scoring rubric for math problem solving

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Math Resources

Sample tasks, anchor papers, assessment tutorial, student communication, getting started, tips for using, k-5 printables, classic math integration, tech support.

Exemplars math rubrics are excellent tools for assessing student work and for encouraging student self- and peer-assessment. Our performance material includes standards-based rubrics that define what work meets today's standards, allowing teachers (and students) to distinguish between different levels of performance. We also provide tips on how to introduce your students to rubrics .

See all Exemplars math rubrics »

Our differentiated, problem-solving tasks promote critical thinking and reasoning, and call on students to practice and apply mathematical ways of thinking to real-world issues. Material can be used for instruction, assessment, and/or professional development.

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In addition to rubrics for teachers and students, Exemplars performance material in mathematics also includes student anchor papers and scoring rationales.

Samples of student work are provided at each of the four performance levels of the Exemplars rubric: Novice , Apprentice , Practitioner (meets the standard), and Expert . Our scoring rationales identify important distinctions for teachers to look for when assessing students. Learn more »

The more you practice, the stronger your skills become. That's why we've launched the interactive K–5 Exemplars Scoring Tutorial. This online tool lets you hone your assessment skills in problem solving through practice as you score sample student work in accordance with the  Exemplars Standards-Based Rubric . The time you spend reinforcing your assessment skills pays off in gaining a clearer picture of where your students stand and where your instruction should take them next. So put yourself to the test and  give it a try !

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Communication is fundamental. It is not only the vehicle by which we convey our thinking to others, but it is the way in which we process information. As we organize our thoughts to communicate, we learn content – understanding how to communicate that content must be considered a basic skill in our schools today.

Asking your students to communicate their thinking or to write about their problem-solving process on a particular math task encourages them to analyze their work more closely. Student's work must include communication, or it will not meet the (Exemplars) standard.  Learn helpful techniques for encouraging communication in math »

For 30 years, Exemplars has worked with schools and districts to integrate performance-based assessment and instruction into math curriculum. To help your school or district get started, check out our Administrator's Tools for Success . 

Administrators, teachers, and coaches can also read our 5 Days of Exemplars blog series to see what classroom application looks like.

Exemplars makes it possible for schools, districts, and teachers to implement excellent performance-based assessment and instruction. Below are some suggestions from experienced Exemplars users and workshop participants to assist with your success. 

• Select an Exemplars math task of the month
• Select several Exemplars math tasks to do in common and then get together to assess the work and discuss students' performance
• Correlate Exemplars math tasks with your textbooks, frameworks, and/or curriculum
• Use the Exemplars assessment rubrics
• Share anchor papers and kid-friendly rubrics with students
• Refer to the "Getting Started" section of the Math Library
• Be sure your teachers are aware that Exemplars math tasks are available and readily accessible for use in their classrooms
• Support your staff with  professional development
• Select and train "mentor teachers."
• Read Exemplars Math Blogs
• Check out Exemplars YouTube Channel to see and learn how schools/districts are implementing our material.

Five and Ten Frames

• Five Frames, 3 to a page
• Five Frames, 6 to a page
• Ten Frames, 4 to a page
• Ten Frames, 12 to a page

Number Lines

• Blank number lines
• 0-100 by 5s
• Fraction number lines: halves, thirds, fourths, fifths, sixths, eighths, tenths, twelfths

Number Charts

• 0-99, 1 to a page
• 0-99, 4 to a page
• 1-100, 4 to a page

Bar Graph/Grid Paper

• Blank bar graph paper
• Bar graph paper by 1s to 12 on y-axis, blank x-axis
• Bar graph paper by 2s to 22 on y-axis, blank x-axis
• Bar graph paper by 10s to 100 on y-axis, by 1s to 7 on x-axis
• Bar graph paper by 2s to 48 on y-axis, by 1s to 18 on x-axis
• Bar graph paper by 5s to 130 on y-axis, by 1s to 16 on x-axis

Fraction Resources

• Fraction strips from 1 whole to twelfths

Exemplars Getting Started Guide offers suggestions on how to integrate our classic "Best of Math" products.

Learn more »

Find support and instructions for installing, using, and maintaining our classic "Best of Math" products.

Learn more »

emergent math

Lessons, Commentary, Coaching, and all things mathematics.

A rubric to assess the eight Common Core State Standards of Mathematical Practice

Update 8/2/21. After reviewing feedback from teachers who have implemented the rubric in its draft form, I feel confident in removing that modifier of “draft.” Consider the rubric below for the Standards of Mathematical Practice as Version 1.0.

The Common Core Standards of Mathematical Practice (MPs) have been available for a while now. They lay out eight habits that mathematicians embody. They’ve been instructive in what to teach and how to teach. They’ve also been helpful in providing a comprehensive vision of what math classrooms can be.

They’re also painfully challenging to interpret and assess. What does it mean for a student to “look for and make use of structure?” And how can we measure student achievement and growth in these areas?

To these questions, I offer a rubric. There’s a phrase I heard at a High Tech High PD once – “ possibly incorrect and definitely incomplete .” I would apply that sentiment to this rubric. I drew upon a few individuals and a few books and other resources to guide its creation. When I worked for New Tech Network I was part of a team that created rubrics with Stanford’s Center for Assessment and Learning for Equity (SCALE) which helped me craft rubrics for non-content outcomes (while also teaching me just how hard it is to create a rubric).

I find rubrics eminently helpful in understanding what students know and can do and where to go next. Rubrics are as much a scaffolding tool as they are an assessment tool.While I was unable to find a CCSS MP rubric, it’s possible that another, better one exists. If that’s the case feel free to use that one, this one, a combination, or whatever you like. Personally the act of creating a rubric and doing the work helps clarify and challenge my own thinking. At the bottom of this post, I’ve listed some of my other blog posts on assessment and rubrics.

A rubric that accurately and equitably assesses the eight standards of mathematical practice could be a boon for schools and teachers desiring to develop a system of student portfolios, as I often advocate. I would absolutely consider using this rubric throughout a school year for your portfolio problems.

I want to acknowledge that this rubric and assessment and teaching of the MPs is probably not top-of-mind for teachers. At the current writing, we’re figuring out how – if at all – we’ll be able to meet with students in person or virtually, whether it’s safe to teach in person during an unrestrained epidemic of COVID-19, while in the midst of a real reckoning with our systemic oppression of communities of color. Also, in education there’s a particular thorniness around assessment and race. Standardized tests are weaponized to prevent access to education and opportunity.

While this rubric is an attempt to move to a more equitable way of assessment, rubrics have also been tools of oppression, and it would be foolish to think that this particular rubric couldn’t be used in such a manner. This rubric is being dropped into an environment which did not ask for it.

Before we get to the rubric itself, I’d like to submit a few principles for rubric use:

Rubric Assessment Principle 1 : Approach any and all forms of assessment, particularly rubrics, with a great deal of humility. You, nor I, are the arbiter of student knowledge. My interpretation of student work can differ and be incorrect. Make sure you’re approaching student work with willingness to be convinced that your rubric score may not be the best rubric score.

Rubric Assessment Principle 2 : Be aware of your own biases and be aware that you have biases you don’t know you have. Dovetailing from the previous principle, it’s crucial to understand that you have biases. You have racial biases, behavioral biases, and biases around what you value in students and student work. It’s important to acknowledge these biases while also acknowledging you have biases that you are unaware of.

Rubric Assessment Principle 3 : Don’t try to assess every row on every problem . Large rubrics such as this one are not meant to be used wholesale. Also, most problems are ill suited to assess more than a handful of MPs effectively. Instead, take a couple of rows for a particular problem and assess those in laserlike fashion.

Rubric Assessment Principle 4 : Assessing is not the same as grading. This rubric is not necessarily meant to have score totals afixed to each column. It’s meant to be a diagnostic as well as a pathway of improvement. Grades can stunt both of those goals.

There are many more tips, tricks, strategies, do’s, don’ts and best practices around rubrics, but I’ll leave it at those four principles for now.

I also want to acknowledge my instructional background is in secondary education. As such, I can’t truly say how useful this rubric is at the elementary (or even lower level junior high) level. I’m writing and crafting from a vantage point of a high school teacher. Also, one of the things I really struggle with when creating a rubric is that first column (in this case, I’ve dubbed it “Emerging.” I end up using more negative language than I would care to: “fails,” “does not,” etc. Right off the bat, I know that’s something I need to improve about the rubric.

At this point I’d like to state that I’m by no means an expert. Maybe I’ll be able to claim expertise when I complete my PhD program (which I’ve yet to start), but for now I’m just someone who’d like to have a good tool to assess and teach the MPs, and currently I’m not able to find a satisfactory one. It’s very possible (probable) I’ve misinterpreted the MPs and how they show up in student work. I genuinely struggle with differentiating between MP7 and MP8. It’s quite possible this rubric isn’t particularly useful in a virtual environment. It’s certainly not top of mind for most educators right now. However, I wanted to put it out into the world so that A) you’d have it for the following school year, particularly if you intend to use some sort of portfolio assessment system, and B) so that we can improve it. I hope you’ll offer the gift of constructive feedback so we can make this tool more useful, more instructive, and more edifying for a student and teacher.

Some of the MPs (and therefore, the rubric indicators) are as much behavioral as they are artifactual. For example, how do students demonstrate “perseverance?” Unless you have students journal about their problem solving experience (which is an entirely valid task) it is hard to measure “perseverance” based on the student work alone. You may have to assess that row based on conversations with students, evidence based observations, or other method.

Now let’s get to the rubric. You’ll find a google doc and PDF version below.

• CCSS MP Rubric ( Google Doc )

I leaned heavily on this rubric throughout my mini-series on crafting and using rubrics. I recommend checking out those posts, and we explore terms like “common indicators” to help us consider how to use this rubric in class.

Here are a few of my posts on rubrics and assessment that may be instructive.

• Equalizing practice and assessment (Part 1)
• Equalizing Practice and Assessment (Part 2): What You Value Should Be What You Assess
• Specifics before Strategies (the creation of a rubric)
• Your Student Portfolio System Begins Now
• Portfolio Problems: Rebuilding Assessment with Rich Tasks
• Assessment via audibles

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