Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 7 do not meet the expectations for alignment to the CCSSM. In gateway 1, the instructional materials do not meet the expectations for focus on major work because they devote an insufficient amount of time to the major work of the grade, and the materials do not meet the expectations for coherence because they do not make sufficient connections between the standards. Since the materials do not meet expectations for focus and coherence in gateway 1, they were not reviewed for evidence of rigor and the mathematical practices in gateway 2.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
6
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 Course 2 do not meet the expectation for focus and coherence in the CCSSM. For focus, the instructional materials do not meet the criteria for the time devoted to the major work of the grade with a 45.3 percent of the days allocated in the timeline aligning to the major work. For coherence, supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, and the materials will not foster coherence between the grades. Content from prior or future grades is not clearly identified and materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and do incorporate some natural connections, but they do not do enough to prepare a student for upcoming grades. The material also lacks some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade level learning is not explicit.

Criterion 1a

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

The instructional materials reviewed for Course 2 do not meet the expectations for focus within the grade. The materials reviewed for Course 2 do assess mostly grade-level content with some above grade-level topics, but If the future grade content was removed, it would not change the underlying structure of the assessments. The instructional materials do not meet the expectations for majority of class time on the major clusters of this grade. Only 45.3 percent of the days are suggested in the materials for major work of this grade. Overall, the instructional materials meet the criteria for grade-level assessments, however it does not spend the majority of time in the major clusters of this grade.

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.
2/2
+
-
Indicator Rating Details

The assessments that are included in the web version of Springboard were reviewed for Course 2 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 2 addressed the major areas of focus for this grade level in a challenging and effective manner with most units having little or no above grade level standards addressed.

Quality, on grade-level examples are:

  • Unit 1, question 18 asks students to demonstrate their knowledge of 7.NS.A.2.C by using order of operations to solve a real world problem.
  • Unit 3, question 16 asks students to demonstrate their knowledge of 7.RP.A.3 by using a real world example of how the mark up of a cost is important in everyday life.

Areas of improvement are:

  • Unit 4, question 1- 1 asks students to discuss corresponding line segments given similar triangles which is 8.G.A.2.
  • Unit 4, question 8-1 asks students to give two similar triangles and select the true statement which is 8.G.A.2.
  • Most of the questions in Unit 7 address the MP standards and are not connected to the content standards at this level. Question 7 addresses what type of tax paid to the Federal Government, which is not a mathematics standard within any of the grades for CCSSM, however it can be connected to the practice standards.

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 Course 2 do not meet the expectations for focus within the grade. The materials reviewed for Course 2 do assess mostly grade-level content with some above grade-level topics, but If the future grade content was removed, it would not change the underlying structure of the assessments. The instructional materials do not meet the expectations for majority of class time on the major clusters of this grade. Only 45.3 percent of the days are suggested in the materials for major work of this grade. Overall, the instructional materials meet the criteria for grade-level assessments, however it does not spend the majority of time in the major clusters of this grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The teacher edition and consumable student edition reviewed for Course 2 do not meet the expectations for spending the majority of class time on the major cluster of each grade. To determine this we evaluated three perspectives: 1) the number of activities devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. Along with major work of the grade, parts of the materials addressing non-major work were also examined for increasing focus on major work through coherent connections. The number of days devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts, and the conclusion was drawn through this data.

We determined our evidence from the Contents Page, pages v - ix and the number of days suggested in "Planning the Unit" found in the the teacher edition and written by the publisher.

  • Activities – 13 out of 27 activities which is 48.1 percent of time spent on major work.
  • Lessons – 34 out of 71 lessons which is 47.9 percent of time spent on major work.
  • Days – 64 out of 141 days which is 45.3 percent of time spent on major work.

Including Embedded Assessment Days:

  • Unit 1: 21 days, all days on major work
  • Unit 2: 12 days, all days on major work
  • Unit 3: 22 days, all days on major work
  • Unit 4: 3 days out of 31 days on major work of the grade level
  • Unit 5: 6 days out of 33 days on major work of the grade level (It is not explicitly written that any of the standards in this unit are major work.)
  • Unit 6: 0 days out of 17 days on major work of the grade level
  • Unit 7: 0 days out of 5 days on major work of the grade level

This allows for 64 days out of 141, or 45.3 percent, to be spent on major work of Grade 7 including support from parts addressing non-major work.

Excluding Embedded Assessment Days:

  • 7.RP.A has 20 instructional days out of 127 total days (16 percent).
  • 7.NS.A has 20 instructional days out of 127 total days (16 percent).
  • 7.EE.A and 7.EE.B has 15 instructional days out of 127 total days are addressed (11.8 percent).

This allows for 55 days out of 127 which is 43.3 percent to be spent on major work of Grade 7 including support from parts addressing non-major work.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
4/8
+
-
Criterion Rating Details

The instructional materials reviewed for Course 2 do not meet the expectations for being coherent and consistent with the standards. Supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, and the materials will not foster coherence between the grades. Content from prior or future grades is not clearly identified and materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades, however the material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade level learning is not explicit.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Course 2 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not.

Examples where connections are present, but the connections to major work are not well explored and, therefore, support a partial rating include:

Non-Major Cluster: 7.SP.B (draw informal comparative inferences about two populations) is used to support major clusters in Unit 6.

  • Activity 26, pages 361-390 supports 7.NS by having students compare populations which involves working with rational numbers.

Non-Major Clusters: 7.G.A (draw, construct and describe geometrical figures and describe the relationships between them) and 7.G.B (solve real-life and mathematical problems involving angle measure, area, surface area, and volume) are used to support the major clusters in Unit 4:

  • Activity 13, pages 137-146, supports 7.EE and 7.NS by having students find angle pairs which involves working with rational numbers and creating/solving equations.
  • Activity 15, pages 159-168, supports 7.RP by having students create and solve ratios and proportions to find similar figures.
  • Activity 16, pages 169-178, supports 7.EE by having students create and solve equations in real-life mathematical problems based on circumference and area of circles.
  • Activity 17, pages 179-189, supports 7.EE by having students create and solve equations in real-life mathematical problems based on composite area.
  • Activity 18-2 and 18-3, pages 199-212, support 7.EE by having students create and solve equations in real-life mathematical problems based on lateral and total surface area of pyramids.

Examples where connections are missed:

  • Activity 20, pages 227-250, has students working with exploring probability which could have been used to support 7.RP.A by connecting proportional reasoning and percentages when extrapolating data from random samples.
  • Activity 21, pages 251-274, has students working directly with probability which again could have been used to support 7.RP.A by connecting proportional reasoning and percentages when looking at data from random samples.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 partially meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. With embedded assessment days not included there are approximately 127 days of lessons in the materials. There needs to be additional material, other than assessment days, to ensure a student's grasp of all major work at this grade level. Overall, the amount of content that is designated for this grade level is short of the amount of material needed to make it truly viable for one school year.

  • According to the pacing guide, each period is 45 minutes in length and there is a suggested 127 days of lessons.
  • When Embedded assessments are also included in the pacing guide and if all are given during the course of the year the total would be 141 days.

The guiding focus taken for this indicator for our team was, "Will the non-major and major work of this material be enough to prepare a student for the next grade level?" With the amount of days, many of those days not focusing on major work, the non-major work days not often supporting the major work of the grade, it will require the teacher to make significant modifications to prepare the student for the next grade level and supports this indicator receiving a partially meets rating.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The teacher edition, consumable student edition, and summative end of unit assessments reviewed for Course 2 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from lower/above grade standards are not clearly identified, and a teacher will have to spend much time unpacking the activities to identify the non-grade level material. Also, materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not explicitly made to content in future grades. However, in general, the progression of standards are followed throughout this course.

Some examples of areas where identification of standards from lower/upper grades would be beneficial are:

  • In Unit 3, Activity 8-1 works with ratios and proportions. The connection given is "In previous courses, students have written ratios of two quantities." For a new teacher it would be beneficial to have standards marked and an explanation of how that prior learning is connected to this activity.
    • The activity also begins with writing of ratios and this is not marked as below grade level and should be expressed as 6.RP.A.1 at least in the teacher edition.
  • In Unit 4, Activity 13-1 works with angle pairs. It also makes a connection to previous grade learning on angle definitions and classification, but does not give any standards for a teacher to refer to.

The instructional materials reviewed for Course 2 partially meets the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

For each activity there are one to five standards attached and there are two to four lessons based on that activity to extend and develop the understanding of the standards included in the activity. For struggling learners or those that need enrichment, the book does provide pointers interspersed throughout the units with ideas on how to differentiate or teach the topic in a different way.

Examples of this are:

  • Unit 1, Activity 1, Lesson 1-2 on multiplying and dividing decimals has an ELL support box that provides another way to think about multiplying decimals to assist students that may struggle with this concept.
  • Unit 3, Activity 9, Lesson 9-2 on constants of proportionality has a differentiating instruction box that helps students to extend their thinking (especially the students that can reason abstractly).

Examples that are not at the depth of knowledge needed to prepare a student for the next grade are:

  • The summative assessments reviewed for this course were limited in nature, containing multiple-choice responses and no significant performance tasks found.
  • Unit 4, Activity 13, Lesson 13-1 on complementary, supplementary, and adjacent angles is very procedural. Though the standards 7.EE.B.3, 7.EE.B.4, and 7.G.B.5 are attached to this entire activity the lessons are low in rigor and may not prepare a student for more advanced geometry.

Examples of lessons that do give a student extensive work at the grade level and are real-world application problems covering the major work of the grade are:

  • Unit 2, Activity 6, Lesson 6-2 on writing and solving equations uses a music scenario to introduce students to writing two-step equations. It is real world, moves the students from concrete to abstract by using variables to represent quantities that vary and are attainable, but rigorous enough to prepare a student for upcoming mathematics courses.
  • Unit 3, Activity 9, Lesson 9-1 on equations representing proportional relationships has a great deal of real-world problems and questions that make a student defend their answer.

The instructional materials reviewed for Grade 7 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials only generally relate grade-level concepts explicitly to prior knowledge from earlier grades.

Each unit begins with an overview that explains what earlier knowledge will be extended in the activities themselves and then each activity has an "Activity Standards Focus" section that will explain the connections between the previous grades and the new learning. This is a rather general overview and is never specific as to where the connections are actually happening and between which grades.

Example of the general overview:

  • Unit 4, Activity 16 begins with the "Activity Standards Focus" saying, "In earlier grades, students learned basic facts about plane figures-how to classify them, distinguish them from one another, and, in certain cases, find their perimeters and areas." This or with "Until now" is how many of the activities begin and then a slight change in what was learned based on what the new learning is.

Indicator 1f

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

The instructional materials reviewed for Course 2 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • The Unit titles are clearly labeled and aligned to the standards without a need for much interpretation.
    • Unit 1 - Number Systems (7.NS)
    • Unit 2 - Expressions & Equations (7.EE)
    • Unit 3 - Ratio and Proportion (7.RP)

The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 2.

  • For the majority of the work, most standards were taught and covered within one lesson out of the entire series and not aligned with any other concept throughout the year.

Some examples of where connections were made, and supported a partially meets rating, are:

7.EE.B.3

  • This standard is first taught in Unit 2, Activity 6.
  • It is reinforced all throughout the book with real world problems involving rational numbers.
  • For example, this standard is covered in the following units and activities:
    • Unit 2, Activity 7
    • Unit 3, Activity 11
    • Unit 3, Activity 12
    • Unit 4, Activity 13
  • This standard is discussed in three out of the seven units of the course.

7.NS.A.1

  • This standard is taught in Unit 1, Activity 1
  • It is reinforced in Unit 1, Activities 2 and 4
  • It is also reviewed throughout the book when rational numbers are being used in problems.

7.NS.A.2

  • This standard is taught in Unit 1, Activity 2
  • It is reinforced in Unit 1, Activity 3
  • It is also reviewed throughout the book, especially within the activity involving scale drawings.

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 Jan 22 00:00:00 UTC 2016

Report Edition: 2014

Title ISBN Edition Publisher Year
null 1457301490 null null null
null 1457301563 null null null
null 9781457301490 null null null
null 9781457301568 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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