Indicator 2c

Indicator 2c Materials are designed so that teachers and students spend sufficient time

working with engaging applications of the mathematics.

Scoring

2 points

● Materials include multiple

routine and non-routine

applications of the mathematics

throughout the grade level.

AND

● Materials provide opportunities

for students to independently

demonstrate multiple routine

and non-routine applications of

the mathematics throughout the

grade level.

1 point

● Materials do not include multiple

routine and non-routine

applications of the mathematics

throughout the grade level.

OR

● Materials do not provide

opportunities for students to

independently demonstrate

multiple routine and non-routine

applications of the mathematics

throughout the grade level.

0 points

● Materials do not include multiple

routine and non-routine

applications of the mathematics

throughout the grade level.

AND

● Materials do not provide

opportunities for students to

independently demonstrate

multiple routine and non-routine

applications of the mathematics

throughout the 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. Materials should include activities with a

variety of contexts for both routine and non-routine applications. Students should apply mathematical knowledge

in real-world contexts to make meaning of and access the content.

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 2c Guiding Questions:

Do the materials develop students’ ability to utilize mathematical concepts and skills in engaging applications

throughout the grade level?

Do the materials provide opportunities for students to independently demonstrate application of mathematical

concepts and skills in real-world contexts throughout the grade level?

Evidence Collection

Application problems often, but not always, present a real-world scenario. Students employ a prescribed

mathematical strategy or choose their own strategy to find a solution. Example: students apply knowledge

about multiplication (Grade 3) to calculate volume (Grade 5).

Collect evidence of problems/activities that align to the standards/clusters for each grade level that address

application. Note whether the materials include a specific section in units/chapters/lessons, etc. that is

specifically designed for application.

Collect evidence of problems/activities where students independently demonstrate applying mathematics.

Evidence should include students solving problems in a variety of contexts, and students should be able to

make their own assumptions or simplifications in order to model the contexts mathematically.

Routine applications are prescriptive word problems that provide a situation and a question. They have a real

world context, but the problems generally include all necessary (and no extraneous) information. The problems

are designed to elicit particular mathematical strategies. The correct answers are usually pre-determined.

Non-Routine applications include unfamiliar/novel contexts. These problems often present a real world

scenario, and students employ their choice of mathematical strategies to find a solution. Thus, the problem is

open in the middle and closed at the beginning and end. Target answers are known, although the solutions

may be allowed to have some variation.

Collect evidence from the materials of multiple routine and non-routine applications of the mathematics

throughout the grade level.

Collect evidence of opportunities for students to independently demonstrate multiple routine and non-routine

applications of mathematics throughout the grade level.

Examples of specific standards/clusters that address application include, but are not limited to:

Grade Standards

Kindergarten K.OA.2

K.G.1

Grade 1 1.OA.A

1.MD.4

Grade 2 2.OA.A

2.MD.5, 8, 10

Grade 3 3.OA.3, 8

3.MD.A, D

Grade 4 4.OA.A

4.NF.3d, 4.NF.4c

4.MD.2

Grade 5 5.NF.2, 6, 7c

5.MD.5b

5.G.2

Grade 6 6.RP.3

6.NS.1

6.EE.7, 9

Grade 7 7.RP.A

7.NS.3

7.EE.3

Grade 8 8.EE.8c

8.F.B

8.G.7

Cluster Meeting

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

● How do the materials include multiple routine and non-routine applications throughout each grade?

● How do the materials provide opportunities for students to independently demonstrate multiple routine

and non-routine applications throughout each grade?

● Do the materials have a consistent lesson structure for including multiple routine and non-routine

applications?

● Based on the student-facing materials, how do students independently demonstrate multiple routine and

non-routine applications?

Gateway 2: Rigor & Mathematical Practices

Criterion 2.1 Materials reflect the balances in the Standards and help students meet the

Standards’ rigorous expectations by giving appropriate attention to:

developing students’ conceptual understanding; procedural skill and fluency;

and engaging applications.