## Big Ideas Math: A Common Core Curriculum - Algebra 1, Geometry, Algebra 2

##### v1
###### Usability
Our Review Process

Showing:

## Report for High School

### Overall Summary

The instructional materials reviewed for the Big Ideas Traditional series do not meet expectations for alignment to the CCSSM for high school. The materials do meet the expectations for allowing students to spend the majority of their time on the content from the CCSSM widely applicable as prerequisites, but they do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. The materials partially meet the expectations for the remainder of the indicators within Gateway 1, and since the materials did not meet the expectations for focus and coherence, evidence for rigor and the mathematical practices in Gateway 2 was not collected.

##### High School
###### Alignment
Does Not Meet Expectations
Not Rated

### Focus & Coherence

##### Gateway 1
Does Not Meet Expectations

#### Criterion 1.1: Focus & Coherence

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).

The instructional materials reviewed for Big Ideas Traditional do not meet the expectation for Focus and Coherence within the CCSSM. For focus, even though the students spend the majority of time on the WAP standards, not all of the high school, non-plus standards are taught to the depth expected in order to give students the opportunity to fully learn each standard. The context of problems are appropriate for high school students; however, the numbers used to model situations are often integers, and the full intent of the modeling process is minimally applied to the modeling standards. For coherence, there is a partial connection between and among standards and courses. Explicit and purposeful connections to the middle school standards are limited.

##### Indicator {{'1a' | indicatorName}}
The materials focus on the high school standards.*
##### Indicator {{'1a.i' | indicatorName}}
The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The instructional materials reviewed for the Big Ideas Traditional series partially meet the expectation that materials attend to the full intent of the mathematical content contained in the high school standards for all students. For this Indicator, the materials were examined, guided by included correlation documents: Common Core State Standards for Mathematical Content Correlated to Algebra 1, Geometry, and Algebra 2 and a course specific table at the beginning of each book which listed the standards addressed in each lesson. Overall, most of the non-plus standards are included in the materials; however, some aspects of the non-plus standards have not been completely addressed by the instructional materials. Additionally at least two standards are completely omitted.

• G-CO.3: In Geometry, Lesson 4.2, students are asked about lines of symmetry but are not directly asked to describe the reflections that carry a specific polygon onto itself as called for in the standard. Lesson 4.3 does ask students to describe rotations that map a figure onto itself, page 195, problem 20, and to select angles of rotational symmetry for a given regular polygon, page 195, problems 21 - 24.
• S-IC.4: In Algebra 2, Lesson 11.5, students are given a version of the Margin of Error formula and use it, but they do not develop the concept using simulations as required by the standard.
• S-IC.5: In Algebra 2, Lesson 11.6, problems 3-4 and 7-9 do "use data from a randomized experiment to compare two treatments," yet no evidence was found requiring students to "use simulations to decide if differences between parameters are significant."
• S-CP.5: In Geometry, Lesson 12.2, students are asked about a variety of everyday situations and whether they are independent (problems 3 - 10). However, there is no evidence of students connecting the concepts of conditional probability and independence.
• N-Q.2 and N-Q.3: No evidence was found where students had to define their own quantities or determine the appropriate level of accuracy of quantities. These standards are indicated to be present throughout sections of Algebra 1 and Algebra 2 but are not noted as a primary focus in any lesson as stated on page xxxii in both the Algebra 1 and Algebra 2 Teaching Editions. Upon examining the identified sections in Algebra 1 and Algebra 2, no evidence of N-Q.2 or N-Q.3 was found to be incorporated into the lessons.
##### Indicator {{'1a.ii' | indicatorName}}
The materials attend to the full intent of the modeling process when applied to the modeling standards.

The instructional materials reviewed for Big Ideas Traditional Series do not meet the expectations that the materials attend to the full intent of the modeling process when applied to the modeling standards. For this indicator, materials were examined for the extent to which the modeling process is incorporated. The series shows the intention to incorporate the modeling process within each chapter; however, the majority of the problems lack the incorporation of the full modeling process as described in the CCSSM. Overall, very few problems throughout the materials integrate the entire modeling process.

Many of the modeling tasks include heavy scaffolding, and the following are some examples of this:

• Geometry, Chapter 11: Page 655 contains a performance task which asks students how much it would cost to reopen a water park if some of the structures have to be repainted, pools filled with water, and some flat surfaces have to be resurfaced. The prompt, however, takes away the modeling intent by directing students towards specific calculations and steps.
• Algebra 1, Chapter 6: The performance task asks students, given a map, to find the best place to locate bicycle rental stations. The question has the potential to incorporate the modeling process, but by providing leading questions the “formulate” and “validate” aspects of the modeling process are lost.
• Geometry: On page 469, problems 13 and 14 are denoted as Modeling with Mathematics problems, yet the right triangles needed to solve the problems are superimposed on the real life pictures and labeled, students are instructed to use the Pythagorean theorem in order to solve and students are directed to look back at a previous example for support in solving. Being provided the physical model as well as the computations needed, the students are unable to experience the modeling process.

The following are two of the few tasks that incorporate the full intent of the modeling process.

• Algebra 1, Chapter 3: The performance task asks students to analyze and compare t-shirt ordering proposals from four different companies, then determine the best company to order from and create a proposal for the class officers as to why that company is the best deal.
• Geometry, Chapter 12: The performance task asks students to put themselves in the shoes of a graphic designer and design a new dartboard. Students are placed into design teams, and each member of the team is given a different scenario for what the dartboard should look like and the probability of hitting certain colors. Students are asked to get creative and design various dartboards keeping probability in mind. The task does include a significant amount of questioning; however, the questions asked push student thinking and do not hinder the implementation of the full modeling process.
##### Indicator {{'1b' | indicatorName}}
The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
##### Indicator {{'1b.i' | indicatorName}}
The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

The instructional materials reviewed for the Big Ideas Traditional Series meet the expectation that the materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, post-secondary programs, and careers.

• The materials provided for teachers suggest a timeline and show an overall focus on WAPs.
• In Algebra 1, the majority of the 160 days focus on the widely applicable prerequisites.
• In Geometry, of the 160-162 days, there is not a majority of days that focus on the widely applicable prerequisites.
• In Algebra 2, the majority of the 160 days focus on the widely applicable prerequisites.
• Viewing the series as a whole, the majority of days focus on the widely applicable prerequisites.
• In Algebra 2, students build upon their basic function concepts from grades 6-8 while exploring various functions: Linear Functions (Chapter 1), Quadratic Functions (Chapter 2), Polynomial Functions (Chapter 4), Radical Functions (Chapter 5), Exponential and Logarithmic Functions (Chapter 6), Rational Functions (Chapter 7), and Trigonometric Functions (Chapter 9).
• Geometry lessons 11.1 and 11.2 review and extend measures of center and variation as well as box-and-whisker plots. Lesson 11.3 builds on these concepts from grades 6-8, addressing standard S-ID.2 in the WAPs.
##### Indicator {{'1b.ii' | indicatorName}}
The materials, when used as designed, allow students to fully learn each standard.

The instructional materials reviewed for Big Ideas Traditional Series partially meet the expectations that the materials, when used as designed, provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics. Overall, the lessons are presented in a way that will allow students to fully learn many of the standards. Throughout the series, students are not spending time on content previously learned but are constantly moving forward. Students, however, are frequently not given the opportunity to develop their own definitions, and where the standards expect students to prove or develop a concept, the materials often provide students the information.

The following standards were included in the materials, yet were not presented in a way that would allow students to fully learn that standard.

• S-ID.4: In Algebra 2, Lesson 11.1 includes practice on using "the mean and standard deviation of a set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate." The materials make use of calculators and tables to estimate areas under the normal curve; however, they do not make use of spreadsheets as called for in the standard.
• N-RN.3: In Algebra 1, Lesson 4.1, problems 99 and 100, students do a limited number of calculations with pre-selected numbers then use that information in problem 100 to answer if this is always, sometimes, or never true. This is the only place where the standard is located. With this limited amount of exposure to the standard, students may not reach the full depth of understanding.
• G-MG.1: Students are frequently provided or told the exact geometric shape to use to solve a problem; the material does not offer students a chance to select for themselves the appropriate shape to model a situation. Throughout the series only one problem was located that asked students to “draw an object (or part of an object) that can be modeled” by a certain shape (problem 40 on page 237 in the Geometry materials).
• G-GPE.2: In Algebra 2, Lesson 2.3 the derivation of a parabola is given to students on pages 68-69. Students are not given the opportunity to derive the equation of a parabola given a focus and directrix for themselves.
• G-C.5: In Geometry, lesson 11.1, page 597, students are provided with the derivation of the fact that the length of the arc intercepted by an angle is proportional to the radius. Students are not given the opportunity to complete this derivation for themselves.
• G-CO.1: Throughout the geometry materials, students are not provided the opportunity to develop their own definitions as required by the standard; instead, the definitions were given to them. The textbook does tell students that there are undefined terms in geometry (with the exception of distance around a circular arc) and point, line, and plane are mentioned to be “undefined terms;” however, the textbook does not build the definitions through this notion.
• A-APR.1: Students add, subtract and multiply polynomials, but the “understanding” aspect of this standard is not developed. In Algebra 2, Lesson 4.2 the closed nature of polynomials is explicitly stated; however, students are not required to demonstrate understanding of the concept.
• A-SSE.1a: Problem 49 of lesson 3.2 in Algebra 1 is the only problem that addresses this standard. The materials list various other lessons in both Algebra 1 and 2 as addressing this standard; however, evidence of meeting the full depth of this standard was not found.
• A-REI.4a: In Algebra 1, page 515, students are given the derivation of the quadratic formula and then work with a partner to provide the justification for the given steps. Students are never given the opportunity to derive the formula as stated in the standard.
• G-CO.10: The standard calls for students to “prove theorems about triangles;” however, many proofs are simply provided by the materials throughout the geometry materials. For example, proof that the measures of interior angles of a triangle add to 180 degrees is provided as an example on page 234, proof that the base angles of isosceles triangles are congruent is provided as an example on page 252, and proof that the medians of a triangle meet at a point is offered as a theorem on page 320 with the proof provided online.
• G-C.1: Proof that all circles are similar is provided for the students on page 541 of the Geometry textbook.
• S-CP.2: There were four problems—Geometry, lesson 12.2, problems 3-6 with an identical chapter in Algebra 2—throughout the series that fully addressed this standard Geometry.
• S-CP.6: Problem 23 in lesson 12.2 of the Geometry textbook is the one problem which addresses the standard.

The following standards provide students thorough exposure through multiple experiences to fully learn each standard.

• G-C0.4: Students are given several explorations throughout Chapter 4 of the Geometry materials through which they can develop the ideas of transformations before the mathematical definition is provided for them.
• G-CO.12: Students are given opportunity to explore constructions using “a variety of tools” (i.e., compass, straightedge, paper folding, and dynamic software) as called for in the standard.
• A-CED: The entire Creating Equations cluster is thoroughly developed throughout the algebra 1 and algebra 2 materials.

The materials offer additional resources to help all students fully learn each standard.

• Each section begins with two or three exploration activities that offer students an opportunity to engage with the content before formal presentation of the terms, definitions, facts, theorems, or procedures. These explorations help students with content mastery by allowing them to "play" with the mathematics and familiarize themselves with the concepts in a seemingly informal way. Many of the explorations present content from different perspectives. For example, in Algebra 1, Lesson 1.4, students explore the concept of absolute value first by considering it as an equation and looking for values that make it true, then as a number line, and finally numerically using a spreadsheet.
• The end of each section offers suggestions for students who may need extra help as well as for students who may need additional challenge problems. The Resources by Chapter book provides on grade-level, additional problems for struggling students and extension problems for students who need a challenge. The extension problems focus on moving the learner forward. For example, in Algebra 1, section 5.2, the lesson dealt with solving systems of equations algebraically. The extension asks students to consider how to solve a system of three equations.
• "Laurie's Notes" in every chapter and lesson provide guidance to teachers in presenting lessons, which in turn could help all students better learn all aspects of standards. Furthermore, the beginning of each chapter includes "Scaffolding in the Classroom" notes in the margin. Each lesson also includes "Differentiated Instruction" and "English Language Learner" boxes providing strategies for teachers to use in order to reach all learners. "Assignment Guide and Homework Check" boxes included before student exercises break down what problems teachers could use for Basic/Average/Advanced assignments and homework checks. After each Chapter Test in the book, teachers are given ideas on what materials to use if students need help or if students got the info. Students are given opportunities to use paper and pencil, graphing calculators, and dynamic software.
##### Indicator {{'1c' | indicatorName}}
The materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The Instructional materials reviewed for Big Ideas Traditional Series partially meet the expectation that all students engage in mathematics at a level of sophistication appropriate to high school. Overall, the materials offer real-life and relevant situations to high school students; however, problems often involve integers and avoid more complex solutions.

• The materials present a majority of problems with integer values. In Algebra 1, Chapters 3 and 4 deal with linear functions, both graphing them and then writing equations. Students do not see non-integer y-intercepts until they are introduced to the linear regression feature of the calculator in Lesson 4.5. The majority of y-intercepts are integer values. Likewise, Chapter 5 (solving systems of equations) primarily contains solutions that consist of integer values. Algebra 2, Lesson 1.4 extends the ideas of solving a system of equations to three variables but still has a large majority of solutions that are integer values and rarely involves non-integer values. Similarly, the Geometry textbook remains focused on integer values much like that of the Algebra 1 and Algebra 2 textbooks.
• The materials offer students problems frequently based on real-life and relevant situations.
• Geometry, page 198, problem 19 connects the Tetris game to rigid transformations.
• Geometry, page 608, problem 37 connects pizza with circle/sector area and reasoning.
• Algebra 1, in the Chapter 6 Performance Task "The New Car," students weigh the many costs of a car when deciding which is the best buy.
• In the Algebra 2, Chapter 2 Performance Task "Accident Reconstruction," students analyze car speed and braking distance.
• Daily journal entries, either online or utilizing the Student Journal book, are age appropriate for high school students.
• One worksheet per lesson provides problems for students working below course level as well as students working above level. These enrichment and extension worksheets are similar to that of the chapter.
##### Indicator {{'1d' | indicatorName}}
The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

The instructional materials reviewed for Big Ideas Traditional Series partially meet the expectations that the materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the standards. Overall, Chapter Summaries are provided at the beginning of each chapter that indicate what content the students should already be familiar with from previous grades and courses. The Common Core Progression offered at the beginning of each chapter indicates skills learned in previous courses, however does not make connections to specific standards.

• Notes for teachers are abundant in the margins and before each lesson; however, they focus mainly on identifying common errors, teacher’s actions, and ideas for next steps for students. Connections within a course and across a series are not made explicit for the teacher.
• Each course is presented in a traditional progression. Chapters are presented as isolated concepts or skills with little to no connection between mathematical concepts made explicit.
• For example, Algebra 1: Lessons 8.1-8.4 each focus on graphing various forms of quadratic functions (8.1 - "Graphing f(x) = ax^2", 8.2 - "Graphing f(x) = ax^2 + c", 8.3 - "Graphing f(x) = ax^2+bx+c", and 8.4 - "Graphing f(x) = a(x-h)^2 +k"), however not until Lesson 9.2 do students discuss solving a quadratic function by graphing. Lesson 9.2 makes no reference to concepts learned in Lessons 8.1 - 8.4.
• “Common Core Progression” boxes located at the beginning of each chapter indicate general connections to previous courses; however, no standards are cited, simply skills and concepts.
• For example, the "Common Core Progression" box at the beginning of Chapter 3 in Algebra 1 lists multiple skill focused statements not rooted in the standards in order to show connection among standards within and across courses.
• "Identify linear functions, using graphs, tables, and equations."
• "Use function notation to evaluate, interpret, and graph functions."
• "Find the slope of a line and use it to write a linear equation in slope-intercept form."
• "Solve real-life problems using function notation, linear equations, slopes, and y-intercepts."
• "Translate, reflect, stretch, and shrink graphs of linear and absolute functions, and combine transformations of graphs of linear and absolute functions."
##### Indicator {{'1e' | indicatorName}}
The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The instructional materials reviewed for Big Ideas Traditional Series partially meet the expectations that the materials explicitly identify and build on knowledge from grades 6-8 to the high school standards. Chapter Summaries and the Common Core Progression boxes indicate skills and procedures students should already be familiar with from previous mathematics classes; however, they do not explicitly identify the middle grades standards which they are referencing. Occasionally throughout the materials, explicit connections to middle grade standards are made in the Teacher Edition, specifically in “Laurie’s Notes” and the “Maintaining Mathematical Proficiency” sections. In some lessons, topics that are middle school standards are presented as if they are high school standards being presented for the first time.

• “Maintaining Mathematical Proficiency” sections are included throughout the materials and clearly state that these are below grade-level problems that have been included to help students retain previously learned skills necessary for further growth in mathematics. The Teacher Edition explicitly references these middle school standards.
• Connections to middle grades are typically mentioned for teachers in notes for the “Maintaining Mathematical Proficiency” sections at the beginning of each chapter. Explicit middle school standards are not referenced in these sections, but rather basic skills such as “Finding x-intercepts” and “The Distance Formula” (Algebra 2, page T-45). These notes are not included for the students.
• At the beginning of each chapter, the Teacher Edition does identify skills, not standards, from grades 6-8 that students should already be proficient at performing. Individual lessons, however, do not reference these connections.
• Multiple lessons present middle grades standards as if for the first time without identifying the standards are middle school standards but rather labeling them as high school standards. For example:
• Algebra 1, Lesson 1.1 is about solving one-step, one variable equations, which is 8.EE.7, but is labeled as A-CED.1, A-REI.1, and A-REI.3. There is no mention in Lesson 1.1 that this is a concept that was previously learned and will be built upon.
• Algebra 1, Lesson 6.1 is a re-teach of the rules of exponents, 8.EE.1, but does not indicate this. The rules of exponents are extended to rational exponents in Algebra 2, Lesson 5.2.
• Algebra 1, Chapter 5 presents systems of equations to students as though the material is new, not a review of standards introduced in Grade 8, 8.EE.8.
• The Overview of Algebra 1, lesson 3.1 explicitly states “Students have prior knowledge of functions from Grade 8 (8.F.1 - 8.F.5). Their understanding may be limited to discrete functions.” However, the lesson then proceeds as though the students have no understanding of the material.

Middle grades standards are rarely explicitly noted throughout the materials. Specific reference to middle grade standards are only found in the Teacher Edition in "Laurie’s Notes" and the Maintaining Mathematical Proficiency sections.

##### Indicator {{'1f' | indicatorName}}
The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

The plus standards, when included, are not clearly identified, and though some of the included plus standards do not unduly interfere with the course, there is no indication that they are optional or extensions.

• Plus standards are not explicitly identified throughout the materials. The correlation charts of lessons to standards and standards to lessons found in the front matter of the Teacher Editions does not denote which standards are plus standards. Furthermore, the plus standards are not identified at the beginning of the lessons when they are present.
• Plus standards are present in both the Geometry and Algebra 2 textbooks.
• Algebra 2 materials include plus standards N-CN.8,9; A-APR.5,7; F-TF.9; S-CP.8,9; and S-MD.6,7 throughout Lessons 1.4, 4.2, 4.6, 7.3, 7.4, 9.8, 10.2, and 10.5.
• Geometry materials include plus standards G-SRT.9-11; G-C.4; and G-GMD.2 throughout Lessons 9.7, 10.1, 11.5, and 11.8.
• Materials do not identify plus standards as optional or additional extension opportunities, rather they are presented in a way as being an expectation for all learners.
• Algebra 2, Lesson 4.6 is the Fundamental Theorem of Algebra and proposes to cover two plus standards (N-CN.8,9). While an appropriate extension into higher level mathematics, the textbook does not indicate that this should be considered optional or as an extension. It would not unduly interfere with the course for all students to complete it, but it is not necessary and could take time from other required standards.
• Some plus standards are presented in a way that is distracting to the learning of the non-plus standards.
• The Binomial Theorem is presented on page 574 of the Algebra 2 materials, and it is part of the lesson on probability. This standard is not necessary for the understanding of probability as called for in the non-plus standards and could detract from the focus of the lesson.

### Rigor & Mathematical Practices

Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One
Not Rated

#### Criterion 2.1: Rigor

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.
##### Indicator {{'2a' | indicatorName}}
Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
##### Indicator {{'2e' | indicatorName}}
The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
##### Indicator {{'2f' | indicatorName}}
The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
##### Indicator {{'2g' | indicatorName}}
The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
##### Indicator {{'2h' | indicatorName}}
The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.

### Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
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.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
##### Indicator {{'3d' | indicatorName}}
Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
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.
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
##### Indicator {{'3n' | indicatorName}}
Materials provide support for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
Materials provide 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).
##### Indicator {{'3v' | indicatorName}}
Materials provide support for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology Use

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
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 Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners.
##### Indicator {{'3ac.i' | indicatorName}}
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
##### Indicator {{'3ac.ii' | indicatorName}}
Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
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.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

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### Overall Summary

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###### Usability
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