# Quantile framework for mathematics

## Quantile math level chart

A Quantile® calculation and a Quantile® scale make up the Quantile® Framework. The complexity of a mathematical ability, concept, or application, as well as a student’s comprehension of these mathematical skills and concepts, is represented by a Quantile® scale. Quantile® measurements are numerical values accompanied by a “Q” (for example, 850Q) that indicate a location on the Quantile® scale.
From below 0Q (Emerging Mathematician) to above 1600Q, the Quantile® System covers the developmental spectrum from Kindergarten mathematics through the content traditionally taught in Algebra II, Geometry, Trigonometry, and Pre-calculus.
Quantile® tests eliminate the guesswork from evaluating which mathematical skills a developing mathematician has mastered and which still need to be taught. They help educators and parents target instruction and track student development against the mathematical demands of college and employment, which enhances mathematics teaching and learning.
Additional mathematics assessments and instructional programs may use Quantile® metrics to report on students’ results. Visit MetaMetrics to find a list of assessments that include student Quantile® measures organized by assessment form.

## Quantile math at home

Quantiles® are used to set student achievement benchmarks and goals. You can use them to see how your child compares to others, learn what they know, and decide where additional assistance might be needed.
A student’s math achievement, not their grade level, is calculated by a Quantile®. Educators would likely use a variety of Quantile® student interventions to target curriculum and remediate as required in a class.
Students will see where mathematics comes from and how it is used in daily life through recognizing mathematical principles. Students gain an understanding of why mathematical methods function by studying underlying mathematical principles.
Practice is important in all sports, including music, dance, athletics, and others. Practice helps students solve more complicated problems by increasing their calculation speed (automaticity) and versatility with numbers (fluency).
This free website contains a variety of resources and family-friendly activities to help your child learn. You and your child can use [email protected] to practice basic mathematical skills and concepts at the appropriate level of difficulty. This tool has it all, from making personalized lists of resources and learning goals to partnering with your child’s teacher to create activities to practice outside of school.

### Metametrics

Quantiles are cut points in statistics and probability that divide a probability distribution’s range into continuous intervals with equal probabilities, or divide the observations in a sample in the same way. The number of groups generated is one less than the number of quantiles. Quartiles (four groups), deciles (ten groups), and percentiles are all names for common quantiles (100 groups). The groups formed are referred to as halves, thirds, quarters, and so on, though the words for the quantile are often used for the groups formed rather than the cut points.
q-quantiles are values that divide a finite set of values into q (nearly) equal-sized subsets. There are q 1 q-quantiles, one for each integer k that is satisfied by 0 k q. In certain cases, such as the median (2-quantile) of a uniform probability distribution on a set of even size, the value of a quantile may not be uniquely determined. Quantiles can also be used on continuous distributions, allowing rank statistics to be applied to continuous variables (see percentile rank). The q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values 1/q, 2/q,…, (q 1)/q when the cumulative distribution function of a random variable is known.

### Quantile range

The Quantile Framework for Mathematics is a scientific method for assessing mathematical achievement and determining the complexity of mathematical abilities and concepts. A Quantile calculation and a Quantile scale make up the Quantile Framework. In the fields of Geometry, Calculation, Number Sense, Computational Operations, Algebra and Algebraic Reasoning, Data Analysis, Statistics, and Probability, a Quantile measure reflects the complexity of a mathematical skill, principle, or application, as well as a developing mathematician’s comprehension of these mathematical skills and concepts. Quantile measurements are numerical values preceded by a “Q” (for example, 850Q) that indicate a position on the Quantile scale.
From below 0Q (Emerging Mathematician – EM) to above 1600 Q, the Quantile System covers the developmental spectrum from Kindergarten mathematics through the content traditionally taught in Algebra II, Geometry, Trigonometry, and Pre-calculus.
As shown in Figure 2, quantile measures can be used to chart a student’s progress toward career and college readiness. The spectrum of mathematical demands of post-secondary pursuits can be found near the upper right-hand corner, ranging from approximately 1220Q to 1440Q. Individual grade level ranges for students’ mathematical skills are also visible, forming a road toward college and career readiness once more. This trajectory can be used by students, their parents, and their teachers to track their growth and development over time.  