Reflections and Resources from Tarheelstate Teacher: What is a Leveled Math Assessment?
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What is a Leveled Math Assessment?

I've had this idea stewing in my mind for quite a while {almost an entire year} and quite frankly, I'm pretty embarrassed that it has taken me this long to get to a final draft. I spent the whole summer thinking about math assessments, brainstorming and drafting some ideas for different areas of the curriculum. Finally, this month
{with my "New Year, more motivated New Attitude"}, I put together butt + chair to finally get something done.
Today I'm going to tell you all about what my leveled math assessments are and some of the thought processes behind them. Currently, I have the 4th Grade Multiplication and Division assessment sets ready.

The idea to create leveled math assessments really came from a need for better resources to help communicate how a child is truly doing on grade-level standards in math. I have always had classes with high concentrations of gifted students and average/high average students who can really hang with going beyond grade level expectations. The resources I create and choose to use in my classroom are never busy work nor would I call them "easy." I always aim for challenge and rigor because it keeps the math classroom alive and students' motivated to learn. However, I knew that there had to be a better way to communicate the expectations of grade-level standards and student growth to parents and other stake-holders. I also realized that I wasn't always making students aware of the fact that a challenging activity or problem was higher than grade-level expectations and for students who lack confidence in math, this may have caused them undo stress.

I realized that while I am able to look at a math problem and know whether or not it is below grade level, on grade level (and my students really need to master the task), or above grade level standard (meant to challenge my students' thinking skills), I wasn't making these levels of mastery and understanding clear to my students. My average students deserved to see that although they may not be able to solve the most challenging problems on a test, they were meeting grade-level expectations. It was also important to me for my math assessments to provide my highly gifted students with questions that allowed them to show they were capable of more than the typical grade-level standards. For the handful of truly struggling students in my classroom, they deserved to begin a test at an entry point where they could feel some level of success.

In comes the idea to visibly level my math instruction and assessments. I came up with three categories for levels of mastery--building blocks, goals, and gold. I decided to use 2 dots, 3 dots, and 4 dots to represent the individual levels. I have since changed the "gold" level to "stretching beyond" because I felt it better communicated what students at that level were doing with the standards and NOT communicating that students able to do more challenging math were "winners" of something like a gold medal. I'm in love with "Stretching Beyond" for that level!

Building Blocks (oo) : Building Blocks are pre-requisite skills and understandings that students need to have in order to meet grade-level expectations (a.k.a. GOALS ooo ). Building blocks may include 2nd and 3rd grade standards and are built from a lower form of the 4th grade standard.

Goals (ooo) : Goals are the “on grade level” expectations based directly on the 4th grade standards. You may also find some “Goal” questions that are based directly on the 3rd grade standards, but taken to the next level because it is an understanding that 4th graders need in order to be proficient with the focus concept.

Stretching Beyond (oooo) : Stretching Beyond questions are “above grade level” expectations. The Stretching Beyond level provides you with ideas to stretch students who easily meet grade-level expectations. You may still expect your 4th grade students to achieve understanding of some “stretching beyond” leveled questions, but these are above the expectations as written in the Common Core standards. (For example, I taught my 4th graders the standard algorithm for multiplication and expected them to master it, but Common Core standards do not require mastery of the algorithm until 5th grade.)

My school uses a leveled report card. The dots (oo ooo oooo ) correlate really well with a leveled grading system where a 3 is “meeting expectations” and a 4 is “exceeding expectations.”

I then began thinking about how I could design math assessments based on these levels. I analyzed the Common Core standards for 3rd grade, 4th grade, and 5th grade and began tracing concepts and thinking about what students needed to know and be able to do in order to meet the 4th grade standards. {I'm also working on 5th grade assessments, but 4th grade will be my main focus. Because of the STRETCH level questions in the 4th grade assessments, I'm able to use them to pre-assess my 5th grade math students for many of our learning units.}

Building Blocks grew from previous grade-level standards that directly relate to the 4th grade skill being assessed. If a related standard is not found in the previous grades, I simply reduced the size of the numbers, the steps needed to complete the problem, or thought about what scaffolded instruction a student would need in order to meet the grade level goals.

Stretching Beyond questions are based on 5th grade expectations, when applicable, or were designed to show that the student is able to complete grade-level tasks at a much higher level than expected.

Each assessment set:
• contains three sections of questions: below grade-level, on grade-level, and beyond grade-level expectations
• includes three comparable versions of each of the assessments, allowing you plenty of materials for pre-assessing, mid-unit checks, post assessing, and reviewing concepts (I've even used some of the versions for homework practice or a unit review)
• includes one summative assessment version for each level of understanding using the Version 3 test questions from each concept
• allows you to encourage students who are not yet meeting grade level expectations while challenging students whose skill level is beyond grade level—all within one assessment!
• is aligned to the Common Core Standards for 4th grade {and aligned to previous grade-level standards or 5th grade standards where applicable}
• allows you to provide your students with math assessments that are aligned with a growth-mindset approach to learning using the “building blocks,” “goal,” and “stretching beyond” language
• includes a multi-step word problem assessment with all of the assessment sets
• integrates writing algebraic equations within many of the individual assessments on many concepts
In the Multiplication Computation Assessment above, you can see that each level of understanding contains two problems for students to solve. Problems become increasingly more challenging so that you can see at what point a student "taps out" in their understanding. Students are expected to solve each problem two ways and in the "stretching beyond" standard, they are required to use the standard algorithm as this is required of the 5th grade standards. Here's how the problems increase in difficulty:

Building Blocks: 2 digit by 1 digit and 3 digit by 1 digit
Goal: 4 digit by 1 digit and 2 digit by 2 digit
Stretching Beyond: 3 digit by 2 digit and 3 digit by 3 digit

Since students are not introduced to multiplication like this in 3rd grade, I use this assessment once I have taught multiplication and begin to see that we have different levels of ability and understanding happening in our whole-group lessons. After giving this assessment, I can quickly group my students to target where they are--remediate, support, and enrich!

In Part 2, I talk more about why I'm committed to leveled math assessments.
In Part 3, I share a variety of ways you can use leveled math assessments.

Ready to jump right in with leveled math assessments? Head over to TPT and add to your cart!
 Differentiated Math Resources for 4th and 5th grade; Growth Mindset math assessments, tests, and differentiated quizzes

Click for the Multiplication Leveled Math Assessments and the Division Assessments.

Multiplication Set Assesses: 

•Factors, Multiples, Prime, and Composite {Foundational Multiplication Concepts}
•Multiplicative Comparison Word Problems (includes Writing Equations)
•Multiplying by Multiples of 10
•Multiplication Computation
•Multi-Step Word Problems

 Differentiated Division Quizzes, Tests, and Assessments
Division Set Assesses: 
* Factors, Multiples, Prime, and Composite {Foundational Multiplication/Division Concepts-also found in my Multiplication Assessment Set
* Dividing With Multiples of 10
* Division Computation (using two methods)
* Multi-Step Word Problems (includes Writing Equations and Explaining Reasonableness of Answers)
* Division Problems with Interpreting Remainders (all three assessment versions use a cohesive theme! So engaging)
These are also bundled together here

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