We offer several fact sheets and informational materials on the Quantile® Framework for Mathematics and how to use it.

## Quantile Map

Our Quantile map helps demonstrate the interconnections of skills and concepts and how you can use the Quantile scale to identify how skills and concepts relate to one another and student learning. There are two versions of the map, our printer-friendly version and poster version. ## How are math content standards and materials aligned and calibrated to the Quantile Framework?

Access this flyer to find out.

## General Questions about the Quantile Framework® for Mathematics

### What is the Quantile Framework for Mathematics?

The Quantile Framework for Mathematics is a scientific approach that evaluates the difficulty of mathematical skills and concepts as well as a student’s ability to learn new mathematical concepts. Each of these measures are on a single scale so that the skill demand and student ability can be matched for targeting instruction. Learn more about Quantile measures.

### What impact does the Lexile® measure of text have on the difficulty levels of mathematics materials?

There is a considerable amount of discussion and research about the type of text that is used in mathematics. The readability of technical text is very different from such reading experiences as reading trade books, novels, magazines or newspapers.
In order to minimize the reading demand of some mathematics materials, most parts of a Quantile assessment are built with Lexile measures that are traditionally below expected reading levels of the students addressing the work. The effort is to diminish the reading demand so that the mathematics demand is what is being measured. Learn more about Lexile measures.

### What does a student Quantile measure mean?

A student’s Quantile measure helps to forecast their ability to successfully learn mathematical concepts and master skills (Quantile Skills and Concepts or QSCs) at the introductory level with classroom instruction. As the Quantile measure of a student increases, the mathematics concepts they are able to learn become more complex.

### Why do we only get one Quantile measure for a student?

All content strands are woven together to form the field called mathematics. The Quantile measure indicates overall mathematics ability so it is given as a single value and does not disaggregate a score into various branches of mathematics.

### If a student has a significantly higher Quantile measure than his peers should that student be placed in a higher level mathematics course?

Any decisions made about student placement in their course work should not be made based upon a single measure or test result. Many factors can impact a student’s readiness for more complex concepts in mathematics. Those factors include background knowledge, academic motivation and the ability to independently problem-solve at an abstract level.

The Quantile measure indicates a student is probably ready for the difficulty of material presented at a particular level but is not an indicator of mastery. Students need to be ready for the demand of the material, which is what the Quantile measure shows. In the discipline of mathematics, however, students also need to have learned and been successful with previous material in the curriculum. Mathematics concepts are highly dependent on one another. The Quantile measure demonstrates readiness for instruction but does not indicate which topics have been learned.

### How does a student get a Quantile measure?

A student receives a Quantile measure by taking an assessment which reports Quantile measures. Many state departments of education have their year-end accountability assessments reporting student Quantile measures. Learn more about how to get a Quantile measure.

### How do grade levels relate to Quantile levels?

Quantile measures help educators and parents track student growth in mathematics over time, regardless of grade level. Within any classroom, students will have varying mathematical abilities. Since growth is expected from one school year to the next, Quantile measures do not translate specifically to grade levels. The Quantile Framework provides two sides to the same coin: a measure for students and a measure for skills and concepts. The student Quantile measure describes what the student is capable of understanding. The Quantile Skill and Concept or QSC measure describes the difficulty, or mathematical demand, of that skill. More information about Quantile ranges and grade levels is available using the Quantile® Grade Level Charts on the Lexile® & Quantile® Hub.

### Why emphasize “readiness for instruction” and introductory problems?

A student Quantile measure does not indicate that a student has mastered all of the material at or below the student’s Quantile measure. Introductory problems tend to be straightforward assessments of concept knowledge. More advanced problems that blend with other concepts cloud the picture in terms of predicting the difficulty of the primary concept. Therefore, the Quantile measure of a skill or concept is the mathematical demand at an introductory level.

### What does a Quantile measure on a particular math skill (QSC) mean?

A unique element of a QSC (Quantile Skill and Concept) is that it has a Quantile measure. The measure of a QSC indicates the difficulty of math skills and concepts at an introductory level (first night’s homework). The taxonomy of math skills, concepts and applications has been through field studies and other research efforts in order to determine these difficulty measures. Read more about QSC measures.

### What does the QSC ID mean? (Example: QSC333)

Each QSC has an identification number that consists of two elements: the letters QSC followed by a unique 1, 2, or 3 digit identifying number.

### What is a Knowledge Cluster?

The entire Quantile framework is interconnected through the Quantile Skills and Concepts or QSCs (a skill description with its measure). The Knowledge Cluster for a QSC contains that QSC and its links to other QSCs. The links are determined by prerequisite skills and their measures. Each Knowledge Cluster is assembled to a single focus QSC with supporting, prerequisite and impending QSCs. These connections to the focus QSC are built to inform both the content and the measure of the mathematical progression of skills and concepts.

The power of a Knowledge Cluster allows parents to scaffold instruction by identifying gaps in students’ mathematical backgrounds that frustrate student success in a content area. Additionally, the Knowledge Cluster enriches instruction by informing the interconnectivity and progression of skills and concepts in the field of mathematics. Read more about Knowledge Clusters.

### What is a “prerequisite QSC”?

Prerequisite QSCs describe skills and concepts that are important for students to learn before beginning instruction on the focus QSC. For example, the focus QSC described as “Use patterns to continue numerical sequences; identify the rule” has prerequisite QSCs that expect students to be able to identify missing addends among addition facts and use various counting strategies and manipulatives. The various QSCs are combined from different content strands which demonstrates the interconnectivity and the developmental progression in the study of mathematics.

### What is a “supporting QSC”?

Supporting QSCs represent skills that are not necessary but could be useful to enrich a lesson, make connections across topics as well as strands and help students integrate different mathematical concepts. For the same QSC mentioned above, “Use patterns to continue numerical sequences; identify the rule”, numerous supporting QSCs in the Knowledge Cluster are applications in skip counting such as reading thermometers, telling time or interpreting graphs whose scales are counting in multiple units.

### What is an “impending QSC”?

An impending QSC to a focus QSC means that the focus QSC is a prerequisite to a new skill or QSC that students will likely learn in their future mathematics studies as they logically progress through their coursework. This insight provides a more global perspective of the process, connections and relationships that support a student’s understanding of mathematics.

### What does “EM” stand for?

Emerging Mathematician (EM): Measures below 0Q are reported as EM—Q (e.g., a Quantile measure of -120 is reported as EM120Q) where “EM” stands for “Emerging Mathematician” and replaces the negative sign in the number. This code is predominantly seen for material and student measures at the early grade levels.

### What does “NMQ” stand for?

Not Measurable in Quantiles (NMQ): Material designated as “NMQ” is content that is extensively diverse in QSCs or strands so it cannot be classified within the Quantile framework. Some examples are quizzes, tests, riddles, review sheets/activities, and process skills such as working backwards, justifying, drawing pictures, etc.

### What does “HMC” stand for?

Higher Mathematical Content (HMC): Material designated as “HMC” is content for which we have QSCs but the QSCs have not yet been researched to identify their measures. These QSCs are currently in statistics and precalculus.

### What is a “foundational” QSC?

A foundational QSC describes a skill or concept that only requires readiness to learn. Readiness is based upon the learner’s cognitive experiences rather than knowledge of specific mathematical concepts. Most often these QSCs appear in the pre-K level.

### How do teachers use Quantile measures in the classroom?

The real power of the Quantile Framework for Mathematics is in examining the growth of students’ mathematical achievement wherever the student may be in the development of his or her mathematical thinking. Students can be matched with resources and engaged in instruction that they will find challenging enough to promote growth with a minimum level of frustration for them. Classroom teachers can confidently forecast students’ ability to be successful with lessons based upon matching the student measures to the Quantile measure of the material in the lessons.

### What resources are available for families to help their child in mathematics?

With Quantile®Math@Home, parents and students can access free math resources that are tailored to a student’s individual state, grade, math topic and Quantile measure or math level. Resources include activities, online games, tutorial videos and worksheets.

The Quantile® Summer Math Challenge is a six-week online free math skills maintenance program for students who have just completed grades 1-8. Students can access math learning activities on weekly topics that are aligned with state math standards to help them retain math skills learned during the previous school year.

### What is the Math Skills Database tool?

The Quantile® Math Skills Database is a tool that allows users to see Quantile measures for each state standard and detailed views of Knowledge Clusters. Users can access free resources aligned to Quantile Skills & Concepts (QSCs), state standards and Quantile measures.

### What is the Find Your Lesson tool?

The Quantile® Find Your Lesson tool aligns the Quantile Framework with textbooks and other math curricula. Users can see each lesson’s associated Quantile measure and explore further to identify prerequisite, supporting and impending math skills.

### What is the Quantile® Teacher Assistant?

The Quantile® Teacher Assistant helps educators to differentiate student instruction based on an individual’s or classroom’s Quantile measure. The tool organizes each state’s standards into Knowledge Clusters and aligns them to the Quantile Framework.

### Can I still use Quantile resources if a student doesn’t have a Quantile measure?

The Quantile tools mentioned above are useful for gaining insight into the difficulty and the content sequencing of curricula. Math@Home has a built-in math level estimator.