Alignment: Overall Summary

The instructional materials reviewed for the CME Traditional series do not meet expectations for alignment to the CCSSM for high school. The materials do not meet the expectations for focus and coherence as they partially meet the expectations in the following areas: attending to the full intent of the modeling process, allowing students to spend the majority of their time on the content widely applicable as prerequisites, allowing students to fully learn each standard, requiring students to engage at a level of sophistication appropriate to high school, making meaningful connections in a single course and throughout the series, and identifying and building on knowledge from Grades 6-8 to the High School Standards. 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.

The alignment document provided by the publisher in the front matter of each textbook includes numerous alignment errors. The pacing guide is often inconsistent with the notes within the chapters and lessons. If a lesson is deemed “optional” in the notation in the chapter, that notation should be specified in both the pacing guide and any standards aligned to that section should be specified in the alignment document as optional, too.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
7
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
N/A
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
21
30
36
N/A
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

Criterion 1a - 1f

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).
7/18
+
-
Criterion Rating Details

Focus and coherence is not met in the series of materials reviewed. The most critical factor is that not all high school standards are included in the lessons in the Algebra 1, Geometry, Algebra 2 sequence of courses. Furthermore, there are a significant number of standards that are not attended to fully and/or the instructional materials provide limited opportunities. Early in the sequence of courses (Algebra 1), a significant number of lessons focus on middle school concepts and distract from emphasis on high school standards. The Algebra 2 course has an overemphasis on plus standards that distracts from the HS standards. Although there are some lessons that fully attend to the high school standards, overall, the courses lack an ease of flow and focus between and within each course.

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
0/4
+
-
Indicator Rating Details

The instructional materials do not meet the expectation for attending to the full intent of the mathematical content contained in the high school standards for all students. Although many lessons included instruction that attended to the full intent of standards, there were many standards that were not fully addressed throughout the materials, and many standards were not addressed at all. It is also important to note that there were several discrepancies between the alignment the publisher provided in the front matter of the textbook and the alignment completed by the reviewers. Those instances are noted at the end of this section.

The following are standards whose full intent was not met:

  • F-IF.7c: Graphing of polynomial functions is limited to linear, quadratic, and cubic functions (no other higher order polynomials). Materials are missing opportunities to identify zeros and end behavior for polynomial graphs.
  • F-IF.9: No opportunities are provided to compare functions represented in different ways. (The alignment of lessons from Algebra 1 in the publisher alignment is incorrect.)
  • F-TF.5 Modeling periodic phenomena with trigonometric functions is not addressed.
  • S-IC.1: There were no opportunities for students to make inferences about populations based on random samples.
  • S-IC.2: There were no opportunities for students to determine whether a model is consistent with a data-generating process.
  • S-IC.4: There were no opportunities for determining margin of error.
  • S-IC.6: There were no opportunities for evaluating reports based on data.
  • S-ID.2: Standard deviation is not included.
  • S-ID.4: There were no opportunities for students to address standard deviation and normal distributions.
  • S-ID.6a: Quadratic and exponential models are not used for fitting data.
  • S-ID.6b: There were no opportunities for assessing the fit of a function by plotting/identifying residuals.
  • S-CP.1-7: There were no opportunities for students to address S-CP.1-3,6,7. In Algebra 1, 3.09, S-CP.4 and S-CP.5 are partially addressed, but these standards are not aligned to any lessons in the publisher’s correlation.
  • S-MD.1-7: not aligned to Algebra 1, Geometry or Algebra 2. (The textbook aligns some statistics and probability standards to the series' precalculus textbook, which is not part of the instructional package reviewed.)
  • G-GPE.3: There were no opportunities for students to address this standard.
  • G-GPE.7: There were no opportunities for students to use coordinates to compute perimeters and areas.
  • G-MG.2: There were no opportunities for students to address concepts of density based on area and volume.
  • G-C.5: There were no opportunities for students to derive the definitions for arc length and radian using similarity.

The following are standards which are not aligned correctly:

  • F-IF.4: Algebra 1 and Algebra 2 instructional materials do not teach end behavior. The publisher aligns Algebra 1 Lessons 5.06 and 5.07 and Algebra 2 Lessons 6.01-6.04, 8.06, 8.08 to the standard; however, these sections are misaligned. Although graphing is included in these sections, the interpretation of key features of the graphs is not the focus of these lessons. In Algebra 1, Lessons 8.06-8.08 address the key features of the functions such as increasing, decreasing, maximum, etc.
  • F-IF.9: Algebra 1 lessons identified by the publisher are misaligned. An example in Lesson 8.06 has students find the minimum using two representations (a table and a graph) and those representations are compared. However, the two representations are not of two different functions.
  • A-APR.6: Despite being identified by the publisher as aligned, Algebra 2 Lesson 2.10 does not ask students to write rational expressions in the given form (though it is a related topic, polynomial division, and does address remainders).

The following are standards whose full intent was partially met:

  • F-IF.2: Algebra 1 and Algebra 2 instructional materials do not consistently use function notation throughout the series. A combination of transformation notation (x -> x+3), function notation (f(x)), and y= notation is used. However, examples of appropriate function notation are found in the instructional materials. For example, Algebra 1, Lesson 5.10, page 484, problem 6 provides a real world problem in the lesson that has students use function notation in a real-world context. Lesson 5.12 addresses real world application of this concept and offers rich context ranging from interest rates on a credit card (page 496) to the build up of antibiotics in the body (page 500).
  • F-IF.7e: Algebra 1, Lesson 6.14 and Algebra 2, Lesson 5.07 address graphing exponential functions; Algebra 2, Lesson 5.14 addresses graphing logarithmic functions. Instructional materials do not have students identify intercepts or end behavior of these graphs. Algebra 2, Lessons 8.07 and 8.08 address graphing sine, cosine, and tangent functions. The concept of periodicity is mentioned once, but the materials do not include amplitude and midline.
  • F-TF.5: Students graph sine, cosine, and tangent functions in Algebra 2 Lessons 8.07 and 8.08, but they do not need to use amplitude, frequency, or midline to model these functions.
  • A-REI.2: Instructional materials do not discuss extraneous solutions when solving rational or radical equations.
  • A-CED.1: Linear, quadratic, and exponential equations are all addressed. Rational functions are not addressed. In Algebra 1, Chapter 2, along with Lessons 4.13, 4.14, 5.10, and 5.11, has students create linear equations or inequalities to solve problems. Linear equations are also revisited in Algebra 2, Lesson 1.07. Algebra 1 Lesson 8.06 has students create quadratic equations. There are examples of exponential functions in Algebra 2 Lesson 5.09. Algebra 2, lessons 5.07-5.09 has students create exponential equations.
  • A-REI.4b: Algebra 1 Lessons 7.03, 7.11, and 8.04 include solving quadratic equations by factoring. Algebra 1, Lesson 7.12 includes solving quadratic equations by completing the square. Algebra 1 Lesson 8.02 includes solving quadratic equations by quadratic formula. Instructional materials do not address how to solve a quadratic function by taking the square root or through inspection.
  • G-GPE.6: Geometry Lesson 7.07 has students determine midpoint but no other partitions of a line segment.
  • G-GMD.4: In Geometry, Lessons 1.0, 6.10, 6.11, and 6.12 identify the shapes of two-dimensional cross-sections of three-dimensional objects. Evidence for the three-dimensional objects generated by rotating two-dimensional objects was not located.
  • S-IC.3: Algebra 2 Lesson 4.14 has students identify the need for randomization within the context of an experiment, yet it does not discuss randomization for sample surveys or observational studies. In Lesson 4.14 of Algebra 2, students compare theoretical probability with experimental results. They are asked to differentiate between the two.
  • A-REI.7: Algebra 1 Lesson 4.13 has students solve a simple system consisting of a linear equation and a quadratic equation. Students use a graph to determine solutions to the system. Students do not algebraically confirm their solutions, and no other related examples were found that would allow students to algebraically find solutions.
  • A-REI.11: Students determine that the intersection of two functions represents the solution for linear functions (Algebra 1 Lessons 3.15, 4.13), quadratic functions (Algebra 1 Lesson 8.10), polynomial functions (Algebra 2 Lesson 2.08), exponential functions (Algebra 2 Lesson 5.07), and logarithmic functions (Algebra 2 Lesson 5.14). The materials do not include rational functions and absolute value functions. Graphing is not used to solve rational and absolute value equations.
  • S-ID.2: Algebra 1 Lessons 3.06-3.08 use statistical measures to compare center of data, and Lesson 3.08 uses Inner-Quartile Range (IQR) to compare spread of data. Standard deviation is not addressed as an additional way to compare spread of data.
  • S-ID.3: Algebra 1 Lesson 3.08 does compare the shape, center, and spread of data sets. However, there is no explicit discussion of outliers.
  • S-ID.5: Algebra 1 Lesson 3.09 has students use two-way frequency tables to summarize categorical data and identify associations and trends in the data. Joint, marginal, and conditional relative frequencies are not used as a method to interpret relative frequencies.
  • S-ID.6a: Lessons in Algebra 1 and Algebra 2 have students fit a linear function to a data set, but the materials do not emphasize quadratic or exponential models.
  • G-CO.1: Precise definitions are provided for parallel lines (page 12) and line segments (page 12). No definition is provided in lessons for angles, circles or perpendicular lines (although these terms are in the glossary). A definition for perpendicular bisector is provided and uses "perpendicular" even though this term is not previously explicitly defined.
  • G-CO.3: Geometry Lesson 7.04 allows students multiple opportunities to describe transformations for a rectangle, parallelogram, and trapezoid (all found in table on page 574) as well as equilateral triangle, square, regular pentagon, and regular hexagon (all found in table on page 575). Rotations and reflections that carry a parallelogram or trapezoid onto itself are not addressed.
  • G-CO.4 The definitions of rotations, reflections, and translations in terms of circles are not addressed.
  • G-CO.9: A proof for "when a transversal crosses parallel lines, corresponding angles are congruent" was not found.
  • G-CO.13: Exercise 9 on page 32 of Geometry Lesson 1.06 has students construct an equilateral triangle. Materials are missing constructions for a square and regular hexagon. Constructing figures inscribed in a circle is not addressed.
  • G-GPE.1: Geometry Chapter 7 Project incorporates equations of circles on a coordinate plane; however, there is no derivation of the equation of the circle made with connection to the Pythagorean Theorem.
  • G-GPE.2: Geometry materials do not address deriving the equation of a parabola given a focus and directrix.

The following are standards whose full intent was met:

  • F-TF.8: Algebra 2, Lesson 8.04 on page 730 provides students three methods for proving the Pythagorean identity and asks students to choose one method to complete the proof.
  • G-SRT.2: Geometry instructional materials support student understanding of similarity with Lesson 4.04. Students are encouraged to determine whether triangles are scaled copies or not scaled copies of each other and asked to compare lengths of corresponding sides. Lessons 4.10, 4.14, and 4.15 establish the definition of similarity in terms of similarity transformations, and it is used to show that similar triangles have proportional sides.
  • S-ID.1: Dot plots are used on page 408 in Algebra 2 to represent the results of an experiment. Later on page 409, the data is compiled into a histogram. Algebra 1 Lesson 3.08 offers extensive practice with histograms, dot plots, and box and whisker plots

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. While some components of the modeling process are frequently required of students, students are not required to go through all of the steps as outlined by the CCSSM.

Aspects of the modeling process that are frequently addressed throughout the series expect students to formulate, compute, interpret and validate in problems.

  • In many For You to Do problems and chapter projects, students are encouraged to develop their own solution strategy - formulate and compute. In the Algebra 2 Chapter 3 Project, students are asked to use their knowledge of factoring to factor polynomials of the form x^n-1, identify patterns, and formulate a conjecture relating the number of factors of x^n-1 to the number of factors of n.
  • In many lesson discussions, students are interpreting and validating findings. Very often students have to critique the process that the fictional students in the materials use to solve problems. In Algebra 1, Lesson 4.02, students have to determine who correctly found the slope in a the problem given.

Although the components of the modeling cycle are included, the entirety of the modeling cycle was not located throughout any of the materials.

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

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.
1/2
+
-
Indicator Rating Details

The Instructional materials reviewed partially meet the expectation for allowing 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 (WAPs). Overall, there are parts of the materials that address topics which are distracting from spending the majority of the instructional time on the WAPs.

Some examples of topics that are distractions from the WAPs are as follows:

  • In Algebra 1, Chapter 1 allots 16 instructional days (according to the publisher's pacing chart) to arithmetic rules for integers, decimals and fractions. This material does not align to the high school CCSSM, so it is distracting from the WAPs.
  • In Algebra 1, Chapter 2 allots 17 instructional days (according to the publisher's pacing chart) on simplifying expressions and solving equations. The majority of the questions in this chapter utilize linear expressions and equations which more closely align to standards from grades 6-8.
  • In Geometry, lessons 3.01-3.08 address cutting/rearranging figures to compose new figures and use this as a lead-in to area. Thirteen instructional days (according to the publisher's pacing chart) are dedicated to these lessons, but these lessons align more closely with standards from grades 6-8.
  • In Algebra 2, lesson 4.03 solves systems of equations using matrices, and lessons 4.04-4.13 address algebra with matrices and applications of matrices. The materials allot 11 instructional days (according to the publisher's pacing chart) to these lessons which align to plus standards.
  • In Algebra 2, lessons 6.05-6.10 address affine transformations which are beyond what is required by the standards. The materials allot six instructional days (according to the publisher's pacing chart) to these lessons, and they are distracting from the WAPs as the transformations explored are beyond the requirements of the CCSSM.

In addition to including topics that are distracting from the WAPs, the instructional materials, when used as designed, include insufficient opportunities for students to engage with the WAPs as the number of instructional days allocated to each course varies greatly.

  • In Algebra 1, the instructional materials reviewed are designed to be completed in 119 days.
  • In Geometry, the instructional materials reviewed are designed to be completed in 157 days.
  • In Algebra 2, the instructional materials reviewed are designed to be completed in 114 days.

Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
2/4
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectation for, when used as designed, allowing students to learn each standard. Overall, the instructional materials provide limited opportunities to practice several standards.

In the instructional materials, examples of standards with limited opportunities for practice include, but are not limited to, the following:

  • F-IF.3: The lessons this standard is aligned to by the publisher address recursive functions, but sequences are not the emphasis nor were they defined. The fact that the domain is the subset of the integers was not made explicit, either. It is not aligned to Algebra 1, lessons 5.07 and 5.08 as denoted in the teacher edition. It is aligned to lesson 5.09.
  • F-IF.4: Instructional materials provide several opportunities to graph different types of functions; however, students are not always asked to identify key features. In Algebra 1, lessons 8.06-8.08, students are asked to determine where a function is increasing/decreasing, find maximums and minimums, find the line of symmetry, and determine zeros of a quadratic function. In Algebra 2, lessons 5.07 and 5.14, students are asked to determine whether a logarithmic or exponential graph is increasing or decreasing as well as determine the domain of these two types of functions when graphed. No other functions are interpreted for increasing/decreasing intervals, end behavior, maximums/minimums, symmetries, or end behavior.
  • F-IF.5: Algebra 2, lesson 2.02 has students graph a function, find the domain, and reverse the process by finding the domain of a function and then graphing. Algebra 1, lesson 8.06 is misaligned (no examples in which students relate domain to a graph). Throughout the series, no examples were identified in which students need to interpret domain of a function provided within a context.
  • F-IF.7b: Although instructional materials show students how to graph square root functions and absolute value functions, there is limited practice provided and may not be sufficient for every student to master the content of the standard.
  • F-BF.1b: Although Algebra 2 lesson 2.08 has students combine functions using arithmetic operations, this section provides limited practice that may not be sufficient for every student to master the content of the standard.
  • F-BF.3: The publisher aligns Algebra 1 lessons 3.16 and 3.17 to this standard. In these two sections, selected problems in the "Maintain Your Skills" portion of the materials (lesson 3.16, problems 17 and 18; lesson 3.17, problem 16) have students graph functions that have been translated or stretched from a parent function. However, there is no instruction on generalizing these effects until lesson 3.18. Students are expected to use a graphing calculator to complete these problems and don't rely on their knowledge of the "rule" for translating and/or stretching graphs. These skills are later addressed in Algebra 2 lessons 6.01, 6.03 and 6.04.
  • F-LE.5 Interpreting parameters in an exponential function in terms of a context is mainly limited to compound interest.
  • A-APR.4: There are limited opportunities to prove polynomial identities (correlation guide lists Algebra 1 lesson 7.01, problem 14 and Algebra 2 lessons 2.11, 2.13, 2.14, but also found in Algebra 1 lesson 7.02 pages 614-615).
  • N-Q.1: There is evidence of using units appropriately in all three textbooks; however, using units is not emphasized as a guide to solving multi-step problems throughout lessons.
  • N-Q.2: Defining appropriate quantities for descriptive modeling is limited to rates of change (Algebra 1 lesson 4.03). [Algebra 2 lessons 1.07 and 1.11 are specified by the publisher correlation to be aligned to this standards but evidence of this standard was not found in the lesson.]
  • N-CN.7: Limited opportunities are provided for students to solve quadratic equations with complex solutions. Algebra 2 lesson 3.03 first introduces solving quadratic equations that have complex solutions. Subsequent lessons in Chapter 3 have students practice these skills in the On Your Own exercises and Maintain Your Skills exercises. Algebra 2 lesson 3.04, problem 15 and 3.07, problems 10 and 11.

A lack of consistency with how lessons are labeled in the teacher materials could also impede students from fully learning each standard because lessons that allow for the full depth of the standard to be realized are identified as optional. This type of inconsistency occurred several times throughout the courses. For example, in Algebra 1, Chapter 4 Investigation 4D (lessons 13-15) is noted as optional in the materials with the lessons (page 394). However, the lessons are not noted as optional in the pacing guide at the beginning of the chapter or book, and the standards for these lessons in the alignment guide are identified as met (not optional).

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to high school. In general, the Algebra 1 materials tend to spend excessive time reviewing the grade 6-8 standards while Algebra 2 tends to do the opposite, including many of the plus standards and extending the instruction beyond what is expected for the high school mathematics standards.

  • There are a significant number of lessons and problems aligned to middle school content and/or considered prerequisite skills. In Algebra 1, lesson 1.08, for example, students are asked to convert decimals to fractions. They are also asked to plot numbers on a number line. Neither of these tasks align to a high school standard. Most lessons that align to middle school content are included in the Algebra 1 course; the lessons in the Geometry and Algebra 2 courses do not have a significant amount of content that aligns to middle school standards.
  • The end-of-chapter project in Algebra 2, Chapter 7 goes beyond the scope of the high school mathematics standards and contains notation and formulas that extend past the appropriate level of mathematics for a high school course. The project contains tasks that lead to a proof of "for any set of data, the line of best fit contains the balance point." The line of best fit is appropriate to high school. Then the students are asked to find the centroid and the error for each point. From there, the materials go on to find the sum of squares which, with the notation and equations, addresses plus-standards and beyond.
  • The units and lessons aligned to the non-plus high school standards generally feature a range of activities that address procedural knowledge, conceptual understanding, and problem solving. For example, Algebra 1 Unit 2, titled “Expressions and Equations,” has lessons that address A-CED.1 and A-REI.1, two standards that deal with solving equations. Lesson 2.09 includes some number puzzles that introduce the topic. Lesson 2.10 gives models intended to help conceptually understand the logic of equation solving, while lessons 2.11 and 2.12 focus more on the procedures involved in solving equations and lessons 2.15 an 2.16 address solving word problems by solving equations that model the word problems. The context, numbers used, and habits of mind addressed engage students in mathematics at a level of sophistication appropriate to high school.
  • The diversity of numbers, representations, and equations in the materials is appropriate for high school. Expressions and equations used throughout the series incorporate integers, decimals and fractions.

Indicator 1d

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for fostering coherence through meaningful mathematical connections in a single course and throughout the series, where appropriate and where required by the Standards.

In some cases, the lessons do provide mathematical coherence between and within courses. Some examples include:

  • Algebra 2, lesson 4.01, begins with a link back to Algebra 1. The lesson addresses solving systems of equations, and then the chapter moves into an emphasis on using matrices to solve similar problems.
  • Algebra 2, lesson 5.12, connections are made between the properties of logarithms and the connection to the properties of exponents that were addressed earlier in the chapter showing that connections are made within the course.
  • Algebra 1, Chapter 8 has students solve quadratic equations, and Algebra 2 extends to including solving quadratic equations with complex solutions.
  • Another example that shows coherence but lacks explicit connections is in an introduction to exponential expressions and functions in Algebra 1 and 2. Algebra 1, Chapter 6 provides the framework for a more deeper understanding of exponential functions in Algebra 2, Chapter 5.

However, connections to prior course and series learning is not always explicit for teachers and students. For example, lessons on scatterplots and positive versus negative associations of data are introduced before lessons on slope and graphing lines in Algebra 1. This builds the foundation for learning about best fit lines in lessons 1.06-1.09 in Algebra 2; however, these connections are not explicit for teachers or students.

Some examples that demonstrate that the lessons are not always coherent include:

  • Geometry lessons 2.15 - 2.19 addressing quadrilateral properties do not continue the coherence of the lessons in the beginning part of the chapter on congruence and proof.
  • Conceptual understanding of area builds in the Geometry materials as students learn about area formulas in lessons 3.06-3.08, then coordinate geometry in lessons 7.06-7.10, and applying this knowledge in optimization examples related to area in lessons 8.04-8.06. Although the concept of area is part of each of these lessons, the lessons do not build on one another nor provide teachers or students prompts for recalling information about area from previous lessons.
  • Not all Statistics and Probability topics fit coherently throughout the courses. Interpret Linear Models (S-ID.7-9) fits naturally into the Graphs and Lines units, but Summarize, represent, and interpret data (S-ID.1-6), which includes mean, median, and two-way frequency tables, is not as natural a fit in those units.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards.

For example, Algebra 1, Chapter 1: Arithmetic to Algebra addresses basic arithmetic of integers, fractions, and decimals. The pacing guide in the teacher edition of the materials indicates that these lessons build upon grades 6-8 standards in order to prepare for a high school content standard. For example, Lesson 1.05: The Basic Rules of Arithmetic "builds on 6.EE.3, 7.NS.1, and 7.NS.2 to prepare for A-SSE.2 and A-APR.1." Furthermore, the instructional materials sometimes, but not always, indicate when lessons review grades 6-8 content. For example, Algebra 1 lessons 4.01 and 4.02 review 8.EE.6. In Algebra 1, the pacing guide aligns the entire first chapter as "builds on" standards for grades 6, 7 and 8. There is not notation in the chapter or individual lessons that reiterates that the content is review or preparation for later lessons.

Not all connections from content taught in grades 6-8 and high school are clearly and explicitly articulated. For example, Investigation 3C in Geometry has students build upon their knowledge of the Pythagorean theorem developed in Grade 8 by investigating several different proofs of the theorem. However, no connections are explicitly made between the Grade 8 cluster "Understand and apply the Pythagorean Theorem" and the high school domain G-SRT: Similarity, Right Triangles, and Trigonometry.

Indicator 1f

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.
0/0
+
-
Indicator Rating Details

The plus standards, when included, are not always explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

In the Algebra 1 and Geometry courses, there are a limited number of plus standards, and therefore the inclusion of those standards does not distract from the work on the non-plus standards. The Algebra 2 materials, however, have a greater number of lessons that include plus standards which is distracting from focus on non-plus standards.

The lesson or chapter overviews do not note that plus standards are included within or are the focus of a lesson. The lessons that include plus standards are not usually noted as optional and are included in the pacing guide for the course (but are not noted as such on that pacing guide). The plus standards often distract from the standards or add extra lessons in the center of a unit. Because they are intertwined with standards that must be taught, the lessons cannot always be skipped. For example, in Algebra 2, lesson 8.4, three standards are aligned to this lesson. Two are plus standards and one is not. The three previous lessons include plus standards. So, it is challenging for a teacher/student to only separate out the part of the lesson that aligns to proving the Pythagorean Identity (non-plus standard) without also using the unit circle and trigonometric functions.

Alignment of the materials to the plus standards is as follows:

Met:

N-CN.3, N-CN.4, N-CN.5, N-CN.6, N-CN.8, N-CN.10, N-VM.2, N-VM.4b, N-VM.4c, N-VM.5a,N-VM.5b, N-VM.6, N-VM.7, N-VM.8, N-VM.9, N-VM.11

A-APR.5, A-REI.8, A-REI.9

F-BF.1c, F-BF.4b, F-BF.4c, F-BF.4d, F-BF.5, F-TF.9, F-TF.3

G-SRT.9,G-SRT.10, G-SRT-11, G-C.4, G-GMD.2,

Partially Met:

N-VM.1: Algebra 2 lesson 3.09 (only magnitude and direction of vector); Geometry lesson 7.12 and 7.13

N-VM.4a: Geometry lesson 7.12 teaches component-wise addition and parallelogram rule for addition, but not end-to-end addition of vectors; Algebra 2 lesson 3.08 teaches parallelogram rule for addition

N-VM.10: Identity matrix included in lessons 4.08 and 4.09, but lacking proof of the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

N-VM.12: 2 x 2 matrix transformations included in lesson 4.11, but lacking proof of the absolute value of the determinant as a representation of area.

A-APR.7: Algebra 2 lesson 2.10 provides opportunities for students to add, subtract, and simplify rational expressions; no evidence found for students multiplying and dividing rational expressions

F-IF.7d: Algebra 2 lesson 6.01 "On Your Own" part of lesson has students graph rational functions, however, there is no explicit instruction. They are not asked to identify zeros and asymptotes.

Not Met:

N-VM.3,F-TF.4, F-TF.6, F-TF.7, G-GPE.3,

None of the Statistics and Probability Standards are met.

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2a - 2d

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

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.
N/A

Indicator 2b

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.
N/A

Indicator 2c

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.
N/A

Indicator 2d

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.
N/A

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

Indicator 2e

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.
N/A

Indicator 2f

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.
N/A

Indicator 2g

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.
N/A

Indicator 2h

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.
N/A

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

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.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

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.
N/A

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

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.
N/A

Indicator 3h

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.
N/A

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
N/A

Indicator 3j

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).
N/A

Indicator 3k

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.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
N/A

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

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).
N/A

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

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.
N/A

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 Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners.
N/A

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
N/A

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

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.).
N/A
abc123

Additional Publication Details

Report Published Date: 09/08/2016

Report Edition: 2009

Title ISBN Edition Publisher Year
978-1-256-74146-6
978-1-256-74147-3
978-1-256-74148-0
978-1-256-74180-0
978-1-256-74181-7
978-1-256-74182-4

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School 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 High School 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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