Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 did not meet the expectations for alignment to the CCSSM. The instructional materials did not meet the expectations for Gateway 1 and therefore were not reviewed for Gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 4 enVision Math 2.0 did not meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for assessment and coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of Grade 4, but the materials do not appropriately focus on assessment nor always meet the full depth of 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 instructional material reviewed for Grade 4 do not meet the expectations for focus within assessment. Overall, above grade-level content, including statistical distributions, was included on assessments.

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 assessment materials reviewed for Grade 4 do not meet expectations for focus within assessment. There are many lessons in the materials that would need to be modified or omitted because of their alignment to above grade-level standards.

The series is divided into topics, and each topic has a topic assessment and a topic performance assessment. Additional assessments include a placement test found in Topic 1, four cumulative/benchmark assessments, and a End-of-Year Assessment.

The assessments that have items that assess future grade-level standards are listed below.

  • Topic 5, item 13 has students using a procedure for division with no ties to place value. The directions for the students are "Use an algorithm to find a quotient." This is more closely aligned to 6.NS.B.
  • Topic 9, item 6 has addition/subtraction with unlike denominators which would be a Grade 5 alignment; however, students are asked to use their knowledge of benchmark fractions to answer this item.
  • Topic 10 questions 1A and 1B and Assessment Master questions 1A and 1B require students to simplify their answer from a fraction greater than one to a mixed number (5.NF.3). On page 584, in questions 5 and 6 students are multiplying whole numbers and mixed numbers. 4.NF.B includes multiplying fraction by a whole number. In Grade 5, 5.NF.B requires multiplication of a fraction by a mixed number.
  • Statistical distributions are assessed and do appear in the Grade 4 materials. Topic 11, item 9a assesses if the data has an outlier; this assesses 6.SP.5c giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. A closer examination of the instruction related to this item revealed the following work on statistics which distract from focus. The following pages include instruction on outliers which demonstrates the prolific amount of off grade-level work and how removing it would heavily modify the materials.
    • Page 587A: "Ask questions about the data set such as: Is there an outlier?"
    • Page 588-590: My Word Cards.
    • Page 591A: Vocabulary.
    • Page 591A in the ELL section: "Display 'outlier' and ask students to read it out loud. Underline 'out.' You know the word 'out,' as in outside. An outlier is a number that is far away from, or outside of, the other numbers in a data set."
    • Page 592: mentions the word outlier 11 times.
    • Page 597: "MP6 Be Precise Listen and look for students who use a line plot to find outliers in a data set about pets." "A line plot can help you find an outlier in a data set." "What is an outlier?"
    • Outlier is used in direct instruction, activities, students pages, intervention, reteaching, and homework on the following pages: 587A, 587D, 581I, 587E, 588-590, 591A, 592, 593, 594, 595, 596, 597, 597A, 598, 599, 600, 601, 602, 616, 617 and 618.

Note:

  • There are many items that require a particular strategy (bar model, array, compensation, etc.), especially in Topics 1-5.
  • Topic 3 page 161, question 5 part B: Only one lesson discusses the distributive property and uses an area model (lesson 3-3), and this question specifically calls for drawing an area model to answer the question.
  • Topic 4, item 9 and Topic 14, item 2, do not require the students to do any mathematics.

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 materials reviewed for Grade 4 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to 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 4 meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade.

To determine this, three perspectives were evaluated: 1) the number of topics 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 is the same as the number of lessons. A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent, and we drew our conclusion based on that data.

Grade 4 enVision Math 2.0 includes 16 Topics with 109 lessons. At the topic level ten of the 16 focus on major work. Two of the 16 topics focus on supporting work and are supporting the major work of the grade, and four of the 16 topics focus on supporting work without supporting the major work. At the topic level approximately 75 percent of the topics are focused on major work.

As mentioned above, a lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level 69 lessons focus on major work, 13 lessons focus on supporting work and support the major work of the grade, 18 lessons focus on the supporting work without supporting the major work, and 9 lessons focus on off grade level topics. Approximately 16 percent of the lessons focus on supporting work and do not support the major work of the grade, and approximately 8 percent of the lessons focus on off grade-level topics. At the lesson level approximately 63 percent of the lessons focus on major work. Supporting work which continues major work learning was included, bringing this up to 75 percent.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
3/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 4 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do not have enough materials to be viable for a school year and do not always meet the depth of the standards. The majority of the instructional materials do not have supporting content enhancing focus and coherence simultaneously but do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 4 do not exhibit enough characteristics of coherence.

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 4 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade, and many natural connections are missed.

The following detail supporting work in the instructional materials.

  • Topic 7 is focused on factors and multiples and somewhat supports the major work of the grade. The connections to the major work are weak. If this topic was earlier in the materials the connections would be stronger since the connections are one-digit by one-digit or one-digit by two-digit multiplication. However, no instruction in Topic 7 is explicitly tied to multiplication/division strategies (e.g., splitting a number into factors, using associative property to rearrange); connections to creating common factors is mentioned in the teacher guide but not tied to instruction in this topic.
  • Topic 13 is focused on conversion of measurements 4.MD.A and does support the major work of the grade. Lesson 13-1, Lesson 13-2, Lesson 13.3 and Lesson 13.6 connect measurement standards to operations with fractions (4.NF).
  • Topic 14 is focused on generating and analyzing patterns 4.OA.C. This topic is treated separately and does not support the major work of the grade.
  • Topic 15 is focused on angles and angle measurement, 4.G.A. This topic is treated separately and does not support the major work of the grade.
  • Topic 16 is focused on lines, angles, and shapes (4.G.A). This lesson is treated separately from 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.
0/2
+
-
Indicator Rating Details

The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-23A. The enVison Math 2.0 Grade 4 program consists of 109 lessons, grouped in 16 topics. Assessments are not included in this count; if the 16 days of assessment are added in this would bring the count to 125 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to 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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 4 partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade-level.

Material related to future grade-level content is not clearly identified or related to grade-level work. The exception is the topic titled "Step up to 5th grade" where the materials are clearly identified as Grade 5 materials. The Grade 4 materials have some instances where future grade-level content is present and not identified as such. For example:

  • Lessons 3-7, 3-8, 3-9, and 4-10 align to using a procedure for multiplication, which is 5.NBT.5.
  • Lessons 5-8 and 5-9 align to using a procedure for division, which is 6.NS.2.
  • Lessons 11-1 and 11-2 have students finding the outlier in a set of data, which is 6.SP.5c.

The content does not always meet the full depth of the standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:

  • 4.OA.3, "Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding" is the focus of three lessons. Within these three lessons (6-3, 6-4 and 6-5), some of the problems are one-step problems. A few other lessons do list 4.OA.3 as a supporting standard; however, they do not have multistep problems in the lessons.
  • 4.NBT.5, "Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models" is the focus of three lessons. One of the lessons (3-1) teaches students to write zeros after the product of the first two numbers if you are multiplying by a power of 10. For example, for 3 x 50, you would multiply 3 x 5 and then add one zero to get the answer. There is no connection made to place value, which could lead to misconceptions later for students.
  • 4.NF.2 is the focus of three lessons, and this standard encompasses the major work of comparing fractions with unlike numerators and unlike denominators.
  • 4.NF.5 is mentioned in two lessons, and when further examining those lessons, the standard is not present in lesson 12-5 and is briefly mentioned in the examples in lesson 12-4.

The materials extensively work with grade-level problems, for example:

  • All students complete grade-level materials, and suggestions for re-teaching and intervention are included with each lesson and at the end of each topic.
  • Online resources include extra-, on-level and advanced-practice materials.
  • A math and science project is available for each topic taught.
  • Homework practice problems are identified in the teacher edition as intervention, on-level, and advanced.
  • The numbers of topics focusing on Grade 4 domains are as follows: 5 out of 16 topics address number and operations in base ten; 4 out of 16 topics address number and operations - Fractions; 3 out of 16 topics address operations and algebraic thinking; 3 out of 16 topics address measurement and data; and 1 out of 16 topics address geometry.

The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:

  • "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 4, explaining connections to the content within the topic, and explaining what will come later in Grades 4 and 5. An example can be found on pages 325c-325d for Topic 6.
  • Individual lessons also include coherence headings. An example is in lesson 6-1 on page 327A that includes the heading, "Coherence: In Topic 2, students developed fluency in adding and subtracting whole numbers. In Topics 3 and 4, ... In this lesson, students use these skills to solve problems involving comparisons."
  • In lesson 9.1, for 4.NF.B, students are extending their simple equivalent fraction knowledge to add fractions using models.
  • In lesson 1.4, for 4.NBT.A, students are extending their knowledge of number lines to round whole numbers.

Indicator 1f

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

The instructional materials reviewed for Grade 4 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.

The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.

  • The focus of Topic 2 is 4.NBT.B, Use place value understanding and properties of operations to perform multi-digit arithmetic, and 4.OA.A, Use the four operations with whole numbers to solve problems. Lesson objectives in Topic 2 include: L4 - Use place value and an algorithm to subtract whole numbers and L6 - Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations.
  • A similar example for Topic 15 can be found on pages 765I - 765J.

The materials for Grade 4 enVision Math 2.0 partially foster coherence through grade-level connections. Most lessons in the Grade 4 program focus within a single domain and cluster. Of 109 lessons, 70 lessons focus within a single cluster and domain.

  • In Topic 1, 0 of the 5 lessons address standards within two or more clusters.
  • In Topic 2, 4 of the 6 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 3, 4 of the 10 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 4, 8 of the 11 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 5, 4 of the 10 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 6, 5 of the 5 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 7, 1 of the 5 lessons address standards in two domains (4.OA and 4.NBT).
  • In Topic 8, 0 of the 7 lessons address standards in two or more clusters.
  • In Topic 9, 0 of the 11 lessons address standards in two or more clusters.
  • Four of the 6 lessons within Topic 10 are within a single cluster and domain.
  • Two of the 4 lessons within Topic 11 are within a single cluster and domain.
  • In Topic 12, 3 of the 6 lessons address standards in two domains (4.NF and 4.MD).
  • Two of the 7 lessons within Topic 13 are within a single cluster and domain.
  • All of the 4 lessons within Topic 14 are within a single cluster and domain.
  • Five of the 6 lessons within Topic 15 are within a single cluster and domain.
  • In Topic 16, 0 of the 6 lessons address standards in two or more clusters.

Gateway Two

Rigor & Mathematical Practices

Not Rated

Criterion 2a - 2d

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

Indicator 2a

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

Indicator 2b

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

Indicator 2c

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

Indicator 2d

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

Criterion 2e - 2g.iii

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

Indicator 2e

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

Indicator 2f

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

Indicator 2g

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

Indicator 2g.i

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

Indicator 2g.ii

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

Indicator 2g.iii

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

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

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

Indicator 3z

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

Additional Publication Details

Report Published Date: Wed Apr 20 00:00:00 UTC 2016

Report Edition: 2017

Title ISBN Edition Publisher Year
null 978-0-328-82739-8 null null null
null 978-0-328-82745-9 null null null
null 978-0-328-82781-7 null null null
null 978-0-328-82787-9 null null null
null 978-0-328-82794-7 null null null

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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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