Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 2 do not meet the expectations for alignment. The amount of time spent on major work is not consistent with the expectations for focus and the materials include assessment questions above grade-level content. The instructional materials do not attend to Mathematical progressions and, therefore, do not meet the expectations for coherence. All three teacher editions (traditional, STEM, literacy/arts) do not meet the expectations for coherence at Grade 2. The materials do not meet the expectations for focus and coherence in gateway 1 and 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 2 do not meet the expectations for indicators 1a and 1b. The amount of time spent on major work is not consistent with the expectations for focus and the materials include assessment questions above grade-level content. The instructional materials do not attend to Mathematical progressions and, therefore, do not meet the expectations for coherence. All three teacher editions (traditional, STEM, literacy/arts) do not meet the expectations for coherence or focus in Grade 2.

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 2 do not meet the expectations for assessing material at the grade level. The materials assess topics that are in future grades. The content assessed in the Cake Walk STEM project is more appropriately aligned with Grade 4, 4.G.A.3, when students are asked to use symmetry as part of their assessment and with Grade 4, 4.NF.B, when students are asked to partition into sixteenths as the denominator. The content assessed in Math Mini-Choppers STEM project is more appropriately aligned with Grade 3, 3.NBT.A.3 when students are asked to demonstrate a multiplication with up to three digits.

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

Materials considered for review for this indicator were STEM projects. The instructional materials reviewed for Grade 2 do not meet the expectations for this indicator. The review team found that the instructional materials assess grade level content beyond the scope of the grade. The out of grade level standards assessed are not Mathematically reasonable for this grade level.

STEM Materials that assess grade level content beyond Grade 2.

  • The Cake Walk STEM project on pages 73 – 88 of the teacher STEM project edition:
    • This project asks students to decorate their cake symmetrically. This is not to be addressed until Grade 4 according to 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw line of symmetry.
    • This project asks students to partition into sixteenths as the denominator. This is not to be addressed until after Grade 4 according to 4.NF.B. Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers. (Grade 4 Expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
  • Math Mini-Choppers STEM project on pages 17 – 52 of the teacher STEM project edition:
    • This project asks students to demonstrate a multiplication with up to three digits. This is not to be addressed until Grade 3 according to 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations.
    • This project asks students to demonstrate estimation. This is a structural part of this activity. This is not to be addressed until Grade 3 according to 3.OA.D.8 Solve two-step word problems using the four operations. 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.

Review Team Note: A separate supplemental digital assessment database is available for an additional purchase cost. The review team did not analyze this supplemental digital assessment database as evidence for indicator 1a due to the fact that this additional component is not provided as part of the core materials.

*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 2 do not meet expectations for focus because the material did not spend the large majority of time on the major clusters in the grade.

  • There is little work with multi-step problems and work is often single- and double-digit computation.
  • There was evidence found where actual student activities do not align with the standards labeled in the materials and where students are engaging in work both below and 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 2 do not meet expectations for focus because the material did not spend the large majority of time on the major clusters in the grade. A total of 54 activities/lessons are provided, and some may be repeated or take additional class periods to complete. However, of the 54 only 37 of the lessons are aligned to major work of the grade. This would mean that if the 37 lessons were fully aligned, 68.5% of the time is spent on the major work, which places it in the lower range of grade level expectations. Looking more closely, the percent of time spent on major work is below 68.5% because there are lessons that are labeled as aligned to major work of the grade, but with activities in the lessons that do not actually align. Student exercises are generally weak in building conceptual understanding and lack opportunities for students to explain their reasoning or critique the reasoning of others. Here are a few examples of the misalignment:

  • STEM "Museum Heist" is not a focused alignment and a few of the standards that are labeled are not addressed.
  • The lesson in the teacher edition on page 218 does not incorporate concrete models, drawings or work with properties. The lesson introduces regrouping taught as a procedure rather than with concrete work decomposing tens or hundreds.

In addition, there are examples of work beyond the grade level:

  • ART, page 77, has a measurement and data lesson titled "Frank is a Gentleman." The visual has the radius drawn and labeled, measurements are in tenths and yards need to be converted to meters. Measurements in the teacher edition appear to use millimeters.
  • Teacher edition, page 121, has work above the grade level. Memorizing the times tables is not a required fluency in Grade 2.
  • Teacher edition, pages 2-18 include both one- and two-step word problems.

Because of these misalignments, the actual time spent on major work would be less than 68.5%, below the expected percentage for this grade.

Criterion 1c - 1f

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

The review team found that the coherence between the standards at the Grade 2 level fall short of meeting expectations for these criterion. Overall, there is very limited use of visual models which students could utilize to help build upon their knowledge of story problems as well as partitioning.

Indicator 1c

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

The instructional materials for Grade 2 do not meet the expectation for coherence. Examples of missing coherence include:

  • Teacher edition lesson, page 387, does not support the major work because it skips student counting and iterating in the unit. There may be an error in the graph for the sunflower, which is not a line plot, but labeled as such.
  • Teacher edition lessons in 2.MD are not extended to standards in 2.OA to provide context and support.
  • Teacher edition lesson page, 425, does not partition rectangles into arrays to use for repeated addition and skip counting which would support 2.NBT and 2.OA work.
  • The STEM project "Cake Walk" does not enhance coherence with major work at the grade. It does not fully address the additional work that it appears to cover as indicated by the label.
  • Student edition, page 37-52 includes only minimal connections to adding (2.OA.C.3-2.OA.C.4).

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 school year viability do not meet expectations for the indicator because the amount of content is not viable for one school year. There are only 54 activities and lessons provided for the year. Additionally,

  • Lessons that allow for in-depth work in 2.OA.A.1 and 2.OA.B.2 should be here and are not. There are six lessons between the three resources labeled with standards in 2.OA.A.1 and 2.OA.B.2 out of the 54 total lessons. Beyond that, not all of these lessons are fully aligned to 2.OA. (e.g., STEM lesson, "Museum Heist").
  • The STEM lesson "Math Mini-Choppers" does not fully address 2.NBT.A.2 and 2.NBT.A.3 which is also major work that calls for specific attention and activity.

The amount of time on major work in Grade 2 instructional materials is not viable for one school year and does not foster coherence between grades. Teachers would need to find supplemental resources in order to cover the content for Grade 2.

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 for Grade 2 do not meet the expectations for consistency with the progressions in the standards.

  • The progression of the problem types and moving from one-step to two-step problems in 2.OA.A.1, specifically ART, page 1, does not support the progressions from previous grades. It also does not develop the types of problem solving situations students need to work on in Grade 2.
  • 2.G.A.3 on ART page 114 does not fully develop the idea of equal shares, the unit fraction of three/thirds as a whole and does not fully build from halves and fourths of Grade 1 as consistent with the progressions.

Grade 2 materials do not give students extensive work on grade level problems.

  • The STEM project "Growing Flowers" is labeled 2.MD.A.2 but does not address or identify as fluency and strategies aren't developed to support fluency within 100.
  • Computation throughout all three resources is a rush to fluency and little development and understanding of place value and groups is evident. 2.G.A.2 does not address repeated addition as a strategy for multiplication in any of the labeled lessons, but instead multiplication is seen in lessons.
  • Work from prior grades in teacher edition on page 387 is not explicitly identified, aiding in coherence between grades. Connections between Grade 3 category data and Grade 4 category data is not evident.
  • Finally, it is stated on page 101 in the teacher tip to "Remind students they are revisiting work they did in prior grades," but the connections between concepts are not clearly articulated for teachers and are not explicitly named for students, just merely mentioned.

For all these reasons, the expectations for materials being consistent with the progressions in the standards is not met.

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 Grade 2 instructional materials reviewed for coherence at the grade do not meet the expectations. Learning objectives are written and either address learning at the individual standard level, or do not really accurately express what is happening in the lesson. For example:

  • In teacher edition on page 425, students are folding paper to make equal-sized squares, or they are covering a rectangle with equal-sized pieces. This is perhaps early area and connects more closely to 2.G.A.2 and the 2.G.A.3 label is inaccurate as students are not asked to describe shares. In addition, the summary on page 429 asks for covering the surface of 16 and specifically mentions dividing the squares.
  • The teacher edition on page 3, offers no visuals in the material to help build from work in the previous grade.
  • In other instances the objectives show that above grade-level work is being covered in the lesson, such as decimals on page 446 of the teacher edition.

Lessons are generally not connecting multiple clusters or domains in the teacher edition. Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. Some standards are placed where there is a natural connection in lessons covering 2.NBT and 2.MD. The STEM project "Cake Walk" does not fully provide evidence of where in the activities the standards cross domains.

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: Fri Feb 13 00:00:00 UTC 2015

Report Edition: 2012

Title ISBN Edition Publisher Year
null 9781587807228 null null null
null 9781587807235 null null null
null 9781847008374 null null null
null 9781847008695 null null null
null 9781908018435 null null null
null 9781908018800 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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