Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 8 partially meet the expectations for alignment to the CCSSM. The instructional materials meet the expectations for gateway 1 because they meet the expectations for focus on major work and partially meet the expectations for coherence. Since the materials meet the expectations for gateway 1, evidence was collected in gateway 2. The instructional materials do not meet the expectations for rigor and balance and meet the expectations for practice-content connections. Since the materials meet the expectations for gateway 1 and partially meet the expectations for gateway 2, they partially meet the expectations for alignment to the CCSSM.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
13
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

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 8 meet the expectations for focus and coherence in the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Seventy-four percent (74%) of the days allocated in the timeline align to the major work of this grade. For coherence, supporting work is rarely connected to the focus of the grade. Coherence is evident in the instructional materials including problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. Overall, the Grade 8 materials are partially coherent and consistent with 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 material reviewed for Grade 8 meets the expectations for focus within both assessment and time on major work. The summative test of each packet assesses topics at this grade level without assessing any content from future grades with one exception, that is test 3, problem 3. Seventy-four percent (74%) of the days are suggested for major work of the grade and there is some support from content in the non-major clusters that directly reinforces major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of class time in the major clusters of the grade.

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 Grade 8 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each packet with one exception, namely test 3 problem 3.

For this indicator, the summative test for each packet was evaluated.

  • All assessments and topics relate to Grade 8 standards or below except for one question on Test 3.
  • Test 3 problem 3 asks students to state the “recursive rule” which is in the high school functions standard – Building Functions: HSF.BF.A.1.A - Determine an explicit expression, a recursive process, or steps for calculation from a context. The Grade 8 standard simply requires verbal descriptions and does not introduce recursive vocabulary. Recursive versus explicit rules are embedded throughout the instruction for this entire unit. The content could easily have been addressed without introducing the recursive rule; however, because of its extensive use, the work could not be completed without knowing what recursive means. This test question could easily be modified or skipped completely in the assessment with no impact. Therefore, it does not impact the score of 2 for this indicator.

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.
4/4
+
-
Criterion Rating Details

The instructional material reviewed for Grade 8 meets the expectations for focus within both assessment and time on major work. The summative test of each packet assesses topics at this grade level without assessing any content from future grades with one exception, that is test 3, problem 3. Seventy-four percent (74%) of the days are suggested for major work of the grade and there is some support from content in the non-major clusters that directly reinforces major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of class time in the major clusters of the grade.

Indicator 1b

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

The instructional materials reviewed for Grade 8 meet the expectations for focus within major clusters. Overall, the instructional material spends the majority of class time on the major clusters of each grade.

To determine this, three perspectives were evaluated: 1) the number of units/packets devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts. The conclusions are based on that data.

The number of days suggested by the publisher for the “enriched” pacing option is the one most dedicated to grade-level work with the least review.

  • Units/Packets – percentage of time spent on major work is 80 percent.
  • Lessons – percentage of time spent on major work is 70 percent.
  • Days – the percentage of time spent on major work is 74 percent.
  • Days allotted to review lessons are minimal.
  • Also, the non-major clusters were evaluated to determine if they could count due to how strongly they support major work of the grade. Some evidence, such as Packet 10: Bivariate Data, does a significant amount of work with writing and using the equation for a line of best fit which supports 8.F: Functions.
  • At 74 percent within the 65 percent - 85 percent standard, Grade 8 spends the majority of time on major work.

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 Grade 8 partially meet the expectations for coherence and consistency with the CCSSM. There is limited evidence of supporting content enhancing coherence by reinforcing the major work of the grade because so much of the content is stand-alone. The Grade 8 materials provide a list of previous skills/knowledge that is foundational for the current work, but they don't explicitly tie the previous skills/ knowledge to the lessons. The materials include lessons that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials also develop by the grade-by-grade progressions in the standards. However, most of the lessons meet individual standards and do not consistently promote the coherent connections that allow students to apply and transfer the learning. Overall, the Grade 8 materials partially address the key aspects of coherence and consistency with the standards

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 Grade 8 partially meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. To determine this, the connections that the teacher guide stated were considered, and the student lessons were reviewed to validate the connections from the teacher guide as well as determine if there were missed opportunities to make strong connections.

Some examples include:

  • The strongest support comes from statistics supporting the major work of functions. Units 4 (Patterns and Linear Functions) and 10 (Bivariate Data) support 8.F. Both of these require the students to use functions to model relationships between quantities.
  • Unit 10 also has a strong connection to Equations and Expressions (8.EE.C) solving line of best fit equations.
  • There were instances where the supporting work missed opportunities to connect to major work such as developing work with equations in both Unit 15 (Geometry) and Unit 16 (Real Number System).
  • In Packet 4, Lesson 3, standards 8.F.A, 8.F.B and 8.SP.A are connected as students measure and record heights of stacked cups. Only one day is allotted for this lesson, and this amount of time does not allow for the connection to be fully developed for all students.
  • There were only 5 out of 16 packets that include supporting work; Packet 15 is "stand-alone" and did not support major work.

Indicator 1d

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

The instructional materials reviewed for Grade 8 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades.

The teacher guide offers six different pacing plans –

  • Three for traditional schedules.
  • Three for block schedules.
  • Each has the Modified Plan for students who require extensive review.
  • The Basic Plan for students who require some review.
  • The Enriched Plan for students who only need minimal review.
  • All of them plan for 32 weeks of instruction.

For the report the Traditional Enriched Plan was used since it best represented a focus on grade-level work.

The pacing provided by the publisher is reasonable for lessons to be completed in the time suggested.

  • Lessons plus a catch-up day (built into each unit) and the assessment day equal 158 days.
  • This Falls within the 140-190 range suggested.
  • According to the scope and sequence, all Grade 8 standards are included.

However, there is concern about the three pacing suggestions.

  • Students needing more review early in the year spend equal or less time on Units later in the year, which is new material.
  • It is not clear how students who need Modified Plan A could finish all packets in the same amount of time as students on Enriched Plan C, though there are suggestions about items that could be omitted.

Overall, the number of days suggested is viable and provides the content needed to be prepared for the next grade level.

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 Grade 8 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grades is clearly identified, although materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not made to content in future grades. Overall, the materials in Grade 8 identify the progressions from prior grades in the standards.

  • The teacher guide includes a page delineating how the major work standards for Grade 8 intersect with major clusters in grades 6-HS.
  • Each packet lists an overview of standards being addressed including foundational standards that have been taught and learned previously.
  • In general, lessons are taught as a series of 3, where each builds or connects to the one before.

· Teachers are provided with sufficient information to help see the connections in the standards, tasks, packets and lessons.

· There are standards where the materials are only partially representative of the progressions. For example: 8.F is included in seven units (Units 3, 4, 7, 8, 9, 10 and 13). In Units 4 and 7, 8.F is addressed through specific examples (Growing Shapes, Going to the Park, Stacking Cups and Rate Graphs). However, the knowledge may not transfer to other functional relationships. The work with functional relationships is very specific to certain tasks throughout the units. Overall understanding of the concept of a function as a whole and representation of a functional relationship as an equation may be limited.

The instructional materials reviewed for Grade 8 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

  • Not all students have the opportunity to engage deeply with problems related to grade-level standards as the material is not as rigorous as needed and doesn't have the depth that is needed to truly master the standards.
  • Each packet primarily contains problem sets designed to help develop students' procedural skill/fluency.
  • Some of the performance tasks and proficiency assessments do allow for more application and rigorous engagement with the standards.
  • It is recommended, in the teacher guide, that struggling students spend the majority of time on basic lessons, skill builders, and review and to avoid extensions and more challenging questions. This is limiting their interaction and mastery of grade level standards.

The instructional materials reviewed for Grade 8 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials only generally relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • Each module lists the foundational standards at the beginning of the module to explicitly connect prior learning to current learning.
  • It would be more beneficial to see these connections listed in the lessons as they occur.
  • Connections to lessons and/or topics from previous grade levels that will be helpful in upcoming lessons are frequently reviewed in the “warm-up” at the beginning of a given topic, though no explicit connections are made for the students.

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 Grade 8 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • Each packet lists the lessons with the student outcomes clearly stated, which are easily aligned to CCSSM standards and cluster headings.
  • In general, lessons and tasks require students to demonstrate the standards. However, they rarely connect these concepts beyond what naturally occurs with lessons following one another.
  • The teacher guide provides a page of content emphasis by cluster.
  • Each packet identifies the standards addressed and bolds the major cluster.
  • Occasionally a lesson title will not have a clear connection – such as “Going to the Park” – however the learning objective clarifies the connection.

The instructional materials include problems and activities that serve to connect two or more clusters in a domain. They include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Overall the materials foster coherence through connections at Grade 8.

  • In packets 3, 4 and 9, students connect the ideas of functions and linear equations (8.EE.B, 8.F.B).
  • Students continue this work by using functions to determine best buys in packet 7 (8.EE.B, 8.F.A).
  • However, one missed opportunity that is visible is that 8.EE.B and 8.G.A are not connected with the linear function work. Here, the concept of similarity could have been connected to slope through the use of similar triangles. Those are connected in a later lesson in packet 15.
  • There are other natural connections evident such as using formulas to solve problems (8.EE.C, 8.G.C).

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional material for Grade 8 partially meets the expectation for rigor and mathematical practices. The materials reviewed for Grade 8 only partially meet the expectation for rigor by not providing a balance of all three aspects of rigor throughout the lessons. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. In Grade 8, procedural skill and fluency is evident in almost every unit, which develop the relevant standards. However, application of the mathematical concepts is lacking throughout each unit. Overall, while conceptual development and procedural skills and fluency are fairly strong, the application is so disproportionately lacking that the three aspects are not balanced within the units. Therefore, the Grade 8 materials only partially meet the criteria for rigor and balance.

However, the materials reviewed for Grade 8 do meet the criterion of meaningfully connecting the CCSSM and the MPs. Materials attend to the full meaning of each practice standard in limited opportunities. Throughout the lessons, though, the materials are lacking in prompting students to construct viable arguments concerning grade-level mathematics. The teacher’s guide will occasionally assist teachers in engaging students in this task. On the other hand, materials very explicitly attend to the specialized language of mathematics. Correct mathematical terminology is consistently used, enforced, and reinforced. Overall, the materials partially meet the expectations for Gateway 2 in rigor and mathematical practices.

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.
4/8
+
-
Criterion Rating Details

The materials reviewed for Grade 8 only partially meet the expectation for this criterion by not providing a balance of all three aspects of rigor throughout the lessons. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. In Grade 8, procedural skill and fluency is evident in almost every unit, which develop the relevant standards. However, application of the mathematical concepts is lacking throughout each unit. Overall, while conceptual development and procedural skills and fluency are fairly strong, the application is so disproportionately lacking that the three aspects are not balanced within the units. Overall, the Grade 8 materials partially meet the criteria for rigor and balance.

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.
2/2
+
-
Indicator Rating Details

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings meeting the expectations for this indicator.

  • Generally, lessons develop understanding through explicit discussion outlined in the teacher lessons. Conceptual understanding is evident throughout the majority of lessons and lesson plans of teacher instruction. Students are consistently being asked to verify their work and explain for understanding. Teacher questioning during instruction is designed to lead to conceptual understanding.
  • Sentence starters often include terms like introduce, discuss, review, demonstrate, compare, explain, challenge, etc.
  • 22 of the 48 lessons include significant conceptual development of ideas.
  • Units 2 - 4, 7 - 9 and 12-14 all include work related to the major work clusters that address conceptual understanding (8.F.A, 8.EE.B, 8.G.A).
  • The materials provide evidence of high-quality conceptual problems, such as discovering patterns, that lead to rules, using concrete representation, verbalization, multiple representations, and interpretation of models. Some examples include:
    • Balance scales for comparing expressions (unit 2)
    • Cups and Counters (similar to algebra tiles) for equations (units 5, 6)
    • Connections between picture, table, graph, rule, slope-intercept, scatterplots (units 3, 4, 5, 7, 8, 10)
    • Looking at an unlabeled graph and describing a situation that would create it as well as generating a table that would work (unit 7)
    • Finding patterns to generalize exponent rules (unit 11)
    • Exploring Pythagorean Theorem with grid paper (unit 12)
  • However, it needs to be noted that beyond the lessons, most of the units did not call for students to demonstrate conceptual understanding on the summative assessments.

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

Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

  • There is abundant evidence of the opportunity to develop fluency and procedural skills. Examples include:
    • Every packet starts with a warm-up that is a review of basic background skills.
    • In every lesson, students have a practice section that includes ample "naked" practice such as the integer problems in 1.1 where there are 35 computation problems involving all 4 operations or 6.2 with 10 solving equations problems.
    • Besides an abundance of practice throughout the lessons, there are also Skill Builder activities in each unit designed to develop procedural skill and lead to fluency.
    • There is also a Knowledge Check at the end of each unit that reviews the skills learned.
    • The last thing in each lesson is a Home-School Connection where students have a page of problems to take home and do with their family that also reviews the skills in the unit.
  • Procedural skill and fluency that develop the major clusters that emphasize it (8.EE.C.7, 8.EE.C.8.B , 8.G.C.9) is predominantly evident in 5 of the 16 units.
  • In the teacher’s guide, there are often multiple "Introduce, Explore/Summarize, and Practice” sections depending on lesson content that develop procedural skill and fluency.

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 Rating Details

Materials are designed so that teachers and students do not spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

  • Some lessons have application type problems included in them. However, most of these are traditional “word problems” with no relevance to students and fit more within fluency.
  • Only 8 out of the 48 lessons include significant application of grade-level concepts.
  • The material has very limited opportunities for the students to engage in work that is authentic in context or that is non-routine.
  • Only two assessments allowed students the opportunity for application questions.
  • Only 1 Task and 6 Proficiency Challenges included application problems.

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
+
-
Indicator Rating Details

The three aspects of rigor are not always treated together and are not always treated separately, meeting the expectations for this indicator. However, there is not a balance of the three aspects of rigor within the grade.

  • Conceptual understanding was sufficient.
  • Procedural skill was the strongest aspect.
  • There is very little opportunity for the students to dig deep into the standards with application problems.
  • The lack of opportunity for students to engage in applications and deep problem solving in real world situations was significantly noticeable.
  • There were many missed opportunities to build from the fluency/procedural problems to move to having the students apply their knowledge.
  • The program is very heavy in fluency, but very weak in application.
  • In addition, there is not a balance of the three aspects of rigor on included assessments.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
+
-
Criterion Rating Details

The materials reviewed for Grade 8 meet the criterion of meaningfully connecting the CCSSM and the MPs. The latter are often identified and used to enrich mathematical content. Materials sometimes attend to the full meaning of each practice standard. Throughout the lessons, the materials are lacking in prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Students are occasionally directed to explain responses in practice sets and tasks. Occasionally, the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others. On the other hand, materials very explicitly attend to the specialized language of mathematics.Correct mathematical terminology is always used, enforced, and reinforced. Overall, the materials meet the expectations for the practice-content connections criterion.

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 MPs are identified and used to enrich mathematics content within and throughout each applicable grade.

  • There is a clear articulation of connection between MPs and content. Materials regularly and meaningfully connect MPs to the CCSSM within and throughout the grade.
  • Every unit identifies the MP used in the unit both on the student and teacher overview page.
  • In the teacher guide, each unit specifically relates how the listed standards are used in the unit. These are logical connections and integrated with the content.
  • The MPs have also been identified for the quizzes, proficiency challenges, tests, and tasks.
  • Compared to the others, MPs 4 and 8 are relatively underrepresented.

Indicator 2f

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

Materials attend to the full meaning of each practice standard.

  • Materials attend to the full meaning of each practice standard, though opportunities are limited.
  • Each practice is addressed multiple times throughout the year, though modeling and repeated reasoning are relatively under-represented compared to the others.
  • There are opportunities to engage in every mathematics practice fully at least a couple of times during the year. For example:
    • “Reason abstractly and quantitatively” as well as “Look for and express regularity in repeated reasoning” has students developing integer rules through discovering patterns.
    • Or “Make sense and persevere” when students must make sense of a money saving problem and need to identify relevant information and extend a simpler problem from previous work.

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 materials reviewed for Grade 8 partially meet the expectation for appropriately prompting students to construct viable arguments and analyze the arguments of others. Materials occasionally prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, there are problem structures that lead a student to explain and justify their reasoning and some to analyze the arguments of others, however.

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

  • The materials rarely provide directives for students to help them make connections to constructing viable arguments concerning grade-level mathematics detailed in the content standards. Occasionally materials prompt students to analyze the arguments of others.
  • Students are asked to “explain” often, however that often falls short of the full meaning of the practice.
  • Throughout the discussion portion of each lesson, students are expected to explain the mathematics leading to understanding content and solving problems.
  • Students are also directed to explain responses in problem-set and tasks.
  • There are rare opportunities for students to analyze the work of another - but it is usually in a problem set and not with another student's work within the classroom.

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.
2/2
+
-
Indicator Rating Details

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.

  • Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
  • The teacher guide encourages the teacher to put students in pairs/groups and have them explain their thinking to each other (Lesson 1.1).
  • The teacher guide encourages the teacher to ask the students to explain their thinking orally and in writing (Lesson 2.2).
  • Suggested questions are provided for students to explain their thinking in the lesson summary (Lesson 4.1).
  • Suggested questions for introducing the lesson to relate previous learning (Lesson 5.1).
  • There were some instances where this practice was connected/described in the teacher guide, but not carried through in the lesson (Units 10 and 15).

Indicator 2g.iii

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

Materials explicitly attend to the specialized language of mathematics.

  • Materials very explicitly attend to the specialized language of mathematics.
  • Correct mathematical terminology is consistently used, enforced, and reinforced.
  • Explicit detail is always used in student-teacher discussion and explanation of process
  • Each unit starts with a vocabulary list of words used in the unit and students have a “resource guide” to refer to. Throughout the unit, these terms are used in context during instruction, practice, and assessment.
  • Teacher notes include hints such as “avoid sloppy language” such as the negative number is bigger rather than the negative has a greater absolute value. Or attending to differences such as expression/equation, solve/simplify. This is evident and strong throughout each unit.
  • The terminology that is used in the modules is consistent with the terms in the standards.

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: Fri Jan 22 00:00:00 UTC 2016

Report Edition: 2015

Title ISBN Edition Publisher Year
null 978-1-61445-209-6 null null null
null 978-1-61445-210-2 null null null
null 978-1-61445-211-9 null null null
null 978-1-61445-212-6 null null null
null 978-1-61445-213-3 null null null
null 978-1-61445-214-0 null null null
null 978-1-61445-215-7 null null null
null 978-1-61445-216-4 null null null
null 978-1-61445-217-1 null null null
null 978-1-61445-218-8 null null null
null 978-1-61445-219-5 null null null
null 978-1-61445-220-1 null null null
null 978-1-61445-221-8 null null null
null 978-1-61445-222-5 null null null
null 978-1-61445-223-2 null null null
null 978-1-61445-224-9 null null null
null 978-1-61445-225-6 null null null
null 978-1-61445-230-0 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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