Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Kindergarten partially meet the expectations for alignment to the CCSSM and do not fully meet expectations for gateway 1 or gateway 2. The instructional materials partially meet the expectations for gateway 1, as they did not appropriately focus on the major work of the grade while partially demonstrating coherence within the grade and across other grades. The instructional materials partially meet the expectations for gateway 2 as they partially address rigor within the grade-level standards, and there are missed opportunities in the materials when it comes to attending to the full meaning of the standards for Mathematical practice. Overall, the instructional materials partially address the content standards and identify and partially integrate the practice standards. 

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
12
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

Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Kindergarten partially meet the expectations  for Gateway 1.  The materials do not meet the expectations for focusing on major work of the grade and only partially meet the expectations for coherence. While the instructional materials do not assess above grade level standards, they also do not allocate a large enough percentage of instructional materials to major standards of the grade. Many strengths are found and noted in the coherence criterion, and the instructional materials meet some of the quality expectations for coherence. Overall, the instructional materials do not allocate enough time to the major clusters of standards for Kindergarten to meet the expectations for focus.

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 grade-level content. Standards assessed are clearly identified in "Data Driven Decision Making," and each item assessed is correlated to a Kindergarten standard. Overall, the instructional materials do not assess content from future grades within the summative assessments provided for each chapter.

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 the expectations for assessing grade-level content. Overall, the instructional materials do not assess content from future grades within the summative assessments provided for each chapter.

  • In the planning guide there is a section called "Getting Ready for First Grade." Planning resources for this are described on pages 40 and 41, and the section is aligned to Grade 1 CCSSM, which is clearly identified. Students are not being assessed on the content.
  • Standards assessed are clearly identified in a textbox titled "Data Driven Decision Making." For an example, see chapter 4, page 226A in the teacher edition.
  • Each item assessed is correlated to a standard. For example, test item 6 assesses standard K.CC.A.2, as listed on page 226A.
  • The assessment for chapter 8, question 11, addresses students' ability to write numbers above 20, which is an expectation for Grade 1, but the question aligns to K.CC.A.1 because of counting to 100 by 10s.

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 the expectations for spending the large majority of class time on the major clusters of the grade. In Kindergarten, about 85% of the instructional materials should address the major work of the grade. Go Math Kindergarten consists of 12 chapters, and only eight (about 67%) address major work of the grade. Overall, the instructional materials allocate a large percentage of instructional time to clusters of standards that are not major work of Kindergarten.

Indicator 1b

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

large majority of class time on the major clusters of the grade. Overall, the instructional materials allocate a large percentage of instructional time to clusters of standards that are not major work of Kindergarten.

  • In Kindergarten, approximately 85% of the instructional materials should address the major work of the grade.
  • Go Math Kindergarten consists of 12 chapters. Eight (about 67%) address major work of the grade.
  • Four of the 12 chapters (about 33%) address supporting work of the grade. The four units that are supporting work have some counting and writing of numbers up to 20.
  • Chapter 10 focuses on the supporting cluster of data interpretation. Chapters 11 and 12 focus on geometry, which are additional clusters.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for being coherent and consistent with CCSSM. The instructional materials have a portion of content designated for Kindergarten that is partially viable for one school year, and they also give students extensive work with grade-level problems. The instructional materials have only some of the supporting content enhancing focus and coherence simultaneously, but they do have materials foster coherence through connections at a single grade. Overall, the instructional materials for Kindergarten exhibit characteristics of coherence as noted in indicators 1E and 1F, and for the entire criterion, the instructional materials partially meet the expectations.

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 the expectations for having the supporting content enhancing focus and coherence simultaneously. Overall, the instructional materials miss opportunities to connect non-major clusters of standards to major clusters, and as a result, the supporting content does not always engage students in the major work of Kindergarten.

  • Chapter 11 treats measurement separately from the major work of the grade level.
  • Chapter 9 mostly treats the supporting content separately, but there are three lessons (9.6, 9.8, and 9.10) that support the major work of counting and writing the corresponding number.
  • Chapter 10 mostly treats the supporting work separately with the exceptions of lessons 10.3 and 10.4.
  • Chapter 12 mostly treats the supporting work separately with the exceptions of lessons 12.4 and 12.5.

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 the expectations for having the amount of content designated for one grade level as viable for one school year. Overall, the amount of time needed to complete the lessons is appropriate for a school year of approximately 170-190 days.

  • The suggested pacing for Kindergarten is between 130 and 160 days (depending on which parts are included) according to the pacing chart provided in each chapter on the pages labeled "Chapter at a Glance," which includes assessment days in the series.
  • Additionally, if time permits there is a unit preparing for Grade 1, which has 25 days total in the unit.
  • Given the instructional materials not allocating enough time to major clusters of the grade as addressed in indicator 1B, these instructional materials would have to be supplemented with other materials, which means these materials may not be viable for one school year.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for having materials that are consistent with the progressions in CCSSM. Overall, the materials give students extensive work with grade-level problems, and grade-level concepts are explicitly related to prior knowledge from earlier grades. Also, the materials develop according to the grade-by-grade progressions, with non-grade-level content clearly identified.

  • Each chapter identifies grade-level work, and how it ties into previous and future grades. For example, see chapter 1, teacher's manual, page 9J.
  • Off-grade-level material is captured in the end-of-year resource guide in the teacher edition's planning guide.
  • Additionally, at the beginning of each chapter, there is a connection to the learning progressions (see chapter 5, page 227J for an example) that identifies in the progression what students should do at grade level and what students will do in Grade 1 (this is a consistent structure throughout the program).
  • Each chapter has a page titled "Learning Progressions and Content Standards," which highlights the learning progressions as well as the standards before and after the grade level. Chapter 5, teacher edition, page 227J is an example.
  • RTI activities are provided for work in tier 1, tier 2 and tier 3. Differentiated instruction is clearly mapped out.
  • There are 99 lessons covering approximately 160 days of instruction; 96 provide work with grade-level problems.
  • Students are assessed on prior knowledge at the beginning of each chapter. For example, see chapter 1, teacher's manual, page 10. In addition, a graphic on page 9J shows skills before Kindergarten.
  • Each chapter begins with a page intended to "review prerequisite skills;" it provides two activities to prompt prior knowledge.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for having materials foster coherence through connections at a single grade. Overall, the materials do include learning objectives that are visibly shaped by CCSSM cluster headings, and the materials connect two or more clusters in a domain or two or more domains in a grade when appropriate.

  • Each lesson contains a section titled "Lesson at a Glance," which states the Common Core State Standards, MPs and learning objectives. For an example, see chapter 2, lesson 2.1, teacher's manual, page 81A.
  • There is evidence that the cluster headings were used to shape the objectives. For example, chapter 1 is titled "Represent, Count and Write Numbers 0-5."
  • Materials connect domains where they are natural and important. The beginning of each chapter clearly defines where these connections take place.
  • In chapter 2, lesson 2.2, students are asked to both count the number of objects and to compare them, K.CC.B and K.CC.C, respectively.
  • Chapters 1 and 4 connect counting and cardinality with operations and algebraic thinking.
  • Chapter 7 connects counting and cardinality with numbers in base ten.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Kindergarten partially meet the expectations for rigor and Mathematical practices. The instructional materials partially meet the expectations for the criterion on rigor and balance, and they only partially meet the expectations of the criterion on practice-content connections because they do not fully attend to the meaning of each Mathematical practice standard. Overall, the instructional materials are strong in regards to procedural skill and fluency, identifying Mathematical practices, and the language of Mathematics, but improvements can be made in keeping balance among the three aspects of rigor and consistently attending to the full meaning of practice standards where they are identified.

 

*Evidence updated 10/27/15

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.
5/8
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten partially meet expectations for rigor and balance. The instructional materials give appropriate attention to procedural skill and fluency, and they partially give appropriate attention to conceptual understanding and application. Overall, because of not fully meeting expectations for application and conceptual understanding, the instructional materials partially reflect the balances in the CCSSM, which help students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for giving attention to conceptual understanding. Overall, the materials identify many opportunities for students to develop conceptual understanding of mathematical concepts where called for in specific content standards or cluster headings, but some of these identified opportunities do not actually allow students to develop conceptual understanding.

  • Each chapter includes a “Teaching for Depth” page. This page identifies strategies, research, mathematical practices, and professional development videos to help teachers attempt to achieve a deep understanding of content among students. For example, chapter 1, in the Teacher Guide on page 9E.
  • The beginning of each lesson has an “About the Math” section to give teachers direction on teaching for depth and reasoning for teaching the specific skill. For example, chapter 1, on pages 13A and 19A in the teacher guide.
  • In chapter 5, lesson 1, there are follow-up questions included that require conceptual thinking and are aligned to K.OA.A.1. The questions are: how many children are playing with the soccer ball? How many children are being added to the group? And, what will you do to find how many children are there now?
  • Many of the sections marked as conceptual understanding do not have students understanding concepts; instead many are very procedural. For example, chapter 1, lesson 6, on page 44 of the teacher edition; chapter 2, lesson 1, on page 82 of the teacher edition; and chapter 3, lesson 7, on page 156 of the teacher edition are more procedural than conceptual.

There are instances where the lesson for the advanced learners is conceptual even though the on target lesson is not. For example, chapter 3, lesson 7, on page 156 of the teacher edition, and chapter 5, lesson 1, on page 232 of the teacher edition are excellent examples of a conceptual lesson. Unfortunately, the lessons in these materials are labeled for advanced learners; this does not allow all students access.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for giving attention to procedural skill and fluency. Overall, the materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

  • The beginning of each lesson includes a “Fluency Builder.” For example, see chapter 11, lesson 2 on page 655B. These naturally weave into the targeted skill.
  • The materials give attention throughout the year to procedural skills and fluency through daily routines, fluency builders, and practice and homework exercises that ask students to practice those skills. For instance, in chapter 1, lesson 1, the daily routine asks students a set of questions on how they could use crayons to show sets of numbers 1 and 2. Which of your sets show one crayon? Which of your sets show two crayons?

The practice and homework exercises provide the majority of the planned procedural skill and fluency. For examples, see the following: chapter 3, lesson 6, pages 153 and 154; chapter 5, lesson 6, pages 265 and 266; and chapter 11, lesson 2, pages 659 and 660.

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
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for giving attention to applications. Overall, the materials identify many opportunities for students to engage in applications with Mathematical concepts, without losing time on the major work of the grade, but some of these identified opportunities do not actually allow students to engage in applications. 

  • Real-world applications are identified in each lesson. An example can be found in chapter 12, lesson 4, on page 708 in the teacher’s guide. Kindergarten students are asked to use cubes to show what they know about making a graph.
  • In the materials, each chapter and lesson include a “Think Smarter” and “Go Deeper” question which are intended to be application problems.
  • Many of the problems marked as applications are not applications. For example, in Chapter 1, lesson 4, and chapter 3, lesson 4, the “Think Smarter” problems labeled as applications are conceptual understanding.
  • In chapter 4, lesson 1, and chapter 5, lesson 9, the “Think Smarter” problems labeled as applications are conceptual understanding.

In chapter 2, lesson 3, the “Think Smarter” labeled as application is a procedural problem.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for balance. Overall, there are many instances where problems or activities are labeled as conceptual understanding or application, and the problems or activities do not accurately align to those labels. These inaccurate labels disrupt the balance among the three aspects of Rigor within the materials.

  • The materials claim all three are present in each lesson. However, many of the conceptual understanding problems are not truly conceptual problems and most of the application problems have the same issues. This creates an imbalance in the materials, with procedural skill and fluency being the strongest of the three aspects.
  • The three aspects of rigor are identified in a balanced manner throughout the material. These aspects are identified in each lesson under Rigor: Understanding Concepts (Share & Show), Procedural Skills & Fluency (On Your Own), and Applications (Think Smarter & Go Deeper). An example can be found in chapter 2, lesson 1, on page 81A in the teacher’s guide.

In the materials, each element of rigor is identified. They are all touched upon in each lesson and sometimes overlap, but they are not always treated together or always separately. For example, chapter 1, lesson 1, on page 13a, the lesson identifies the three areas of rigor and where they are addressed (Share and Show, On Your Own, Think Smarter & Go Deeper).

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
7/10
+
-
Criterion Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for practice-content connections. The materials meet expectations for identifying the practice standards and explicitly attending to the specialized language of Mathematics, as addressed in indicators 2E and 2G.iii, respectively. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and for engaging students in Mathematical reasoning as addressed in indicators 2F, 2G.i and 2G.ii. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice, the instructional materials should carefully pay attention to the full meaning of every practice standard, especially MP 3 in regards to students critiquing the reasoning of other students.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the Mathematical content. Overall, the instructional materials do not over-identify or under-identify the MPs, and the MPs are used within and throughout the grade.

  • The MPs are clearly identified and used to enrich content. Each chapter includes a “Teaching for Depth” page that has an explanation of how the Mathematical practices will be used throughout. For example, in chapter 3, on page 115E in the teacher's guide, it discusses how students might encounter and explore patterns in a counting sequence, and it relates the extension of these patterns to MP 8 (look for and express regularity through repeated reasoning).
  • Each lesson has a “Lesson at a Glance” where the practices are noted for that particular lesson. For example, chapter 3, lesson 1, on page 119A in the teacher’s guide, notes that students will be able to use appropriate tools strategically as they learn to count with the possible tools being counters and ten frames (MP 5).
  • Each lesson has an “Explore and Explain” section for the teacher to prompt students to apply and work through the mathematical practices. An example of this can be found in chapter 3, lesson 2, on page 125 in the teacher’s guide, where teachers prompt students to reason abstractly and quantitatively by having them compare the number of cubes to the number of hats (MP 2).
  • In the teacher’s edition on page 23, there is a list of the MPs with prompts you can ask each student to address the practice.

Each lesson has MPs identified, and they are used to enrich the content of the work. The identified MPs are found in the “Lesson at a Glance” of each lesson. For example, chapter 5, lesson 2, on page 237A in the teacher edition states that students will model with Mathematics when students start writing addition sentences to describe how they are working with counters in ten frames (MP 4). The practices are not over identified or under identified.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the instructional materials carefully attend to the full meaning of some of the practice standards but not all of them. 

  • The materials attend to the full meaning of most of the Mathematical practice standards. An exception is in regards to MP 5. In the materials for Kindergarten, there are many instances when MP 5 is listed, and students are given or directed to use a specific tool, which does not allow students to consider and choose the appropriate tool. An example of this can be found in chapter 3, lesson 3, on page 131 in the teacher’s guide. Teachers are directed to give students seven two-color counters for counting. Another example can be found in chapter 4, Lesson 1, on page 181 in the teacher’s guide. Teachers are directed to give students counters for counting work.
  • On page 24 of the teacher’s guide, the materials identify the standards for Mathematical practice and where the lessons include these. For example, there are problem-solving lessons in lessons 1.9 and 2.4 for MP 1.
  • Each chapter has MPs listed, but they do not always attend to the full meaning of the practice standard. For examples, in chapter 5, lesson 2, on page 237 of the teacher edition, MP 2 is referenced along with a question to ask the students. The question is very direct and does not require the students to reason abstractly or quantitatively. By asking the questions the way they are stated, the teacher is taking the thinking and reasoning away from the students.

In chapter 6, lesson 7, on page 347 of the teacher edition, makes a reference to MP 5; however, the students are given the tools to use, which means they are not selecting their own tool as the practice requires. This happens again, in chapter 7, lesson 5, on page 385 of the teacher edition, because students are not choosing their own tools as they are given counters and ten frames to use.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level Mathematics detailed in the content standards. Overall, the materials consistently allow students to construct viable arguments, but they do not consistently prompt students to analyze other students' arguments.

  • Examples can be found in the materials for opportunities to apply SMP 3. Two examples can be found in chapter 2, Lessons 2.2 and 2.3, on pages 88 and 94 in the teacher’s guide. Lesson 2.2 asks students, “How can you tell which set has a greater number of counters?” Lesson 2.3 asks students, “How can you tell which set has a number of counters that is less? Which number is less?”
  • There are several places where MP 3 is identified in the student materials, but these identifications do not always meet the intent of the standard. For example, MP 3 is identified in chapter 11, lesson 2, page 649 of the student edition; lesson 3, page 655 of the student edition; and lesson 4, page 667 of the student edition, but the questions provided do not have students constructing viable arguments or analyzing the arguments of others.
  • chapter 10, lesson 7, page 609 of the student edition; lesson 9, page 623 of the student edition; and lesson 10, page 627 of the student edition all identify SMP 3, but the prompts/questions do not have students engaging in the practice.

In chapter 11, lesson 3, page 661 of the student edition, students are asked to construct an argument, but they do not analyze another student’s argument.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level Mathematics detailed in the content standards. Overall, the materials consistently assist teachers in having students construct viable arguments, but they do not consistently assist teachers in having students analyze other students' arguments.

  • In the planning guide for the materials, page 26 is dedicated to identifying where examples of MP 3 are located throughout the materials. The planning guide also lists examples of MP 3 on page 98.
  • In the materials, the “Think Smarter” problems and “Go Deeper” sections of each lesson prompt teachers to help engage students in constructing viable arguments. For instance, in chapter 5, lesson 5, page 257, teachers are prompted to ask students “What happens if you turn your counters over to the opposite color? Do you get another way to make 10? Explain your thinking.”
  • In the “Go Deeper” section in chapter 10, Lesson 10.9, on page 623 of the teacher’s guide, teachers are prompted with the following: “Children should understand that the traffic cone they circled is beside an object shaped like a cube. The other cone inside the truck is not beside an object shaped like a cube. Help children see that they can also describe the position of the object shaped like a cube as being beside the traffic cone.”
  • In the Math Journal in chapter 10, Lesson 10.7, on page 612 in the teacher’s guide, students are asked to make drawings of a square, discuss, and share their models. The teacher is then directed to ask students to explain how building models of solid real-world shapes helps them learn more about the shapes.
  • On page 23 of the teacher planning guide, there are a list of prompts to ask students to help them construct viable arguments.

There are several places where MP 3 is identified; however, these identifications do not meet the meaning of the practice standard.  For example, chapter 3, lesson 9; chapter 7, lesson 1, on page 362 TE, and lesson 9, page 410, all identify MP 3. An explanation does not exist to show teachers how to get kids to participate in a conversation using viable arguments and analyzing the arguments of others. The questions often have right or wrong answers, and when they do not, they still are not asking students to explain how they went about solving a problem and then talking with others about how they solved the problem.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Kindergarten meet the expectations for explicitly attending to the specialized language of Mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of Mathematics that are consistently present throughout the materials.

  • Each chapter begins with vocabulary builders and vocabulary games. An example can be found in chapter 12 on pages 685-686B.
  • The lessons attend to using correct vocabulary. For example, the questions for teachers to ask use correct vocabulary. In chapter 10, lesson 4, on page 591B in the teacher’s edition, the problems are asking students to name cylinders, cubes, and spheres.
  • There are routine sections of each lesson that are connected to math language. This happens specifically in the “Math Talk,” “Vocabulary Preview,” and the “Developing Math Language” section of each lesson. For example, in chapter 5 on page 227H, vocabulary words are identified for the chapter as well as how to plan for ELL students and activities. Pages 229-230B include vocabulary games to introduce the lesson. In the lesson, there is a daily routine for building vocabulary, such as lesson 5.1 on page 231 in the Vocabulary Builder section.

Each lesson has a “Language Objective” and “Vocabulary Builder” exercise. An example can be found in chapter 3, lesson 3.1, teacher’s guide pages 119A-B.

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: Sun Feb 15 00:00:00 UTC 2015

Report Edition: 2015

Title ISBN Edition Publisher Year
null 9780544390508 null null null
null 9780544433342 null null null

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

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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