Open Ended "Real" Algebra 2 Problems

Do you ever ask yourself, do my students get the big picture?  Could they solve a "real" problem, work with others, and communicate the results in a clear write up with graphics?  Wow, I am asking for a lot.  One of my goals this year, is to get my students to think on their own, and at least attempt these "real" problems.  In my Algebra 2 classes, they get a problem for each unit.  I give the problem early in the unit with a deadline.  That's it!  I don't help them, they can collaborate with other students, research solving methods, use graphics, whatever they want.  But, and here is the catch, they must communicate clearly their answer and justify in words and mathematical work why their answer is the best (or simply correct).

Here is an example of a systems of equations (my unit 3) problem:

Unit 3 Problem

Solutions must be neat, printed in pencil, all work shown, and all variables defined!

                                                                                                                                                                                                                               

Shonda is organizing the printing of tickets for a show her friends are producing.  She has collected prices from several printers and these two seem to be the best.

                                                       SURE PRINT

Ticket printing

25 tickets for $2

                                                       BEST PRINT

                                                    Tickets printed

$10 setting up

plus

$1 for 25 tickets

Shonda wants to go for the best buy.  She doesn’t yet know how many people are going to come.  Show Shonda a couple of ways in which she could make the right decision, whatever the number of tickets.  Illustrate your advice with a couple of examples.

---------------------------------------------------------------------------------------------------------

The student solutions were varied and I was impressed.  Some students will not turn in anything.  They cannot get past the thinking that there is only one way to work a problem (which is NOT true!).  Since they don't know how to start, they won't.  So, I copied an A+, B-, and C paper (without student names), then projected them up and discussed the different methods, and that they only needed to get started to earn the C.  I hope it opened their eyes.  I hope more will try the next problem.

This problem is from the Mathematics Assessment Project (MAP) website:
http://map.mathshell.org/materials/index.php

Here are some quadratic equations problems on The Futures Channel website:
http://www.thefutureschannel.com/algebra/quadratic_equations_functions.php

There are several sites that have problems you may use.  I hope to incorporate more "real" open ended problems as in-class team projects.

First 3 weeks of SBG

Three weeks down, 33 to go.  My SBG (Standards Based Grading - see first post) journey in Advanced Algebra, Geometry, and Statisitcs is enlightening, informative, and exhausting (but worth it).  The first quiz in all my classes showed me what skills the kids learned (and did not) in each class.  This helped direct instruction (review and new stuff).  A big and important piece of information that usually takes several weeks to discover is which students are getting it quickly and which students need more time.  Also, after the 2nd quiz, I identified the kids who probably belong in a lower level class.  Identifying these students early is very important.  I can make the recommendation and ask them to meet with their Counselor.

There is a learning curve (for both me and the kids).  Students get a 2nd chance to improve a skill score on the next quiz.  But if they choose to work out a previous learning skill on the quiz , and they do worse than before, they get that new score.  However, they can come in on their own time to retake that skill(s).  Some students that earned a lower score on a skill, are commenting "Oh no, I thought I knew it."  They are disappointed with themselves.  When I remind them they can come in to try a third time, they feel better about it (even if they never come in).  I have reminded the classes several times to make sure you know the material before you try to work out a past skill - maybe I should make a poster.

So far, it is going great.  I have to keep up in Stats with writing the skills quizzes, and with Geometry (I am writing the learning targets (skills), as I go along with the quizzes).  I wish I could get more teachers interested.  I really need the help.  Maybe next year.  :)

SBG for AP Statistics

If you are just starting SBG (Standard Based Grading), see my post Starting SBG (July 2012).

Finally finished the first semester of Learning Targets for SBG for my AP Statistics class.  If you are looking for Learning Targets aligned with The Practice of Statistics (YMS 3rd ed.), I posted mine at: http://apstatssbg.wikispaces.com/
Thanks to Jared Derksen for starting this wikispace.

As with Advanced Algebra, most of the students grade (60%) is for SBG assessments.  The other components of their grade are: Daily Pracitice (10%), FRAPPYs (10%), and End of Quarter Summative Assessments (20%).  FRAPPYs are past AP problems, to learn more go to: http://apstatsmonkey.com/StatsMonkey/FRAPPYs.html
There are several other resource at StatsMonkey.  Check it out!

The Learning Targets I use are designed from Dr.Robert Marzano's teaching strategies. For a list of his researched instructional strategies go to: http://www.marzanoresearch.com/research/researched_strategies.aspx

It's count down time.  The first day of school is Aug 20th!  :)

SBG Grade Weighting and Rubric

Just finished planning the first semester of Standard Based Grading (SBG) for my Advanced Algebra classes.  As I go through this process, I continue to revise my syllabus.  I realize from reading other blogs, that SBG must be a large part of the grade (otherwise, why should they take it seriously?).  So I updated my semester grade weights and have separated daily practice (having materials/textbook, staying on task, working on problems together) from unit problems (an end of chapter "big picture" problem that ties several learning targets together).  As of this posting, here are links to 2 teacher blogs that I have found useful:

     dy / dan
     druin

My revised semester grade weights:
Daily Practice   10%
Unit Problems  10%
Learning Target Assessments (SBGs)  60%
Chapter Assessments  20%

Some teachers asked me about my grading rubric and how that rubric is calculated in my grade book (I am not an expert!).  In the past I have used a 4 point scale and then converted the scores to percents for an overall test grade.  Now with SBG assessments I want the grade book program to do the work for me.  My current plan is to assign these percents to the rubric scores:

Rubric    Percent
        0 =   0%  (blank or nonsense)
     0.5 = 60%  (glimmer)
     1.0 = 65%  (getting started)
     1.5 = 70%  (little understanding)
     2.0 = 75%  (getting there)
     2.5 = 80%  (almost there)
     3.0 = 85%  (some minor errors)
     3.5 = 90%  (minor arithmetic errors)
     4.0 = 95%  (got it!)
     4.5 = 100% (perfect)
     5.0 = 105% (beyond perfect)

Except for the 4.5, I will not give 1/2 scores on the SBGs.  The students have multiple chances to improve their SBG grade on any learning target.  So if they want to improve their grade, they need to move up to a solid letter (whole number on the rubric).  No more, "What do I need to do to just get a B?"  They want to just "squeak by" to get the next letter grade.  My district does not give plus or minus letter grades, so a C - is just a C on the transcript.

A perfect (4.5 = 100%) is for no errors, including all directions followed.  Beyond perfect (5 = 105%) is for the bonus problem on the chapter tests.

I'm sure there will be revisions as I move along.  At this point, I am optimistic for a great school year.  :)

Starting SBG (Standard Based Grading)

How do you start sbg?  Good question.  Honestly, I thought I knew the answer until Internet research showed me I was off base.  Way off base.  This school year (2012-2013) will be my first real attempt at sbg.  My colleagues and I developed learning targets and common assessments, but missed the mark on how to give students useful feedback.  I teach high school, so this post is written for math subjects (not grade levels).  Here is what I have learned this summer:

1.  Start with a copy of the subject (grade) standards, your textbook and/or support materials, and past assessments.

2.  Get help (at least one other teacher).  This is a lot of work.

3.  Look at the past assessments and ask yourself; What do I expect my students to learn?

4.  Make a list of learning targets (objectives, skills) that are not too specific, yet not too broad.  We use Marzano's "I can . . . ." statements.  This is tricky.  I noticed that for Advanced Algebra I am averaging about 2 learning targets per week.  I have no idea if I have too many or not enough.  It is important that the learning targets include everything you are going to assess.  Sample student learning targets:

2a	Ø I can identify and evaluate a function.	Getting started…       Getting there…       Got it!          1             2              3             4
2b	Ø I can find the slope and graph linear equations.	Getting started…       Getting there…       Got it!           1             2              3             4

5.  Start planning around your learning targets.  Students need to know you are going to assess them on the learning targets, and that they will have multiple opportunities to master those learning targets.  To do this you must have some type of scoring table in the header of your assessments.  Sample assessment header:

Learning Target	2a	2b	0 = F (Blank or Nonsense)     1 = D (Getting started) 2 = C (Getting there)    3 = B (Minor errors)    4 = A (Got it!)
LT score

6.  Allow students to improve their LT score.  On the 2nd quiz I have some learning target 2a and 2b problems with 2c and 2d.  Note the header will have two more columns added for 2c and 2d.  Any student who mastered the first two LTs may skip those problems.  Any student who needs another (3rd) opportunity to master a LT must come in outside of class time with the quiz corrected and at least one additional problem worked out for each LT before they can retake an assessment on that LT.

7.  In the gradebook, the LTs are listed; 1a, 1b, 1c, 2a, and so on.  When a student retakes an assessment, I will simply change the grade. Note, if they do worse on a LT they get that score.  But they can come back after remediation to take it again.

This is how I am starting sbg for Advanced Algebra.  Currently, I plan to break down the grade into 3 categories:  Daily Practice 20%, Mastery of Learning Targets 40%, and Chapter Tests 40%.  I want to elimate chapter tests and have only one summative assessment at the end of each quarter, but I haven't developed enough material to do that yet.