Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 3 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 3. 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 3 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 3.

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 topics that are in future grades. The content assessed in Delivery Route, STEM project, is more appropriately aligned with 4.NF.B.4 when students are asked to convert between unlike units, multiplying fractions with whole numbers and with Grade 5 5.NBT.B.7 when students are asked to multiply decimals with whole numbers. The content assessed in Tetrahedron Kite, STEM project, assesses fractions with denominators outside the range of Grade 3 expectations. This is not to be addressed until after Grade 3 according to 3.NF.A.

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 3 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 3.

  • Antique Calculator STEM project on pages 25 – 42 of the Teacher STEM Project Edition:
    • The assessment does not align to the objectives of this STEM project and does not completely address 3.NBT.1 and 3.NBT.2.

Rounding and subtraction are not addressed. Neither standard is stated to be addressed in any of the other STEM projects for Grade 3.

3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100

3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

  • Delivery Route STEM project on pages 63 – 104 of the teacher STEM project edition:
    • This project asks students to convert between unlike units, multiplying fractions with whole numbers on page 70. This is not to be addressed until Grade 4 according to 4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
    • This project asks students to convert feet to miles. This is not to be addressed until Grade 4 according to MD.A.1
      Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
    • This project asks students to multiply decimals with whole numbers on page 73. This is not to be addressed until Grade 5 according to 5.NBT.B.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • Tetrahedron Kite STEM project on pages 43 – 62 of the teacher STEM project edition:
    • This project asks students to assess fractions with denominators outside the range of Grade 3 expectations. This is not to be addressed until after Grade 3 according to 3.NF.A. Develop understanding of fractions as numbers (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8)

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 material reviewed for Grade 3 do not meet expectations for focus because the material did not spend the majority of time on the major clusters in the grade. There are multiple above grade level examples in 3.NF.A including teacher edition, page 283 (beyond Grade 3 denominators); teacher edition, page 318, 320 and 332 (adding fractions); teacher edition page 350 (beyond Grade 3; ART page 71 (beyond Grade 3 denominators); ART page 77 (fractions outside CCSSM); and ART pages 95-97  and 101 (beyond Grade 3).

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 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 focus because the materials do not spend the majority of class time on the major cluster of each grade.

A total of 68 activities/lessons are provided between the three resources, and some may be repeated or take additional class periods. However, only 46 of the lessons are aligned to major work at the grade according to the table of contents in the teacher edition, ART and STEM materials. This would mean that if the 46 lessons were fully aligned, 68% of the time is spent on the major work placing it at the lower end of the expected range. Looking more closely, the percent of time spent on major work would be below 68% considering there are lessons labeled as aligned to major work of the grade do not actually align. Examples of this misalignment are below:

  • In the teacher edition on page 161, a lesson that is labeled as aligned to 3.OA.D.8 has limited development on two-step word problems, especially of the types suggested by the progressions document.
  • In ART on page 25, students make flash cards.
  • Page 383 in the teacher edition goes outside the scope of standard 3.MD.A.2 and includes ounces, pounds, and subtracting fractions.
  • Page 72 in the teacher edition has limited alignment to the range of multiplication and division situations as indicated in the progressions document.

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

  • In the 3.NF lessons (teacher edition, pages 292-294), there are denominators included that are beyond the scope of the grade-level work. The progressions document refers to fractions outside the scope of the Grade 3 expectations.
  • In teacher edition, page 350, the lesson has connections between fractions and money, with denominators outside of the scope of Grade 3. There is also limited opportunity for students to explain reasoning as student exercises rely on filling in blanks (e.g., "cents as fractions of a dollar," page 350).
  • In teacher edition, page 551 is off grade-level content. Symmetry is not far off Grade 3, considering the standard is to partition shapes into equal areas. The bigger problem is that students do little investigating or reasoning about shapes in lessons for 3.G.A.1 and 3.G.A.2. Students do not find the area of partitioned parts of shapes.
  • In the lesson "three-dimensional figures," on page 557, students classify three-dimensional shapes by counting faces, bases and vertices. This is outside the scope of the grade.
  • The decimal work in the STEM project "Ski Math" is beyond the scope of the grade.

Because of these misalignments, the actual time spent on major work would be less than the amount of time noted according to the table of contents.

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 3 level fall short of meeting expectations for these criterion. The absence of connection between 3.NF and 3.G standards, as well as missing area models connected to skip counting and grouping to support multiplication understanding lack coherence.

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 3 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 ART lesson "Geometric Design" does not support the major work of 3.NF.
  • The ART Lesson "Delivery Route" does not support the major work of addition and subtraction at the grade level; one data representation is a pie chart, and the standards call for a scaled bar or picture graph.
  • The STEM project "Antique Calculator" includes errors with the intent of 3.NBT.A.1 about rounding.
  • Teacher edition page 517 does not connect the labeled 3.G.A to 3.NF work.
  • Standards in the series are taught overwhelmingly in isolation, with insufficient evidence that supporting standards enhance the teaching of major standards.

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 coverage for one school year.

  • A large portion of Grade 3 lessons should align with 3.NF as it is considered major work.
  • Between the three resources, 15 lessons are labeled as 3.NF out of 68, which is 22% of the work.
  • Beyond that, not all of these lessons are fully or appropriately aligned to 3.NF and do not fully allow for students to partition shapes, (e.g., tape diagrams, page 65 in ART resource).
  • Work of partitioning from Grades 1 and 2 in their geometry domains are coherently connected and build on in the 3.NF lessons.
  • While lessons could be each be repeated multiple times, the amount of content for instruction is limited and would not fulfill a typical instruction for a normal 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.
0/2
+
-
Indicator Rating Details

The instructional materials for Grade 3 do not meet the expectation for consistency with progressions. The review team did not find that the materials were consistent with the progressions in the standards as evidenced by:

  • Denominators outside of scope of grade are scattered throughout the teacher edition (pages 283-350) but are not labeled.
  • In the 3.OA.B.5 lessons in the teacher edition (pages 132-151), it does not need to be explicit of the properties in terms and vocabulary but should have more about application and the progression to two-step word problems, which are not evidenced here.
  • Connections between skip counting and groups with area representations are not evident in any lessons in teacher edition pages 84-151.
  • The teacher edition lesson on page 530 is more about attribute of shape then partitioning units. Symmetry, a Grade 4 standard, is addressed as well.
  • Other examples are on teacher edition pages 283, 313, 350, 383, 428, 535, 538, and 557.

In addition, above grade-level work is not identified. There are no references to the progression documents. Due to the low amount of grade-level work and the nature of student exercises, the depth of student work is limited. There is limited work with grade-level problems for students. Materials are not consistent with CCSSM intent and lack use of equal groups and arrays. Standards for Mathematical Practice are not aligned throughout lessons and instead are provided their own set of activities at the end of the book and in the STEM lessons. Neither of them are connected thoughtfully to the work, but presented as blanket problem-solving tools.

Finally, connections between concepts are not clearly articulated for teachers. Although standards and objectives are listed for each lesson, they do not always cohesively connect. For example, the classroom activity on pages 79-83 show one picture of measurements broken up and then asks students to complete word problems such as "How many feet are there in 3 yards? Write your equation here. Which is the right answer? Put a checkmark in the correct box." This does not ask students to demonstrate their thinking through drawings or written/verbal explanations for how they got to the answer. The standard 3.OA.A.3 requires students to use multiple examples to demonstrate learning rather than just writing the equation.

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 do not meet the expectations for this indicator. Learning objectives are written and either address learning at the individual standard level, or simply restate the cluster. Examples can be found in ART on pages 118 and 167; the STEM project "Tetrahedron Kites" on page 44; and the STEM project "Geometric Design" on page 105.

Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. No evidence of lessons/activities where standards across domains are made. For example lessons for 3.MD.B do not follow the intent of the standard and cluster, they include pie graphs (not standard) and include graphs that are not scaled. Lessons provided for 3.G are not grade-level material or do not follow the intent of the standards.

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 9781587807242 null null null
null 9781587807259 null null null
null 9781847008381 null null null
null 9781847008701 null null null
null 9781908018442 null null null
null 9781908018817 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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