In any classroom, in every grade, you’ll find a wide variety of math abilities. Quantile® measures provide educators with useful data to help track their students’ growth in math no matter what grade they’re in. Quantile measures provide an alternative — and possibly more useful — measure of mathematics ability than grade-equivalent scores.

• Quantile measures are the same across many different state assessments and math programs.
• Quantile measures show a clear growth path over time.

There’s no direct correspondence between a specific Quantile measure and a specific grade level. Given that there is a range of student abilities within each grade, you might find it useful to see what the typical Quantile measures are within a given grade. Based on research studies conducted by MetaMetrics®, the chart below provides ranges for typical student performance at a particular grade or math course. Data for these norms came from a large sample of students who were administered tests that reported Quantile measures in the years 2010 through 2016. However, please note:

• This information is for descriptive purposes. The goal is to give you a sense of how a student’s Quantile measure (mathematics ability) compares to Quantile measures for students in the same grade. The ranges are not intended to be a guide or standard that students are expected to reach. See our FAQ on performance and content standards, norm-referenced interpretations, and criterion-referenced interpretations of test scores for more information.
• The Quantile range shown is the middle 50 percent of student measures for each grade. This means that 25 percent of students had Quantile measures below the lower number and 25 percent had Quantile measures above the higher number.

*Measures below 0Q are reported as EM—Q where “EM” stands for “Emerging Mathematician”.

 Grade Student Measures (25th to 75th percentile, Mid-Year) 1 EM70Q to 205Q 2 130Q to 390Q 3 305Q to 555Q 4 455Q to 700Q 5 570Q to 820Q 6 670Q to 915Q 7 765Q to 1010Q 8 845Q to 1090Q 9 915Q to 1160Q 10 975Q to 1225Q 11 & 12 1030Q to 1280Q

Emerging Mathematician (EM)
is a code given to students and mathematics materials that measure below 0Q on the Quantile® scale. The lower the number following the EM code, the more complex the materials or the more skilled the student. The higher the number, the less complex the materials or the less skilled the student.

MetaMetrics has also studied the difficulty of lessons in mathematics textbooks commonly used in the United States to help understand the mathematics demand that students will likely encounter in their elementary through high school mathematics courses. Results are shown in the table below. In a related study, MetaMetrics found that the mathematics ability needed for college and career readiness ranged from approximately 1220Q to 1440Q, and the median mathematics demand for college and career readiness was 1350Q. Read our research briefs describing this work: A Quantitative Task Continuum for K-12 Mathematics and The Quantile Framework for Mathematics Quantifies the Mathematics Ability Needed for College and Career Readiness.

## Quantile Lesson Measures to Guide Mathematics Instruction for College and Career Readiness

 Grade Lesson Complexity Measures (25th to 75th percentile) 1 EM50Q to 80Q 2 40Q to 300Q 3 240Q to 490Q 4 390Q to 680Q 5 560Q to 810Q 6 680Q to 890Q 7 800Q to 950Q 8 840Q to 1050Q 9 900Q to 1150Q 10 1070Q to 1230Q 11 1100Q to 1350Q

Grade equivalents are scores based on the performance of students in the test’s norming group. The grade equivalent represents the grade level and month of the typical (median) score for students. For example, a 5th-grade student who earns a 5.9 on a norm-referenced test has earned a score similar to the 50th percentile students in the test’s norming group who were in their ninth month of fifth grade.

### Common Issues with Grade Equivalents

Grade equivalent scores are often misinterpreted as being a grade level standard. A grade equivalent of 5.9, for example, does not necessarily represent the desired level of achievement for all grade 5 students at the end of the school year. It simply represents the norming group’s median score, or projected score at that point in time. Achieving the same score as the average student in the norming group may not be an appropriate goal for all students. In contrast, Quantile measures are not generated from grade level norms and do not presume a specific grade level interpretation. When using Quantile measures, struggling students are not stigmatized with a grade equivalent that labels them as “below grade.” Rather, students have an independent Quantile measure and can be matched to appropriately challenging mathematics materials within their Quantile range.

Grade equivalent scores do not represent the appropriate grade placement for a student or the level of the material the student should be studying. Imagine a student who takes a fourth-grade math test and receives a grade equivalent score of 6.9. The 6.9 does not mean that she’s mastered sixth-grade mathematics material or that she should be studying sixth-grade math. All you know for sure is that the student scored well above the average third-grade student in the norming group in math on the material presented on the test. Because the Quantile measure does not suggest grade level placement, this type of misinterpretation does not occur. The Quantile measure can be used to identify material at the appropriate difficulty level for the student regardless of the student’s grade level.

### Measuring Growth

In addition to potential misinterpretations, the grade equivalent scale makes it more difficult to accurately measure growth. The grade equivalent scale is not an equal-interval scale. In other words, a student who moves the same number of grade equivalents at one level on the scale (e.g., from 2.5 to 2.9) has not necessarily “grown” the same amount as a student who moves the same number of grade equivalents at a different level on the scale (e.g., from 8.5 to 8.9). Because grade equivalents are not equal-interval, comparisons should not be made between the amount of growth at different locations on the scale.

In contrast, the Quantile scale is an equal-interval scale. Regardless of the point on the scale, the amount of growth in ability required to move between two points is the same. In other words, moving from 240Q to 340Q on the Quantile scale represents the same increase in ability as moving from 840Q to 940Q. Because Quantile measures are equal-interval units, they can be used in mathematical calculations. Read our paper The Hippocratic Oath and Grade Equivalents for a more in-depth discussion of Lexile or Quantile measures and grade equivalents.

## Looking for More Research?

MetaMetrics has gathered years of research as well as conducted its own research on better ways to measure student math ability and report growth.