Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 3 do not meet expectations for alignment. The materials do not devote the large majority of time to grade-level work and topics from future grades are assessed. There is little explicit connection made to the progressions of learning in the standards. Since the materials do not meet the expectations for focus and coherence in gateway 1, they were not reviewed for gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
0
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 3 do not meet expectations for focus on major work and coherence. The materials do not devote the large majority of time to grade-level work and topics from future grades are assessed. There is little explicit connection made to the progressions of learning in the standards.

Criterion 1a

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

The instructional materials reviewed for Grade 3 do not meet the expectations for assessing material at the grade level. The materials assess many topics that are above grade level, and statistical distributions, specifically, should not be assessed before Grade 6.

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 Grade 3 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A, “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.”. There are also many other sessions in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. For this indicator, all of the identified assessments and end-of-unit assessments for the nine units were reviewed. Units and sessions accompanying above grade-level assessment items are noted in the following list.

  • Assessment 2.3A in unit 2 assesses how to: describe the shape of ordered, numerical data; describe where data are spread out or contracted, where there are few data, highest and lowest values, and outliers; and describe data using the term range. These expectations align to standards within 6.SP. According to Table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6.
  • Unit 4, session 2.6, assesses how to: design a shape for a given area; find area by counting or calculating whole and partial square units; find the perimeter of an irregular shape; and find the area of an irregular shape. These expectations partially align to 3.MD.C.7.Aa, “Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths,” and 3.MD.C.7.D.d, “Recognize area is additive. Find the areas of rectilinear figures by decomposing them into non-overlapping parts, applying this technique to solve real world problems.” There are four sessions that align to these expectations, and these four sessions would need to be modified or omitted in order for the expectations to align to the grade-level standards.
  • In Unit 6, the end-of-unit assessment expects students to: read and interpret positive and negative temperatures on a thermometer and on a line graph; use tables to represent the relationship between two quantities in a situation with a constant rate of change; and compare situations by describing differences in the tables that represent them. These expectations align to 6.NS.C.5 , “Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g. temperatures above/below zero, elevations above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation,” and 6.RP.A.3., “Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.” There are twelve sessions that align to these expectations, and these twelve sessions would need to be omitted because modifications would eliminate the underlying structure and intent of the lessons.
  • In Unit 7, the end-of-unit assessment expects students to: divide a single whole or quantity into equal parts; name those parts as fractions or mixed numbers; identify equivalent fractions; and find combinations of fractions that are equal to one and to other fractions. Adding and subtracting fractions with unlike denominators most closely aligns to 5.NF.A, “Use equivalent fractions as a strategy to add and subtract fractions.”. There are four sessions that align to this expectation, and these four sessions would need to be modified or omitted in order for the expectations to align to the grade-level standards.
  • Problems 1 and 2 on the end-of-unit assessment for unit 8 involve computing with money. These problems align to 4.MD.A.2 , “Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals and problems that require expressing measurements giving in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale,” and these problems could be modified or omitted from the assessment without significantly affecting the underlying structure of the materials.
  • Unit 9, session 3.3, assesses how to: design patterns (nets) for boxes that will hold a given number of cubes; see that the cubes filling a rectangular prism can be decomposed into congruent layers; and determine the number of cubes that will fit in the box made by a given pattern (net). These expectations align to 5.MD.C, “Geometric measurement: understand concepts of volume”, and 6.G.B.4, “Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems”. There are seven sessions that align to these above, grade-level standards, and these seven sessions would need to be omitted because modifications would impact the underlying structure and intent of the lessons.

*Evidence updated 10/27/15

Criterion 1b

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

The instructional materials reviewed for Grade 3 do not meet expectations for focus. The materials do not spend the majority of time on the major clusters in the grade. There were lessons in the CCSSM book that addressed one standard but that is not adequate time to teach content in major focus areas. The review team found evidence where actual student activities do not align with the standards labeled in the materials/table of contents and where students are engaging in work above the grade level, thus diminishing the focus.

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 Grade 3 do not meet expectations for majority of class time spent on the major clusters of the grade. There are 166 sessions between assessments and lessons in the materials. Excluding assessments, there are 154 sessions that would be taught throughout the year. Within that 154, only 99 lessons are focused on the major concepts of grade three. This results in 64% of the year being dedicated to the major work. This percentage does not meet the recommended range of time spent on the major work (65%-85%). The following are examples where work is not accurately aligned to the standard as marked, thus diminishing the focus. Examples include:

  • When in unit 9 students are asked to work with measuring volume, the problems include alignments with Grades 4, 5 and 6 standards and introduce transformational geometry which is a Grade 8 standard.
  • The 6 sessions on division in unit 5 are insufficient material for 3.OA.B.6, and two of these are the same lessons for 3.OA.C.7 for fluency.
  • Unit 7 investigation 3 on decimals is above the scope for the grade.
  • 1.3 in unit 7 has students adding the unit fraction, which is more suitable for Grade 4.
  • Unit 4, lesson 2.1 has transformations, which is a Grade 8 standard. Students are using slides, flips, and turns to prove congruence of shape.
  • Unit 6 includes questions and activities on the shape of the data, which is more appropriately aligned with Grade 6.

In addition, much focus is given to straight addition computation (3.NBT.A), which is an additional cluster, and to addition and subtraction word problems (3.OA.D.8). The majority of these are not two-step problems as required in the standard. Addition and subtraction computation and word problems are the focus for 3 units, while multiplication and division is found in one 25-day unit, and fractions in a 15-day unit (of which many lessons are not sufficiently aligned to the standards).

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
0/8
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 3 do not meet expectations for coherence in the grade. The materials are not coherent with the progressions, as volume work goes beyond the scope of the grade and the consistency with the standards within the grade is only evident on rare occasions.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
0/2
+
-
Indicator Rating Details

Instructional materials reviewed for Grade 3 do not meet expectations for coherence because the content in the materials does not support focus and coherence. Overall the review team concluded that there were very few lessons that had supporting/additional clusters that supported the major work. Examples include:

  • Unit 4, investigation 3 teaches standard 3.G.1 in isolation.
  • Unit 6 is Data Analysis: Investigation 1 focused on reading a graph about temperatures on the hour, and all lessons did not simultaneously engage students.
  • All lessons in investigation 2 focus on patterning which is not a standard for Grade 3.
  • Supporting content 3.MD.B.3 involves scaled pictographs and bar graphs which could be used as an appealing context for one- and two-step word problems involving multiplication (OA.A.3). However this opportunity was missed as the scaled graphs are taught in unit 2, prior to the multiplication work taught in unit 5. There are no scaled bar or picture graphs utilized in unit 5 in order to make this connection.
  • In unit 9, the use of nets as representations for 3D shapes is included, which is work of Grade 6.

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 Grade 3 do not meet expectations for viability of content for the scope of one year. The curriculum consists of 166 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, the review team found that the major work is not adequately covered in the materials and therefore, would not be viable for the year in order to support students as they prepare for Grade 4. The domain of number and operations-fractions, which is major work, is greatly under-represented in this series. Only unit 7 teaches fractions and of its 16 lessons, only 2 (sessions 1.1 and 1.2) are aligned correctly to Grade 3 standards.

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 Grade 3 do not meet expectations for consistency with the progressions. The materials do not develop according to the progressions, and they do not give students extensive work with grade-level problems. In addition, while there are teacher notes in the "Looking Back" section of each unit, there is not explicit connection to specific standards addressed in prior grades. Examples of evidence include:

  • In unit 2, line plots focus on numerical data and the focus is on the "shape of data" and includes references to mode and outlier, which is future work.
  • Unit 6 focuses on patterns and line graphs, and neither concept is a Grade 3 expectation.
  • Angles are introduced in unit 4 as an attribute which helps define and categorize squares and rectangles. A Math Note on page 126 explains that teachers can use the angle vocabulary in this grade, but the concept is formally introduced and becomes an expectation in future grades.
  • In unit 7, students are introduced to a few decimal fractions in the context of money. In the Mathematics in this Unit section on page 11, it is explicitly stated that there is no benchmark for this work with decimals and that the extensive work will be in Grades 4 and 5. With the limited focus on fractions in the Grade 3 materials, this is not consistent with the progressions in the standards.
  • A good deal of "extensive work" is missing - there are no real two-step problem-solving opportunities. Most of these opportunities have been simplified by guiding students through the steps by using parts a, b, c in the problems.
  • The "Looking Back" note in unit 1 (page 10) specifically refers to how students work with place value and the properties of addition and subtraction, as well as their work with addition and subtraction fluency with 1-digit combinations. While this is the foundation for their work within addition and subtraction problems in Grade 3, this is not made explicit with connections to CCSSM from prior grades.
  • Units 6 and 9 are not aligned with grade level content.

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 Grade 3 do not meet expectations for fostering coherence through connections at a single grade. The materials do not include learning objectives that are shaped by cluster headings and do not include some problems that connect clusters and domains. Examples include:

  • In unit 7, 11 lessons and 2 assessments are labeled with an alignment between 3.G.A.2 and 3.NF.A, however, upon further review only four of the lessons actually support this coherence. The lessons, investigation 2.2, 2.4, 1.4, 1.5 and 3.1-3.3 may have partitioning but it is with a denominator outside of the scope of the grade. The work also includes dividing parts of a set and involves dividing decimals in money context to hundredths which is all outside of the scope for Grade 3.
  • All focus points are in units 6 and 9, as these units are not aligned with grade level content.
  • Unit 2 aligns with Grade 6, such as when describing the shape of ordered, numerical data, or where data are spread out or concentrated, where there are few data, highest and lowest values and outliers.
  • Unit 4 aligns with Grade 8, such as when determining the geometric moves needed (slides, flips and turns) to prove or disprove congruence between two shapes.
  • Unit 7 aligns with Grade 4, such as when using mixed numbers to represent quantities greater than 1.
  • In unit 2, scaled graphs are taught in isolation and before the multiplication work in unit 5, so a natural connection between the two is missed.

Gateway Two

Rigor & Mathematical Practices

Not Rated

Criterion 2a - 2d

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

Indicator 2a

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

Indicator 2b

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

Indicator 2c

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

Indicator 2d

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

Criterion 2e - 2g.iii

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

Indicator 2e

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

Indicator 2f

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

Indicator 2g

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

Indicator 2g.i

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

Indicator 2g.ii

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

Indicator 2g.iii

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

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

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

Indicator 3b

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

Indicator 3c

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

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

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

Indicator 3h

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

Indicator 3i

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

Indicator 3j

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

Indicator 3k

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

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

Indicator 3p.ii

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

Indicator 3q

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

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

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

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

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

Indicator 3ab

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

Indicator 3ac

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

Indicator 3ad

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

Indicator 3z

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

Additional Publication Details

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

Report Edition: 2012

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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