Alignment: Overall Summary

The instructional materials reviewed for the CORD 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: spending a majority of time on the widely applicable prerequisites from the CCSSM, allowing students to fully learn each non-plus standard, engaging students in mathematics at a level of sophistication appropriate to high school, and making connections within courses and across the series. Since the materials do 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
5
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).
5/18
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Criterion Rating Details

The instructional materials reviewed for the CORD Traditional series do not meet the expectation for focusing on the non-plus standards of the CCSSM and exhibiting coherence consistent with a logical structure of mathematics. Overall, the instructional materials partially attend to spending a majority of time on the widely-applicable prerequisites from the CCSSM, allowing students to fully learn each non-plus standard, engaging students in mathematics at a level of sophistication appropriate to high school, and making connections within courses and across the series. The materials do not attend to the full intent of the non-plus standards, the full intent of the modeling process when applied to the modeling standards, or explicitly identifying standards from Grades 6-8 and building on them to the High School Standards.

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
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Indicator Rating Details

The instructional materials reviewed for the CORD Traditional series do not meet the expectations for attending to the full intent of the mathematical content contained in the High School Standards for all students. The instructional materials include many instances where aspects of the non-plus standards are partially or not addressed across the series.

The following are standards that are partially addressed across the series:

  • N-RN.1: In Algebra 1, Lesson 7.2, the Laws of Exponents for monomials are addressed for positive integer exponents, but the properties are not extended to rational exponents. Algebra 2, Lesson 2.3, page 72 shows rational exponents, but no explanation is provided of how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
  • N-RN.3: In Algebra 1, Lesson 1.4, the materials do not contain an explanation that the sum of a rational number and an irrational number is irrational and that the product of a nonzero rational number and an irrational number is irrational.
  • A-SSE.4: In Algebra 2, Lesson 9.3, students use the formula for the sum of a finite geometric series. Evidence was not found where the materials derive the formula for the sum of a finite geometric series.
  • A-APR.1: In Algebra 2, Lesson 6.1, the materials address that polynomials are closed under addition and subtraction, but closure under multiplication is not addressed. Furthermore, there is no connection to the system of integers.
  • A-REI.3: Throughout Algebra 1, Chapters 2 and 3, students solve equations and inequalities in one variable. Evidence was not found where the materials solve equations when the coefficients are unknowns.
  • F-TF.5: In Algebra 2, Chapter 10, Math Lab Activity 3, "Swing of a Pendulum" Question 6, students choose the trigonometric function, and in Lesson 10.4, Problem 25 students match a sinusoidal function to a situation. However, the materials do not choose trigonometric functions to model periodic phenomena with specified midlines.
  • S-IC.1: In Algebra 1, Chapter 4, Math Lab Activity 1, students make probability calculations about a population. Algebra 2, Lesson 11.3 discusses populations, bias, and how to design a study. No evidence was found in either course on understanding statistics as a process for making inferences about population parameters based on a random sample from that population.
  • S-CP.2: In Geometry, Lesson 12.3, Chalkboard Examples, students identify events as independent or dependent, but the materials do not characterize two events as independent based on finding the product of the probabilities of the two events.
  • S-CP.3: Geometry, Lesson 11.6 defines conditional probability, and in Lesson 12.4 students find the probability of a conditional event. The materials do not contain an interpretation of the independence of A and B as the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
  • S-CP.4: In Algebra 1, Lesson 11.6, students construct two-way frequency tables and use them to compute answers for conditional probabilities of events. In Geometry, Lesson 12.7, Activity 1, students use a two-way frequency table to answer what relief pitcher should be used if the next batter is a right/left handed hitter. The materials do not use a two-way table to decide if events are independent.

The following are standards that are not addressed across the courses of the series. The lessons listed are indicated by the materials as addressing the standards. However, these lessons do not address the standard cited, and no other evidence was found in the remainder of the materials where these standards are addressed.

  • A-SSE.3c: In Algebra 2, Lesson 5.1, students evaluate exponential functions, but the materials do not transform exponential functions or demonstrate how to transform.
  • A-REI.11: In Algebra 1, Lesson 6.1, students solve equations where both functions are the same type. The materials do not contain an explanation 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). Other than a linear-quadratic system, the materials do not contain mixed-type systems of equations with graphs, tables, etc. Throughout the series, approximation of solutions is not addressed. The materials do not include cases where f(x) and/or g(x) are polynomial, rational, absolute value, exponential, or logarithmic functions.
  • F-IF.6: In Algebra 1, Lesson 4.2, students calculate constant rates of change from two endpoints or the graph of a line. The materials do not contain calculations or interpretations of average rate of change for non-linear functions presented by any representation over a specified interval, and the materials do not contain estimations of the rate of change from a graph.
  • F-BF.1b: In Algebra 2, Lesson 3.2, students combine functions using addition and subtraction. However, the functions are linear, so the function type does not vary. Combining functions with multiplication and division is not addressed.
  • F-LE.3: Algebra 1, Lesson 9.5 provides examples of graphs and tables involving exponential growth and decay. However, the materials do not contain comparisons of linear, quadratic, polynomial, and exponential growth in a table or graph to observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Although the series includes comparisons of exponential functions with different bases in Algebra 1, Chapter 9, Applications, Problem 9.9, in the end behavior of polynomial functions in Algebra 2, Lesson 6.4, there is no evidence that the materials include comparisons of the end behavior of different types of functions.
  • G-SRT.1a: Evidence was not found regarding dilations taking a line not passing through the center of the dilation to a parallel line.
  • G-SRT.2: Geometry, Lessons 6.2 and 6.3 contain an explanation of similarity using corresponding angles that are congruent and corresponding sides that are proportional instead of in terms of similarity transformations.
  • G-C.3: The materials do not contain a construction of the inscribed and circumscribed circles of a triangle, and the materials do not include a proof of properties of angles for a quadrilateral inscribed in a circle.
  • G-GPE.6: The materials do not address finding a point of a directed line segment between two given points that partition the segment in a given ratio.
  • S-ID.2: Evidence was not found where comparisons are made across different datasets for center and spread.
  • S-ID.6b: The materials do not include informally assessing the fit of a function by plotting and analyzing residuals. Residuals are not addressed in this series.
  • S-IC.2: The materials do not contain a determination of whether or not a model is consistent with a data-generating process. Simulation is not used in conjunction with the distribution of the sampling statistics.
  • S-IC.4: The materials do not include an estimation of population mean or calculation of a margin of error. Students find the population proportion indirectly through probability, but they do not distinguish between sample proportion and population proportion.
  • S-IC.5: In Algebra 2, Lesson 11.4, the materials contain a simulation that was used to estimate probabilities rather than to compare differences in parameters.
  • S-IC.6: There were no opportunities for evaluating reports based on data.
  • S-CP.5: In Geometry, Lesson 12.4, the materials do not contain an explanation of the concepts of conditional probability and independence in everyday language and everyday situations.

Indicator 1a.ii

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

The instructional materials reviewed for the CORD Traditional series do not meet the expectations for attending to the full intent of the modeling process when applied to the modeling standards. The series shows the intention to incorporate aspects of the modeling process within each chapter; however, the majority of the problems lack the incorporation of the full modeling process as described in the CCSSM.

Aspects of the modeling process that are lacking throughout the series include: interpreting results of the mathematics in terms of the original situation, validating conclusions by comparing them with the situation, and either improving the model or, if it is acceptable, reporting on the conclusions and the reasoning behind them. Students do not make decisions about problems that would lead to a modeling scenario. Students apply and analyze given problems and scenarios but only after units, equations, methods, procedures, and other parameters are defined for them. Students do not make choices on which model to use, assumptions, and approximations throughout this series.

While the materials present opportunities for students to engage in a part of the modeling process, scaffolded procedures and given information on variables, representations, and tools limit students full engagement with the modeling process. For example:

  • In Algebra 1, Chapter 2, Math Lab Activity 2, Marching in a Band, students collect data to determine a unit rate of step marching then use that rate to predict the amount of time it would take to march a certain distance and predict the distance marched in a given time. Students follow a 10-step procedure that leads them directly to the solution.
  • In Algebra 2, Chapter 8, Math Lab Activity 1, Work Efficiency, students determine the optimum number of 2-inch squares and 2-inch circles that can be drawn and cut out in a given time period. The 6-step procedure includes how students should arrive at a solution: record time as a rate in seconds, use given variables to represent what quantities, and write an equation for the number of squares and circles that can be drawn in 5 minutes and cut out in 2 minutes. Students use their equations to find a solution.
  • In Algebra 1, Chapter 2, Math Apps Problem 7, students find the cost associated with renting a car while going on vacation in Paris. Students are given the variables and how to change the equation in order to isolate a variable and find the solution. Students compare one rental company that charges per mile and one that charges per week to determine when the number of miles Zach could drive is the same as the cost of renting a car for a week.
  • In Geometry, Chapter 11, Math Apps Problem 7, students use a diagram of an elevated grain storage bin to determine the total weight to be supported by each post in order to make sure the bin is safely constructed. Students are given the weight in lbs/sq foot of the material that will be used, the conversion for cubic feet to bushels, the weight for each bushel, and the process to calculate the surface area of the bin. Questions are scaffolded, for example, as in finding the weight of the empty bin. Students follow this prescribed sequence of steps given in the problem rather than making their own assumptions, choosing their own model, and evaluating the effectiveness of the model.

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
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Indicator Rating Details

The instructional materials reviewed for the CORD Traditional series, when used as designed, partially meet expectations for spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers. Overall, the materials spend a majority of the time on non-plus standards from CCSSM. However, the instructional materials do not spend a majority of time on the WAPs, and some of the remaining materials address prerequisite or additional topics that are distracting.

Examples where students are distracted from the WAPs by engaging in prerequisite materials from earlier grades include:

  • In Algebra 1, Chapter 1, the majority of the lessons (according to the provided pacing guide) address the real number system, operations with real numbers, absolute value, expressions and equations, and unit analysis. These lessons align with standards from Grades 6-8.
  • In Algebra 1, Chapter 2, the majority of the lessons address properties of addition, subtraction, multiplication and division, and solving proportions and percent equations, multi-step equations, and equations with variables on both sides. These lessons align with standards from Grades 6-8.
  • Algebra 1, Lesson 3.1 addresses solving inequalities that align to 6.EE.8 and 7.EE.4b.
  • Algebra 1, Lessons 7.2 and 7.3 address the properties of exponents for simplifying expressions and simplifying expressions containing zero and/or negative exponents which align to 8.EE.1.
  • In Algebra 1, Chapter 11, the majority of the lessons address: finding mode, median, and mean of a set of data; determining which measure of central tendency best describes a data set; organizing data into a frequency distribution and histograms; creating and interpreting dot plots and boxplots; calculating measures of dispersion; and creating and interpreting two-way frequency tables. Measures of center and displaying numerical data in plots align with 6.SP.4,5.
  • Geometry, Lesson 1.1 addresses drawing points, lines, line segments and rays which aligns with 4.G.1, and Lessons 1.2 and 1.3 address measuring line segments and angles using a protractor with all measures in whole-number degrees which align to 4.MD.6.
  • Geometry, Lessons 9.1, 9.2, 9.3, and 9.5 address areas of squares, rectangles, irregular figures, parallelograms, triangles, rhombuses, trapezoids, and the circumference and area of circles which align to 6.G.1,3 and 7.G.4.

Examples where students are distracted from the WAPs by engaging in topics outside the CCSSM include:

  • Geometry, Lessons 2.1 through 2.5 address patterns, inductive reasoning, deductive reasoning, converse, inverse, contrapositive, valid arguments, and types of proofs. These lessons are not aligned to any standards from CCSSM.
  • Geometry, Lesson 3.2 addresses vectors on a coordinate plane which aligns to plus standards, N-VM.A.
  • Geometry, Lesson 4.6 addresses tessellations which does not align to any standards from CCSSM.
  • Geometry, Lesson 11.2 addresses perspective drawing which does not align to any standards from CCSSM.
  • Algebra 2, Lesson 10.6 addresses the secant, cosecant, and cotangent reciprocal identities, and Lesson 8 addresses double-angle and half-angle identities. These identities are not aligned to any standards from CCSSM.
  • Algebra 2, Lesson 12.1 addresses distance and midpoint formulas, and Lesson 2 addresses general conic sections. These topics do not align to any standards from CCSSM.

Indicator 1b.ii

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

The instructional materials reviewed for the CORD Traditional series partially meet expectations, when used as designed, for letting students fully learn each non-plus standard. Overall, students are frequently not given the opportunity to develop their own definitions, and where the standards expect students to prove or develop a concept, the materials often provide students the information.

The following are some examples of how the series instructional materials, when used as designed, do not enable students to fully learn some of the non-plus standards. (Those standards that were not attended to by the materials, as noted in indicator 1ai, are not mentioned here):

  • N-Q.1: In Algebra 1, Lessons 11.2, 11.4, and 11.5, students do not choose and interpret the scale and the origin in graphs and data displays; rather, students are provided with pre-labeled tables or graphs with pre-determined scales making the quantities that they represent obvious to the student.
  • N-Q.3: In Algebra 1, Lessons 1.7, 1.8, and Math Labs, students have few opportunities to choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
  • A-REI.5: In Algebra 1, Lessons 6.4 and 6.5, students solve systems of linear equations, but students do not have the opportunity, in this chapter or the rest of the materials, to prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
  • F-IF.3: In Algebra 1, Lesson 5.6 and Lesson 9.7, students write explicit and recursive functions for sequences, but students do not recognize that the domain of a sequence is a subset of the integers.
  • F-IF.7b: In Algebra 1, Lessons 5.1-5.5 and 8.2 and Algebra 2, Lessons 3.1-3.5, 5.1-5.2, 7.4, 10.2-10.4, students graph square root and piecewise-defined functions but do not have an opportunity to graph cube root functions in the materials.
  • F-IF.8b: Students use exponential functions to solve problems, but students do not interpret the relationship between the growth and decay factor and the exponent in the function. Students do not use the properties of exponents to write equivalent exponential expressions with different growth/decay factors.
  • F-LE.1a: In Algebra 1, Lesson 9.6, students read that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals, but there are no opportunities for students to prove these things on their own.
  • G-CO.6: Geometry, Lesson 5.4 states two triangles are congruent if one triangle can be carried onto the other triangle by a rigid motion. There are limited opportunities for students to use geometric descriptions of rigid motions to transform figures and predict the effect of a given rigid motion on a given figure.
  • G-CO.7: Geometry, Lesson 5.4, Activity 1, Identifying Congruent Triangles uses the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding sides and corresponding pairs of angles are congruent. However, there are no opportunities for students to use the definition of congruence in terms of rigid motions to show that two triangles are congruent.
  • G-CO.8: In Geometry, Lesson 5.5, students are given the criteria for triangle congruence and to identify the triangle congruence; however, there is no opportunity for students to explain how the criteria follow from the definition of congruence in terms of rigid motions.
  • G-CO.9,10: In Geometry, Lessons 2.7, 2.8, 5.1-5.8, 6.2, and 6.3, many of the proofs listed in these standards are completed in the examples. There are no opportunities for students to prove the theorems or demonstrate that they understand how to complete the proofs given.
  • G-CO.12: Students are given opportunities to create the constructions listed within this standard; however, all constructions are created using a compass and straightedge. No other tools or methods, such as using string, reflective devices, paper folding, dynamic geometric software, etc., are used.
  • G-SRT.1b: In Geometry, Lesson 4.7, students are provided one example and one activity to verify experimentally the dilation of a line segment being longer or shorter. There are no other opportunities in the materials for students to develop their knowledge of this standard.
  • G-SRT.6: In Geometry, Lesson 7.4, students are given several opportunities to work with tangent ratios. Lesson 7.5 defines the sine and cosine ratios, but students do not have an opportunity to use similar triangles to understand that the sine and cosine ratios are properties of the acute angles in the right triangle.
  • G-SRT.7: In Geometry, Lesson 7.5, students are given the relationship between sine and cosine. In Problem 24a, students prove sin A = cos(90 - m∠A). This standard is not revisited for practice or application in the remainder of the materials.
  • G-C.1: In Geometry, Chapter 10, Math Lab 1, Activity 1, students use step-by-step procedures to determine that all circles are similar by showing that the ratios of the lengths of the circumferences to the lengths of the radii are proportional. Students do not formally prove that all circles are similar.
  • G-C.5: In Geometry, Lesson 10.3, students are given a description of arc length and a procedure to calculate it, but similarity is not addressed. In Problem 4, students explain how to find the area of a sector of a circle, but students are not required to derive the formula. In Algebra 2, Lesson 10.2, students have no opportunities to discover or define radian.
  • G-GPE.1: In Geometry, Lesson 10.1, students use the distance formula to derive the equation of a circle given center and radius. Students have no opportunities to find connections between the Pythagorean Theorem and the distance formula.
  • G-GPE.5: Students make a conjecture about slopes for parallel and perpendicular lines, but they do not prove the criteria as addressed in the standard.
  • G-GMD.4: In Geometry, Lesson 11.10, students identify the two-dimensional cross sections of various three dimensional objects. In Activity 2, students rotate a line at a 30 degree angle around a vertical line to create a three-dimensional object. There are no other opportunities for students to generate three-dimensional objects from rotations of two-dimensional objects.
  • S-ID.4: In Algebra 2, Lesson 11.5, students are given limited opportunity to use tables and no opportunities to use spreadsheets to estimate areas under the normal curve as described in the standard.
  • S-ID.6a: In Algebra 1, Lesson 4.8, students calculate least squares regression lines and use the lines to solve problems in the context of given data. Students are not given opportunities to fit quadratic or exponential functions to a set of data and use those functions to solve problems in the context of given data.
  • S-ID.7: In Algebra 1, Chapter 4, students identify but do not interpret the slope of a linear model in the context of the data. In Math Applications, Problem 9a, students state the slope of the graph but do not interpret it. In Problem 11b and c, students state the slope but do not interpret it, and they do interpret the y-intercept.
  • S-CP.6: In Geometry, Lesson 12.4, students find the conditional probability as a ratio of probabilities. Evidence was not found where students are required to interpret a conditional probability in terms of the given model.
  • S-CP.7: In Geometry, Lessons 12.2 and 12.4, students apply the Addition Rule in multiple problems. However, evidence was not found where students are required to interpret the answer in terms of the given models.

Indicator 1c

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

The instructional materials reviewed for the CORD Traditional series partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age-appropriate contexts. Materials do not always vary the types of real numbers being used, and some of the key takeaways from Grades 6-8 are not applied.

Each chapter has one section called MathLab which contains problems that engage learners in the mathematics through contexts where students take measurements and/or interpret data given a set of constraints. Contexts include a variety of different levels of interests:

  • Algebra 1, Chapter 1, Math Lab 1: Comparing Pulse Rates
  • Algebra 1, Chapter 5, Math Lab 1: Price and Size of Pizza
  • Geometry, Chapter 3, Math Lab 1: Two-Dimensional Coordinates with Stairs
  • Geometry, Chapter 6, Math Lab, Activity 1: Indirect Measurement of Height
  • Algebra 2, Chapter 3, Math Lab 1: Calculating the Value of a Used Car
  • Algebra 2, Chapter 8, Math Lab 2: Man Your Battle Stations

The instructional materials do not vary the types of real numbers being used. For example:

  • Algebra 1, Lessons 6.3 and 6.4 address solving systems of equations, and the practice problems for solving by substitution use whole number coefficients. Within Lesson 6.3, all of the solutions are integers. Within Lesson 6.4, the coefficients of the practice and problem-solving questions are integers; there is one fractional solution, but there are some decimal solutions on the extra practice worksheet.
  • In Algebra 1, Chapter 7, the coefficients in polynomials are mostly integers between -10 and 10.
  • In Geometry, Chapters 9 and 11, the majority of the given dimensions that students use to find the area, surface area, and volume of two- and three-dimensional shapes are positive integers.
  • In Algebra 2, Chapter 1, almost all of the solutions to the equations are integers.

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

  • In Algebra 1, Lesson 6.1, students are given step-by-step instructions to solve a system of equations (8.EE.8) by graphing and creating a table. The materials do not have students apply this key takeaway from Grades 6-8 within the materials.
  • In Algebra 1, Chapter 11, examples show how to create histograms, box plots, and dot plots and to calculate measures of center (6.SP.B) without applying key takeaways from Statistics and Probability in Grades 6-8.
  • In Geometry, Lesson 3.1, students find a point on a directed line segment which divides the segment by a given ratio. The materials give the formula for finding the midpoint of a segment, but students do not apply the key takeaway from ratios and proportional relationships in Grades 6 and 7 (6.RP.A and 7.RP.A).
  • Geometry, Chapter 4 materials address reflections, translations, rotations, and dilations (8.G.A) without applying key Geometry takeaways from Grades 6 through 8.

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
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Indicator Rating Details

The instructional materials reviewed for the CORD Traditional series partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. The instructional materials partially foster coherence through meaningful mathematical connections in a single course and throughout the series where appropriate and where required by the CCSSM.

In each course, chapters include lessons that present mathematical concepts or skills but few connections are made between them. Connections between clusters and domains of standards are not always made for the teacher or student, and these missing connections decrease the coherence of the materials across courses.

The instructional materials miss opportunities to make coherent connections between courses throughout the series. For example:

  • Materials address Statistics and Probability at the end of each course in isolation from the rest of the topics within each of the courses. Algebra 1 contains calculation of descriptive statistics and linear regression. Geometry focuses on probability, in particular, probabilities of conditional and compound events. Algebra 2 addresses probabilities of compound events and data distributions. These chapters addressing Statistics and Probability do not make connections to each other or to other chapters within each course.
  • The Geometry standards are predominantly addressed in the Geometry course with minimal connections to the Geometry standards occurring in the other courses. Conversely, the Geometry course is largely devoid of connections to Number and Quantity, Algebra, and Functions. For example, there are no connections to quadratic functions in Geometry. There is no connection between an area model and a quadratic function for finding a maximum area of a shape within the Geometry course.
  • Algebra 2, Chapters 3, 5, 6 and 7 have no meaningful connections made between these chapters in order to increase coherence across the course and develop students’ understanding of functions.

Some examples of how the instructional materials display coherence between courses and provide opportunities for students to make meaningful connections are as follows:

  • In Algebra 1, Chapter 8, students solve quadratic equations through a number of methods. In Algebra 2, Chapter 4, students use those methods to solve quadratic equations with no real solutions.
  • In Algebra 1, Chapter 3, The Addition Property of Inequality Start-Up states: “Students already will know how to solve equations using addition and subtraction. All they need to know in order to succeed is to bring down the inequality symbol in each step of their solution.” In Algebra 1, Chapter 8, The Quadratic Formula Start-Up states: “Point out to students that, like completing the square, the quadratic formula can be used to find exact solutions to any quadratic equation.”
  • Algebra 1 starts with linear equations, moves to systems of linear equations, extends to monomials with some factoring of trinomials, and then quadratics. This sequence of topics makes meaningful connections to provide coherence throughout the Algebra I course.
  • The Geometry course progresses from triangle congruence in Chapter 5 to similarity in Chapter 6. In Chapter 7 right triangle trigonometry meaningfully connects to triangle similarity criteria to provide coherence across these three chapters.

Indicator 1e

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

The instructional materials reviewed for the CORD Traditional series do not meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. Throughout the materials, standards from Grades 6-8 are presented as new standards for students to learn. In many cases, the correlation documents align middle school concepts and procedural skills to High School Standards.

Throughout the series, the materials provide a “Start Up” section in the Teacher Edition for each lesson. These discuss how to start a lesson and include reminders teachers can give to students regarding previously-learned concepts. These sections do not contain indications of Middle School Standards. The following are examples where the materials do not explicitly identify and/or build upon standards from Grades 6-8:

  • Algebra 1, Lesson 2.4, Start Up states: “Refresh students’ memories on the order of operations. Point out that when solving a multi-step equation, the order is reversed in order to isolate the variable.”
  • In Algebra 1, Lesson 1.1, students classify rational and irrational numbers and order them from least to greatest. Students classify numbers and order sets of numbers from least to greatest and do not build upon standards from Grades 6-8 (6.NS.C and 8.NS.A.) to the High School Standards.
  • Algebra 1, Chapter 2 makes no connections to Grades 6-8 Standards. However, in Lessons 2.1, 2.3, and 2.4, students identify properties of operations and solve linear equations of the form px = q and px + q = r where p, q, r and x are rational numbers (7.EE.A and 8.EE.7). In Lesson 2.2, students use cross multiplication to solve proportions and use proportions and percent equations to solve percent problems (7.EE.3 and 7.RP.3). In Lesson 2.5, students solve equations with variables on both sides, including equations whose solutions require expanding expressions using the distributive property and collecting like terms (8.EE.7).
  • In Geometry, Lesson 7.2, students complete a proof of the Pythagorean Theorem with no connection to 8.G.6, which states: “Explain a proof of the Pythagorean Theorem and its converse.”
  • Geometry, Chapter 11 addresses area, volume, and surface area, all concepts from Grades 6-8. However, there are no standards from Grades 6-8 identified, and there are no connections between the standards from Grades 6-8 and the High School Standards.
  • Algebra 2, Lessons 11.1, 11.2, and 11.4 address the fundamental theorem of counting to find probabilities of simple and compound events and to use probability to model random events with no connections to 7.SP.C.

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.
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Indicator Rating Details

The instructional materials reviewed for the CORD Traditional series identify the plus standards in the correlation document for each course, and these plus standards are used to coherently support the mathematics which all students should study in order to to be college and career ready.

Plus standards are addressed in the Geometry and Algebra 2 courses. The Geometry course includes: G-SRT.9-11; G-C.4; S-CP.8,9; and S-MD.6,7. The Algebra 2 course includes: N-CN.8,9; A-APR.5,7; and S-MD.6,7. The lessons in which the plus standards do occur can easily be omitted if needed. For example:

  • N-CN.9: In Algebra 2, Lesson 6.6, students use the Fundamental Theorem of Algebra to determine the type and number of roots of polynomial equations.
  • A-APR.5: In Algebra 2, Lesson 9.5, students use Pascal’s triangle and the Binomial Theorem to expand powers of a binomial.
  • A-APR.7: Algebra 2, Lessons 7.1 and 7.2 address operations on rational expressions and make the connection to a system that is analogous to the rational numbers. In Lesson 3, students simplify complex fractions and solve rational equations with complex fractions.
  • G-SRT.9: In Geometry, Lesson 7.6, Activity 2, students complete a derivation of the formula A = 1/2 ab sin(C).
  • G-SRT.10: In Geometry, Lesson 7.6, Activities 1 and 3, students complete derivations for the Laws of Sines and Cosines and use the laws to solve multiple problems.
  • S-CP.8,9: In Geometry, Lessons 12.3 through 12.6, students find and interpret probabilities of independent events and use permutations and combinations to compute probabilities of compound events and to solve problems.
  • S-MD.6,7: In Geometry, Lesson 12.7 and Algebra 2, Lessons 11.3 through 11.5. students make decisions based on probability.
  • N-VM: Geometry, Chapter 3 introduces vectors, but the correlation document for the course does not align any lessons to this domain.

Of the plus standards incorporated into the materials, the following are not fully addressed:

  • N-CN.8: In Algebra 2, Lesson 4.6, students solve quadratic equations with complex solutions, but they do not extend polynomial identities to the complex numbers. In Algebra 2, Lesson 6.6, students create polynomial equations based on given complex roots, but the students do not extend polynomial identities to the complex numbers.
  • F-IF.7d: In Algebra 2, Lesson 7.4, students graph rational functions and identify their asymptotes, but they do not identify zeros. Students solve equations that would lead them to finding zeros; however, this is not explicit in the work, nor is it identified as part of the lesson.

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
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Additional Publication Details

Report Published Date: 02/07/2018

Report Edition: 2014

Title ISBN Edition Publisher Year
CORD: Learning in Context Algebra 1 978-1578377730 Student Edition CORD Communications 2014
CORD: Learning in Context Geometry 978-1578377749 Student Edition CORD Communications 2014
CORD: Learning in Context Algebra 2 978-1578377757 Student Edition CORD Communications 2014
CORD: Learning in Context Algebra 2 978-1578377927 Teacher Edition CORD Communications 2014
CORD: Learning in Context Geometry 978-1578377935 Teacher Edition CORD Communications 2014
CORD: Learning in Context Algebra 1 978-158377897 Teacher Edition CORD Communications 2014

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.

The publisher has not submitted a response.

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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