Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Kindergarten do not meet expectations for alignment. The materials do not devote the large majority of time to grade-level work with the inclusion of the pattern unit, but the materials can be utilized to appropriately assess grade-level content. In addition, there is no explicit connection made to the progressions of learning in the standards. Since the materials do not meet the expectations for focus and coherence in Gateway 1, they were not reviewed for Gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
6
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
0
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials reviewed for Kindergarten do not meet expectations for focus on major work and coherence. The materials do not devote the large majority of time to grade-level work with the inclusion of the pattern unit, but the materials can be utilized to appropriately assess grade-level content. In addition, there is no explicit connection made to the progressions of learning in the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for assessing material at the grade level. Although there are multiple units and sessions noted that align to and assess standards that are beyond Kindergarten, the inclusion of these sessions and units is either Mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet expectations for assessment because above grade-level assessment items and their accompanying lessons, sessions, or units, could be modified or omitted without a significant impact on the underlying structure of the instructional materials. For this indicator, all of the assessment checklists and end-of-unit assessments for the seven units were reviewed. All assessments are student observation/interview in nature, and units and sessions accompanying above grade-level assessment items are noted in the following list.

  • In unit 3, sessions 1.5 and 3.1 assess how to: construct, copy, and extend patterns; break a pattern into units; and construct a pattern from a known unit. These expectations for students align to 4.OA.C.5. The materials explain the inclusion of these expectations by saying they “raise student awareness of pattern and regularity which is what math is mostly about…relationships among mathematical objects” (page 13), but these topics are not clearly identified as beyond Kindergarten. Due to these topics aligning to a standard four grade levels above Kindergarten, the inclusion of these topics is not Mathematically reasonable within the materials, and the omission of these lessons and sessions would not significantly alter the underlying structure of the materials.
  • In unit 4, session 1.1 assesses how to: measure the length of objects in non-standard units; line up units the length of the object; and accurately count the number of units used. These expectations align to 1.MD.A. These topics are not clearly identified as beyond Kindergarten, but their inclusion is Mathematically reasonable since the topics are only one grade level beyond Kindergarten and do not constitute a large number of lessons. Also, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials.

In unit 7, session 1.1 assesses how to: represent accurately the number of pieces of data; represent data so that others can produce representations from the data; and represent and organize data. In Unit 7, Session 3.5 assesses how to: identify and represent data needed to solve a problem; solve the problem accurately; represent the method used to solve the problem. These expectations align to 1.MD.D. These topics are not clearly identified as beyond Kindergarten, but their inclusion is Mathematically reasonable since the topics are only one grade level beyond Kindergarten and do not constitute a large number of lessons. Also, the omission of these lessons and sessions would not significantly alter the underlying structure of the materials, especially since this would more than likely be the last unit of the school year.

*Evidence updated 10/27/15

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
0/4
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten do not meet expectations for time spent of the major clusters of the grade. This is largely due to one unit of the seven that is spent on additional work and one unit of the seven that is spent on work outside the grade level.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten do not meet expectations for class time spent on the major clusters of the grade. According to the unit instructional plans, there are 163 days of lessons and assessments. Within that, there are areas where the work is aligned to supporting and additional clusters or is work outside of the grade level. For example:

  • In unit 2, sessions 2.10-2.14, students in Kindergarten should be comparing two quantities, however these activities extend to comparing more than two quantities and ordering them.
  • One major cluster, K.NBT is barely addressed; only three lessons in unit 6 are devoted to the composing and decomposing numbers 11-19 to gain a foundation for place value.
  • Unit 3 focuses primarily on patterns. Patterns would be considered more of a mathematical practice and are not formally introduced until Grade 4.
  • Unit 5 is aligned to geometry, which is additional work of Kindergarten. There are 18 lessons in the unit that do not focus on major clusters.
  • There are 22 lessons in unit 3 aligned to patterns and 20 lessons in unit 5 aligned to geometry, additional clusters. This shows a percentage of possible alignment to the major clusters at 73%. That is not enough of a focus in Kindergarten on the major work of the grade, especially considering the near absence of K.NBT.A.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten do not meet expectations for coherence. With the inclusion of Unit 3, the amount of appropriate content for the year and the extensive work on grade level materials diminishes.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet expectations for enhancement of supporting content with major content at the grade. The review team found evidence where supporting content enhances focus, particularly in the area of counting and cardinality, but not for all major work of Kindergarten. For example:

  • In units 3 and 5, the K.CC cluster is used in workshop activities within lessons dealing with additional content and also by including it in the Classroom Routines for the day.
    • Specifically, in unit 5, lesson 2.2, "pattern block puzzles" asks the students to create a composite shape and to count the number of different shapes used and record the number of each shape.
  • Unit 2 uses measurement standards as a support for K.CC. An example of this is name towers, where students build towers with snap cubes to represent the number of letters in their name. Each snap cube has a dot sticker placed on it that has a letter written on it. In this activity students gain a visual representation of the number that matches the number of letters in their names. Students also directly compare the length of their "name tower" to other students' name towers. This activity uses direct comparison of length, measurement vocabulary (longer than, shorter than) paralleled with counting and representing numbers 1-10 and comparison vocabulary (more than, less than).

On the contrary,

  • In unit 4, measuring and counting, all lessons within investigation 1 focused on non-standard measurement which is not a Kindergarten standard. All lessons in investigation 2 simultaneously engage students in the major work of K.CC.A, K.CC.B and K.CC.C. 

*Evidence updated 5/20/2015, score unchanged

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet expectations for viability of content for the scope of one year. The curriculum consists of 163 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, with the inclusion of unit 3 on patterns, the review team determined that the amount of content was not fully viable for one school year to foster coherence between Kindergarten and Grade 1. The depth of content needed to prepare students for Grade 1 needs to be further developed for K.NBT.A as well. Teachers would need to find supplemental resources in order to cover the content for Kindergarten.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet expectations for consistency with the progressions. There is partial alignment to development of grade-by-grade progressions and to the amount of work with grade-level problems. Since there is no grade level prior to Kindergarten, there are no opportunities to explicitly relate the grade-level concepts to prior grade level standards. In the front of each unit, there are detailed explanations of the content addressed in a section called "Mathematics in this Unit." Within this section, the "Looking Back" and "Looking Forward" pieces explains content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. Some examples of alignment and misalignment with the indicator include:

  • In unit 1, work in data analysis (surveys) is a future expectation, but its use is articulated as a means to count and compare quantities in a meaningful, real-world context.
  • In unit 7, session 1.1, a math note provides a rationale for counting objects slightly beyond 20, acknowledging that this goes beyond Kindergarten expectations.
  • Five of the lessons in unit 2 (sessions 2.10-2.14) extend comparing two quantities to ordering more than two is given no explanation or acknowledgement that this goes beyond Kindergarten expectations of comparing two quantities.
  • Pattern work is not identified as future work in unit 3.
  • In unit 4, non-standard length and weight with cubes and other non-standard units is not identified as future work, but is connected to Kindergarten counting work.
  • Every lesson in unit 2 includes one or more of these differentiation suggestions.
  • The one cluster lacking in extensive work is K.NBT.1 as only three lesson opportunities for students to work on gaining foundations for place value exist.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for fostering coherence through connections at a single grade. The materials include some instances where learning objectives are shaped by cluster headings and include some problems that connect clusters and domains. Examples for both arguments include:

  • In unit 6, "Composing and decomposing the teen numbers into one ten and some number of ones" can be found as learning objectives. In sessions 5A.3-5A.5, students build teen numbers using ten frames and record using an addition of 10+ some number of ones in order to develop an understanding of place value.
  • In unit 4, "modeling the action of combining and separating situations," "combining two amounts," and "adding or subtracting from a number" can be found in sessions 3.2-3.7; investigation 2 includes "finding the total after a small amount (1,2,3) is added to a set;" investigation 3, sessions 3.2-3.7 demonstrate "modeling the action of combining and separating situations," "combining two amounts," and "adding or subtracting from a number"; and investigation 4, sessions 4.2 and 4.5 include "recording decompositions and compositions of a number using addition and subtraction notation."
  • In unit 6, investigation 1, six lessons involve "using numbers and addition notation to describe arrangements (combinations) of object;" investigation 2 includes "finding the total after a small amount (1,2,3) is added to or subtracted from a set;" and investigation 3 demonstrates "combining two single-digit numbers with totals to 10," "modeling action of combining and separating situations," "separating one amount from another," and "using numbers and addition notation to represent an addition situation." All support the K.OA.A cluster heading.
  • In unit 2, session 1.4 connects number words, numerals, and quantities (shaped by K.CC.3).
  • In unit 6, sessions 5A.3-5A.5 combine and connect K.NBT and K.CC.B.5 and K.CC.A.3.
  • Unit 5 sessions 1.3-1.5 and most lessons in investigations 2 and 3 combine and connect work in K.G.A.2 and K.G.B.4 with counting in K.CC.A.3, K.CC.B.5 and comparing numbers in K.CC.C.6.
  • Unit 1 investigation 3 lessons and Unit 7 investigations 2 and 3 lessons combine and connect work in sorting and classifying K.MD.B.3 with opportunities to rote count and write numbers K.CC.A.3 and comparing quantities K.CC.C.6.
  • However, with the inclusion of Unit 3 on patterns, not addressing cluster headings in Kindergarten, or containing grade level problems, the review team saw that the math focus points and work students were engaged in were not shaped by Kindergarten clusters.

Gateway Two

Rigor & Mathematical Practices

Not Rated

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
0/8

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
0/2

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
0/2

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
0/2

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
0/2

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
0/10

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
0/2

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Wed Feb 11 00:00:00 UTC 2015

Report Edition: 2012

Title ISBN Edition Publisher Year
9780328687121 0

About Publishers Responses

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Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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