Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 5 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 5. 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 5 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 5.

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 5 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 M-Class Hydroplane Racing, STEM project, is more appropriately aligned with Grade 6, 6.G.A.4, when students are asked to address surface area and 6.RP.3.C when students are asked to find the percent of a number. The content assessed in the Engines STEM project is more appropriately aligned with Grade 7, 7.G.B.4, when students are asked to find the area of a circle and with Grade 8, 8.G.C.9, when students are asked to find the volume of a cylinder. The content assessed in the Fractional Playground STEM Project is more appropriately aligned with Grade 6, 6.SP.B.5.c when students are asked to find the average.

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 5 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 5 include:

  • M-Class Hydroplane Racing STEM project on pages 55 – 78 of the teacher STEM project edition.
    • This project asks students to address surface area. This is not to be addressed until Grade 6 according to 6.G.A.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.
    • This project, on page 37 of the student STEM project edition, asks students to find the percent of a number. This is not to be addressed until Grade 6 according to 6.RP.3.C.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
  • Engines STEM project on pages 15 – 38 of the teacher STEM project edition:
    • This project asks students to find the area of a circle. This is not to be addressed until Grade 7 according to 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
    • The project asks students to find the volume of a cylinder. This is not to be addressed until Grade 8 according to 8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
  • Fractional playground STEM project on pages 39 – 54 of the teacher STEM project edition:
    • This project asks students to find the average. This is not to be addressed until Grade 6 according to 6.SP.B.5.C 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.

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 5 do not meet expectations for focus because the material did not spend the majority of time on the major clusters in the grade. For example, there were misalignments within the 5.NF and Grade 5 procedural work as well as a lack of visual models to build understanding of operations. The review team found evidence of student activities that do not align with the standards as labeled in the materials 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 5 do not meet expectations for focus. The materials do not spend the majority of class time on the major cluster of each grade. A total of 74 activities/lessons are provided between the three resources, and some may be repeated or take additional class periods. However, only 47 of the 74 lessons are aligned to major work at the grade according to teacher edition, ART and STEM table of contents. If the 47 lessons were fully aligned, 63.5% of the time is spent on the major work. In looking more closely, the percent of time spent on major work would be below 63.5%. These lessons are labeled as aligned to major work of the grade but the activities in the lessons do not actually align and some of the lessons include content that is beyond the scope of the grade. Examples of these misalignments include:

  • The ART lesson on page 14 is about factors and prime factorization which can connect to expressions, but the activity does not follow the full meaning of the standard.
  • The 5.NF.A.2 lesson beginning on teacher edition page 233 limits use of visual fraction models, no use of benchmark fractions and few experiences with adding/subtracting fractions in word problems.
  • The STEM project "M-Class Hydroplane Racing" does not include work of counting unit cubes or include a jump to surface area.
  • The teacher edition lesson on pages 35-47 only addresses one-step numerical patterns and students are not generalizing patterns themselves.
  • Most of the pages in teacher edition pages 48-62 are limited to writing numbers, identifying the value of digit in a number and comparing numbers, which is not what is meant in the standard 5.NBT.A.1.
  • In the lessons on pages 95-106, the >, = and < symbols are mentioned on page 97 and one student exercise on page 105 uses the symbols, but the rest of the lesson does not use the symbols to compare decimals to thousandths. The lesson doesn't show students how to place numbers together to demonstrate comparing each digit on both sides of a decimal to determine if the numbers are greater than, equal to, or less than. It also waters down the symbols by referring to the numbers as merely bigger or smaller rather than the vocabulary of the grade level (5.NBT.A.3.B).
  • In the teacher edition on pages 113-121, all the problems round to exactly one place to the left of the last digit in the number; e.g., numbers in the hundredths always rounded to tenths, thousandths always rounded to hundredths (5.NBT.A.4).
  • Teacher edition pages 263-299 are supposed to build on student understanding of fractions and use visual fraction models, but they merely have students perform a procedure to solve the problems (5.NF.B.4).
  • Teacher edition pages 300-316 provide additional multiplication practice with no real connection to scaling or comparing product to factor size (5.NF.B.5.A).
  • Teacher edition pages 317-337 provide no opportunities to have students explain why multiplying a number by a fraction less than one results in a smaller product (5.NF.B.5.B).
  • Teacher edition pages 338-350 instructs students to always turn a mixed number into a fraction to perform an operation on it, even when that is not the most efficient strategy (5.NF.B.6).
  • Teacher edition pages 351-360 do not have students use visual fraction models or create story context to solve problems (5.NF.B.7.A).

Therefore, the percentage would be considerably less than 63%, making the content connections to major work less focused.

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 5 fall short of meeting expectations for these criteria. Overall there is little opportunity for explanation offered in these lessons and multiple strategies, representations and division situations (which promote coherence) are not evident.

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 5 do not meet the expectation for coherence so that supporting content would enhance the major work of the grade. Examples of missed opportunities for coherence include:

  • The STEM lesson "Cryptology," which does not support the major work of 5.NBT.
  • The ART lesson on page 146 does not support the major work of 5.NF fully at the grade level; all fraction calculation has been done for students, additional units could have been added so that students had to use conversion and the connection to 5.NBT.

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 Grade 5 instructional materials reviewed for school year viability do not meet expectations for the indicator. The amount of content is not viable for one school year for the following reasons:

  • Between the three resources, 63.5% of the time is spent on major work. Beyond that, the lessons do not all align with major work. There would be gaps in understanding with only one lesson in the teacher edition on page 122 specifically on fluency (5.NBT.B.5), and little to no connection made to multi-digit multiplication in other lessons in the teacher edition, STEM or ART resources.
  • The liquid volume example in ART, page 157, with the cylinder is a Grade 8 example. "Cube nets" on two ART lessons, pages 162 and 167, are aligned with 6.G.
  • The examples show that the amount of time on major work in the Grade 5 instructional materials decreases, meaning less time is spent on major work connecting to prior and future grade levels.

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 materials reviewed for Grade 5 do not meet expectations for consistency with the progressions in the standards.

  • All three resources are void of a tape diagram model, which is an essential representation in the coherent development of whole number and fraction understanding in the standards progressions.
  • The ART lesson on page 54 on fluency has a problem with an array model, a great strategy that was not fully developed in prior grades. At this point, students should move to an open area model and partial products methods in connecting with other standards in the 5.NBT domain, which allow student work to reach fluency.
  • Considering 5.NBT is major work in Grade 5 and division is a large portion of the standards in 5.NBT, it is not enough to have three lessons on 5.NBT.B.6.
  • Teacher edition page 134, ART page 60 and the STEM project "Engines" connect to 5.MD, but are not labeled as such.
  • Connections between multiplication and multiplication with fractions misses groups of fractional amounts or fraction-sized parts to multiply by a whole group or situation. This is evidenced in ART lesson page 94. Additionally, ART lesson page 100 should allow for students to tile fractional units, and see the overlap in the product on the area model, not just the shaded product.
  • The classroom activity on pages 519-530 on the standards 5.G.B.3 and 5.G.B.4 requires students to classify two-dimensional figures in a hierarchy based on properties and understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. However, the student exercises focus on using equations to find the missing angles instead of classifying or organizing shapes by categories.
  • Mathematical practices are not indicated nor aligned throughout lessons and instead are provided their own set of activities at the end of the book. This exact same set of activities appears in all teacher editions, Grades 3-5.

There are further examples where content from future grades is inconsistently identified as such:

  • Teacher editions pages 155-157 (5.NBT).
  • Teacher editions pages 351-373, beyond grade fraction work (5.NF.B.7).
  • ART pages 125, 128 and 134, beyond grade level fraction work (5.NF.B.7.A and 5.NF.B.7.B).
  • Teacher editions page 409, Grade 2 level line plot (5.MD.B.2).
  • Teacher editions page 453, lacking real world problems, beyond grade level.

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 5 do not meet expectations for fostering coherence through connections at a single grade level. Learning objectives are written and either address learning at the individual standard level, or they restate the cluster. Although standards and objectives are listed for each lesson, it does not always cohesively connect together in the following examples:

  • STEM project "Planetary Exploration"
  • ART lesson, page 44
  • Teacher edition lesson, page 1
  • Teacher edition, page 210
  • Teacher edition, page 388
  • STEM project "Cryptology"

Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. There are missed opportunities for connections including:

  • Missing 5.OA and 5.NBT connections in teacher edition pages 2-47, mostly whole number smaller numbers.
  • Missing coherence between 5.MD.B and 5.NF.A with use of fractions within line plots for real-world problems.

With the exception of the ART lessons having a family theme (21st Century Families), there is no mathematical connection from one lesson to the next within a domain and materials do not make connections between domains or clusters when appropriate. Connections between concepts are not clearly articulated for teachers and therefore the criteria is not met.

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 9781587807280 null null null
null 9781587807297 null null null
null 9781847008404 null null null
null 9781847008725 null null null
null 9781908018466 null null null
null 9781908018831 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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