Indicator 2d

Indicator 2d The three aspects of rigor are not always treated together and are not always

treated separately. There is a balance of the three aspects of rigor within the

grade.

Scoring

2 points

● All three aspects of rigor are

present independently

throughout each grade level.

AND

● Multiple aspects of rigor are

engaged simultaneously to

develop students’ mathematical

understanding of a single

topic/unit of study throughout

each grade level.

1 point

● All three aspects of rigor are not

present independently

throughout each grade level.

OR

● Multiple aspects of rigor are not

engaged simultaneously to

develop students’ mathematical

understanding of a single

topic/unit of study throughout

each grade level.

0 points

● All three aspects of rigor are not

present independently

throughout each grade level.

AND

● Multiple aspects of rigor are not

engaged simultaneously to

develop students’ mathematical

understanding of a single

topic/unit of study throughout

each grade level.

About this indicator:

What is the purpose of this Indicator?

This indicator, along with 2a, 2b, and 2c, determines the shift of Rigor. Grade-level materials must include a

balance of conceptual understanding, procedural skill and fluency, and application, and this balance should be

evident in supporting students as they develop mathematical understanding.

Research or Standards connection:

● Common Core State Standards for Mathematics (CCSSM)

● K-8 Publishers' Criteria for the CCSSM (Summer 2012)

● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics

● Achieve EQuIP Rubric for Lessons & Units

● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments

Resources:

● SAP Coherence Map

● Institute for Mathematics Education Progressions Documents

● Reading: “Principles To Actions”, (NCTM) p. 42-48

● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)

● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)

● Video: “Building Conceptual Understanding in Mathematics” (NCTM)

● Video: “Conceptual Understanding Excerpt” (The Hunt Institute)

● Concrete Representational Abstract: Instructional Sequence for Mathematics

● Achieve the Core: Situation Types for Operations in Word Problems

Indicator 2d Guiding Question:

Do the materials balance the three aspects of rigor?

Evidence Collection

Note: Consider the intent of the program to balance the three aspects of rigor, not the quality of the

materials—indicators 2a-c focus on the quality of materials. Evidence should be different than the evidence

collected for 2a, 2b, and 2c.

Collect evidence demonstrating how the three aspects of rigor are present independently throughout each

grade level.

Collect evidence demonstrating where multiple aspects of rigor are engaged in simultaneously to develop

students’ mathematical understanding of a single topic/unit of study throughout each grade level, for example:

● Consider whether materials use conceptual understanding to develop procedural skill and fluency.

● Consider if students use multiple representations (i.e. manipulatives, drawings, expressions, equations,

tables, graphs, charts, number lines, etc.) and written/oral explanations to support their work in application

problems.

Do the materials emphasize one aspect of rigor over the others in specific units? If so, do the materials work to

maintain balance throughout the grade level?

Cluster Meeting

Consider the following question(s) as evidence is synthesized:

● How are the three aspects of rigor present independently throughout each grade level?

● How are multiple aspects of rigor engaged simultaneously to develop students’ mathematical

understanding of a single topic/unit of study throughout each grade level?

● Do the materials emphasize one aspect of rigor over the others in specific units? If so, do the materials

work to maintain balance throughout the grade level?

Gateway 2: Rigor & Mathematical Practices

Criterion 2.2

Standards for Mathematical Practice

Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical

Practice (MPs).

What is the purpose of this Criterion?

The purpose of this criterion is to ensure the Standards for Mathematical Practice are identified and connected

to grade-level mathematical content, and the materials present opportunities for students to both learn and

independently demonstrate each of the MPs.

Research Connection

● Common Core State Standards for Mathematics (CCSSM)

Scoring

Note: If the materials do not identify the MPs for teachers, evidence of this will be included in the

Practice-Content Connections criterion report. The lack of identification of the MPs will result in the deduction

of 1 point in the scoring for indicator 2e only.

Meets Expectations

● 9-10 points

Partially Meets Expectations

● 6-8 points

Does Not Meet Expectations

● <6 points

Gateway 2: Rigor & Mathematical Practices

Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and

the Standards for Mathematical Practice.