Building Enduring Mathematical Understanding, one lesson at a time.

Archive for the category “SBG”

Made4Math Monday: Formative Assessment Forms

I definitely left some things “hanging” on my last SBG post, so I thought I would “kill two birds with one stone,” so to speak, and write about some of the ways I incorporate formative assessment into my daily routine.

A lot of people have written about “Exit Tickets,” and I guess, in a way, that’s what this is. I LOVE Sarah’s recent post at Everybody is a Genius (I’m not sure about everybody, but she IS a genius!) about the laminated dry erase ones 🙂 I think I might try that for my more “reflective” tasks to end the period, but I like the “permanence” of the system that I have set up.

Here is my:


Question of the Day
After we have spent a bit of time on a concept (but before it is time for a Mini-Assessment (Quiz)) I use Question of the Day to assess where students are at on a concept and us it to guide my instruction for the next few days. I will put up a slide such as this:


at the end of class and given them about five minutes to work on it. (Depends on the task.) Rather than just using quarter sheets of paper (or anything dry erase) I wanted to have a tool that I could use to provide feedback and also to have students keep as a record of their growth. I came up with the following simple “form”:

I print out four copies and then use the “booklet” app on our copy machine so that it shrinks it down and prints all four onto an 8.5 x 11 sheet. The original copy has more “space” on the top section because when it shrinks down there is an extra “gap” at the bottom of the page. This provides opportunities for 8 QOD’s before the students need a new sheet. They will store them in the “pocket” of their Math Notebook once they receive them back the following day. I use colored markers to write their number at the top so it’s easier to sort and hand back to color or number groups. The specific standard (CCSS) is written on the form, and we update scores on their Tracking Sheets (see SBG post) fairly regularly. When the forms are “full” students store them in their Math Portfolio – a hanging file folder in a crate that contains their tracking sheet as well as other “larger” formative assessments. Since there is only one question (ok, there’s usually two to three parts though) they don’t take long to grade and record. I can also “sort” the forms to create “Just for Today” seats (also on Sticks and Seats post) to either differentiate instruction or provide support for students who have not yet mastered the concept.

Writing About Math
I have students write in math class quite often,

20120903-130039.jpg but I haven’t always spent the time reading and commenting on their responses as I should. This year we are implementing the Common Core State Standards, and there are more than a few that employ the use of the verb “explain” or “describe.” I am looking forward to challenging students to meet standard on those in addition to the more skill-based ones. I decided to modify my Question of the Day form to use it for Writing About Math prompts as well.

Sometimes the prompt will be tied to a particular standard and graded/recorded as such, but other times I am just looking into their thinking about a concept and wanting a way to provide feedback.

Recording System
Since I record multiple scores for each standard (and multiple standards on each assessment) I needed a way to organize that information so that I can see the progressions of scores in each area. I created a “grade book” form that allows for up to four scores (more if I sneak in a re-assessment score next to the original) for each standard with room for three standards on each sheet:

Once I have my class lists I will enter them on a blank copy, make four copies of that, and again use the booklet feature on the copy machine. This time I transfer them to the 8.5 x 14 size, otherwise it shrinks down more than I want. When folded they create a nice size for up to twelve standards. I usually don’t have more than that in any one unit, so I create a new “grade sheet” for each unit. When I am entering grades into the online Gradebook, I just have to look at the most recent column and update scores that have changed from previous assessments.

Final Note: QOD and WAM are not always relegated to “end of period tasks.” I also use them at the beginning of the period. After I collect them we discuss possible responses. I am excited to use “My Favorite No” either when we do them at the beginning of the period, or the following day as a re-cap / remediation activity!


SBG: Grades

In my last post on Standards Based Grading, I focused on choosing, organizing, and tracking Standards. This post will focus on assigning levels of achievement and overall grades. I have tweaked my procedures bit by bit over the past few years, and I am happy with what I have put together (for now.)

I put together a general scoring rubric that I use for all types of assessments.



I know some teachers create a specific rubric for every assessment, but I find that a bit too overwhelming, and I know it would cause me to assess far less often. On larger assessments, I often sketch out some guidelines for myself in regards to at least some of the standards, especially if there are quite a few questions that fall under the same standard.

I differentiate between types of errors quite often as I am scoring assessments. Conceptual errors can quickly cause a student’s score to fall below standard, whereas arithmetic errors are less significant, as long as the response is reasonable. I have also been known to give scores of 2.5 or 3.5 when students are right on the edge.

Assigning grades is challenging in a Standards Based Grading. Rather than throwing it all in a computer and letting it spit out the grade, (which I have played around with in the past) I have created a rubric that I follow each time I update students’ overall grades.


As I mentioned in the previous post, I only use the most recent score for each standard, although in the comments of the grading program I list the progression of the scores so that parents can see if the student is “headed in the right direction” for that particular standard.

I would love to be able to use something like Active Grade or BlueHarvest, but we are required to use the same online grading program throughout our district. So, I am faced with the task of scanning through the row of scores for a particular student, evaluating where they fall on the grading rubric, and then assigning a value in the “overall grade” column. I have set up the weighting so that this column is worth 100% of the grade. Early on during each quarter, this is not at all difficult, but as the number of standards increases, my effort seems to increase exponentially 🙂 I will often find it necessary to actually write down the number of 4, 3, 2, 1, and 0 scores for each student and then go back and assign grades. This is where my system may collapse on itself this year, since I have tripled the number of classes I am teaching! (For the past few years, as a part-time teacher I have had one section of either seventh or eighth grade math along with a two-period block of sixth grade, whereas this year I have three sections of Algebra 8 and three sections of Math 8.) I will need to find extra time in order to keep up!

I use a variety of types/levels/sizes of assessments. Generally smaller assessments while we are developing concepts and larger assessments at the end of each Unit.


Each standard receives a score whenever it is included on an assessment, so on a Unit Assessment students will be looking at a “chart” indicating the standard, the problems in which it was assessed, and their score for that standard. At this point (or earlier in the Unit as well) students may choose to sign up for a re-assessment on just the particular(s) in which they did not meet standard, along with a remediation plan in order to help ensure their success.

In my opinion, Standards Based Grading marches step by step alongside developing Enduring Mathematical Understanding. Frequent repeated assessments requiring process and/or explanations allow me to judge the depth of their comprehension and forces me to modify my plans in order to encourage deeper understanding. Students are regularly informed of their level on specific targets and receive the feedback necessary to improve.

In the next post on SBG, I will describe some organizational strategies that I use to help facilitate the implementation of my plan.

SBG: Standards

Over the past few years I have traveled far down the path of Standards Based Grading. A LOT of people have written about it (here, here, and here) online, and I have taken bits and pieces to create something I am comfortable with, for now.

Starting with Standards
Our school district is “converting” to the Common Core this year while maintaining the need to include the current Washington Performance Expectations since students will still be tested on these in the Spring. The Math 8 curriculum is Common Core plus some work with angles and probability. The Algebra 8 curriculum is Common Core (which overlaps/expands on quite a few of the eighth grade CC standards) along with Pythagorean Theorem. (These students were exposed to most of the non-algebraic Washington standards for eighth grade last year, but I am sure some review will be in order.)

Student Tracking
I have created a tracking chart for each student based on samples I have seen from others. (See images below – sorry not the whole form.) All scores on any type of assessment are labeled by the Standard, and students update scores on a weekly basis. After recording the date and score, they shade in the “bar” to show their level – using pencil, because the level may change in the next assessment!



Some of the Standards I have broken down into smaller chucks while others are just “as is.” The lists are fairly long, but we submit grades quarterly, so in each quarter there are roughly 15-20 Standards. There is a separate page for the Mathematical Practices Standards, but those are more difficult to assess.

Teacher Tracking
I record scores “by standard” and only include the most recent score when updating grades. This is not a “quick and easy” task in an electronic gradebook. I “override” scores on a regular basis rather than entering in a whole new set of scores. On a Unit Assessment there will be about 7-10 scores, one for each Standard on the assessment. As I am moving from part time to full time this year, I hope I won’t get bogged down too much 😦 After the Unit Assessment (or any other time) students may re-assess on individual learning targets, not the entire Unit.

Only including the most recent score allows students time, when necessary, to fully understand the concepts, but also requires that students retain their understanding. We have been implementing quarterly Benchmark Assessments in our district, but I have yet to include those scores in the gradebook, as they are just a “snapshot” of the skills.

In the next post, I address my rubrics for assigning levels and overall grades.

Post Navigation