Tiered Math Assessments

Tiered assessments allow students to show their understanding at varying degrees of challenge. Besides tests, we also  offer tiered projects and performance assessments. Below, you’ll find examples of tiered tests. We’ve worked to improve these over the years. Recently, we’ve worked to merge the three choices into a single test.  Students can now choose green, blue, or black challenges for each intended learning goal after showing grade-level proficiency with the questions required of all students. Here is an example. This innovation has increased choice (kids can choose green for some learning goals and blue or black for others) and eliminated the need for retests as a safety net for kids who try blue or black tests (since all students are asked to demonstrate grade level proficiency on the “all” questions).

*** 8th Grade (Mostly) Algebra ***

Solving Linear Equations and Evaluating Expressions
Green Assessment Solutions
Blue Assessment Solutions
Black Assessment Solutions

Problem Solving with Linear Equations
Green Assessment Solutions
Blue Assessment Solutions
Black Assessment Solutions

Analyzing Patterns, Relations, and Functions
Green Assessment Solutions
Blue Assessment Solutions
Black Assessment Solutions

Linear Functions – Numerical, Symbolic, and Graphical Representations
Green Assessment Solutions
Blue Assessment Solutions
Black Assessment Solutions

Solving, graphing, and applying linear systems of equations
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Solving Problems in 2 and 3-D Space
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Angle Relationships
Green Assessment
Blue Assessment
Black Assessment

Exponents, Radicals, and the Pythagorean Theorem
Green Assessment Solutions
Blue Assessment Solutions
Black Assessment Solutions

Polynomials and Quadratic Equations
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

*** 7th Grade ***

Algebraic Expressions and Integers
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Simplifying Expressions and Solving Basic Equations
Green AssessmentSolutions

Factors, Fractions, and Exponents
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Operations with Fractions
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Ratios, Proportions, Percents, and Probability
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Solving Multi-Step Equations
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Area and Volume
Green AssessmentSolutions
Blue AssessmentSolutions
Black AssessmentSolutions

Data Analysis (Histograms and Box and Whisker Plots)
Green Assessment
Blue Assessment
Black Assessment

*** 6th Grade ***

Number Sense and Algebraic Thinking
Green Assessment
Blue Assessment
Black Assessment

Decimal Operations and Applications
Green Assessment
Blue Assessment
Black Assessment

Number Patterns and Fractions
Green Assessment 1
Blue Assessment 1
Black Assessment 1

Green Assessment 2
Blue Assessment 2
Black Assessment 2

Ratios, Rates, Proportions, and Percents
Green Assessment 1
Blue Assessment 1
Black Assessment 1

Green Assessment 2
Blue Assessment 2
Black Assessment 2

Area and Volume
Green Assessment
Blue Assessment
Black Assessment


26 responses

16 07 2010
Carlos Valencia

First, let me say that I enjoyed working through all of the “Black” level assessments for the “8th Grade Algebra Course (and a touch of Geometry)”! They were indeed quite challenging.

Second, I wanted to point out what I consider an error in the wording of problem #3 of the 8th grade “Problem Solving with Linear Equations” Black assessment. The final solution one arrives at algebraically is indeed n = 80 bags of flour (which I note your solution key also shows); however, the solution of 80 bags of flour at the outset does NOT satisfy the problem requirement for “all transactions involving whole bags.” In fact, after the first gate, which leaves the merchant w/ 74 bags (i.e., 7/8 * 80 = 70, plus the four bags returned to the merchant…), all other tax transactions involve fractional amounts of bags!

The problem statement should probably say something like “If the merchant starts and ends w/ a whole number of bags, find the value of n” as its last sentence if you wish to retain the final answer of n = 80 bags.

17 07 2010
Carlos Valencia

In looking over the online solution key for the “8th Grade Algebra Course (and a touch of Geometry) – Analyzing Patterns, Relations, and Functions” Black assessment, I wanted to point out something that as a Physics and Math teacher I would consider an error in your posted solution: Your vertical axis for problem #3 (the two colliding trains w/ a fly traveling between them…) should NOT be labeled “Distance.” Instead, the appropriate term for that particular axis quantity should be “Position.”

In the case of your solution graph, what you’ve really shown is the position of each quantity (Trains A & B, as well as the fly) relative to the starting position of both Train A and the fly. In physics this makes a huge difference whether we use the appropriate term “position,” since velocity then can be easily defined as an appropriate signed quantity corresponding to the slope along the position vs. time graph.

The earlier you can get students used to the difference between “position” and “distance,” the better! (Esp. while working w/ nice, simple 1-D motion graphs!)

17 07 2010
David Suarez

Thanks a lot for the feedback, Carlos. I’ll pass your comments along to our 8th grade team so they can think about what you’ve said when they arrive at that unit during the coming school year. It feels really good to hear you say that you enjoyed working through the problems, and that they seemed quite challenging. You clearly know your stuff, and if you found the problems challenging while finding only those two errors, then I think we’re doing pretty well. If you find anything else, please let us know. Thank you again!

21 11 2010
Jen

I just found your site, and am blown away by the assessments your team has created. I work in an urban school, where the need for tiered assessments and instruction stems from a broad range of readiness for Algebra. I was wondering if you could describe (or post examples) of the type of work you have students do in class – or how you structure your classes. Do all students receive the general instruction, and then divide up afterward? Any information/resources would be much appreciated, as I am always trying to catch my lower skilled kids up, while pushing my higher level students as far as they can go.

Thanks!

21 11 2010
David Suarez

Thanks for the comment, Jen. Where do you work? I don’t think it’s a coincidence that this work started in an urban school in Oakland (though we were applying it in science classes at the time). The range of readiness in our classes was huge, which had a major impact on classroom managment, culture, and learning in general. The strategy helped in a big way.

About running a class – Could you check out the comments section of the “Tiered Instruction and Assessment” page. A similar question was asked and I discussed some lesson design approaches we use.

5 01 2011
Rachel

Hi, David.

I am *so* impressed by these assessments, and find myself referring to them, constantly, when planning my own instruction. I noticed, however, that all the beautiful and incredible sixth grade math assessments are no longer available! I’m hoping this is a glitch – ? I’d LOVE access to them, again. They are amazingly useful! Any way to get them on the site, again? (I’m sure others would benefit, too.)

Thanks,
Rachel

6 01 2011
David Suarez

Rachel,
I’m thrilled to hear these resources have been useful. Realizing that teachers use these assessments as examples to learn and build from, I’m trying to make sure they all represent tiered assessment at its best – problem solving challenges that are natural conceptual extensions for the knowledge and skills assessed during a given unit. I’m sorry if the absence of the 6th grade assessments is holding you back at all. I hope to upload improved 6th grade assessments in the near future.
David

16 01 2011
Rachel

Oh, great! Thanks so much. I’ll be glad to have them back, but can definitely make do without them, for a while. =)

Rachel

10 11 2011
Marc Alvarez

This is incredible! I teach 5th grade G.T. math, and have found the tiered assessments to be invaluable…especially as I work on making my own assessments. Thanks!

10 11 2011
David Suarez

It’s great to hear a comment like this, Marc. Thanks for the feedback and enjoy!

12 05 2012
kacavill@yahoo.com

Hi there!

Excellent job on the tiered assessments! A lot of work has gone into what your team has created and is so helpful to us teachers who care to reach all of our students. Using Challenge by Choice in my classroom has made a great difference in the students’ motivation to work out their tasks! Anyhow, I was wondering if you could share your textbook/workbook resources used for 8th grade Pre-Algebra/Algebra?

Thanks,
Kristin

12 05 2012
David Suarez

Thanks so much for the positive thoughts, Kristin. At the time these assessments were developed, 7th grade teachers were using Prentice Hall Pre-Algebra and 8th grade teachers were using McDougal Littell’s Algebra 1 Concepts and Skills. Supplemental problems were offered from a wide variety of sources. http://challengebychoice.files.wordpress.com/2007/09/7th-and-8th-grade-problem-set-bibliography.pdf

5 07 2012
Irene Davy

The other posts say it all, this is wonderful work. Do you have plans to extend the resources down to lower grades?

Thanks,
Irene

5 07 2012
David Suarez

Thanks, Irene. I’d love to be part of team effort to develop resources for lower grades, but that isn’t in the cards at the moment.

19 07 2012
Laurie Byrne

FYI, in 7th grade, the blue assessment for simplifying expressions and solving basic equations is a repeat of the blue Algebraic Expressions and Integers. I really love this tiering!!!! Thank you for sharing them.
Laurie

19 07 2012
David Suarez

thanks, Laurie! I just tried to fix… look and see.

3 06 2013
Chris Sykes

Will there be a posting for solutions to Grade 6?

3 06 2013
dsuarezteacher

sorry, Chris. i don’t have plans to post grade 6 solutions.

15 08 2013
Kathy Borst

So, there is nothing to keep students from finding this site, right? Do you share the contents of the tests with your students ahead of time or are these just sample tests for the rest of us?

15 08 2013
dsuarezteacher

Yes, that’s right. Our tests have evolved over the years, and these are samples. Here’s an example of a recent test if you’re interested.

15 08 2013
Kathy Borst

Thanks. That is interesting. Still very skill based tests. Do you do anything with more conceptual or applied kinds of questions? Maybe shorter tests that target a couple or a few skills and require students to do more thinking than recall? I’m super interested in multiple levels of things like that.

17 08 2013
dsuarezteacher

We enjoy supplementing tests like these with more conceptual and/or applied tasks. For an example, check out the tiered performance task on the classroom videos page. This was given in addition to the test you looked at.

15 10 2013
ejohn

Are there solution keys to the 6th grade assessments?

15 10 2013
dsuarezteacher

Sorry. No, these were provided by some generous 6th grade teachers a while back, and I don’t have solutions to share.

15 10 2013
ejohn

I apologize — I meant to reply to your post, but I made a new one instead :)

15 10 2013
ejohn

Very generous indeed — they are excellent assessments, and I am so grateful for this resource! I am trying this approach with my Math 6 Accelerated class –beginning our unit on number patterns and fractions with a formative assessment. It was so interesting to see my students choose the color/challenge of choice. Several went for black and then soon asked to try blue. Some went for blue and asked to go to green. I am trying to think about how I will use these assessments to inform my teaching. I saw the sample tiered questions (practice) — I will continue to look through this site to learn more. Thank you!

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