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.

Examples of how standards were fully met in the materials:

• A-REI.6. Modules 11 and 12 in Algebra 1 include ample opportunities for students to solve linear systems exactly and approximately using various methods. In these modules, students solve systems of linear equations with numerous algebraic and graphical techniques as specified in the standard.
• F-IF.A. The use of function notation and the underlying concepts as specified by the standards in this cluster can be found abundantly throughout the materials. Specifically, lessons 3.2, 3.3, 3.4, and 4.1 in Algebra 1 focus on domain, range, function notation, and recognizing sequences as functions that can be defined recursively. Moreover, the use of function notation as specified by these standards can be found throughout the Algebra 2 materials.
• G-CO. The materials do an excellent job of attending to the entirety of all of the standards in this domain. Students are required throughout the Geometry coursework to experiment with transformations in the plane, understand congruence in terms of rigid motions, prove geometric theorems, and make geometric constructions. Notably, the materials thoroughly focus on congruency and similarity in terms of transformational geometry. For example, modules 2 and 3 in the Geometry coursework continually require students to use rigid transformations to look at congruency. Lesson 3.2 is appropriately titled “Proving Figures are Congruent Using Rigid Motions.”

The following standards were not fully met: N-RN.3, A-SSE.3, A-REI.2, A-REI.10, F-IF.9, and S-ID.4.

• N-RN.3. In lesson 14.2 of the Algebra 1 materials, students will look at the properties of rational and irrational numbers. In this lesson, students will determine whether sums and products of numbers are rational or irrational as well as prove that rational numbers are closed under addition and multiplication. However, there was no evidence that students are required to explain that the product of a nonzero rational number and an irrational number is irrational.
• A-SSE.3. Students factor and complete the square in order to rewrite quadratic expressions throughout the Algebra 1 and 2 materials (e.g., Algebra 1, lessons 20.2, 21.3, and 22.2; Algebra 2 lessons 3.1, 3.3 and 6.4). However, this 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. That is, students were directed to produce specific forms without opportunity for student choice. For example, Algebra 1, lesson 22.2, student exercises 17-18 (TE, page 1055) ask students to “rewrite the equation into vertex form, and solve the problem.”
  
• A-REI.2. The materials require students to solve simple rational and radical equations in one variable, yet evidence was not found where students are required to give examples showing how extraneous solutions may arise. Algebra 2, lessons 9.3 and 11.3 work with rational and radical equations that give rise to extraneous solutions. Although students regularly check for extraneous solutions, evidence was not found to show students are required to explain how, why, and when extraneous solutions may arise.
• A-REI.10. Lessons 6.1, 6.2, and 6.3 in Algebra 1 are noted by the publisher to address A-REI.10. However, no evidence was found that any of these lessons attend to A-REI.10. The Geometry and Algebra 2 materials do not specify any lessons dealing with A-REI.10, and evidence was not found that the materials address this standard. While looking for other potential occurrences, lesson 5.1 in Algebra 1 was found to require students to regularly “make a table, plot the points, and then connect the points.” However, students are not required to explain or indicate how they understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Students are asked in question #11 (TE, page 205) “What is a solution of a linear equation in two variables?” yet they are not required to explain how this relates to the entirety of the set of all solutions or how the solution relates to the graph of the equation.
• F-IF.9. Lesson 6.5 in Algebra 1 requires students to compare the properties of two linear functions represented in different ways, yet evidence students were required to do this with other function types was not found. Notably, there was no evidence found that students are required to compare properties of two quadratic or two exponential functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
• S-ID.4. Lessons 22.2, 23.2, and 23.3 in Algebra 2 require students to look at mean and standard deviation, determine when data sets appear to be normally distributed, calculate the percentage of data occurring within a given standard deviation from the mean, and estimate population percentages by using normal distribution curves. However, evidence was not found that students are required to recognize that there are data sets for which it is not appropriate to use a fitted normal distribution curve to estimate population percentages.

The materials partially meet the expectation for providing students with opportunities to work with all high school standards without distracting students with prerequisite or additional topics. The materials, when used as designed, allow students to fully learn most, but not all, standards.

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.3. Lesson 14.2 of Algebra 1 requires students to determine if products and sums of numbers will result in rational and irrational numbers. Students also discuss whether the product of two rational numbers will yield an irrational number. Students also discuss closure of number systems under various operations. However, students rarely work with the product of a nonzero rational number and an irrational number.
• A-SSE.1. Lesson 2.1 of the Algebra 1 materials provides opportunity for students to both identify and interpret components of expressions. Beyond this single lesson, however, the authors rarely call out further opportunities for students to interpret expressions in context. Later lessons in the Algebra 1 materials, including 14.2 and 17.1, are identified by the authors as supporting this standard, yet they do not provide opportunities for students to interpret structure in terms of a context. For example, section 14.2 of Algebra 1 has students rewriting radicals but does not attend to the full measure of the standard by interpreting structure in context.
• G.CO.13. Students work on this standard only in lesson 6.1 in Geometry. Students are directed on how to construct these polygons in a circle, yet they are not given opportunities to practice.
• A.APR.3. Lesson 20.2 in Algebra 1 requires students to graph a quadratic function and each of its linear factors in the four problems on TE, page 957. Throughout the Algebra 1 and 2 courses, students graph and factor polynomials. Students thoroughly practice finding zeros of polynomials, writing them in factored form and matching roots with factored forms of polynomials. In lesson 5.2 of Algebra 2, students are given factored forms of polynomials to sketch graphs by finding zeros. However, students are not required to factor polynomials in order to identify zeros and then create graphs.
• F-IF.8.B. The only example found that would give support for F-IF.8.B alignment would be item 16 on TE, page 665 in the Algebra 2 materials where students are asked to “Use the properties of exponents to show why the function f(x) = 2^-x is an exponential decay function.” Typically though, students are not required to use the properties of exponents to interpret expressions for exponential functions. In contextual situations, students will be given formulas they are specified to use (e.g., example 3, TE, page 658, which states “Given the description of the decay terms, write the exponential function in the form f(t) = a(1 – r)^t and graph it with a graphing calculator”) without any need to write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Materials partially foster coherence through meaningful connections in a single course and throughout the series, where appropriate and where required by the standards.

Throughout the series, lessons within modules regularly build upon the work of previous lessons. For example, Algebra 1 module 17 progresses from the nomenclature of polynomials to adding and subtracting polynomials.

However, connections between and across multiple standards are rarely made in meaningful ways to support understanding of multiple standards at the same time. Modules typically contain 2-4 lessons with a sharp focus on specific standards or parts of standards. Rarely do the materials look at multiple standards at the same time in order to foster deep connections. Namely, the materials lack problems and activities that serve to connect two or more clusters in a domain, two or more domains in a category, or two or more categories, in cases where these connections are natural and important.

For example, module 14 in Algebra 1 looks at rational exponents and radicals. Although the next module focuses on geometric sequences and exponential functions, module 14 requires students to work on simplifying and evaluating expressions without making meaningful connections to standards outside of N-RN.A.

The Geometry standards are called out explicitly in only the Geometry materials. Nowhere in the Algebra 1 or Algebra 2 materials are there any explicit indications that students are working with Geometry standards. Similarly, the Geometry materials never explicitly call out any standards from the Number and Quantity, Algebra, or Functions conceptual categories. Even though connections are being made or could be made, the materials do not make the connections clear to teachers or students. Calling out the connections between standards to students and teachers would foster coherence throughout the series.

Additionally, Algebra 2 lessons 19.1-21.2 exactly duplicate Geometry lessons 21.1-23.2. These three modules, nine lessons in total, differ only in page and lesson numbers.