address any needs the following day, prior to assessment.

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As always, this is a work i  progress, suggestions and ideas are welcomed!
PDF:  http://db.tt/DWfJUqLL
Foundations in Geometry doc

Intro to Matrices:

Intro to Matrices pdf
Intro to Matrices doc