Alignment: Overall Summary

The instructional materials reviewed for the Pearson 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 and explicitly 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.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
8
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).
8/18
+
-
Criterion Rating Details

The instructional materials reviewed do not meet expectations for focus and coherence. The materials allow students to spend the majority of their time on the widely applicable prerequisites and attend to the full intent of much of the mathematical content contained in the high school standards for all students. However, the materials do not attend to the full intent of the modeling process, and more connections could be made within and across courses in order to foster more coherence among mathematical concepts.

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.
2/4
+
-
Indicator Rating Details

The instructional materials reviewed partially meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. In general, the series included the majority of all of the non-plus standards, but there were some instances where the full intent of the standard was not met.

Below are the non-plus standards that were not fully addressed and descriptions of how they were not fully addressed:

  • A-SSE.1: Students are often shown how the information from a context is related to an equation or expression, yet evidence was not found where students interpret expressions in terms of the represented context. The materials regularly highlight and provide nomenclature for the parts of expressions, yet students are not required to interpret the parts of the expression in terms of the context. For example, Lesson 4-7 of Algebra 1 highlights the first term, term number, and common difference in arithmetic equations. In these cases, students are regularly shown the parts of an expression in order to replicate an example without needing to interpret the parts of an expression in terms of the context the expression represents. Furthermore, the materials focus on words within the standard (like “factors”) without requiring students to interpret the structure. For example, the cumulative review in the TE on page 610 in Algebra 1 asks students to “Factor the expression 3x^2 + 23x + 14” as the single task aligned with A-SSE.1a. This example is representative of the focus of the materials on words like “factors” within the standard without attending to the requirement for students to interpret expressions in terms of their context.
  • A-SSE.3: Students regularly factor and complete the square throughout the series, yet the standard requires students to “Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.” Evidence was not found that the materials require students to choose a form in order to reveal information. For example, the Algebra 1 TE on page 576 directs students to factor to find zeros. Similarly, students are directed to “solve by factoring” in the Algebra 1 TE on page 571 and “Find the vertex of each parabola by completing the square” on page 579 of the Algebra 1 TE. The standard requires students choose and produce an equivalent form in order to reveal information, but the materials regularly direct students which form they should use.
  • A-APR.3: Although students graph functions to find solutions to equations (e.g., 3x2 – 12 = 0, Algebra 1 TE on page 564 and x2 – 11x + 24 = 0, Algebra 2 TE on page 229), evidence was not found where students identify zeros of polynomials by factoring and then use the zeros to construct a rough graph of the function defined by the polynomial.
  • A-APR.6: No evidence was found where students rewrite a rational expression, a(x)/b(x), in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials.
  • A-REI.1: Throughout Algebra 1 and Algebra 2, students solve equations. The examples provided (e.g., problem 3 on page 111 in the Algebra 1 TE) detail the operations, formulas, and properties used in order to solve the equation. Examples like these regularly provide students with sample justifications that "explain each step in solving a simple equation," yet students themselves are not required to explain their steps in solving simple equations.
  • A-REI.5: The textbook provides reasoning as to why the “elimination method” works (Algebra 1, Lesson 6.3), yet students are not required to prove that replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions as required by the standard.
  • A-REI.11: Evidence was not found where students explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x). Students regularly follow a prescribed method for solving equations. For example, page 596 of the Algebra 1 TE states “Step 1: Graph both equations in the same coordinate plane. Step 2: Identify the point(s) of intersection, if any. The points are (-2,4) and (2,0). The solutions of the system are (-2,4) and (2,0).” Similarly, the Concept Byte on pages 260-261 for Lesson 4-4 of the Algebra 1 TE provides a prescriptive method to solve equations like -4 = -3t + 2.
  • F-LE.3: Evidence was not found where students use graphs and tables to observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Students look at rates of change of various function types (e.g., on page 559, Algebra 1 TE), yet they are not required to observe exponential functions overtaking others in these situations.
  • G-CO.13: Students construct squares given a side length (in the Geometry TE on page 187), equilateral triangles (in the Geometry TE on page 255), and circumscribed polygons. However, no evidence was found that students construct an equilateral triangle, a square, or a regular hexagon inscribed in a circle.
  • G-MG.3: Evidence was not found that students would apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
  • S-ID.3: The materials require students to recall definitions as well as calculate measures of center and spread (e.g., Lesson 12-3 in Algebra 1). However, no evidence was found where students are required to interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • S-ID.8: The materials require students to compute correlation coefficients of a linear fit with technology (on page 339 of the Algebra 1 TE), yet no evidence was found were students interpret the meaning of the correlation coefficient.

Many standards are addressed fully only with the incorporation of the teacher notes and features such as “Concept-Bytes” which are not present in the student materials.

Below are examples of how standards and clusters were fully addressed in the materials:

  • N-RN.2: Lesson 6.4 of Algebra 2 includes work specifically around rewriting expressions involving radicals and rational exponents using the properties of exponents.
  • A-CED.A: The materials attend to the entirety of this cluster. Throughout the series, students create equations to describe relationships. Students begin writing simple linear equations in the first chapter of Algebra 1, and as the series progresses, students write equations with various functions. Students also create equations to highlight quantities of interest throughout the series, in particular in Algebra 1 and Algebra 2.
  • F-IF.2: The series regularly uses function notation and expects students to evaluate inputs for various function types. Additionally, students are required to interpret statements that use function notation in terms of a context (Algebra 1, Lesson 4-6).
  • G-CO.C: The entirety of this cluster is fully addressed in the materials. Throughout the geometry course, students prove various theorems about lines, angles, triangles, and parallelograms.
  • S-CP.6: In lesson 13-6 of Geometry and lesson 11-4 of Algebra 2, students find conditional probabilities by using the fractional part of desired outcomes that belong to the restrictive event.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
0/2
+
-
Indicator Rating Details

The instructional materials do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. Overall, while there are a few opportunities throughout the program for students to engage in some part(s) of the modeling cycle, students do not have opportunities to work with the full intent of many of the modeling standards.

The materials provide isolated opportunities for students to access the full modeling cycle in items like the “Apply What You’ve Learned” and “Concept Byte” sections. However, students are typically led through a series of guiding questions and established scenarios rather than engaging in the complete cycle which involves: “(1) identifying variables in the situation and selecting those that represent essential features, (2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables, (3) analyzing and performing operations on these relationships to draw conclusions, (4) interpreting the results of the mathematics in terms of the original situation, (5) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable, (6) reporting on the conclusions and the reasoning behind them.”

Below are some examples of where the materials allow students to engage in only a part of the modeling process or interrupt the development of it:

  • In “Got It?” in Algebra 1 TE on page 256, students are required to choose the scale in graphs, an element of identifying variables and formulating a model. However, the situation is given, the essential features are called out, and a model is given rather than formulated by the student.
  • The “Pull It All Together” in Algebra 1 TE on page 282 gives students an established scenario, formulates a model, and directs assumptions students should make, although the task is identified as aligning with the modeling standard F-IF.4.
  • The performance task in Algebra 2 TE on page 346 and the connected task in TE on page 279 notes that students are modeling, yet the tasks fail to incorporate the full modeling cycle. In both cases, students are limited to providing an equation to describe the situation.
  • In the “Pull It All Together” in Algebra 2 TE on page 552, the task is scripted and the assumptions are given, even in the "On Your Own" portion of the task.
  • Lesson 3-4 in Geometry notes alignment with G-MG.3 but includes no tasks that attend to the full intent of the modeling process.
  • How the materials address F-BF.2 does not give students opportunities to engage in the modeling cycle with the content of arithmetic and geometric sequences. In Algebra 1 Lessons 4-7 and 7-8, students write function rules, defined both explicitly and recursively, given a sequence and also write terms of the sequence defined by a function rule. In Algebra 2, lessons 9-2 and 9-3 continue that work with the same content. In Algebra 1 TE on page 473, “Pull it All Together” is a culminating performance task for arithmetic and geometric sequences, and it asks students to engage in calculations for a given scenario using a given model. However, students are not asked to identify variables in a situation, instead a situation is given. Students don’t formulate a model to describe relationships, but a model is delineated. Students aren’t asked to analyze and draw conclusions, but they perform calculations and follow procedures. Students cite the meaning of the numerical answer they calculated in many cases, but they are not required to interpret the results or to validate their conclusions. Instead, the calculated answer is accepted. Students are not given opportunities to improve the model that was given by the materials, and they do not need to report on the reasoning behind the conclusions drawn. In Algebra 2 TE on page 576, question 62 provides a scenario and again specifies the model to use to complete a series of calculations with minimal opportunity for students to engage in any part of the modeling cycle.
  • Similarly, for A-SSE.2, A-APR.3, A-CED.1, F-IF.7, F-BF.2, G-SRT.8, G-MG.1 and S-ID.6b, the materials provide few opportunities for students to engage with elements of the modeling cycle.

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.
2/2
+
-
Indicator Rating Details

The Instructional materials reviewed for the High School Pearson Traditional series meet the expectations 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). (Those standards that were not attended to by the materials, as noted in indicator 1ai, are not mentioned here.)

In Algebra 1, students spend most of their time working with WAPs from Number and Quantity, Algebra, and Functions. The Geometry course focuses daily attention on all the WAPs in the Geometry category. During Algebra 2, students spend most of their time extending their understandings of Number and Quantity, Algebra, and Functions. Throughout all three courses, students also spend time on the Statistics and Probability WAPs.

Examples of students engaging with the WAPs include:

  • Defining arithmetic and geometric sequences as functions and several opportunities with both recursive and explicit formulas to recognize and develop these utilizing such scenarios as an online auction, seating in a sports arena, and evaluation of consecutive bounces of a ball (F-IF.3);
  • Multiple opportunities to work with similarity, both in terms of transformations and problem-solving (G-SRT.A,B), and problem solving with trigonometric ratios in right triangles including contexts such as embroidery, conveyor belts, and building storage containers (G-SRT.C); and
  • In several sections in Algebra 1 and Algebra 2, data sets are used to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more data sets (S-ID.2) and interpret the slope (rate of change) and the intercept (constant term) of a linear model with some discussion of correlation and causation (S-ID.7), and statistics is used as a process for making inferences about population parameters based on a random sample from that population (S-IC.1).

Indicator 1b.ii

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

The materials partially meet the expectation for, when used as designed, allowing students to fully learn each standard.The following are some examples of how the materials, when used as designed, would not allow students to fully learn each standard. (Those standards that were not attended to by the materials, as noted in indicator 1ai, are not mentioned here.)

  • N-RN.1: Students should “Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents…” Lesson 7.2 of Algebra I includes an explanation of this in the Teacher Edition; however, no explanation is noted in the student edition and no indication is noted where students explain. In Lesson 7.3 of Algebra I, there are examples of methods students can use to simplify exponential expressions; however, students are not asked to explain the meaning of rational exponents as the standard requires. Similarly, in lesson 6.4 of Algebra II on page 381, Problem 1 gives an example of this idea; however, students are not asked to explain the meaning of rational exponents.
  • F-IF.8b: Students “Use the properties of exponents to interpret expressions for exponential functions.” Lessons 7-3 and 7-4 of Algebra I work with properties of exponential functions. In Example 1B on page 461, students can see the expression 1.07x (in terms of x years) transformed into 1.0057m (a monthly expression); however, no evidence is found where students are interpreting the new expression.That is, students do not have opportunity to fully work with, practice, and learn this standard. Similarly, Lesson 6-8 in Algebra II, page 416, addresses this idea in a “Think Box” near the bottom of the page. Again, no evidence is found where students are interpreting the meaning of the equivalent exponential expression.
  • F-IF.9: Students “Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).” The evidence of this standard is found to be very limited. For instance, in Algebra I, three problems are found to address this idea: problem 51 (graph and table) in lesson 5-5 on page 327, problem 40 (table and equation) in lesson 7-6 on page 458, and problems 28 and 29 (equation and table) in lesson 9-2 on page 557. In Algebra II, four additional problems are noted: problem 48 in lesson 2-4 on page 87, problem 43 (equation and table) in lesson 4-2 on page 207, problem 38 (equation and graph) in lesson 5-9 on page 344, and problem 58 in lesson 7-3 on page 457. The limited number of problems provide limited opportunities for students to compare properties of functions represented in different ways, and no evidence is found to support students comparing different functions.
  • S-ID.7: Students “Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.” Some discussion of correlation and causation occurs in Algebra I on page 342 in problem 21. While students are given the opportunity to use and determine the slope and intercept, there is no evidence of students being asked to interpret these ideas, either in context or generally.

Opportunities to fully learn the following standards are limited to one Concept-Byte activity.

  • G-CO.2: Concept Byte 9-1 in Geometry includes a tracing paper activity, and Concept Byte 9-2 includes paper folding to represent reflections. The online program shows a solution to problems but does not have an interactive program for students to utilize in creating transformations. No evidence is found of students using transparencies to create transformations. Lesson 12-5 in Algebra 2 addresses “geometric transformations” with matrices. While students are given intermittent opportunities to work with transformations, there is no opportunity for students to describe and/or compare transformations which limits their experience and the opportunity to deeply interact with these concepts.
  • G-CO.3: Geometry Concept Byte 9-3. pages 568-569, addresses this standard; however, evidence is not found in the student edition asking students to translate a figure back onto itself. In the Teacher Edition, notes include questions that push student thinking to this effect; however, students are not asked to “describe” these things in their problem solving.
  • S-ID.5: This standard is addressed in Algebra 1 with Concept Bye 12-5. One more problem was found in Geometry on page 854 with problem 23. This is limited opportunity for students to interact with the topic, understand the use of these tables, and interpret any data revealed within them.
  • S-IC.2: The materials state this standard is addressed in Algebra 2 by Concept Byte 11-3. There is material here for probability distributions and cumulative probability in problems 4a,b. Opportunities on this topic are limited and do not allow students to fully understand and interact with the ideas.

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 materials partially meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Throughout the series, students engage in age-appropriate situations at a level of complexity suitable for students in this grade span. However, the materials require students to apply only some of the key takeaways from Grades 6-8.

Below are examples of how key takeaways from Grades 6-8 are not applied within the materials:

  • Exercises do not regularly require students to perform rational number arithmetic fluently in all the courses. For example, lesson 1-4 in Algebra 2 TE on page 30, “solving equations” provides 23 problems of which only two contain non-integer numbers and only five have non-integer solutions.
  • Throughout the materials, students are directed step-by-step to follow a procedure in order to apply key takeaways from Grade 6-8. For example, in Algebra 1 lesson 6-2 TE on page 374, students are given step-by-step instructions showing how to use a system of linear equations to solve a word problem. Rather than "building on students’ previous knowledge and allowing students to make connections to new learning," the materials direct procedures.
  • The materials do not require students to apply concepts and skills from 6.SP through 8.SP in their work with high school Statistics and Probability throughout the series. For example, in the last chapter of Algebra 1, students work with histograms and measures of center. The lessons articulate how to create histograms and calculate measures of center without extending the work from 6.SP through 8.SP. Additionally, no evidence was found to support the application of 6.SP through 8.SP concepts and skills earlier in Algebra 1. Similarly, Statistics and Probability is addressed late in Geometry and Algebra 2 with no evidence found for the application of concepts and skills from 6.SP through 8.SP.

Below are examples of how key takeaways from Grades 6-8 are applied within the materials:

  • The materials require students to apply ratios and proportional relationships with their work in geometry, namely Chapters 7 and 8 concerning similarity and trigonometry.
  • Throughout Algebra 1 and Algebra 2, students apply basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.

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 materials partially meet the expectations for fostering coherence through meaningful connections in a single course and throughout the series where appropriate and where required by the Standards. The lessons throughout the Algebra 1 and Algebra 2 materials frequently build mathematically from one lesson to the next, in much the same way as the Geometry materials build from work with area of quadrilaterals and triangles to more diverse polygons and then to circles. However, the materials do not make many connections throughout courses and the series.

The Geometry Progressions for the Common Core State Standards describe a coherent growth in student understanding of congruence founded in rigid transformations in a plane and advocates student use of tools like tracing paper. The progressions go on to state that once a foundational definition of congruence in terms of rigid motion in a plane has been established, “it is possible to transition into the traditional way of proving theorems” (page 13). Instead, the materials move into congruence proofs in traditional format early in the materials (Geometry TE lesson 4-1) where congruence is defined as polygons with congruent corresponding parts. In the Geometry TE lesson 9-1, students are introduced to rigid transformations in the form of translations, reflections, and rotations. In a typical example from the materials, students are asked to combine transformations (Geometry TE on page 601) instead of using those transformations to justify congruence. The task asks students to justify the movement of a puzzle piece onto another without connecting the concept of congruence as the standards require. Likewise, the materials present similarity in Chapter 7 in a traditional manner while redefining similarity in Chapter 9 in terms of transformations without explicitly connecting the previous definition to the new.

The Algebra Progression for the CCSSM describe a tight connection between the work in algebra and the functions domain. Students should see the connection that equivalent expressions are in fact describing the same function, the same relationship between quantities. While the materials define and engage students with equivalent expressions and with functions separately- for example Algebra 1 TE Big Ideas on T26, Algebra 1 TE Math Background on page 613A, Algebra 1 TE Lesson 6-1, and Algebra 2 TE Lesson 3-2- the connection that, for example, equations in a consistent and dependent linear system represent a single function, is absent.

Materials addressing Statistics and Probability occur at the end of each course throughout the series. The treatment of these topics occurs in isolation from the rest of the topics within each of the courses. Additionally, some topics are duplicated in different courses without acknowledging the connections or repetition. For example, Geometry lesson 10-5 and Algebra 2 lesson 14-4 both derive the formula A = 1/2 ab sin(C) for the area of a triangle.

Overall, the series fails to make connections across conceptual categories. Work with the geometry category lives predominantly in the geometry course with minimal connections occurring in the other courses. Conversely, the geometry course is largely devoid of connections to number and quantity, algebra, and functions. Even when connections are being made, or could be made, the materials do not make the connections clear to teachers or students.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
0/2
+
-
Indicator Rating Details

The materials do not meet expectations for explicitly identifying and building on knowledge from grades 6-8 to the high school standards. Neither the teacher nor student editions identify standards from grades 6-8, and the materials do not specifically build on connections from middle school content.

The teacher notes throughout the materials, namely in the “Math Background,” make references to previous work, yet these connections are to lessons within the series. For example, the Geometry TE on page 400 notes “An introduction to coordinate geometry is provided earlier in this textbook.” Explicit evidence linking the work of the series to grades 6-8 was not found.

Moreover, the materials presume no previous knowledge when introducing multiple topics, for example:

  • The Geometry textbook introduces similarity in Chapter 7 without any reference to the work from Grade 8. The TE on page 431A provides the mathematics background for teachers for the chapter without any mention of how students worked with similarity in 8.G.4 or any reference to the transformational geometry middle school standards require.
  • Algebra 1 addresses measures of center, histograms, and box-and-whisker plots as new material even though the standards require students to be working with these these tools and concepts since Grade 6.

This disconnect with middle school standards can also be seen in particular with the materials’ treatment of:

  • Ratios and proportions (Geometry lesson 7-1, “Ratios and Proportions”)
  • Variables and expressions (Algebra 1 lessons 1-1 “Variables and Expressions”, lesson 1-2 “Order of Operations and Evaluating Expressions, lesson 1-7 “The Distributive Property”)
  • Operations on real numbers (Algebra 1 lessons 1-2, 1-3, 1-4, 1-5, 1-6, 1-7)
  • Functions (Algebra 1 Chapter 4, “An Introduction to Functions”)
  • Understanding equations (Algebra 1 lesson 1-8 “An Introduction to Equations”)
  • Solving equations (Algebra 1 Chapter 2, “Solving Equations”; Algebra 2 lesson 1-4 “Solving Equations”)
  • Solving inequalities (Algebra 1 Chapter 3, “Solving Inequalities”; Algebra 2 lesson 1-5 “Solving Inequalities”)
  • Systems of linear equations (Algebra 1 Chapter 6 “Systems of Equations and Inequalities”; Algebra 2 Chapter 3 “Linear Systems”)

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 instructional materials reviewed for this series address many of the plus standards, and in general, the materials treat these standards as additional content that extend or enrich topics within the unit and do not interrupt the flow of the course. Of the plus standards addressed in the materials, the following are fully met: N-CN.8,9; N-VM.1-5a; A-APR.5; A-REI.8; F-IF.7d; F-BF.1c; F-BF.4c; F-TF.6,7,9; G-C.4; G-GMD.2; G-SRT.11; S-CP.8,9; and S-MD.6,7.

Below are some examples of how plus standards are addressed:

  • The treatment of vectors can be found entirely in Algebra 2, lesson 12-6. This single lesson addresses N-VM.A,B. As such, the materials that address vectors are not integral to the work of the course and could be included or excluded at the discretion of the instructor without interrupting the flow of the course.
  • Students begin working with matrices in the Concept Byte for lesson 6-3 in Algebra 1 in order to solve systems of linear equations. Students revisit matrices in a similar fashion in lesson 3-6 of Algebra 2. In both cases, the treatment of matrices helps enrich the work within the chapter. Matrices are addressed further in chapter 12 of Algebra 2 where students learn about the structure of matrices and how to perform operations with them. In all of the occurrences, the materials provide extensions to the course and could be used at the discretion of the teacher.
  • Lesson 12-5 of Algebra 2 looks at how matrices can be used to represent geometric transformations in the plane. This lesson adds to the work of the unit while making connections to the geometry course.

Of the plus standards addressed in the materials, the following are not fully met: A-APR.7; N-VM.5b,11,12; and G-SRT.9,10. Below is a description of how each of these plus standards is not fully addressed.

  • A-APR.7 requires students to understand that rational expressions form a system analogous to the rational numbers. Although the materials (Algebra 1, lessons 11-2 and 11-4, and Algebra 2, lessons 8-5 and 8-6) attend to operations on rational expressions, students are not required to make the connection to the analogous system.
  • N-VM.5b requires computation of the direction of scaled vectors. Evidence for this was not found in the materials.
  • N-VM.11 stipulates that students multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector and work with matrices as transformations of vectors. Evidence for this was not found in the materials.
  • N-VM.12 notes that students interpret the absolute value of the determinant of a 2x2 matrix in terms of area. Evidence for this was not found in the materials.
  • G-SRT.9 expects students derive the area formula for triangles. The materials provide the proof (Algebra 2, lesson 14-4, and Geometry, lesson 10-5) without requiring students to derive the formula on their own.
  • G-SRT.10 asks students to prove the laws of sines and cosines. Students use the laws in multiple lessons (Geometry, lessons 8-5 and 8-6, and Algebra 2, lessons 14-4 and 14-5), yet students are not required to prove the laws.

The following standards are noted in the materials as “Studied in a 4th year course”: N-CN.3-6; A-REI.9; F-BF.4b,4d,5; F-TF.3,4; and S-MD.1-5b.

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: 09/23/2016

Report Edition: 2015

Title ISBN Edition Publisher Year
9780133281149
9780133281156
9780133281163
9780133281170
9780133281187
9780133281200
9780133281224
9780133281248
9780133281255

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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