Math Teacher Must Haves

Due to a previously mentioned grant my school received, I basically have free reign for supplies/resources for the math classroom. I obviously have no idea what I need. So here's what I currently have:

Colored Pencils
Electric Pencil Sharpener
Graphing Calculators
Individual white boards
Document Camera
2 Printers (1 is color)
4 Student Computers (that we never use)
Kagan Timer
Student Response System (Clickers)
1 Flip Video Camera

Basically I want supplies that are durable, sustainable, and reusable. But then again, I want to take advantage of the money while we can. Here are the ideas I've found/heard so far.

Classroom Laptops (Don't know how to use them)
Ipads (Have one, not really a fan, rather have laptops)
TI-Inspire and Navigator (scared of these!)
CBL/CBR data collection devices for the TI 83/84 (not sure how to use this)
Deluxe Probability Kit
Geometry Reproducibles (Book)
Folding Shapes: Solids and Nets
Geometric Solids (Are these the same as the above?)
Geoboards (Recommendations? What size do I need?)
Algebra Tiles (Recommendations?)
Easy Smartboard Teaching Templates (Book)

Any other ideas? Professional development is kind of iffy so for now I'm looking more for manipulatives, books, supplies, etc.

What should every math classroom have?


My Favorite Lesson of All Time!

I've never taught a unit on transformations before so I started from scratch. Wait, all my lessons are created from scratch. Just sometimes it's someone else's scratch. I digress. My unit only covered reflections, translations, and rotations and I discovered I suck at teaching rotations. But, my translation lesson went over really well and my reflection lesson was probably the my best lesson idea ever!

Here's what I did. In explicit detail. With bullets. Download PowerPoint here first.

  • Using the questions posed [slide 1] have students answer and discuss. You should get some pretty interesting information. Sum up the discussion by telling students that most fashion models usually have very symmetric features. Also, a study was done using babies. Pictures were put up and babies tended to stare longer at the faces that were most symmetric, alluding to the fact that symmetric faces are more attractive to the eye.
  • [Slide 2] names the objective. [Slide 3] Have students guess which face is the real one. The real face is always the one on top (this is for you to know and them to find out!). The bottom left is the left side of the face reflected and the bottom right is the right side of the face reflected. As you go through [slide 3] through [slide 9] discuss the similarities and differences. Ask students which pictures look realistic and which don’t. Point out birth marks, shadowing, eye shape, mouth shape, etc. Basically, make the conversation as interesting as possible.
  • Now go to your internet browser. Ask the students to pick a celebrity famous for being attractive. Google their name to find a picture. The picture needs to be of them facing forward and preferably with both ears showing (which is harder if the person is female). Classroom management tip: You might want to do this ahead of time or where the students can’t see. You never know what type of picture might come up! Copy the url to the picture you’ve found. Then go to the website http://www.anaface.com. Paste the url into the box that says Enter Image URL. Click submit. Then place the dots as directed. Have the students help guide you. Then click next. The site will analyze your picture and talk about vertical and horizontal symmetry. This is a good place to introduce those as vocabulary terms as well as introducing a line of symmetry.
  • [Slide 10] Put up your picture. Your face. I inserted a 10 x 10 table with a red border and no fill over my picture. Now we start talking about where the lines of horizontal and vertical symmetry would be. Ask the students how we decide if the eyes are symmetrical. What about the ears? We want to lead students to measuring the distance from each eyes to the line of symmetry and comparing the lengths.
  • Before advancing to [slide 11], I had students guess what rating the site gave me. I had previously analyzed my own face and took a screenshot of the website. I put it on the slide to save class time. We want to the next slide and talked about the different aspects of symmetry. I used my own face so that no one else would be offended by the negative comments.
  • Now pass out the notes worksheet. I picked celebrities that I knew my students liked. Please change any of these to pertain better to your class. Have students use a ruler to draw a straight vertical line. Then draw dots in the center of each eye. Use the centimeter side of the ruler to measure the distance from the left eye to the line. Then measure from the right eye to the line. Repeat for each celebrity. Students may get bored doing the same repeated action. If so, jump straight to the geomirror. Have students put the mirror part on the line of symmetry. Have them look at the left and the right side to see the difference in symmetry.
  • Have the students do the back of the worksheet on their own, using the geomirror. For left-handed students, they will need to turn the paper upside down.
  • To end beautifully (pun intended), have the students complete the exit slip [slide 12] on scrap paper. This brings us back to the beginning of our conversation.

OMG if the students did not eat this up!! During this whole unit, I heard students talk abut how math was actually fun now and they looked forward to this class and it went by so fast. It was encouraging to finally find something that they truly enjoyed.

And for the record, their exit slip answers brought out really good comments on what their opinion of beauty was. I shared ALL of them the next day with the whole class.

Students also loved the geomirrors and borrowed them throughout the day to use on their own pictures and yearbooks and so on. They wanted to use them every day!


Does It Work? Wednesday

I sent this as an e-mail to a group of teachers but I would also like to pose it to you my friends!

What do you know about College Preparatory Math?

I am the only algebra and geometry teacher at a small school and I am only in my second year of teaching. I have been creating my lessons every night on my own, loosely based on common core standards and the textbook. Except I hate textbooks. I am working with an instructional coach for the first time and so I feel like other parts of my teaching are improving and I'd like to improve my curriculum as well. I'm intrigued by CPM, College Preparatory Math, and I just have some questions that I would love to have answered by teachers that are using this curriculum already. Thank you in advance for answering any of these questions and any feedback at all is much appreciated!

  • What were your first impressions with CPM and how have they changed over time?
  • How complicated was CPM to implement?
  • What changes did you see in your classroom dynamic and student behavior after starting CPM? What has the student response been to CPM?
  • Is CPM recommended for a range of ability levels, from remedial  to gifted?
  • Does it seem strange to you that CPM homework assignments are based on past concepts instead of current concepts? How does that work for you?
  • When assessing, do your tests include questions from the lesson and the homework? Did you or do you implement team testing and individual tests?
  • In your opinion, do students stay actively engaged? Is the material appropriately challenging?
  • Do students learn to better think, problem solve, and reason?
  • Do students take notes in addition to the work they do in class, as a team, with partners, or on their own?
  • Have you seen an improvement in state/benchmark test scores in a single year or over time? (I hate to ask this but it is something my administration is very focused on this year and while I do not want to teach only 'to the test', I would be doing a disservice to my students to ignore it.)
  • Are students learning and retaining information any more/better with CPM than with a previous curriculum?
  • Overall, what do you think about CPM and what else do I need to know?


    This, My Friend, Is Learning

    I really do attribute the frustration I felt in my last post to the change in weather. I felt a lot better the next day. Also, I was put on another team. Yay another meeting! (insert pom poms and back flips). We've now started student support teams. I am on the freshman/sophomore team since I mostly teach underclassmen. It actually turned out to be the most productive team I've been on yet and we've only had one meeting.

    We look at data to see which students have 5 or more absences and who are failing. Then, as a team made up of teachers, administrators, guidance counselor, coaches, and social worker, we brainstorm. We compare student behaviors in different classrooms and collaborate on ways to connect with the student, get them involved and engaged, and hopefully create some new positive experiences at school. I felt hopeful because we talked about some of the students I was so frustrated with previously.

    I recommend you go back and read the comments from my last post. What I took from them is to focus on the positive and that will change my outlook which will influence the classroom culture. Also, I know that I have improved 100% in my teaching since last year and I am offering my students the very best of me.  It is their choice to learn. I will do my best to influence that choice while accepting that I can't make it for them. And when they are ready to learn, I will still be teaching at a 100% better level than before.

    Another positive thing that I did was to have a discussion with the class that I dread the most. We talked about other teachers they like and learn from and what I gathered is that I need to do a better job of breaking things down step by step. I also need to give students more chances to do examples in front of me during class so I can correct and redirect. (I threw that in just to rhyme. My flow is getting rusty.)  I have not been assigning homework. We decided that if I assign 2-5 problems a day, I still will not letter grade them but I will check for completion. We will go over the problems in class so students can correct their mistakes. If you get 3 zero's which is basically 3 missing assignments, you get a written office referral. This is a rule that other teachers enforce which I'm not sure I was aware of, but that seems to work for the students. They agreed that the amount of problems was low enough that there really was no reason not to do it. And once again, the consistency monster roared it's head. They liked classes where the teacher did what they said they would do and enforced the rule at 3 missing assignments- no more, no less.

    What I am learning from all of this productive frustration is that, I need these feelings. Enduring these feelings is helping me get to the place I need to be in order to really implement classroom management. It is helping me to distance myself from taking every hit personally. I can now be more objective and stay firm.

    This is the way we are doing things. Each choice has a consequence. You decide. You live with the consequence. You suck it up and take it like a big kid.

    If you don't like it, make another choice. If you do like it, then keep making the same choice.

    This, my friend, is learning.


    Every Day for the Rest of My Life?

    Very frustrated.

    I don't know why this is getting to me so bad today, but it just is.

    What do you do with kids that just do not care and will not try and only put forth the smallest amount of work possible?

    We've been doing some partner work on a slope worksheet that I stole borrowed from Mimi. It's a great activity and the kids handled it pretty well. For the most part. But I had a few in each class that just copied off their partners and have no idea how to do any part of it. They don't care, they just want to be done. But I explained to them, I don't grade classwork. What is the point in copying? I told them if they plan on copying to just save their ink and do nothing because it's pointless. I explained that what we do in class is practice for the test.  I told them they can choose to do nothing but the consequence to doing nothing is a bad grade. And they stare at me.

    I keep thinking that once they start failing, they will wake up and realize that they have to put forth some effort. But alas, it is not the case! They are okay with failing as long as they don't have to do anything. I don't know how to deal with this. How do I teach the rest of the class knowing these few are falling farther and farther and behind. How do I look them in the eye when I know they are not learning and I am not doing anything about it? I am supposed to care. I am supposed to remediate. I am supposed to engage them. I am supposed to create individualized interventions. But what is the point if they aren't going to do anything? Is this a classroom management problem that I am not handling correctly? That is totally possible so you can tell me if that's true.

    I thought not grading class work and homework would help but I don't think it has. I don't really give homework, I never have, I just can't rationalize it in my head. But if we assess what we value, am I implying class work and homework are not important?

    How am I supposed to do this every day for the rest of my life? How do I face these students that are failing? And I am letting them. And then we are supposed to do RTI interventions and I am thinking, I cannot possibly face these students a minute more than I already do. If they aren't learning in my class, maybe I am the problem? But in a small school, there really is no other options.

    I do not want to lesson plan. I do not want to spend every night thinking of creative ideas and activities that they are not going to care about. I do not want to rearrange my room and put tape on the floor and set up fun stations and play games and so on when it makes no difference. THEY WON'T CARE ANYWAY.

    And a few of these kids are so far behind that I just no there is no way to catch them up. I can't do it and stay alive. How can we go back and teach so much and still move forward?

    Again, I don't know why I am so irritated today but I just can't shake it. I took a nap, watched tv, ate dinner, ate chocolate...and it still is just weighing on me.

    Is this a frustration I have to learn to live with?


    7 Country Wisdoms of Teaching

    Catchy right? These are some notes I took at our Regional Teacher's Institute.

    Although I'm not an English teacher, I do like hugging and mushy stuff. If you are allergic to that, click away. But every once in a while, some simply practical mush is good for all of us.

    If the notes seem random, it's because they are. Take what you will and chew on the rest.


    Students want to please the teacher. Often, they don't know how or lack the skills.

    If you want a behavior, teach it.

    Students desperately need to like each other and you.

    1. Slow Down

    Figure out what you must teach and teach it well.

    Every kid needs a smile. They need to feel encouraged.

    Kids need to have their physical needs met, a sense of power, freedom, fun, and belonging in order to come to school and keep coming.

    It is not the job of the teacher to fill the cup but to light the fire.

    Create memories and belonging.

    You can care about kids and still be in control.

    Know your students.

    2. Keep It Simple

    Students control their attendance, attitude, and how hard they work.

    Share everything. Play fair. Don't hit people. Put things back where you found them. Say you're sorry. Clean up your own mess. Be aware of wonder.

    Kids want to do stuff. If I'm not having fun neither are they! We need to want to be there.

    Just because we identify misbehavior doesn't mean they will change. But if we don't identify it, they'll never change.

    3. Choose a Positive Attitude

    Attitudes are more easily caught than taught. The kids are watching.

    4. Choose Your Words

    Eliminate the words 'I can't' and 'try'. Do or do not, there is no try. Try is a cue word that we use when we aren't going to do something but we won't come out and day it.

    I can't is an excuse to give up and blame someone else.

    5. Use Humor

    Have fun and laugh every day!

    6. Tell More Stories

    Using stories teaches kids about responsibilities and behaviors without making anyone feel bad.

    7. Challenge Others to Accept Responsibility


    SBG: How To Grade

    I think my issue with sbg is how to grade.

    I know my main problem with sbg is getting students to come in and reassess, but hopefully the conversations I had with 16 parents this week at Parent Teacher Conference will start to move that into motion.

    So for me personally it's the issue with grading. I started out doing two questions per skill per assessment. I created my own rubric with a mixture of C's, P's, and I's with the second question weighted more heavily than the first. But sometimes the rubric didn't serve my students well and I couldn't, in good conscience, always stick to it. Which probably implies I need a new rubric.

    But as I began to work with my instructional coach and discover second-year-teaching wisdom, I realized you all were right and I was assessing way  too many skills. I started to broaden my skills so that one skill contained baby ones. I suppose you understand what I mean. We also started to look at the ACT and the Work Keys and pulling questions from there so that I could backwards plan my lessons to lead up to hard problems I normally would have avoided asking my students. We've already established that I should plan backwards, I've just started it, moving right along...

    So my past couple assessment have only been assessing one skill but I've asked about 8 questions. How do I grade that with a rubric?

    Give each question a score 0-4 and then average them together? I thought averaging was the devil...

    Grade as usual, giving a certain amount of points for each problem, counting off, and then giving a percentage of points correct out of points possible? My twitter peeps said this puts me back into points instead of levels of understanding. But what if I assigned a range of percents to a rubric, say:

    100% =4
    90-99% = 3.5
    80-89% = 3
    70-79%= 2.5
    60-69%= 2
    50-59%= 1.5 
    40-49%= 1
    30-39% = .5

    But I guess that still isn't providing accurate information to the student because a 73% doesn't tell them what they messed up on.

    I previously tried @druinok's idea of asking 3 questions per skill on different levels but that rubric was still confusing to me too.

    Am I asking too many questions per skill? How often do you assess and how long are the assessments?

    We've been working on developing assessments that come naturally at the end of a small unit. My coach has talked to me about balanced assessments: including some more basic, straightforward questions as well as application, word problem, synthesis type of problems. And I like that. I like the assessments we've been creating but I don't know how to give an overall score when I'm asking so many questions. 

    What happens with multiple choice? If they get it right a 4? If they get it wrong is it a 1, 2, or 3?

    @dcox gave the advice:  Say you have one basic, one "proficient" and one application/synthesis problem. Students who can do all three =5, 2/3 =4, 1/3 =3. But what if they do 1.5 out of 3, or 2.5 or 3.5? What then? What if they make small mechanical errors that throw off the whole problem? What if they start off well and then nose dive?

    It's like no matter what rubric I find or create, when I'm grading, I always find a loophole that leaves me staring blankly at a paper trying to estimate how much they know based on the test and what I see in class.

    What am I missing?


    SBG: Error Analysis

    It's the end of the first quarter. I don't want to give up on sbg just yet. I've got to figure out what's going wrong so I can make this thing work.

    I've separated grades in the gradebook according to skill.

    I've been giving shorter,weekly assessments addressing specific skills.

    Students have their own bubble sheets to fill in so that they can self-analyze what they know and don't know.

    I've had 6 out of 68 students come in to reassess.

    And 4 of those 6 were girls who had B's instead of their normal A's.

    Overall, grades are lower than last year. But I have different students. I'd like to say that the grades are a truer picture of their abilities since I am only grading quizzes but with the rubric I was using, I can't necessarily agree with that.

    Pitfall #1: I was forcing my instruction to fit in a quiz every Friday whether or not a skill logically ended that way. It didn't matter if we were in the middle of a skill or not, come Friday, we quiz.

    Solution #1: By creating my assessment first, I can expect more out my students since I can plan better lessons. Creating the assessment first forces me to focus my instruction on the skills that are imperative to build up to the same level of ability that the assessment addresses. This way my teaching covers all the needed parts and class logically ends with an overall assessment.

    Pitfall #2: It's possible that the students do not have enough independent practice to prepare them for taking an independent assessment. I've been trying new strategies to get away from direct instruction but 90% of what the students are doing is with a partner, in a group, or as a whole class. Maybe I am making it too easy for them to tune out and just write things down without holding them accountable for anything. Also, I don't give homework. If we don't finish something in class, I will tell them it's homework. They don't do it. We finish it in class the next day anyway. The whole idea of not grading homework is to give them guidance and correction through constructive feedback. I have morphed into giving no homework at all which translates into no written feedback until the actual assessment. So the only concrete evidence that they know what they are doing is the few minutes I walk around the room while they are working and give minor feedback.

    Solution #2: My instructional coach is advising me to create a chart or some kind of system to check the work the students are doing, even if I'm not actually grading it. I started an Excel sheet where I catalog a C for Complete, I for Incomplete, or a 0 if they didn't turn anything in. This at least gives me a point of reference for discussion with a student/parent/administrator. Another idea I had is to hang up charts (like in Kindergarten or Sunday School) and let a student each day collect the assignments and go mark the C, I, or 0 for their class. That would give the students some involvement and maybe hold them a little more accountable since everyone could plainly see who is completing their work and who isn't. From there I could reward those that constantly complete their homework but I don't really want to start bribing them. Another idea she had is if maybe once a week I randomly checked a couple problems so that students would never know when I would be checking or for what. I really don't want to do that. I just hate grading. I don't want to grade all that and completion grades become fluff.

    Pitfall #3: Students are not retaining information. I was doing my best to assess every skill twice in class to help those students who will never come in for reassessment as well as the retention issue. I don't know that it helped other than highlighting the fact that students are not retaining information.

    Solution #3: Although I have created some thoughtful ideas on how to summarize my lessons, I have yet to do any. When faced with a time crunch, I tend to want to finish the notes or activity we're currently doing rather than stopping to start something new. I guess the truth is I haven't seen the value of summarizing as a tool for retention. Yet. Also, it seems like a waste for students to do the summary for me to glance at it and throw it away. On the other hand, most of the work we do in class gets less than a glance from me.  Touche. I wonder if my students would be more likely to do summaries if they had laptops to type them on? What I'd like to do is give two problems (preferably on index cards, which I heart!) of homework each day. Surely everyone could manage that. But, I still don't want to grade it. And is 2 problems really enough to aid in retention?

    Pitfall #4: Students don't care about their grades. No one wants to reassess. A good portion don't even fill out the bubble chart (skill tracking form) because it's not for a 'grade'. I suppose as long as they are passing, it doesn't really bother them. Report cards come out next week, so I guess we'll see what happens then. We had progress reports at the halfway point of the quarter, but I guess no one was really upset by their grade.

    Solution #4: If I knew how to make students care, I could be rich and famous by now.


    Octoeber Woes

    I have been wanting to blog forever but lacking the time and motivation, I did not. I didn't read any and I only got on Twitter when I was in some type of dire need. My love of teaching has been withering away. This year is much suckier and harder than I remember last year being. Last year, the prevailing feeling was that I had no idea what I was doing. This year my feeling is, I thought I learned what to do and now things are worse than when I didn't know what to and I am too busy to learn anything.

    Let's just recap my current frustations.

    SBG sucks.

    I have been reading other people's blogs that just started sbg this year and how it is more work than expected but soooo beneficial. I am jealous of your juiciness.  I have not had success. I actually kinda hate it. Shhh, don't tell. I have had about 5 out of 70 kids come in for reassessments. Four of the five are geometry students and one.One.ONE was an algebra student. The quiz is clearly labeled with the skill and their score for that skill. Each day in our lesson, I introduce the skill and the skill is at the top of their notes. They don't care that they get bad grades. None of them. And since that's all they are worried about, they aren't even realizing that hey, I don't understand very much.  My quizzes suck. For the most part I give two questions per skill. My past 2 quizzes addressed only one standard and so they each had 8 questions on it. Does that make any sense whatsoever? I'm grading using a rubric but I think I hate it too. I've found myself still trying to give them more points on the rubric if they showed work or 'tried really hard'. I've been using ExamView to create quizzes. I create a bank of all the questions offered for that skill and then I pick the ones that aren't super easy but that I think they will know how to do. What kind of assessment is that? Ugh, I hate it. I am just starting to try backwards design with my coach and hopefully that will solve one of my problems.

    I don't know, everything is just sucking. With the creation of my common core pacing charts, my skill list kind of flew out the window which leaves every day up in the air for me. I have not went to bed before midnight the past two weeks and as a result I am cranky and impatient and unforgiving in class because I just want to go home and take a nap. Our coaches are challenging us to implement new teaching strategies that involve more cooperative learning than my default direct instruction and my beloved powerpoints which I was just beginning to master. Every day I have no idea what to do.

    I am a firm believer of routines and systems. Currently, I hate my notetaking system, homework system, assessment system, and grading system. Not forgetting my downfall of catching students up who have been absent. I literally feel like nothing I am doing is working. I am working harder and accomplishing less.

    I have not been grading homework but my coach has been pushing me toward recording completion, even though I insisted on not giving a grade. I understand that students should be held accountable and I need a paper trail to cover my butt, but right now that paper trail is about 6 inches tall, lying in a chair untouched.

    So I am assigning homework and the kids say, 'oh you said we didn't have to do homewoek,  and me correcting them by saying 'no, I said homework isn't graded'. They still don't do it. We spend time doing it in class. Which is whatever.

    This blog post is just rambling on with no direction because I have none. I can't even complain effectively.

    My coach helped me admit realize that I was rushing to have a quiz every Friday even though the kids weren't ready for it. I liked it just because I like routine. Also because then I don't have to lesson plan for Friday. You know, since I currently hate lesson planning. I currently hate everything. I have no motivation to do anything. Usually I love reading blogs, tweeting, reading pd books, decorating my classroom, and doing fun things for the students. Now, I just want to come home and do nothing. During my plan period last week, I literally sat in a chair and stared out the window for the whole hour because I couldn't even think what I needed to be doing or motivate myself to figure out. Also last week, I feel asleep during tutoring. I only had one student who was studying her terms so I could quiz her for a test. I laid my head down and fell asleep until the principal walked in. Oops.

    We have a 4 day weekend and it's Saturday night and I still haven't attempted to do anything related to school. I have a stack of tests to grade and lesson plans for the week to attempt but I. don't. want. to. do. anything. I spent the last three hours catching up on blog posts that just made me feel bitter toward those of you that are enjoying your year and having success. It de-motivated me, if that's possible. This is sad. I don't want to feel this way. I am too young and inexperience to be burnt out. I have already lost my joy of teaching.

    One specific class has already ended up being something I dread. I spend most of my time at the board with arms crossed giving them the death stare so they might actually stop talking and pay attention. As I'm writing on the board, I'm thinking to myself, "I hate this class. I hate this class. I hate this class.' And as I engage in confrontational conversations with them, I think to myself 'I do not want to come back here tomorrow. I cannot face them one more time.' And then the next day I come back. I've tried a few investigation-y cooperative learning type things but their behavior and my utter failure at classroom management produces a chaotic mess.

    Not to mention all the RTI and 5-step lesson plans and extra meetings and parking lot duty and tutoring and so on that eats up all my time.


    SBG Common Core Geometry Pacing Chart

    Geometry Pacing Chart
    Common Core Standards

    Priority Standards in Bold- Priorities are things we will keep coming back to over and over throughout the year and are assessed on ACT.

    Note: In order to bridge gaps between Algebra I and Algebra II, the following Algebra I skills will be embedded as much as possible:
    • Solving equations and systems of equations
    • Factoring
    • Analyzing and graphing linear, exponential, and quadratic functions

    Quarter I

    Foundational Geometry Terms
    • G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
    • G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*
    • G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. (Note: Include factoring and systems of equations.)

    Parallel Lines
    • G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
    G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

    G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
    • G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

    Quarter 2

    • G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

    Triangle Congruency
    • G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
    • G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Include CPCTC.

    • G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
    • G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
    • G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
    • G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
    o a. A dilation takes a line not passing through the center of the dila- tion to a parallel line, and leaves a line passing through the center unchanged.
    o b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

    Quarter 3

    Area and Volume (Focus on real-world applications not simple use of formula.)
    • G.MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
    • G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
    • G.GMD.4 Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
    G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. (Note: Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale factor k.)
    • G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

    Probability and Statistics
    S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
    • S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
    • S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
    • S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

    Quarter 4

    Right Triangles
    • G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

    • G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle Include factoring.
    G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
    • G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle
    • G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
    • G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
    • G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).*

    SBG Common Core Algebra 1 Pacing Chart

    Algebra I Pacing Chart
    Common Core Standards

    Priority Standards in Bold- Priorities are things we will keep coming back to over and over throughout the year and are assessed on ACT.

    Quarter 1

    A.REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
    Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R
    • A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
    • 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
    • N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
    • N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
    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. For example, interpret P(1+r)n as the product of P and a factor not depending on P.

    • S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
    • S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
    • S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean, and spread of two or more different data sets.

    Quarter 2

    Functions and Graphs
    • 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 f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
    • F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
    • F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries
    • F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
    • F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)
    • S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    o a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.
    o b. Informally assess the fit of a function by plotting and analyzing residuals.
    o c. Fit a linear function for a scatter plot that suggests a linear association.
    • S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    • S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
    • F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
    • F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
    o a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.
    o b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
    o c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
    F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    o a. Graph linear, exponential, and quadratic functions and show rate of change, intercepts, maxima, and minima.
    • 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.

    Quarter 3

    Systems of Equations
    A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
    • 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).
    A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
    • A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

    Rational Exponents
    N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
    • N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
    • N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

    Quarter 4

    Polynomials and Factoring
    A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
    A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
    o a. Factor a quadratic expression to reveal the zeros of the function it defines.
    • A.SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2)

    Quadratic Functions
    • F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    • Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
    • Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
    • F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
    • A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
    • A.REI.4 Solve quadratic equations in one variable.
    o b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

    SBG: Common Core

    Our school recently received a massive grant for school improvement. There are only 2 small schools in Illinois who received this grant and we are one of them (less than 200 students in high school). If we can do this, if we can turn our scores around and make substantial AYP progress, it's likely we will receive national recognition. As a result, we have adopted the turnaround model which means we have employed a turnaround administrator, 3 instructional coaches, and a large amount of change. Change + teachers = not the easiest thing ever.

    We have already started completing and submitting 5-step lesson plans each week. Coaches are rotating classrooms making observations in any classroom they want to and meeting with teachers to suggest new teaching strategies and the like. Soon we will be accumulating and analyzing tons of data in order to make better decisions for students. Starting with math, the coaches are starting to align curriculum to ACT but more importantly, the newly adopted Common Core standards from high school down to elementary. Hopefully this will better guide instruction as well as eliminate knowledge gaps from one grade level to the next.

    Back in September, I had the fantastic opportunity to work with my instructional coach for two entire days building a Common Core/ACT College Readiness Standards SBG skill list.

    First of all, I'm not a fan of Common Core. I think the language is still vague and complicated. I don't know what is so hard about writing things in a way that makes sense to the average person. Also, I hope in the future they create a document with examples or sample assessment questions to better clarify what exactly each concept means. The ACT college readiness standards are much more clear cut and practical and I had just gotten accustomed to them when the CC curve ball hit. These lists are prioritized based on what is assessed by the ACT since a Common Core test won't show up for a few years (if at all). Since all of this work should have been done this summer but couldn't be (thanks, state of Illinois for all the 'delayed' funding), the pacing guide is for next year and this is sort of a transitional year that will be messy.

    I really liked the way my coach helped me create this. She printed the CC standards on colored paper and cut it into strips. I went through and picked out what I considered to be my priorities for Algebra 1 and Geometry, based on the topics assessed on ACT and their College Readiness Skills. Then we had 4 pieces of paper that had each quarter written at the top. We put the standards in an order that made sense and separated it into each quarter by what we thought was doable. We taped the colored paper down and thus we had a rough draft pacing chart.

    As I've mentioned many times once or twice, I am an algebra girl. Geometry is not my cup of tea. The algebra was much easier for me to sequence and more closely aligned to what I've already been teaching. Unfortunately. CC is leaps and bounds above the baby geometry I am teaching. Which isn't a bad thing, but somewhat sobering. This year I will be teaching things I've never taught before or in fact, have never even learned or heard of myself. (dilations, density dissection arguments, Cavalieri’s principle, and informal limit arguments....what??) CC is HEAVY on transformations which I enjoy but haven't done since high school and have never taught or seen taught in any capacity.

    I will be stretched this year. I already am. But that's another post...

    While I was incredibly excited to work with someone who 1) loves math 2) has 30 years of experience teaching geometry 3)could help me, it was not exactly the sbg  high I was anticipating. Our pacing guide has 2-3 units per quarter and 2-3 objectives per unit which gives me about 10 objectives to teach in 9 weeks. Which sounds quit simple actually. The problem is, I need a list to tell me what I need to cover each day in order to accomplish those things in 9 weeks. I need a list people, that's just how I operate. Next year, I think it will be much easier to take your advice on chunking things and creating topics but this year I have felt stranded without a specific day-to-day list. Thank God for my coach. It has been so, so helpful to have a real live breathing person there to listen and strategize with who keeps me from boiling over or melting down and who has tons of her own resources to share. Plus, she gives hugs and chocolate.

    We have now been working together utilizing backwards design to create assessments first and then designing what is needed each day to work up to that level. Backwards design is something I have wanted to do since before I started teaching but is not something I could wrap my head around and do on my own. It is near impossible for me to project my thinking into the future in that way and so her help has been miraculous. We are creating small units and I am creating my own lists, which is my lifeline.

    I started this post with the intention of pasting in my lists of standards but it is already too long so I will link to them here and here and post them in separate entries for your viewing pleasure.


    SBG: Algebra Redo

    The topics listed under Pre-Algebra are skills I'm hoping my students have, but I'm not assuming that they do. Optimistically, I hope to teach and assess all the Pre-Algebra topics in the month of September. The ones in red are what I've already taught. Although I'm not sure they've learned it. I'm going to spend extra time on this in my Algebra support class and keep spiraling skills through Warm Up problems.

    • Operations Using Whole Nunbers Fractions, and Decimals
    • Square Roots
    • Exponents
    • Scientific Notation
    • Ratios, Proportions, and Percent
    • Linear Equations with One Variable
    • Absolute Value
    • Simple Probability

    The topics listed below are the heavy hitters. Now what do I do with them? Do I break them down into more specific skills? Or should I list what they should be able to do? I want to make a new skills list that isn't 95 skills long. These are ACT topics and earlier this summer I listed the specific skills from the ACT College Readiness Standards. Should I just use those, or modify, or...what?

    Elementary Algebra
    • Functions
    • Polynomial Operations and Factoring Simple Quadratic Expressions
    • Linear Inequalities with One Variable
    • Properties of Integer Exponents and Square Roots

    Intermediate Algebra
    • Quadratic Formula
    • Radical Expressions
    • Inequalities and Absolute Value Equations
    • Systems of Equations

    Now for the actual assessing.

    I haven't actually used my idea of exit slips. I think I have to. I'm not assigning homework. They are doing problems in class and I am checking and giving feedback, but I think they need more specific attention/feedback. Ideally, (and hopefully I can achieve this next year) I'd like to be able to make my Exit Slips ahead of time for the week. I could put 2 on front, 2 on back, grade and return each day and that is an instant study guide, in addition to the notes worksheet. And if I could create my assessments ahead of time, that would guide the problems I put on the Exit Slips. Unfortunately, I'm  still at the newb stage where planning ahead is at most 2 days at a time. Last year I planned the next day and that's it. Now I can do 2-3 days, so I am making progress. But at least I have decided what to do and I can now more efficiently work on how to do that.

    I think I have decided that my actual SBG quiz will be 2 problems per skill, 1 easy and 1 hard. But I will assess each skill twice: one the current week and once again the next week.

    My attempt at a grading rubric follows.

    C = Correct
    P = Partial
    I = Incorrect

    Easy Hard Score  Percentage
    C       C       4            100%
    P       C        3.5         95%
    C       P        3            90%
    I        C        2.5         80%
    P       P        2            70%
    C       I         1.5         65%
    P       I         1            60%
    I        I         .5           55%

    To me, it make sense to put more of an emphasis on the harder problem than to give points for any correct problem as in the Marzano 3-level strategy. (At least the way I understand it.)

    The easy problem will be straightforward plug and chug. The harder one will be...I don't know yet? Adding in more steps? Word problems? Short answer? Construction?

    Input needed.

    P.S. I now realize that this is what I should have spent my summer doing. I literally did nothing this summer. I think next summer I will create a pacing guide for myself! lol Or get a job. Or both.

    SBG: Back to the Drawing Board

    Everyone has told me to narrow my SBG list, cluster it, separate by topics, etc.

    I'm an Illinois girl which means we have vague state standards, we're assessed on ACT College Readiness Standards, we recently agreed to Common Core Standards,and basically have to decipher this on our own.

    I have decided to go by ACT Standards until Illinois gets smart enough to write their own state test, which will take at least 3-4 years from now. So using a very helpful ACT resource book, I've listed all the topics addressed in the ACT.

    Now I just need help deciding which topics fit specifically into Algebra 1 as opposed to Algebra II.

    Once I get those nailed down, should I list the prerequisite skills needed? How specific should I get?

    How do I assign grades on topics instead of skills?

    Or maybe I could break down the topics a bit more specifically and use them as shorter skill list?

    Remember, Dan Meyer pulled it off in 34 standards people!

    ACT Math Topics

    • Operations Using Whole Nunbers Fractions, and Decimals
    • Square Roots
    • Exponents
    • Scientific Notation
    • Ratios, Proportions, and Percent
    • Linear Equations with One Variable
    • Absolute Value
    • Simple Probability

    Elementary Algebra
    • Functions
    • Polynomial Operations and Factoring Simple Quadratic Expressions
    • Linear Inequalities with One Variable
    • Properties of Integer Exponents and Square Roots

    Intermediate Algebra
    • Quadratic Formula
    • Radical and Rational Expressions
    • Inequalities and Absolute Value Equations
    • Sequences
    • Systems of Equations
    • Logarithms
    • Roots of Polynomials
    • Complex Numbers

    Coordinate Geometry
    • Number Line Graphs
    • Graphs of Points, Lines, Polynomials, and Other Curves
    • Equation of a Line
    • Slope
    • Parallel and Perpendicular Lines
    • Distance and Midpoint Formulas

    Plane Geometry
    • Properties and Relations of Plane Figures
      • Triangles
      • Circles
      • Rectangles
      • Parallelograms
      • Trapezoids
    • Angles, Parallel Lines, and Perpendicular Lines
    • Translations, Rotations, and Reflections
    • Simple Three-Dimensional Geometry
    • Perimeter, Area, Volume

    • Basic Trigonometry Concepts (SOHCAHTOA)
    • Advanced Trigonometric Concepts (Secant, Cosecant, Cotangent, Pythagorean Identities, Trigonometric Identities, Double-Angle Formulas, Half-angle Formulas)
    • Radians (Conversions)


    SBG: Frustration


    I am so frustrated with myself. I guess I am guilty of just jumping onto the SBG bandwagon and now I am dragging behind the wagon and hitting every pothole. That is filled with mud. And pebbles. And maybe some quicksand.

    SBG just makes so much sense in my analytical brain but the concept is still not sinking in. It's not changing my teaching yet. It's merely pointing out how much my teaching and question writing and grading and assessing suck. But I don't know how to fix it.

    I'm using ExamView to write my quizzes and I'm picking 3 levels of Bloom's to use on the assessment: application, synthesis, and analysis. Here is my sample quiz for the distance formula and midpoint formula. The 3 levels are there but do they make sense? Some twitter people responded with:

    mathhombre @misscalcul8 maybe a line w. slope=1 so tempting to count dots; don't get how #6 checks objective. (Midpt means =, but buried in there)

    mathhombre @misscalcul8 Maybe A=(2,3), B=(5,1). Find the distance from A to C if B is the midpt of AC. Allows multiple methods.  
    mdsteele47 @misscalcul8 Good start, but those are all procedural questions. There's nothing that assesses what they understand conceptually 

    On #6, midpoint means a segment is cut into two congruent halves and you have to know that to set up the equation correctly.

    The problem of using one endpoint and the midpoint to find the other endpoint is a good question, but we didn't do it in class so they won't know how to do it.

    And how do I assess conceptual understanding? My brain can't think outside of the box that is all things procedural.

    Also, I'm reassessing last weeks 4 skills in addition to 2 new skills this week. So with 6 skills and 3 questions per skill, that's 18 questions. Isn't the idea of sbg to have frequent shorter assessments? Should I be assessing after completing one skill? Should I not assess each skill twice? Should I just give one advanced question the second time I assess the same skill? What is the best way to do this?!

    park_star  @misscalcul8 give your quiz when it feels natural to do so. it makes marking them so much better :)  

    This is good advice, but I can't tell when it feels natural. I like doing it every Friday but the students told me today they felt rushed and like they were cramming while at the same time I feel like we're behind. I feel like I need two spend at least two days per skill: one for introducing, one for mastering. If we do that, I feel like we will never get far enough. But if I am about learning, then rushing through material is counterproductive to that.

    Even creating my skills list of things to teach, I still feel like I don't know what to teach. Comparing different textbooks makes me question how deep I should go into a specific skill. One book gives this type of problem, another gives another type. How do I know what is too little and what is too much? I don't have enough experience to know what type of problems aren't as important or what's most important. It took me two class periods just for them to correctly use the distance formula, and that's just procedural.

    What am I doooooooooooooiiiiiiiiinnnnnnnnngggggggggggggg?

    I keep changing the notes we do in class, changing the quiz, and the way I grade. I  think my students have no idea what's going on and neither do I. I owe it to them to find a system that works but in the meantime they have all this confusion to put up with. I'd like to just ask them what would be the best for them but if I don't know, how can I expect them to know? And they aren't mature enough to really answer my questions anyway.

    How did Dan Meyer pull this off in 34 concepts and I have over 100? Maybe I will just steal his list and his sample questions and make my life easier!


    SBG: Homework and Grading Questions

    Had someone on the wiki ask quite a few questions and thought I would throw them out here for some more answers.

    mrlongscience Today 10:02 am:

    I'm slightly late in the game with my students coming tomorrow but still have tons of questions.

    I only have 39 minutes a period so I often struggle to get through an entire lesson, and still have time for the students to work on practice problems from the book.

    1. How many practice/homework problems do you assign for kids to work on?

    I have 45 minutes class periods So I kind feel your pain. What I do is alternate between explaining a concept/group discussion to them working at their seats. So maybe will do 2-3 examples together and I will say do 1-4 on your paper now. They compare with their partner and then I call on random students for answers. Then we will do 2-3 nmore examples and then they will do 5-8, and so on. My goal is to make it all the way through one practice worksheet front and back and then depending on their understanding, assign (parts of) a worksheet for homework.

    2. Do you just give suggestions on what problems to do since homework isn't graded and students have different needs as far as how many problems they need to do to develop competence with a skill?

    I give them all the same worksheet and suggest they work on the ones they had the most trouble with. Our low level students have an extra math support class and so their teacher works through the entire sheet with them. Other than that, I leave it up to them.

    3. Do you spend time going over the practice problems in class?

    We do problems together throughout class so that they have a good grasp on what to do. The homework I correct and give feedback on individually.

    4. Do you just go over the answers and ask for questions on practice problems or do you post the work and answers for practice problems on the board?

    I haven't done either yet but I like the idea of posting them on the board. Actually, I'm thinking about printing them out with the answers on them so that they can make sure they know the correct process to get the correct answer.

    5. What do you do with the kids who didn’t do any/all of the practice problems while you’re going over the answers/work in class?

    I don't go over them in class.

    6. How often do you include old skills on a quiz?

    I plan to asses, for examples, 1234, then 1234567, then 45678910, so each skill is assessed twice. Still debating about doing a cumulative/retention test.

    7. With skills, whenever students see an old skill on a quiz are the questions related to the skill progressively more difficult each time it's assessed?
    I assess each skill twice and yes, the second time is harder.

    8. Do grades carry over from quarter to quarter i.e. A student gets a 3/5 on the skill of Adding a fraction for the 1st quarter. Is that same skill inputed on the 2nd quarter? If the student re-assesses and receives a different score, do you change the grade only for the 2nd quarter or go back and somehow change the grade for the skill on the previous quarter's grades.

    This depends on your admin and gradebook policies. My plan is to change it until that grading period is over. After that, I can't go back. So then I will input it as a new skill in the grading period they are reassessing in.

    9. Does anyone haave written criteria for the score scale for each skill? I'll be the first one in my district to implement SBG and I have a feeling my administration/myself will want something to refer to when parents want to talk about their child's grade.

    Check out the grading page of the wiki and there are some blog posts and sample rubrics explaining this in more detail.


    SBG: Questions Per Skill

    I gave my first sbg skill quiz over 4 concepts in both Algebra 1 and Geometry on Friday. I also gave my first vocab quiz. We went through all the vocab words from the first section together and filled in each square of the Frayer model: Definition, Characteristic, Example, Nonexample. Then in the second section they looked up the definition in the book themselves and I mentioned the other 3 as we went along. Friday was the quiz and here is the example for Algebra  1 and here for Geometry. I reviewed a few minutes during our warm up and gave them 2-4 minutes to study on their own. The results were pretty terrible. The few that did well surprised me. One student missed about 3 out of the 5 days of instruction but told another teacher that we underestimate his abilities because he studies a lot at home. Touché. Another girl assured me that she would flunk it and I believe she has/d a learning disability or just low math scores.  They were my top scorers. Yay!

    I have to say I am pretty happy with the process even though I'm disappointed by the results. I like the Frayer model and I feel like the questions came straight from the information I gave them without being matching or multiple choice. The question I gave about 'modify the expression so it can be evaluated' was too hard and most didn't know what to do. That one was my fault. I felt like the others were within reach. My colleagues told me to stand my ground. It was only the first quiz and now they know what to expect. They will either rise to the challenge or fail. That sounds harsh to me but I will be curious to see what happens at the end of week two.

    Now my first sbg skill quiz...

    Algebra Skill 1 and 2 Skill 3 and 4

    Geometry Skill 1 and 2 Skill 3 and 4

    I didn't really have a clue what I was doing. Still don't. I know you are supposed to make your assessments first but I just don't get that yet. How do I know what to assess when I haven't taught it yet? I know, you're thinking "How do you know what to teach when you don't know what you're assessing yet?". Touché. I had 5 questions per 2 skills and only 4 skills on the quiz. So 10 questions. This really makes no sense. I see that clearly now. I don't know how to grade these. If there are 3 questions for 1 skill, how do I give them one score for that skill? What about when there are only 2 questions per skill? Does it change now? Is each question worth a 2 to achieve the maximum score of 4? I haven't looked at them yet because I have no idea how to assess them.

    I know other people use Marzano's 3 levels of questions per skill but I need someone to explain that to me. And still how do you grade that? How do those 3 pieces work together to create one score? I'd like to ask one question per skill that is purely computation but then I don't know where they would get questions on a deeper level that synthesize, analyze, apply concepts, and you know, actually matter.

    On a positive note, I'd like to brag on myself for actually running out of time to finish the lesson. More than once. That NEVER happened last year. I went from preparing 10-12 slide Powerpoints to 25 or more. No, it is not all direct direct instruction. Yes, I use pictures. What I've started doing is giving them a worksheet as notes. We do examples together on the board. Then they do 3-5 at their seat and compare with their partners.  Then we go back to the board. I have them come to the board and draw examples or work out problems. While they are working I scout the room to check for understanding (oooh nice little sample of edu-jargon for ya) This way I am alternating their focus and while I am 'lecturing' they can actually pay attention instead of scrambling to write. (Yes I need more inquiry and a variety of other strategies and skills. It's week two of my second year. Work with me here people.) Then at the end, I created an overview sheet for them to summarize the important ideas associated with that skill. Hopefully that will be like a quick and dirty study guide refresher with the accompanying worksheet to provide examples. Hopefully.

    I would like to explain that I am doing vocabulary separate from sbg skills because
    1. My admin asked me to
    2. Test scores show our students don't understand standardized testing vocabulary
    3. I know they have the skills but don't know what the question is asking
    This is hard to integrate into geometry. In geometry, understanding the vocabulary is synonymous with understanding the concepts. Hopefully from the examples I linked to, you can affirm my question creating skills in that the vocab quiz built more off of the technical, specific definition and the sbg skill quiz was more identifying, using, modeling, applying, the definition. Hopefully. After some Twitter conversation, I realized that vocab can still fit into sbg. If we are about learning, then we are still about learning vocabulary. If we are about learning, and students can retake, then students can retake vocabulary. If Algebra is broken up into specific concepts, it  can also be broken up into specific vocabulary. And as long as I'm teaching it, they should be learning it, and I can freely assess it. And re-assess it.



    First Days 2010-2011

    So my first week of my second year in my second room.

    I think it went pretty well.

    In every class, every day this week, I kept the students busy until the bell rang. That is an accomplishment I am VERY proud of. Classroom management and procedures are my downfall and what I am really trying to work on this year. My principal has beat it into my head that keeping them busy minimizes disruptions plus it's my job and what the taxpayers are paying for. So...I did it!

    I stole all my first day ideas from my Twitter peeps and they all worked out great.

    The first day I had my algebra students stand, no assigned seat. I gave them mental math problems that they had to solve and then could pick a partner and a chair. Then my algebra students designed an index card with the numbers from -25 to 25 and we hung them up as a visual number line. After that I gave them a 'pop quiz' with multiple choice questions about me. I then had them create 5 of their own questions about themselves. I plan on using these questions as a guess-which-student-trivia on my warm ups. From there we did some lateral thinking puzzles and filled out Who I Am sheets.

    Next day I discussed my syllabus with them. Then I handed out a copy for them to sign and to take home to their parents and sign as well. I mainly did this because of my not grading homework policy and attempting sbg. After that I handed out the Million Words assignment and had them write ANY 3 questions on an index card. I answer every question. I've had great ones like "What are your fears?" "Do you ever feel alone?" "Do you ever feel used by people you trust? as well as random ones like "Who invented baseball?", "What's the fastest rollercoaster in the world?" "What are the three stages of a tornado?" And keep in mind high school boys asking a young female teacher anything. I find a creative way to answer every question. Yes. Every question.

    So on Friday I answered all of those questions in class. They are always very interesting and the students enjoying laughing at me and each other. I hope that it helps build a positive and fun environment as well proving that what they say counts and that I will answer any question they have. Then we did one of my favorite activities yet...a Murder Mystery. I split the students into groups of 4 or 5 and passed out the clues. I had them deal the clues like cards until everyone had some. They had to read aloud, not switch, not share, not show. As a group they had to organize and solve the mystery. I gave them a little sheet asking the 5 questions, Who did it, Where at, What time, What weapon, Why and they filled it out.  I checked their answers and told them if they were right or wrong but not on specific parts. Out of about 15 groups, only 1 group actually got them right. I feel like the students really enjoyed it and some spent over 30 minutes solving this one problem. U used the discussion questions at the end and they really understood the point of why we did it. I'm also going to use this as blackmail when they want to give up: "Remember that time you worked for 30 minutes on ONE problem. You didn't give up then." Ha ha ha

    I have to say I have a really good group of freshman. They are almost scared to death and will hardly move a muscle or talk at all. Also, a lot of the girls really wrote some personal things to me in their Million Words assignment. Some literally brought me to tears. I don't know if it's just because they are girls or if they are an emotional group. Either way, I love that they felt comfortable enough to share all that with me. I wonder how many times they have been invited to freely share their lives with an adult.

    And that's all I have to say about that.