The instructional materials reviewed for the Glencoe Traditional series do not meet the expectation for attending to the full intent of the modeling process when applied to the modeling standards. All of the modeling standards were reviewed for evidence of the modeling process. While there are examples of the use of tangible models, real-world situations, tables, equations, expressions, and graphical representations, there is no evidence of students making sense of a real-world situation to (1) identify essential aspects, (2) interpret and represent the situation mathematically, (3) manipulate the model, and then (4) analyze the quantitative information in terms of the original situation. Students are told the modeling tool or representation to use for many of the situations. Although students do manipulate the model, they are not asked to analyze the results within the context of the situation represented to determine if the model is appropriate. Listed below are examples with components of the modeling process that are attended to and places where the modeling process fell short:

• G-SRT.8: There are application problems for this modeling standard, but there are limited opportunities for students to explore problems using multiple pathways or to think creatively or "formulate" their own strategy to solve. Also, problems frequently bypassed the modeling process by providing clearly drawn and labeled pictures or listing examples that students could reference. Section 8-3 in Geometry lists problem 3 on page 550 and problem 43 on page 553 as modeling for standard G-SRT.8, but these are not fully modeling because they are extensively scaffolded.
• Problem 26 on page 563 is a modeling question, except the material directs the students to an example problem that directs them through the process. Problem 56 on page 575 could match the modeling standard G-MG.3 (though there is no CCSSM stated) and is close to the full modeling (involving units) process, but a picture is provided requiring no creative thinking.
• Lab 11-2 in Geometry for G-MG.2, regarding density, provides examples and asks students to repeat the shown process in an applied situation, but the lab does not attend to the full modeling process. Problem 3 on page 796 is another example for this standard, and does not engage students in the modeling process because the exact steps are given in activity two and leaves little room for students to find multiple approaches to solve the problem.
• Algebra 1 and 2 have data labs (Algebra 1: 2-6; Algebra 2: 4-8, 7-8) that have the potential to engage students in the modeling process. Students collect data using graphing calculators, but they do not solve any type of problem. They are looking at a pattern of data. They do have to answer some interpreting questions, but the students do not have to formulate anything as the book walks them through the data collection and equation-creating processes.
• The activity of finding the limit of a geometric sequence in Extend 10-4 for standard A-SSE.4 in the Algebra 2 book could be adapted for modeling, but the materials give too much information to allow students to fully engage in the modeling process.
• Frequently, there are examples directly next to the student exercises that show students exactly how to work through the problem. One example is problem 9 on page 36 of Algebra 2, which is labeled as a CCSS modeling problem using writing and solving an inequality. Example 4 is listed next to the problem, directing students to follow the completed process made available in this example.
• A-REI.11: There was no evidence of modeling found to support this modeling standard of the CCSSM.
• The “formulate” part of modeling is consistently lacking in the materials. The CCSSM states that students should be formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables. There was limited evidence found that students had to come up with a strategy to solve an open-ended problem with multiple solution paths or were required to formulate a process for solving any problems or work through the modeling process on their own.
• The Interactive Student Guide attempts to provide more modeling problems, but the problems do not attend to the full modeling process as they are either application problems or heavily scaffolded problems.
  • Problem 4 on page 367 of the Geometry Interactive Student Guide addresses standard G-MG.2, but it is an application problem rather than a modeling problem.
  • The amusement park problem on page 396 of the Algebra 2 Interactive Student Guide gives the model, and though the model is a very complicated trigonometric function with lots of reading, the problem is scaffolded to provide information that doesn't allow the student to experience the modeling process.

The instructional materials reviewed for the Glencoe Traditional series do not meet the expectation that students are provided with opportunities to work with all non-plus standards and do not distract students with prerequisite or additional topics. Lessons were examined for evidence that, when used as designed, they would enable all students to fully learn each standard. There are many standards where students are not given an opportunity to fully learn all aspects of the standard. In addition, many standards are only taught in the Interactive Student Guide, which provides no guidance on its appropriate use. Listed below are standards that are not fully taught in the series and standards that are primarily found in the interactive student guide.

• A-APR.4: There was one example of proving polynomial identities in Algebra 2 on page 350. There were a few examples using a calculator, but there is not enough practice for students to fully meet the depth of this standard.
• N-Q.1: Choosing and interpreting units consistently in formulas is found in Section 2.7 of the Algebra 1 Interactive Student Guide.
• G-CO.3: Example 3 on page 656 asks students to describe a single transformation that maps a figure onto itself after copying and reflecting the figure; however, there was no evidence found to describe the rotations and reflections that carry a polygon onto itself.
• G-CO.12: When formal geometric constructions are addressed, the materials provide students with the opportunity to practice each construction at most two times. For instance, the Extend Lab 1-5 shows students the steps to construct perpendicular lines two different ways using a compass and straightedge, then has the students practice each construction once. Even though there are several sections within the Geometry material where students work with perpendicular lines (including Chapter 3 on parallel and perpendicular lines), the students are not required to construct perpendicular lines.
• G-SRT.4: The proof on page 547 of the geometry material uses geometric mean instead of similar triangles to prove the Pythagorean theorem as referred to in the standard.
• G-C.2: Angles, radii and chords are defined in the geometry materials, but there was no evidence found of describing the relationships among inscribed angles, radii and chords as the standard states.
• G-GPE.6: There were some opportunities for students to develop an understanding of midpoint, but not of any other points on a directed line segment that partitions the segment in a given ratio that is not 1:1. Problem 69 on page 34 of the geometry material does offer some understanding of partitioning in thirds, but there was no other evidence of partitioning other than halfway.
• G-GPE.7: Perimeters of triangles and squares are found, but are not generalized to polygons to go beyond the middle school standards.
• G-GMD.1: Informal arguments of the area and volume formulas are not explicit for each aspect of this standard, especially with regard to informal limit arguments.
• S-ID.7: There is brief reference to the the meaning of the slope in context, but there are no exercises that ask students to interpret the slope in terms of the context of the data.
• S-ID.8: There is no evidence of interpreting the correlation coefficient.
• S-CP.6: There was only one problem that fully met the "interpret" part of this standard, and that was problem 6 on page 955 in the Extend 13-5 of the Geometry text.
• In Algebra 1, many standards, including N-Q.2, N-Q.3, A-SSE.3c, A-REI.7, S-ID.5, and S-ID.9, are not addressed and only appear in the Extend lessons, which does not provide students with extensive opportunity to work with those non-plus standards. For example, the N-Q.2 standard appears in the Extend 2-6 for Algebra 1, which only contains four exercises, and only one of the exercises has students defining an appropriate quantity for a modeling purpose.

Additionally, there are several standards for which evidence was found in the supplemental Interactive Student Guide, but either not in the student textbook or minimally in the student textbook. Using only the textbook would cause all of these standards to not be fully developed. There is no teacher guidance or correlation documents to help interpret and know how and when to use the Interactive Student Guide. Some of these standards include:

• A-APR.1: Understanding that polynomials are closed under multiplication was found in section 5.1 of the Interactive Student Guide of Algebra 2.
• A-REI.4b: The Algebra 2 Interactive Student Guide, section 4.6, has exercises that asks students to recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
• G-CO.2: Evidence of comparing transformations that preserve distances and angles to those that do not is not explicitly taught. The concept is there, but it is not explicit in the material but is addressed briefly in the Interactive Student Guide throughout Chapter 1.
• G-C.5: The Geometry Interactive Student Guide includes this standard in lesson 9 - 2.
• G-SRT.7: There are many examples that allow students to engage fully in using the relationship between the sine and cosine of complementary angles; however, problem 64 on page 576 of the materials was the only evidence of asking students to explain the relationship between the sine and cosine of complementary angles, and this one opportunity does not lead students to fully learn this standard. In the Interactive Student Guide, there was a multi-part investigation plus three exercises to further develop the idea.
• G-MG.1: This was taught minimally in the materials and covered a little more in detail on pages 364-366 of the Geometry Interactive Student Guide.
• S-ID.3: Interpreting is addressed in problem 10c of lesson 12-3 in the Algebra 1 material. Additionally there are a few problems in Chapter 12 of the Interactive Student Guide. The problems in the Interactive Student Guide use standard deviations to interpret the differences whereas the standard asks to use shape, center and spread.
• S-ID.4: Recognizing that there are data sets for which such a procedure of fitting a data set to a normal distribution is not appropriate was found only in the Algebra 2 Interactive Student Guide in section 9.7 which states to use after section 11-5 in the textbook.
• S-IC.2: There were a few problems in the Algebra 2 Interactive Student Guide on page 318 that allowed students to experience deciding if a specific model is consistent with results from a given data-generating process; however, more problems are needed to fully develop this standard.
• S-IC.3: The Algebra 2 Interactive Student Guide provides evidence of the aspect of identifying the characteristics of different study types for this standard in section 9.1, which states to use after 11-1 in the textbook. Recognizing the purposes of each of these study types is not explicitly taught, nor is explaining how randomization relates to each of these study types.
• S-IC.4: The Algebra 2 Interactive Student Guide has problems that use the maximum error of estimate to find a confidence interval to estimate a population parameter from a random sample and develops a margin of error in section 9.8 to be used after 11-6 in the textbook.
• S-IC.5: The Algebra 2 Interactive Student Guide has two problems in section 9.1 that compare two treatments. This section states to use this lesson after 11-1 in the textbook.
• S-ID.5: There were only a couple of problems in section 11-5 of the Algebra 2 Interactive Student Guide, and this standard needs more problems for students to master the standard from the aspect of possible associations in the data.
• S-ID.9: There is one example and five total problems for this standard (correlation and causation) in an extend section (4.5 extend on page 254) in Algebra 1. In Algebra 2 there are seven questions in an Algebra lab on page 99. Both of these sections are at the end of the chapter tied to optional extend/lab/explore sections.
• F-LE.3: There was only one problem in the Interactive Student Guide of Algebra 1 in section 10.7 that allowed students an opportunity to observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as a polynomial function. Students need more practice to master this standard.
• F-TF.8: The Algebra 2 Interactive Student Guide includes some conceptual development and the proof of the Pythagorean identify in Section 10.7, which is stated as being used after section 13.1 and 13.2 of the textbook.

The instructional materials reviewed for the Glencoe Traditional series do not meet the expectations that the materials explicitly identify and build on knowledge from Grades 6-8 to the High School Standards. Overall, the materials include Grade 6 - 8 standards; however, they are not identified as such.

• The online materials more clearly identify Grade 8 concepts than the print materials do. Although they indicate topics from Grade 8, they do not clearly identify the standards. There was no evidence of connections being made and/or articulated between the middle school and high school standards. The Grade 8 material is presented, but there is no evidence of how it is extended or built upon to develop high school standards.
• There is no building on knowledge of Geometry from the Grade 8 CCSSM for students and teachers. For example, the standard G-CO.7 is in the cluster "Understand congruence in terms of rigid motions." There is evidence of the converse of this, but there was no evidence found of explicitly using rigid transformations. Students learn the definition of congruence through corresponding parts and not through rigid transformations.
• Other than Chapter 0, any indication of teaching standards from Grades 6-8 is not labeled. All lessons indicate that they align to one or more non-plus standards even if the content in the lesson does not meet the standard indicated. While Chapter 0 in the materials is labeled clearly as containing topics from previous courses, the only standards indicated, if indicated at all, in the Chapter 0 lessons are the Mathematical Practice Standards and the plus standards.
• In Algebra 1 lessons 1.2 on order of operations, 1.4 on distributive property, 2.6 on ratios and proportions, and 7.4 on scientific notation all align to middle school standards; moreover, the problems are mostly routine and neither the rigor nor the depth approach high school standards.