Alignment: Overall Summary

The instructional materials reviewed for Grade 5 do not meet the expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus on major work because of assessing too many above, grade-level topics and devoting an insufficient amount of time to the major work of the grade. The materials also do not meet the expectations for coherence because they do not make sufficient connections between the standards. Since the materials do not meet expectations for focus and coherence in Gateway 1, they were not reviewed for evidence of rigor and the mathematical practices in Gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
1
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
N/A
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
N/A
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 materials for Grade 5 did not meet expectations for focus and coherence. They also did not meet the criteria for indicators 1a and 1b. Connecting Math Concepts assesses future grade level content (ratios, finding the area of triangles, circles and parallelograms, solving equations with multiple variables, calculating volume of cylinders, understanding place value beyond hundredths, converting decimals and fractions to percents, finding averages and determining probability). Additionally, the instructional materials only devote 60 percent of class time to major work of the grade. The instructional materials reviewed for Grade 5 do not meet the expectations for being coherent and consistent with the standards. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, however there are many major modifications that need to be made in order to teach at the depth required for students to master all grade level standards. The instructional materials do not: identify or connect prior or future grade-level work to Grade 5 work, provide students with extensive work with Grade 5 level work, or relate Grade 5 level concepts explicitly to prior knowledge from earlier grades. The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings. Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate. Overall, the Grade 5 materials do not support coherence and are not consistent with the progressions in the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
0/2
+
-
Criterion Rating Details

The materials for Grade 5 did not meet the criteria for focus. A positive of the assessment program is the formative assessments (mastery tests), which are aligned with a specific remedy section for repeated practice of concepts students have not mastered. Unfortunately, the following above grade level topics are assessed: ratios, finding the area of triangles, circles and parallelograms, solving equations with multiple variables, calculating volume of cylinders, understanding place value beyond thousandths, converting decimals and fractions to percents, finding averages and determining probability. Overall, the instructional materials assess numerous topics before they should be introduced. The materials only devote 60 percent of class time to major work of the grade. A larger percentage of major work is presented in Book 2, which is toward the end of the instructional year, and may not allow enough time for students to develop mastery. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 5.

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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) do not meet the expectations for focus within assessment. For this indicator, the review team examined all mastery tests and both cumulative tests. Overall, the instructional material assesses content from future grades within the majority of the summative assessments. The assessments would not be viable if the above grade level material was omitted, as there are too many assessment questions within the series that are above grade level.

Review Team note: The Level F (Grade 5) Teacher Guide identifies the cumulative tests as “optional” in two places (pages 3-4); however, the publisher orientation session identified these assessments as a required component of the grade level program. Therefore, the cumulative tests are included in this review.

Mastery Test 1: All items align or partially align to grade-level standards.

Mastery Test 2: All items align or partially align to grade-level standards.

Mastery Test 3: All items align or partially align to grade-level standards.

Mastery Test 4:

  • Items in part 1 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
  • Items in part 7 assess writing the reciprocal of a fraction which aligns to standards within 6.NS.A.
  • Items in part 12 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Mastery Test 5:

  • Items in part 4 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.
  • Items in part 8 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Mastery Test 6:

  • Items in part 1 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
  • Items in part 7 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.

Mastery Test 7:

  • Items in part 6 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.

Mastery Test 8:

  • Items in part 8 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
  • Items in part 9 assess finding the area of circles which aligns to standards within 7.G.B.
  • Items in part 12 assess finding the volume of a cylinder which aligns to standards within 8.G.C.

Mastery Test 9:

  • Items in part 5 assess finding averages which aligns to standards within 6.SP.B.
  • Items in part 1 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.
  • Items in part 2 assess writing equations with variables which aligns to standards within 6.EE.C.
  • Items in part 3 assess solving with variables which aligns to standards within 6.EE.A.

Mastery Test 10:

  • Items in parts 4 and 11 assess finding averages which aligns to standards within 6.SP.B.
  • Items in part 3 assess solving problems involving probability which aligns to standards within 7.SP.C.

Mastery Test 11:

  • Items in part 10 assess finding averages which aligns to standards within 6.SP.B.
  • Items in part 6 assess solving problems involving probability which aligns to standards within 7.SP.C.

Mastery Test 12:

  • Items in part 4b assess finding averages which aligns to standards within 6.SP.B.
  • Items in part 7 assess solving problems involving probability which aligns to standards within 7.SP.C.
  • Items in part 1 assess writing equations with variables which aligns to standards within 6.EE.C.

Mastery Test 13: All items align or partially align to grade level standards.

Cumulative Test 1:

  • Items in part 5 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
  • Items in part 1 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.
  • Items in part 7 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Cumulative Test 2:

  • Items in parts 12 and 17b assess finding averages which aligns to standards within 6.SP.B.
  • Items in part 10 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
  • Items in part 4 assess finding the area of circles which aligns to standards within 7.G.B
  • Items in part 24 assess solving problems involving probability which aligns to standards within 7.SP.C.
  • Items in part 9 assess finding the volume of a cylinder which aligns to standards within 8.G.C.
  • Items in parts 5 and 10 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.
  • Items in part 21 assess solving with variables which aligns to standards within 6.EE.A.

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 materials for Grade 5 did not meet the criteria for focus. A positive of the assessment program is the formative assessments (mastery tests), which are aligned with a specific remedy section for repeated practice of concepts students have not mastered. Unfortunately, the following above grade level topics are assessed: ratios, finding the area of triangles, circles and parallelograms, solving equations with multiple variables, calculating volume of cylinders, understanding place value beyond thousandths, converting decimals and fractions to percents, finding averages and determining probability. Overall, the instructional materials assess numerous topics before they should be introduced. The materials only devote 60 percent of class time to major work of the grade. A larger percentage of major work is presented in Book 2, which is toward the end of the instructional year, and may not allow enough time for students to develop mastery. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 5.

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 Connecting Math Concepts Level F (Grade 5) do not meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 5.

To determine this, two perspectives were evaluated: 1) the number of lessons aligned to major work by cluster and/or standard. and 2) the number of exercises aligned to major work (based on reviewer analysis). The review team found the second perspective to be the most accurate, as it indicates an amount of class time devoted to major work each day. A third perspective was not evaluated because the materials spiral and are not organized into units or chapters.

The percent of lessons aligned to major work clusters according to “Level F Correlation to Grade 5 Common Core State Standards for Mathematics” document in Presentation Book 1, pages 437-445, and Presentation Book 2, pages 469-479:

  • The percentage of lessons aligned to 5.NBT.A is 64 percent.
  • The percentage of lessons aligned to 5.NBT.B is 100 percent.
  • The percentage of lessons aligned to 5.NF.A is 58 percent.
  • The percentage of lessons aligned to 5.NF.B is 94 percent.
  • The percentage of lessons aligned to 5.MD.C is 19 percent.

In book one, there are 232 out of 451 exercises, about 51 percent, that focus on major work. In book two, there are 302 out of 440 exercises, or about 69 percent, that focus on major work. This is 534 out of 891 total exercises, about 60 percent..

  • Book one has much less work focusing on major work of grade. This leaves the majority of major work toward the end of year, which may lead to not enough time to develop mastery.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
1/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 5 do not meet the expectations for being coherent and consistent with the standards. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work. The amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days, however there are many major modifications that need to be made in order to teach at the depth required for students to master all grade level standards. The instructional materials do not: identify or connect prior or future grade-level work to Grade 5 work, provide students with extensive work with Grade 5 work, or relate Grade 5 concepts explicitly to prior knowledge from earlier grades. The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings. Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate. Overall, the Grade 5 materials do not support coherence and are not consistent with the progressions in 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 Connecting Math Concepts Level F (Grade 5) partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not. There are several missed opportunities to connect supporting work to major work.

Connections between CCSS Supporting Work and Major Work Math Standards are never identified in the Teacher Presentation Books or the Teacher Guide. Connecting Math Concepts is a “direct instruction” program, where teachers are encouraged to use instructional materials as written, with little to no deviation from the prescribed presentation script. The Teacher Guide states: “The script indicates the wording you use in presenting the material and correcting student errors. Once you are familiar with the program, you may deviate some of the exact wording; however, until you know why things are phrased as they are, you should follow the exact wording." (page 9). This structured presentation discourages teachers from making missed connections explicit for students.

Connections between Supporting and Major Work:

  • Lessons 112-120 has students representing and interpreting data (5.MD.B). An explicit connection is made in the standards to multiplication and division with fractions (5.NF.2). Each exercise does involve students using addition and multiplication to create subtotals and totals from a line plot. Students also apply division to find the average. Although meaningful contexts for the data or a meaningful context for creating an average are not found in these lessons, students do apply and connect multiplication and division of fractions. There is no further exploration of the connections between the two standards.
  • Lessons 90-116 has students converting like measurements (5.MD.A). Although there are some exercises where the result is a fraction this connection is not very strong. Students work with numbers that are in the Grade 4 range for most problems when they are multiplying and dividing (5.NF.B).

Missed Connections between Supporting and Major Work:

  • Lessons 90-116 has students converting like measurements (5.MD.A). They teach unit comparison and do not enhance the major work of the grade using operations with decimals and hundredths (5.NBT.B). Instead the curriculum focuses on converting units like yards to inches, hours to minutes, days to hours, years to months, days to weeks, etc.
  • Lessons 112-120 has students representing and interpreting data (5.MD.B). These lessons teach probability and line plots, which do not enhance the major work of fraction clusters (5.NF.A).

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) do not meet the expectations for having an amount of content designated for one grade level as viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is appropriate for a school year of approximately 140-190 days; however, due to the large amount of content that is not aligned to the grade level, there is not enough instruction at the depth required to prepare students for learning in future grades.

  • The curriculum supplies 120 lessons, 12 mastery tests, and 2 cumulative tests. Although remedial worksheets are provided to support students struggling on concepts after each mastery test, these do not comprise the same amount of material as is contained in each lesson. These materials, if each mastery test is conducted in one lesson period (45-60 minutes) would be completed over 134 instructional days.
  • A substantial number of unaligned exercises focus on skills and understandings not included in CCSSM and/or mastery of above-level standards from Grade 6 and beyond (see report for Indicator 1b); this focus on above grade-level objectives takes time and focus away from foundational grade level understandings. Teachers using this program would need to make significant modifications to the daily lessons and/or omissions that would affect the integrity of the grade level program.
  • Measuring volume, 5.MD.4, which is part of a major cluster, appears in only two exercises (lessons 68.3, 69.6).
  • Understanding the concept of volume measurement, 5.MD.3, which is part of a major cluster, appears only in two exercises (lessons 68.3, 69.6).
  • Generating two numerical patterns using two given rules, 5.OA.3, appears in only three exercises (lessons 118.2, 119.2, 120.1).

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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) do not meet the expectations for materials being consistent with the progressions in the standards. Overall, the instructional materials do not: identify or connect prior or future grade-level work to Grade 5 level work, provide students with extensive work with grade-level problems, or relate Grade 5 concepts explicitly to prior knowledge from earlier grades.

i. Materials do not develop according to the grade-by-grade progressions. Prior or future content is not clearly identified.

  • Only 60 percent of the exercises address major work of Grade 5.
  • Prior grade-level topics taught and not identified include: 3.NBT.A, place value and rounding (lessons 1-80), 2.NBT.B, addition/subtraction number families (Lessons 1-116), 3.NBT.A, mental math (Lessons 11-106), 4.MD.B, line plots (lessons 103-117), 4.MD.A, area and perimeter (lessons 40-112), 4.MD.C, angles (lessons 54-112), 3.OA.C, multiply and divide within 100 (lesson 1, exercise 4), 2.NBT.A, expanded notation (lessons 1-6), 4.NF.B.C, add and subtract fractions with like denominators (lessons 4-6) and 3.NF.A, recognizing and generating simple equivalent fractions (lesson 11).
  • Future grade level topics taught and not identified include: 6.RP.A, percent values (lessons 35-106), 6.RP.A, ratio and proportion (lessons 19-75), 6.EE.A, expressions with variables (begins lesson 35), 6.SP.A, probability (lessons 95-116), 6.EE.C, graphing ratios (lesson 69-120), 6.SP.B, finding averages (lessons 82-117), 6.G.A, finding surface area (lessons 106-112), 7.G.B, finding area of circles (lessons 72- 75) and 8.G.C, solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (lessons 76-80).

ii. Materials do not give students extensive work with grade-level problems.

  • Lessons 112-120 are not taught or practiced to the full depth of the standard (MD.B.2).
  • Lessons 68 and 69 contain one exercise each that addresses the concept of relating volume to multiplication and addition (MD.C.3 and MD.C.4).
  • Lessons 61-120 provide limited work with writing and interpreting numerical expressions (5.OA.1). Students learn "the parentheses are a times sign." Students are not taught how and why parentheses are used and are not introduced to brackets or braces.
  • Lessons 90-116 provide limited work with unit conversion (MD.A.1). Students are not given the chance to apply unit conversion to the metric system, which is not only a missed connection, it holds students back from the progression expected to work with decimals and scientific notation in later grades.
  • Lessons 62, 102, 104 and 106 provide limited work with line plots (MD.B.2). Students do not make their own measurements or work independently to create a line plot.
  • The major work of 5.MD.3 is only addressed in two exercises, or about 20 minutes in the entire school year. This is not enough time for students to understand concepts of volume measurement.
  • The major work of 5.MD.4 is only addressed in two exercises or about 20 minutes in the entire school year. This is not enough time for students to master measuring volumes.
  • The work of 5.OA.3 is only addressed in three exercises, or about 30 minutes in the entire school year. This is not enough time for students to master generating two numerical patterns using two given rules.
  • Students who fail parts of the mastery test can be assigned Remedies aligned to standards below the current grade level to complete during independent practice, so these students would not be working with grade-level problems. Opportunities for enrichment of grade-level work do not exist in the program.

iii. Most materials do not explicitly relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • "Coherence in connecting prior work in multiplication to multiplication of fractions or fractions and whole numbers," (5.NF.B ) is not made. For example, in lesson 9, exercise 5, the lesson focuses students on ideas like "the bottom numbers do not have to be the same" and "when you multiply fractions, you don't copy any numbers." No connections are made to previous reasoning or learning with multiplication. Students are not asked to consider or reason about the size of the product relative to the factors.
  • When exercises do occur over subsequent lessons, little of the teacher script connects back to a previous day’s learning or understanding.
  • Opportunities to extend previous understanding are not made because lessons provide isolated practice of the standards.
  • Many of the lessons provide isolated exercises that do not explicitly connect to 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.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) do not meet the expectations for fostering coherence through connections at a single grade level.

The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings.

  • Lessons are composed of exercises that are unrelated. In cases where there could be connections made, they are still treated as separate exercises.
  • Lessons and exercises are not marked with CCSSM.
  • Page 12-13 provides a chart with the Lessons and the CCSSM for Level F.
  • Teacher Guide, pages 145-149, shows how the CCSSM are presented in sample lessons.
  • A comprehensive listing of the CCSSM and the correlating exercises are found in the backs of Presentation Book 1 and Presentation Book 2.
  • CCSSM aligned exercises do not meet the true intent of the standard:
    • 5.OA.A - Students are seldom asked to solve numerical expressions and never asked to write them.
    • 5.MD.C - Students use the formula to calculate volume without having to demonstrate conceptual understanding by counting unit cubes

Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate.

  • Student work with multiplying fractions (5.NF.B) does not extend their understanding of the operation of multiplication (5.NBT.B.5).
  • Student work with converting units within the metric system is not connected to their work with place value (5.NBT.A.1)

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

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.

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.
N/A

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.
N/A

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
N/A

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.
N/A

Criterion 2e - 2g.iii

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

Indicator 2e

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

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
N/A

Indicator 2g

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

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.
N/A

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.
N/A

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
N/A

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

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

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.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

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.
N/A

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

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.
N/A

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.
N/A

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.
N/A

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).
N/A

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.
N/A

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

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.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

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

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).
N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

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.
N/A

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.
N/A

Indicator 3ab

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

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.
N/A

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.).
N/A

Additional Publication Details

Report Published Date: 01/25/2016

Report Edition: 2013

Title ISBN Edition Publisher Year
9780021036417
9780021036424
9780021036455
978021036387
978021036431
978021036448

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.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

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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