Alignment: Overall Summary

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for alignment to the CCSSM for high school, Gateways 1 and 2. In Gateway 1, the instructional materials meet the expectations for focus and coherence by being 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). In Gateway 2, the instructional materials meet the expectations for rigor and balance by reflecting the balances in the Standards and helping students meet the Standards' rigorous expectations, and the materials meet the expectations for mathematical practice-content connections by meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
16
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Meets Expectations

Not Rated

Gateway 3:

Usability

0
21
30
36
35
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets 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).
16/18
+
-
Criterion Rating Details

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for focus and coherence. The instructional materials attend to the full intent of the mathematical content contained in the high school standards for all students, spend the majority of time on the CCSSM widely applicable as prerequisites, let students fully learn almost all non-plus standards, engage students in mathematics at a level of sophistication appropriate to high school, and make meaningful connections in a single course and throughout the series. The instructional materials partially attend to the full intent of the modeling process and partially identify and build on knowledge from Grades 6-8.

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.
4/4
+
-
Indicator Rating Details

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The instructional materials include few instances where all aspects of the non-plus standards are not addressed across the courses of the series.

The following are examples of standards addressed by the courses of the series:

  • N-RN.3: In Algebra I, Module 3, Topic 1, Activity 2.5, students explain how the properties of rational exponents extend from the properties of integer exponents. Students consider calculations between numbers and determine to which number set the answer belongs. For example, students determine if the product of a nonzero rational number and an irrational number is sometimes, always, or never equal to a rational number.
  • A-REI.1: In Algebra I, Module 2, Topics 1 and 2, students use properties of equality to solve equations and inequalities. Students check and justify their solutions.
  • F-IF.7c: In Algebra II, Module 1, Topic 2, Activity 1.1, students identify zeros, predict the shape of a function by sketching the graph and labeling the zeros, and check their solutions using a graphing calculator. Students use technology to graph, identify domain and range, determine intervals of increasing and decreasing, and the x- and y-intercepts. In the same module, Topic 3, Activity 3.2, students encounter the definition of end behavior and complete a table to describe end behavior.
  • G-CO.3: In Geometry, Module 1, Topic 3, Lesson 5, students describe symmetry in a rectangle and reflectional symmetry in a square. Students also determine if shapes have rotational or reflectional symmetry and are asked to “describe the reflections and rotations that can carry each figure onto itself.”
  • S-CP.3: In Geometry, Module 5, Topic 2, students use conditional probability to solve problems and identify independent or dependent events. Also in the topic, students use an example of conditional probability and determine if the probability of A given B is the same as the probability of A.

The following non-plus standards are not fully addressed: 

  • A-REI.5: There was no evidence found where the materials or students prove, or are shown how 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.

Indicator 1a.ii

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

The instructional materials reviewed for Carnegie Learning Math Solutions Traditional series partially meets expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials do not use the full intent of the modeling process to address more than a few modeling standards across the courses of the series.

Examples where the full modeling process was present include:  

  • G-SRT.1: In Geometry, Module 3, Topic 2, Assessments, Topic Performance Task, Trigonometry: “It’s a Bird! It’s a Plane! It’s … a Drone?”, students are given information of drones flown by Jeremy and Leslie. Students determine which drone is higher, the difference between the heights, and the distance between Jeremy’s and Leslie’s locations on the ground. Students consider if Jeremy flies his drone the same height as Leslie’s drone, and they explain why the angle of elevation from Jeremy’s location is different from the angle of elevation between Leslie’s location on the ground and her drone. Students calculate the angle of elevation from Jeremy’s location on the ground to his drone to validate their reasoning. According to the rubric, students provide a labeled drawing, including all given measurements and calculated measurements. Students formulate their own equation in order to compute whose drone is higher and the difference between the heights of the drone. Students compute the distance between Jeremy and Leslie with supporting work. Students provide an explanation as well as validation to support their work.
  • N-Q.2 and S-ID.6a: In Algebra I, Module 3, Topic 2, Lesson 4, students work with probabilities of real-world scenarios. Students complete a series of analysis questions and draw conclusions from the probabilities. In Activity 4.1, students make predictions, create a model with a table, graph, and equation, and define the variables. In Activity 4.2, students summarize the results and write out the work they did in each step of the modeling process while completing Activities 4.1 and 4.2. Students choose functions and utilize statistical skills by creating charts or tables to represent data. Students decide if the function they wrote is a good fit, and they make predictions and explain answers. Students also write an article for the newsletter for SADD.

All aspects of the modeling cycle are addressed throughout the series, however, students are often limited in their opportunities to make choices and assumptions when defining mathematical modeling problems as well as validating their conclusions and improving upon their models when appropriate. Examples of how students engage in some, but not all, elements of the modeling process include:

  • A-SSE.1: In Algebra II, Module 1, Topic 1, Lesson 4, students explore that a distinct line that passes through two points and 3 non-linear points establishes a distinct parabola. Then students compare the forms of parabolas (general, vertex, factored) and write equations from a vertex and point. Next, they write quadratic equations from a specific graph, so only one equation can be written. In the Extension, students solve a problem about laws governing a pool and a diving board. Students explain their reasoning, but there is no evidence that students test solutions, communicate with others, and revise thinking. Students define the variables in the problem.
  • F-IF.4: In Algebra II, Module 1, Topic 2, Lesson 2, students are presented 3 patterns in different contexts. Students answer open-ended questions about the growth patterns and how the quantities change relative to one another. Students extend their thinking and write an expression to determine the next tile. Students choose variables but are encouraged to rethink or revise their expressions. Finally, they are given sample student expressions with descriptions and choose the ones that match and explain their reasoning.
  • F-BF.1: In Algebra II, Module 2, Topic 2, Lesson 3, Activity 3.1, students describe patterns in a table with two quantities and predict a model that would represent a relationship between the quantities. Students used a blank coordinate graph to draw a scatter plot and technology to write a regression line. Students compare their prediction, graph, and regression equation obtained from technology. Students do not rethink or revise. Aspects of the modeling process included were: make a prediction, analyze predictions, and make choices.
  • G-MG.1: In Geometry, Module 4, Topic 1, Lesson 4, students imagine stacking pancakes (circular, square, triangular and decreasing sizes), and students name the shape formed, relating the dimension of a single pancake of that shape to the entire stack and drawing conclusions about the 3D solid created. Students make a pyramid with cubes, explore volume by making changes in dimensions, and build a spreadsheet with the data from the pyramid explored. Students compare their data and write a formula for volume of a pyramid. Students build physical models of 3D shapes, gather data, and make conjectures about volume. Several components of the modeling process are found in this lesson, students ask questions and make assumptions to define the problem, use mathematical tools to solve, and explain if/when their answer makes sense. Students do not test and revise models.

In the materials, many lessons are structured with learning opportunities which contain step-by-step instructions for students with minimal opportunities for creativity, estimation, and student choice of math concepts and skills to combine and utilize for problem solving. At the end of topics and/or lessons, Performance Tasks can be found in assessment sections. The full modeling process is present within these tasks however, the tasks are found within a summary assignment of scaffolded lessons which directs how students should mathematize the problem along with predictions and analyses that should occur.

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 Carnegie Learning Math Solutions Traditional series, when used as designed, meet expectations for allowing students to spend the majority of their time on the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers. The materials do not include distracting content that would keep students from engaging with the standards identified as widely applicable prerequisites (WAPs).

Examples of how the materials allow students to spend the majority of their time on the WAPs include, but are not limited to:

  • In Algebra I, Module 3, Topic 2, Lesson 2, students rewrite radical expressions and rational expressions using the properties of exponents. In Geometry, Module 1, Topic 1, Lesson 4, students rewrite radical expressions arising from the distance formula and Pythagorean Theorem. In Geometry, Module 2, Topic 2, Lesson 4, students use and rewrite rational expressions arising from trigonometric ratios in special right triangles. In Algebra II, Module 3, Topic 1, Lesson 4, students write radical expressions with rational exponents, rewrite the radicands of variable expressions, and compute the sums/differences of irrational numbers in algebraic expressions. (N-RN)
  • In Algebra 1, Module 5, Topic 1, Activity 2.4, students factor quadratic expressions and graph them in order to find the zeros (A-SSE.3a).  Also, in Algebra 1, Module 1, Topic 2, Lesson 4, students complete the square to transform quadratics into vertex form and find zeros in order to graph quadratics (A-SSE.3b). 
  • In Algebra I in the MATHia software, students explore constant change, evaluate linear functions, complete charts, identify the input value, compute the equation by substituting, and determine the output value. In Algebra II, Module 1, Topic 3, students explore the characteristics of polynomial functions. In Algebra II, Module 3, Topic 4, students write equations of exponential functions from patterns.  In Algebra II, Module 4, students explore trigonometric functions. (F-IF)
  • In Geometry, Module 3, Topic 1, students use dilations to create similar figures and establish criteria for determining similar triangles. Students use similarity to establish proportionality theorems and use similar triangles to solve problems (G-SRT.A, G-SRT.B). In Geometry, Module 3, Topic 2, students use similarity to determine constant ratios in right triangles and define trigonometric ratios (G-SRT.C).
  • The Statistics WAPs are addressed in Algebra I and Algebra II, and students have multiple opportunities to engage with the WAPs from this category.

Indicator 1b.ii

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

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series, when used as designed, meet expectations for letting students fully learn each non-plus standard. However, the instructional materials for the series, when used as designed, do not enable students to fully learn a few of the non-plus standards.

Examples of the non-plus standards that would not be fully learned by students when using the materials as intended include:

  • A-SSE.4: In Algebra 2, Module 3, Topic 4, Activity 1.1, students do not derive the formula for a geometric series. An example is provided and students analyze the example to find a pattern in one question with two parts. Underneath the question, the materials give the formula to compute any geometric series. Students use the geometric series to solve problems.
  • A-REI.4a: In Algebra 1, Module 5, Topic 2, Lesson 5, students complete the square in order to solve quadratic equations. The materials derive the quadratic formula by completing the square, but students do not derive the quadratic formula on their own.
  • A-REI.11:  Students have limited opportunities to explain why the x-coordinates of the points where the graphs of two equations intersect are solutions. In Algebra 1, Module 2, Topic 3, Lesson 1, students find the intersection of two linear equations and explain why the x- and y-coordinates of the points where the graphs of a system intersect are solutions. In Algebra 1, Module 5, Topic 1, Activity 1.3, students find the intersection of constant and quadratic equations and explain why the x- and y-coordinates of the points where the graphs intersect are solutions. In Algebra 1, Module 5, Topic 3, Lesson 2, students find the solutions to systems of quadratic equations. Students do not explain this relationship for absolute value, rational, exponential, and logarithmic functions.
  • G-C.5: In Geometry, Module 4, Topic 1, Lesson 2, Getting Started, students use a dartboard of 20 sectors to determine the area of the entire dartboard and the area of one sector. Then students find the area of one sector if the dartboard was divided into 40 sectors. Students do not generalize their findings to a dartboard with n sectors and are given the formula for the area of a sector at the beginning of Activity 2.1.

Indicator 1c

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

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age appropriate contexts, use various types of real numbers, and provide opportunities for students to apply key takeaways from grades 6-8.

Examples of applying key takeaways include, but are not limited to:

  • In Algebra I, Module 1, Topic 1, students interpret key features of graphs in the context of a problem (8.F.4). In Activity 1.1, students read scenarios, determine the graph which represents the scenario, and identify independent and dependent quantities. In Activity 1.2, students compare and contrast the graphs they organized in the first sections.
  • In Geometry, Module 3, Topic 1, students develop similarity standards (8.G.4). In Activity 1.1, students dilate figures to create similar figures. In Activity 1.2, students establish similarity criteria. In Activity 5.1, students apply knowledge of similar triangles in order to solve mathematical problems.
  • In Algebra I, Module 5, Topic 2, Lesson 5, students solve problems and apply knowledge of real numbers to determine to which set the answers belong. In Algebra II, Module 1, Topic 1, Lesson 6, students apply knowledge of real numbers to determine if solutions are a part of the real number system. These activities apply key takeaways from 6-8.NS involving integers, rational numbers, and irrational numbers.

Examples of age appropriate contexts throughout the series include, but are not limited to: 

  • In Algebra I , Module 1, Topic 3, Activity 3.1, students construct a scatter plot that relates speed and braking distance. 
  • In Geometry, Module 3, Topic 2, Lesson 2, Talk the Talk task, students relate road grades of mountainous areas to the angle of elevation. 
  • In Algebra II, Module 1, Topic 1, Activity 1.2, students use a scenario regarding homecoming elections and how the results have been shared. Also in this lesson, students explore the pattern of a rumor spreading. 
  • In Algebra II, Module 1, Topic 1, Activity 5.3, students apply a quadratic model to launching a free t-shirt to fans at a baseball game.

The instructional materials use various types of numbers throughout the series in expected places where numbers are naturally varied, such as trigonometry, regression models, and problems involving radicals and/or rational exponents. Examples of the materials using various types of numbers include, but are not limited to:

  • In Algebra I, Module 5, Topic 2, Activity 5.4, students evaluate the discriminant of quadratic equations and the calculations include real, rational, irrational, and imaginary numbers.
  • In Geometry, Module 4, Topic 2, Lesson 3, students determine the intersection points for each system of equations involving a circle, including rational and irrational coordinates.
  • In Algebra II, Module 4, Topic 2, students use integers, rational numbers, and irrational numbers in trigonometric functions and relationships.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. The instructional materials foster coherence through meaningful mathematical connections in a single course and throughout the series, where appropriate and where required by the Standards.

Examples of connections made across courses include, but are not limited to:

  • In Algebra I, Module 3, Topic 1, and Algebra II, Module 3, Topic 1, students use rational exponents and their definitions in order to solve problems (N-RN.1).
  • In Algebra I, Module 5, Topics 1and 2, and Algebra II, Module 2, Topic 1, factoring, completing the square, and finding equivalent forms are connected. Students write equivalent forms and make connections between solutions, graphs, and other key details using the equivalent forms (i.e., connections between factors and zeros and completing the square to reveal the vertex or as an alternate way of solving an equation) (A-SSE.3). 
  • In Algebra I, Topic 1 of Modules 1, 2, 3, and 5, and Algebra II, Module 2, Topic 1, Module 3, Topics 1-3, and Module 4, students use functions to model different situations. Although often confined to a specific type of function, students complete a process to develop understanding of why a certain function type is used in a context (F-IF.4).
  • In Algebra II, Module 1, Topic 3, and Module 2, Topic 3, Lesson 3, students transform rational and polynomial functions and sketch a graph involving a transformed function. Students apply knowledge of geometric transformations from Geometry Module 1 to transform a graph based on an equation (G-CO). 
  • In Geometry, Module 4, Topic 2, Lesson 2, students use completing the square as a method for writing the equation of a circle. Students also use completing the square as a way to calculate minimum and maximum values in Algebra I, Module 5, Topics 6 and 7, and in Geometry, they determine the equation of a circle in standard form using the same method (A-SSE.B).

The following examples are instances where meaningful connections are made within courses:

  • In Algebra I, average rate of change is addressed through linear functions in Module 2 and students explore average rate of change with exponentials in Module 3, including connections to a constant ratio for geometric sequences and the use of MATHia Software. Average rate of change is explored for quadratic functions in Module 5 (F-IF.6).
  • Transformations are used throughout the Geometry course. In Module 1, Topic 1, students are introduced to the idea of transformations where definitions for both transformations and rigid motion are given. In Topic 3, students explore the different rigid motions using simple geometric transformation machines, similar to function machines. In Module 2, Topic 1, Lesson 2, students use transformations to prove triangle congruence, and in Lesson 3 students use triangle congruence to solve problems (G-CO).
  • In Algebra II, students connect patterns to functions, tables, and graphs. In Module 1, students match scenarios, various function forms, tables, and graphs with linear, exponential, and quadratic functions. In Module 2, students factor, use long division, sketch graphs, and analyze tables. Students also write equations to solve problems from scenarios (A-SSE).

Indicator 1e

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

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

The Teacher Implementation Guide includes “What is the entry point for students” in each topic overview. The instructional materials do not explicitly identify content from Grades 6-8. The materials reference middle school learning but not by specific standards. The materials support the progression of the high school standards by including connections between content from Grades 6-8 and high school that enable students to extend their previous knowledge. Examples from teacher materials include but are not limited to:

  • In Algebra I, Module 2, Topic 2 Overview, “In grade 7, students solved two-step inequalities and graphed the solutions on a number line. Students build from this knowledge in this topic when they solve more complex inequalities in one variable and compound inequalities.” 
  • In Geometry, Module 1, Topic 3 Overview, “Students know that two figures are congruent if and only if there exists a sequence of one or more rigid motions that carries one of the figures onto the other.” 
  • In Algebra II, Module 5, Topic 1 Overview, “Since middle school, students have created and analyzed data in a variety of distributions, and have compared different displays.” “This topic deepens students’ understanding of the importance and usefulness of these measures and provides them with an opportunity to apply these concepts in real-world situations.” 

The Student Editions of the instructional materials include a family guide with “Where have we been? Where are we going?” for each topic. These sections identify connections between middle school content and courses and lessons in the series. The materials refer to middle school but not the standard(s) being built upon throughout the lesson. Examples include but are not limited to:

  • In Geometry, Module 3, Topic 1, “In middle school, students developed their understanding of proportional reasoning through explorations of multiplicative relationships. Students have used scale factor to solve problems.” “Understanding similarity further develops proportional reasoning which began in grade 6 and continues throughout high school mathematics. It provides the opportunity for students to connect spatial and numeric reasoning and lays the groundwork for understanding trigonometric ratios, which students will explore in the next topic.”
  • In Algebra I, Module 2 ,Topic 3, “Coming into this topic, students know that every point on the graph of an equation represents a value that makes the equation true.” “Students have written systems of linear equations and have solved them either graphically or algebraically using substitution.”

Tables are presented as an overview of each module in the teacher editions and contain a column for connections to prior learning. This is evident for each module, but explicit standards are not listed in this overview or anywhere else in the teacher and/or student materials.

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
+
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Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Math Solutions Traditional series explicitly identify plus standards and use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready. The plus standards that are included in the materials typically support the mathematics which all students should study in order to be college and career ready in a coherent manner, and the plus standards typically could be omitted without detracting from the underlying structure of the materials. Examples where plus standards were addressed include, but are not limited to:

  • N-CN.8: In Algebra II, Module 1, Topic 1, and Module 2, Topic 1, students work towards understanding properties of the set of complex numbers and their operations. Students write and manipulate complex number expressions. Students factor polynomial structures across the complex numbers. 
  • A-APR.5: In Algebra II, Module 2, Topic 2, Lesson 2, students explore Pascal’s Triangle and how it is used to expand binomials then extend this work into the Binomial Theorem. 
  • A-APR.7: In Algebra II, Module 2, Topic 3, Lesson 4, students perform operations with rational expressions and determine closure for operations with rational expressions. 
  • F-IF.7d: In Algebra II, Module 2, Topic 3, Lessons 1 and 3, students graph rational functions, compare multiple representations of rational functions, compare rational functions to polynomial functions, analyze key characteristics, identify domain restrictions (continuous and discontinuous), compare removable discontinuities to vertical asymptotes, rewrite rational expressions, and sketch discontinuous rational functions with asymptotes and removable discontinuities.
  • F-BF.4c: In Algebra II, Module 3, Topic 1, Lesson 1 and 2, students explore inverse functions by using graphs and the Horizontal Line Test to determine whether a function is invertible and generalize about inverses of even- and odd-degree power functions.
  • F-BF.4d: In Algebra I, Module 5, Topic 3, Lesson 3, students find the inverse of quadratic functions and restrict the domain and range of quadratic functions.
  • F-BF.5: In Algebra II, Module 3, Topic 3, Lessons 1, 3, 4, and 5, students use exponential and logarithmic models to analyze problem situations. Students solve for the base, argument, and exponent of logarithmic equations. Students solve logarithmic equations using logarithmic properties and equations arising from real-world situations. Students complete a decision tree to determine efficient methods for solving exponential and logarithmic equations.
  • F-TF.3: In Algebra II, Module 4, Topic 1, students apply special right triangles to trigonometric ratios. Students also work with sine and cosine functions as well as transformations of those functions.
  • F-TF.4: In Algebra II, Module 4, Topic 1, Lesson 3, students use symmetry to label coordinates around the unit circle.
  • G-SRT.9: In Geometry, Module 3, Topic 2, Lesson 6, students derive the area formula, A = 1/2 ab(sin C), by completing provided steps.
  • G-SRT.11: In Geometry, Module 3, Topic 2, Lesson 6, students determine when the Law of Sines and Cosines is “useful to determine unknown measures” in Talk the Talk. Then, students find the unknown length of the side of a triangle.
  • G-C.4: In Geometry, Module 2, Topic 2, Activity 5.4, students construct tangent lines to a circle through a point outside of the circle.
  • G-GPE.3: In Geometry, Module 4, Topic 2, Lesson 6, students investigate a constructed ellipse and answer a series of questions that results in finding the general equation of an ellipse using the distance formula. Similarly, in Lesson 7, students find the general equation of a hyperbola. 
  • S-CP.8: In Geometry, Module 5, Topic 1, students apply the general multiplication rule to solve probability problems involving dependent events.
  • S-CP.9: In Geometry, Module 5, Topic 2, students use permutations and combinations to compute probabilities of compound events and solve problems.
  • S-MD.5, S-MD.6: In Geometry, Module 5, Topic 2, Lesson 5, students are given $200 and either keep their money or return their money and spin a wheel to determine their winnings. Students explore probabilities of spinning the wheel and expected values in order to make a fair decision.
  • S-MD.7: In Geometry, Module 5, Topic 2, Lesson 5 Getting Started, students analyze probability and make decisions based on the probability. 

Examples of plus standard that were partially met, include but are not limited to:

  • F-BF.1c: In Algebra 2, Module 3, Topic 1, Lesson 2, students use composition of functions to determine whether two functions are inverses of each other. Students do not use composition of functions in application problems. 
  • G-SRT.10: In Geometry, Module 3, Topic 2, Lesson 6, students derive the Laws of Sines and Cosines but do not prove them. Students use the Laws of Sines and Cosines to solve problems.
  • G-GMD.2: In Geometry, Module 4, Topic 1, Lesson 4, students use Cavalieri’s Principle to understand the formulas for the volume of a cone and pyramid. Students do not use Cavalieri’s Principle for the volume of a sphere, rather, the materials simply state the formula in Activity 4.5.

Plus standards not included in the series:

  • N-CN.3-6
  • N-VM
  • A-REI.8,9
  • F-TF.6,7,9
  • S-MD.1-4


Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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.
8/8
+
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Criterion Rating Details

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet expectations for 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.
2/2
+
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The instructional materials develop conceptual understanding throughout the series and provide opportunities for students to independently demonstrate conceptual understanding. Examples include, but are not limited to:

  • In Algebra I, Module 5, Topic 1, students determine from an equation whether a function has an absolute maximum or minimum and explain their decision. In answering the questions, students demonstrate an understanding of absolute maximum and minimum and other characteristics of quadratic functions. (A-APR.B)
  • In Algebra I, Module 2, students complete steps to create equivalent equations by exploring equal statements and applying a series of arithmetic steps to both sides. Students work collaboratively to use properties of equality to justify how equivalent equations were created through the solution process. Students solve multi-step equations providing a justification for each step, and when justifications are provided, students complete the steps. (A-REI.A)
  • In Algebra I, Module 2, Topic 1, Lesson 1, students explore the concept of arithmetic sequences and build them into linear functions. In Module 3, Topic 1, Lesson 1, students explore geometric ratios and graph the terms of the geometric sequences before working with exponential growth. Students write explicit geometric formulas and exponential functions from the common ratios. In Module 3, Topic 2, Lesson 1, students compare the average rate of change between common intervals of a linear and an exponential relationship in contextual problems while justifying their thinking and processes. (F-LE.1)
  • In Geometry, Module 3, Topic 1, in addition to calculating ratios and angle measures to determine similar figures, students answer a series of questions to develop conceptual understanding. Students answer questions to explain or justify their answers using measurements or transformations, for example: “Explain why this similarity theorem is Angle-Angle instead of Angle-Angle-Angle.” In answering the questions, students demonstrate an understanding of similarity and the characteristics that make two figures similar. (G-SRT.2)
  • In Geometry Module 3, Topic 2, Lesson 1, students explore trigonometric ratios as measurement conversions and analyze the properties of similar right triangles. Starting with two parallel lines, students pick a point on one line and draw a line to another line and create two triangles. Students verify the two triangles are similar by measuring all sides and comparing the ratio of the lengths of the corresponding sides. Students use the triangles to find the ratio of the lengths of the sides that later are defined as sine, cosine, and tangent. Students use the ratios throughout the lesson to develop an understanding of the ratios before the formal definitions are given at the end of the lesson. (G-SRT.6)
  • In Algebra II, Module 3, Topic 1, Lesson 4, students review exponent rules and explore tables and graphs for power functions with integer exponents. Students write conclusions based on this exploration and use their conclusions with rational exponents and radical expressions. Students analyze other student work with rational exponents by comparing, contrasting, and justifying different approaches to rewriting radical expressions. (N-RN.1)

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. The instructional materials develop procedural skills and provide opportunities to independently demonstrate procedural skills throughout the series. The series includes practice problems in the lessons, MATHia software, and an additional workbook. 

Examples include, but are not limited to:

  • In Algebra II, Module 1, Topic 1, Lesson 2, students develop procedural skills with algebraic and geometric patterns. Students compare models and calculations and verify the equivalence of expressions. This topic has additional days of MATHia and skills practice on patterns, algebraically and graphically, modeled by linear, exponential, and quadratic equations. Students explore and analyze patterns, compose and decompose functions, sketch 3rd and 4th degree polynomials, and explore average rate of change. (A-SSE.1b)
  • In Algebra I, Module 5, Topic 2, Lesson 2, students combine terms, multiply expressions, solve quadratic equations using multiple methods, and convert and sketch graphs in the lesson. This topic has additional days of MATHia and skills practice on estimating values of functions, solving equations to determine the zeros, and rewriting expressions using difference of squares. (A-SSE.2)
  • In Algebra II, Modules 1-4, students practice transformations with a variety of parent functions. MATHia software includes additional days of practice with inverse functions, represented graphically and numerically, writing inverses of quadratic functions as square root functions, identifying transformations of quadratic functions, and exponential functions, both growth and decay. The skills practice includes additional problems on transformations, rewriting and solving radical and exponential functions, and properties of exponential graphs. (F-BF.3)
  • In Geometry, Module 1, Topic 1, students use area and perimeter in a coordinate plane and the distance formula as they work with composite shapes. Students demonstrate procedural skills by finding the perimeter and area of polygons. (G-GPE.7) 

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations that 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. 

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematics while providing  opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts throughout the series. 

Examples where students engage in routine and non-routine application of mathematics include, but are not limited to:

  • In Algebra I, Module 1, Topic1, Lesson 1, students read scenarios and determine the independent and dependent quantities. Students then match each scenario to its corresponding graph. For each graph, students label the axes with the appropriate quantity and a reasonable scale, and then interpret the meaning of the origin. Students draw conclusions from the scenarios. (N-Q.A)
  • In Algebra II, Module 1, Topic 2, Lesson 1, students are given a scenario where a drain is built. Students make physical models from paper, compare with classmates, then complete a chart of possible height/width combinations for a certain size of sheet metal to determine the dimensions that produce the most water flow. Next, they write a function to model a cross sectional area and use technology to graph the function. Students interpret points on the graph and describe what that point represents. Then students work on a new scenario with larger dimensions of sheet metal. (A-REI.11)
  • In Algebra I, Module 5, Topic 3, Lesson 3, students engage in a MATHia application scenario about guns on a battleship. Students are given that the guns fire at an initial height above an ocean and an initial upward velocity. Students must define a unit for each quantity, enter a variable for the time, and write an expression for the height of the charge. Students must answer a set of questions in order to plot points. Students use the graph to determine how long after the charge is fired that the projectile reaches certain heights. (F-IF.B)
  • In Geometry, Module 3, Topic 2, Lesson 4.2, problems 5, 6, and 7, provide opportunities for students to engage in applications. Problems 5 and 6 represent traditional inverse trigonometric problems where students are asked to find angles. However, these problems are contextualized in a way that is appropriate for high school courses. Problem 7, represents a less traditional inverse trigonometric problem. This problem requires students to evaluate the given information and solve for more than one triangle in order to arrive at the appropriate answer. (G-SRT.8)

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials and multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

Examples of where the instructional materials attend to conceptual understanding, procedural skills, and application independently throughout the grade level include:

  • Conceptual Understanding: In MATHia, students must see the connections between algebraic representations of functions, graphical representations of different types of functions, and determine from a context the type of function that is being described. In Algebra I, students are exposed to different types of functions (e.g., cubic, polynomial) but asked to categorize them as “Other.” Students must understand the relationships between contextual situations, algebraic representations, and graphs. 
  • Procedural Skills: In MATHia Algebra II, opportunities exist for students to simplify radicals with negative radicands, simplify powers of i, adding and subtracting complex numbers, multiplying complex numbers, and solving quadratic equations with complex numbers. 
  • Application: In Algebra I, Module 5, Topic 1, students write quadratic functions to model contexts. Specifically, Activity 2 includes a handshake activity where students must record and organize data and write a function that models that data. Students are then asked application questions related to minimums, domain, and range. They are also asked to compare the orientation of the graph to a previous problem in the section.

Examples where two or more of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials include: 

  • All sections related to G.SRT.6 represent a balance between solving simple proportions related to trigonometric ratios in right triangles, contextualized word problems involving different trigonometric ratios, and conceptual understanding related to the different trigonometric functions. For example, in Geometry, Module 3, Topic 2, Activity 2.3, students are asked to extend their knowledge of the tangent ratio and apply it to different similar triangles and more abstract representations of angle measures. 
  • In Algebra I, Module 2, Topic 1, End of Topic Test A, students demonstrate all aspects of rigor by rewriting equations in different forms and transforming figures on a coordinate grid. Students are required to recall arithmetic and linear functions and use knowledge of both to solve problems and answer questions. Students also apply knowledge of linear equations by reading a scenario and answering a series of questions involving the function.
  • In Algebra II, Module 3, Topics 1-4, the study of exponential, radical, and logarithmic functions are developed, practiced, and utilized. The study begins in Topic 1 with developing the conceptual understanding of a radical being the inverse of a power. Students develop procedural skills with practice in simplifying, rewriting, and graphing radical expressions and functions. Application occurs in real-world scenarios. In Topic 2, students algebraically and graphically analyze and transform exponential and logarithmic functions expanding upon the concepts from Topic 1. In Topic 3, students use these skills to solve and develop procedural skills with the properties of logarithms. In Topic 4, students model with exponential functions and solve real-world scenarios of growth. 

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/8
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Criterion Rating Details

The instructional materials reviewed for the Carnegie Learning Math Solutions Traditional series meet the expectation for supporting the intentional development of the eight Mathematical Practices (MPs), in connection to the high school content standards. Overall, the materials integrate the use of the MPs with learning the mathematics content. Through the materials, students make sense of problems and persevere in solving, attend to precision, reason and explain, model and use tools, and make use of structure and repeated reasoning.

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for supporting the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards. The majority of the time MP1 and MP6 are used to enrich the mathematical content, and there is intentional development of MP1 and MP6 across the series.

Throughout the series, there is a section labeled “How do the activities promote student expertise in mathematical practices,” which states the MPs included within the module. Each of the MPs are labeled with a symbol, and the MPs are referred to as “habits of mind.” MP1 does not have an icon and the materials indicate that students are expected to continually engage in this practice. MPs are identified for activities but not for specific problems or exercises. 

Examples of where and how the materials use MP1 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

  • In Algebra I, Module 2, Topic 3, Lesson 5, Activity 2, students choose the better cell phone plan. Students solve a system and use the approximation for the number of texts to determine the better plan. The answer is an approximation. 
  • In Geometry, Module 1, Topic 1, Lesson 1, students determine if the size of squares will affect the sum of the measures and use a protractor to test their predictions. Students copy each of the angles on a piece of patty paper and determine how to manipulate the three angles to show that their sum is 90 degrees. The materials state how there are different methods to verify sums.
  • In Algebra II, Module 2, Topic 2, students explore the Binomial Theorem and Pascal’s Triangle. They complete a series of exercises that help them in future lessons related to the Binomial Theorem. Students make sense of the patterns in the triangle and answer questions related to the relationships between the numbers.

The materials use a target icon to explicitly identify MP6 in both teacher and student materials. Examples of where and how the materials use MP6 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

  • In Algebra I, Module 1, Topic 1, Lesson 3, Activities 1 and 2, students attend to precision as they compare functions and non-functions as well as identify domain and range for the functions. Students use the precise definition of a function, and in Activity 2, they use appropriate interval notation to describe domain and range.
  • In Geometry, Module 3, Topic 2, Activity 4, MP6 is identified. In order to arrive at the expected answers, students use the appropriate trigonometric ratios and appropriately use a calculator to find the most precise angle measures for problems both in and out of contexts.
  • In Algebra II, Module 1, Topic 3, Lesson 2, Activity 2.2, students apply the mathematical principles related to rigid motions and accurately find points on a transformed graph. Students understand precise vocabulary and the operations required to find the new points.

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. The majority of the time MP2 and MP3 are used to enrich the mathematical content, and there is intentional development of MP2 and MP3 across the series. In Habits of Mind, MP2 and MP3 are identified by the “brain puzzle” icon.

Examples of where and how the materials use MP2 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

  • In Algebra I, Module 4, Topic 1, Lesson 3, Activity 3.1, students compare data and use the numerical evidence to reason and determine answers to additional questions. For example, a teacher is asked to use data to support the choice for who should compete in a spelling bee based on test scores, and the students must reason quantitatively to reach a reasonable conclusion.
  • In Geometry, Module 1, Topic 3, Lesson 2, students write equations that represent different translations and discuss the similarities and differences between geometric translation functions and algebraic equations which show the translations.
  • In Algebra II, Module 2, Topic 3, Lesson 6, students solve contextualized problems related to Work, Mixture, Distance, and Cost. Students write equations to solve specific problems and then answer specific questions. By having to generate the equations to solve, students reason abstractly and quantitatively.

Examples of where and how the materials use MP3 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

  • In Algebra I, Module 3, Topic 2, Lesson 1, Activity 1, students critique Chloe’s reasoning and use examples to justify their thinking. This activity compares linear functions with exponential functions and their outputs.
  • In Geometry, Module 1, Topic 2, Lesson 4, students critique the conjectures of other students. Students also use mathematical strategies to determine whether or not the conjectures are correct.
  • In Algebra II, Module 1, Topic 3, Lesson 4, Activity 4, students answer the questions “What characteristics did you take into consideration first? Why?” After each set of characteristics in the function game, students share their graphs with other students to determine their accuracy and make corrections as needed. Students answer the question: “Did you use transformations to help select the correct graph? If so, explain.”

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. The majority of the time MP4 and MP5 are used to enrich the mathematical content, and there is intentional development of MP4 and MP5 across the series. In Habits of Mind, MP4 and MP5 are identified by the “tool in hand” icon.

Examples of where and how MP4 is used to enrich the mathematical content and demonstrate the intentional development of the full intent of MP4 across the series include: 

  • In Algebra I, Module 2, Topic 3, Lesson 3, students write systems of inequalities (with constraints), graph the system, and interpret results based on a contextualized problem.
  • In Geometry, Module 4, Topic 1, Lesson 3, students use what they know to describe the volume of two figures. Students use the Cavalieri’s Principle to draw conclusions about the volumes of two prisms.
  • In Algebra II, Module 3, Topic 2, Lesson 1, students complete a table to determine the amount of caffeine at each time interval. In Problem 11, students complete a second table for the half life. Students use both tables to answer questions based on the scenario given at the beginning.

Examples of where and how MP5 is used to enrich the mathematical content and demonstrate the intentional development of the full intent of MP5 across the series include:

  • In Algebra I, Module 2, Topic 3, Lesson 1, Activity 2, students choose and use their own method, along with technology, to solve systems of equations. Students also use graphing tools to verify algebraic solutions to systems of equations.
  • In Geometry, Module 1, Topic 2, Lesson 3, students perform constructions. Students choose from dynamic software, a compass, or other appropriate tools. Students are not told which tool to use and are expected to choose based on availability and/or appropriateness.
  • In Algebra II, Module 2, Topic 1, Lesson 4, Activities 1 and 2, students use graphing utilities to connect algebraic solutions of polynomial inequalities to the graphs of the polynomial functions. The graphs created by the graphing utility also relate to the number line/interval representation of the solutions for the polynomial inequality.

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. The majority of the time MP7 and MP8 are used to enrich the mathematical content, and there is intentional development of MP7 and MP8 across the series. The materials use a box icon to explicitly identify MP7 and MP8 in teacher and student materials.

Examples of where and how the materials use MP7 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

  • In Algebra I, Module 1, Topic 2, Lesson 3, students generate/organize data and then use the patterns revealed in the data to write formulas for recursive sequences. In Activity 3, students repeat this type of activity and write both explicit and recursive formulas and examine the connection between the two.
  • In Geometry, Module 2, Topic 2, Lesson 3, Activity 2, students use triangles having interior angles that sum to 180 degrees to determine the sum of the interior angles of a polygon. Students examine patterns and make conjectures based on the idea of the sum of the interior angles of a triangle.
  • In Algebra II, Module 2 Topic 1, Lesson 2, Activity 2, students factor special binomials building on difference of squares. Students also factor the sum and difference of cubes. By examining long division examples, students determine the structure for factoring the sum and difference of cubes.

Examples of where and how the materials use MP8 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include: 

  • In Algebra I, Module 1, Topic 1, Lesson 4, Activity 1, students use repeated reasoning from scenarios to identify domain characteristics of the function families (linear, exponential, quadratic, absolute value) and compare the graphical behaviors within a family. 
  • In Geometry, Module 1, Topic 1, Lesson 3, Activity 3, students use prior knowledge of parallel lines, perpendicular lines, and slopes to answer questions about horizontal and vertical lines. Students extend their reasoning of slopes to answer questions 2-10 by applying previous understanding of slope as applicable.
  • In Algebra II, Module 3, Topic 4, Lesson 1, Activity 1, students express regularity in repeated reasoning to determine a rule for geometric sequences. Students interpret notations and recognize/describe patterns. Students complete a similar activity using the Sierpinski Triangle. Student describe the iterative process, complete tables, and identify the sequence from the table.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

Each set of materials is divided into five modules, which are then divided into topics, and the topics are divided into lessons and activities. The structure for the topics are as follows: Connections, Getting Started, Activities, Talk the Talk, and Assignment. Each part of the structure has a specific goal. For instance, Connections, located on the topic page, directs students’ instruction through the use of a question or questions. In Getting Started, students access prior knowledge needed to be successful in the activities. Activities provide a variety of teaching strategies to encourage learning, and, in Talk the Talks, students reflect on the lesson by applying mathematics to real world problems. Finally, Assignment is separated into Write, Remember, Practice, Stretch, and Review. In each section, students use concepts learned to solve problems. The MATHia Software provides additional exercises incorporating a variety of instructional tools, such as: explore, animations, classification, problem-solving, and worked examples.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

According to the Carnegie Learning Math Solutions Traditional textbook, “Each lesson of the High School Math solution has the same structure. This consistency allows both you and your students to track your progress through each lesson.” The sequence of every lesson is divided into categories called Engage, Develop, and Demonstrate.

  • Engage establishes “Mathematical Goals to focus Learning.” This section includes the following: a warm-up to activate prior knowledge, the learning goals, connections to previous learning, and a Getting Started page meant for students to solve/think/share and notice other’s work/thinking, usually for a non-routine problem.
  • Develop involves “aligning Teaching to Learning.” It includes lesson activities which allow students to “build a deep understanding of mathematics through a variety of activities.”
  • Demonstrate includes Talk the Talk in which students have “an opportunity to reflect on the main ideas of the lesson.”

After completing the categories within the lesson, students practice their learning in assignments, which includes: Write, Remember, Practice, Stretch, and Review. Students have additional practice with “Learn Individually” lessons using the MATHia software, or if the technology is not accessible, students use the Skills Practice workbooks.

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectation that there is a variety in what students are asked to produce. Students produce a variety of products in digital and written form.

Examples of variety in how students present the mathematics include:

  • In Algebra 1, Module 2, Topic 2, Lesson 2, Activity 2.2, students analyze work to explain errors in students' work.
  • In Geometry, Module 1, Topic 1, Lesson 3, Getting Started, students determine the slope of a line, create a segment parallel to a line utilizing patty paper, and describe the movements needed to complete the segment.
  • In Algebra 2, Module 3, Topic 2, Performance Task, students examine a scenario involving administering the correct dose of medications. Students write functions, sketch a graph with technology, and interpret information.

The materials include performance tasks which usually involve real world scenarios and applying mathematics. Students produce tables, graphs, and charts to model data and solutions using different representations. The assignments provide numerous opportunities for students to write, explain, determine values, describe, and graph on a coordinate plane.

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectation that manipulatives are faithful representations of the mathematical objects they represent and are appropriately connected to written methods.

Virtual manipulatives are embedded within the MATHia Software for each section and include graphing tools, geometry tools for transformation, and the ability to manipulate a graph. Within the instructional materials, physical manipulatives for lessons are listed in the lesson overview. For example, in the Teacher Lesson Plans for Algebra 1, Module 5, Topic 1, the material needed for a specific portion of the lesson is patty paper.

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series have a visual design that is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The student materials are intentional and consistent between modules and across courses. The black and white design of the program does not contain distracting designs and includes models that have a purpose for the mathematics. The text is supported by graphic elements that enhance the lesson, such as a highlighted worked example or various visual models to help with conceptual understanding. Both the textual and graphic elements complement each other and do not crowd the page, allowing for students to work and write answers.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
8/8
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Criterion Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials support teachers by: planning and providing learning experiences with quality questions; containing ample and useful notations and suggestions on how to present the content; containing full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons; and containing explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development. 

Each section has extensive facilitation notes provided in the Teacher’s Edition. There are suggested questions that teachers may use to aid in instruction and mathematical development. There are also suggestions as to what teachers should look for as they observe/examine student work. Within each lesson, there are questions that ask students to explain or justify their answers. For example, in Geometry, Module 3, Topic 1, Lesson 3, teachers are given the following questions to ask while students complete questions 4-7:

  • “Do the ratio and scale factor represent the same thing?”
  • “If all pairs of corresponding angles in the image and pre-image are congruent, is the shape of the image always the same as the shape of the pre-image?”

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.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. The introductory pages of the first volume of the Teacher’s Implementation Guide for each course provide detailed information regarding the instructional design of the series, lesson structure, assignment structure, problem types, thought bubbles to promote student self-reflection, mathematical habits of mind, academic glossary, modeling process, and assessments. Detailed information regarding content alignment within a given course complement a general overview of standards addressed within that course.

The Facilitation Notes embedded within every lesson provide ample and useful annotations and suggestions regarding an overview of the mathematical concepts addressed, standards addressed, essential ideas, pacing, what to look for from students, questions to ask, grouping strategies, common student misconceptions, differentiation strategies, and a summary statement of the mathematical ideas addressed.

Where applicable, the materials include teacher guidance for the use of embedded technology to support and enhance student learning. The introductory pages of the first volume of the Teacher’s Implementation Guide for each course provide guidance for using the MATHia software and collecting data reports generated by MATHia. The table of contents explicitly identifies certain MATHia workspaces that correlate to specific modules in the given course.

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.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Math Solutions Traditional series meet expectations for containing a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

Within MyPL, teachers can view instructional videos that provide adult-level explanations and examples for teachers to enhance their own knowledge of the content. The instructional videos address textbook lessons, MATHia, mathematical content, and classroom strategies. For example, in the video, Approaching Infinity (Algebra 2, Module 2, Topic 3, Lesson 2), teachers view suggestions for implementing the lesson. The Teacher’s Implementation Guide for each course provides detailed information regarding how mathematical content fits into the series overall, and the materials include module overviews that describe the mathematics of the module and how the content is connected to prior and future learning. MyPL also includes 33 videos addressing mathematical content that are not lesson-specific, and the advanced mathematics concepts addressed by the videos include, but are not limited to: ellipses, hyperbolas, and discontinuities and asymptotes of rational functions.

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for containing a teacher’s edition that explains the role of the specific mathematics standards in the context of the overall series.

  • The Module Overview includes information for the teacher with explanations that build the teacher’s understanding of how the lesson content fits into the curriculum. It tells why the module is named, the mathematics included in the module, and how the module connects to prior and future learning.
  • Each Topic Overview provides information on the mathematical content in the lessons as well as where it fits in the scope of mathematics across grades and courses. Knowledge required from prior chapters and/or grades is identified in this section.
  • The Module Overview of each section does not identify specific standards related to each of the connections. For example, in Geometry, Module 3, the prior connections states, “Students have extensive experience with ratios and proportional reasoning in middle school and in previous courses” but does not state the specific standard. In Algebra II, Module 1, Topic 1, the Family Guide explains that students have previously studied linear, exponential, and quadratic functions and also explains that this topic will prepare students to study more complex function  throughout the rest of Algebra II. The Teacher's Edition lists the use of patterns in the course as a way to promote mathematical thinking for the series.

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).
0/0
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series provide a list of lessons in the teacher's edition, cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter, and unit (i.e., pacing guide).

The pacing guide is located within the Module overview before each module. It is titled Leaning Together and is shown in a chart. The chart defines the topic, the standards involved, the number of days for the topic, and the highlights from the topic. There is also a pacing guide for the MATHia software.

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.
0/0
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The Family Guide for each topic is available in a PDF file that can be downloaded. The manual contains general topic information, what the students have learned in the past, what they will be learning, talking points, myths about math, keys for student success, vocabulary, content explanations, examples, and practice problems with answers aligned by topic and chapter.

Families are also provided with generic tips about how to facilitate success, including:

  • “To further nurture your child’s mathematical growth, attend to the learning environment. You can think of it as providing a nutritious mathematical diet that includes: discussing math in the real world, offering encouragement, being available to answer questions, allowing your student to struggle with difficult concepts, and providing space for plenty of practice.”
  • “You can further support your student’s learning by asking questions about the work they do in class or at home.”

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
0/0
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Teacher’s Implementation Guide contains research-based strategies and instructional approaches for the program, including:

  • The instructional approach to learning is “based upon the collective knowledge of our researchers, instructional designers, cognitive learning scientists, and master practitioners. It is based on a scientific understanding of how people learn and a real-world understanding of how to apply that science to mathematics instructional materials. At its core, our instructional approach is based on three simple yet critical components: Engage, Develop, and Demonstrate.” Each of these components is provided in detail. (Algebra 1, Teacher’s Guide, Volume 2, page FM-6)
  • The components of the blended learning program are described in detail and a website is provided to learn more about the approach. (Algebra 1, Teacher’s Guide, Volume 2, page FM-8)

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
10/10
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Criterion Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities to collect information about students’ prior knowledge and strategies for how to utilize the information in the classroom. The materials provide opportunities for identifying and addressing common student errors and misconceptions, ongoing review and practice with feedback, and assessments with standards clearly identified. The assessments contain detailed rubrics and answer keys, and there is guidance for interpreting student performance or suggestions for follow-up.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

  • There is a pretest for every topic in each module that addresses the standards which will be taught. The post-test for the topic is the same test.
  • The Topic Overview provides a list of Prerequisite Skills needed for the topic, which creates an indirect opportunity for teachers to gather information about students’ prior knowledge, although there is no direct guidance provided to the teacher about how to use the information.
  • The MATHia software is used as an assessment and progress monitoring tool, providing personalized data about where a student stands on various skills.
  • In every assignment in the textbook, there is a Review section. Students practice two questions from the previous lesson, two questions from the previous topic, and two questions that address the fluency standards. This provides teachers with information about students' learning gaps as they work through the instructional materials.
  • In the Module Overview, there is a connection to student’s prior learning. This explains to the teacher what students should know or be able to do based on previous learning. At the beginning of each module, there are teacher notes that indicate “Where We Have Been.” This small explanation frames student’s previous learning and knowledge in the context of the new lesson. At the beginning of each lesson is a Warm-Up and a Getting Started portion so that students begin to connect previous learning to new learning. These exercises  allow instructors to gather information related to prior knowledge.

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

The Topic Guide regularly includes Misconceptions with suggestions for teachers to identify and address common student errors and misconceptions. For example, in Geometry, Module 1, Topic 1, Lesson 4, “Students may assume all equiangular polygons are also equilateral polygons...” Teachers are encouraged to engage students in mathematical conversations to address student errors and misconceptions with phrases such as, “Remind the students…, Discuss with students…, Point out that….”

The MATHia software provides a solution pathway for common student misconceptions: “Like a human tutor, MATHia re-phrases questions, re-directs the student, and hones in on the parts of the problem that are proving difficult for the student. Hints are customized to address the individual student, understanding that there are often multiple ways to do the math correctly.”

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Examples include:

  • Each assignment at the end of the Lesson has review questions included.
  • The workbook has the answers to the odd exercises for immediate feedback.
  • Within each assignment, there is practice for the current material as well as practice for past material. 
  • There are Topic Performance Tasks with rubrics to provide feedback based on knowledge for the topic.
  • Warm Ups and Getting Started tasks provide additional practice for students as they start to expand their learning.
  • The MATHia software includes “Hints” which students can select when reviewing and practicing concepts and skills. Just-in-Time Hints automatically appear when a student makes a common error, and On-Demand Hints are provided when a student asks for a hint while working on a problem. Step-by-Step Hints demonstrate how to use the tools in a lesson by providing step-by-step guidance through a sample problem.

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
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Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Math Solutions Traditional series meet expectations for assessments clearly denoting which standards are being emphasized. The series offers several types of assessments, print and digital:

  • MATHia provides information for each student based on standards.
  • Performance tasks clearly note which standards are being assessed. 
  • The student-facing versions of the Pretest, Post test, and the End of Topic Test do not denote which standards are being emphasized.
  • The digital overview contains assessments and an assessment overview document. The document contains each assessment as well as which standard is assessed for each individual problem.
  • The Carnegie Edulastic Assessments Suite displays standards for each problem within each assessment provided. These standards are not student-facing.

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
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Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Math Solutions Traditional series meet expectations for assessments providing sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

  • Expected answers and outcomes are provided for each assignment/assessment, and some guidance is provided to aid teachers in the interpretation of student performance. 
  • Guidance is provided about formative assessments, and strategies teachers can use to address student misunderstandings are included in lesson facilitation notes.
  • Performance Tasks include detailed scoring rubrics.
  • MATHia reports provide teachers with detailed information about student performance in relation to progress on standards and suggestions on the skills that require additional support.
  • The materials offer teachers an APSLE (Adaptive Personalized Learning Score) report which is a predictor for year-end summative assessments. Videos within MyPL explain this report in more detail while outlining the research and models behind the report.

Indicator 3q

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series encourage students to monitor their own progress.

Examples include:

  • The MATHia software encourages students to monitor their own progress using strategies such as: Just-in-time hints, On-demand hints, a Progress Bar showing a summary of major skills, and Skill Tracking Behavior.
  • There is a review for students at the end of every lesson which includes spiral review of previous concepts. 
  • The Family Guide suggests questions for students such as, “Is there anything you don’t understand? How can you use today’s lesson to help?”

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
9/10
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Criterion Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across courses.  The instructional materials provide strategies to help teachers sequence or scaffold lessons, strategies for meeting the needs of a range of learners, tasks with multiple entry-points, and support, accommodations, and modifications for English Language Learners and other special populations. There are opportunities for students to investigate mathematics content at greater depth, but they are intended for all students over the course of the school year with general tips for teachers to expand or deepen lessons.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Scaffolding is evident throughout the series and teachers have support for different types of learners. Every activity has Differentiation Strategies included in the Facilitation notes that provide teachers detailed instructions about the organization of the topic, entry point for the students, how to see students are demonstrating understanding, and the importance of learning the topic as well as how the topic provides expertise in the mathematical standards.

The topic overview provides a detailed chart explaining the scope and sequence of the topic, and it is Learning Together. The chart provides the number of days needed for the lesson, aligned standards, and highlights for the lesson.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

MATHia differentiates the learning experience for every learner, adapting the amount of support based on the students' answers and path through each problem. This level of support is similar to a one-on-one tutoring experience, where the software is adapting based on everything the student is doing.

The differentiation strategy notes for teachers includes strategies for struggling students and suggestions for all students. The Questions to Ask, and other facilitation strategies are intended for all students. The varied activities throughout a topic address different types of learners. For example, in Geometry, Module 1, Topic 3, Lesson 5, “What is the difference between reflectional symmetry and rotational symmetry? How do you determine if a figure has rotational symmetry?” The questions are intended for all students, not a specific subgroup. On the same page, there is a differentiation strategy stating, “To extend the lesson, encourage students to investigate how to describe the location of the center of rotation for each figure in Question 9.”

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations. 

In each module, students complete series of consecutive problems that provide different entry points for students to demonstrate their understanding and skills. For example, Module 2, Topic 1, Lesson 1, Activity 3, scaffolds problems within the student problem set to help students have an entry point and to allow teachers to determine where students may be having difficulty. Facilitation notes at the beginning of the chapter have a section labeled “What is the entry point for students.” Teachers are given instructions such as, “As students work, look for: different translations of triangle ABC. Some students may move a single vertex of the triangle to the origin while others may move vertices to the axes. Share different strategies to accomplish the task.”

There are also problems when the materials provide two possible solution paths for a problem and students choose their path, for example, Geometry, Module 1, Topic 1, Lesson 5, Problem 3.

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).
2/2
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

Throughout the series, there are suggestions for ELL students within the teacher’s materials. For example in Algebra 1, Module 3, Topic 2, Lesson 4, the ELL Tip states, “Students may not understand the term intuitively in the introduction. Discuss the problem-solving strategies that students automatically used to solve the problem and how they relate to the modeling process.” ELL support is evident in all of the teachers guidance, and there are ELL Tips that address other strategies to help ELL students, such as honoring the use of students’ native languages, building relevant background, simplifying sentences, and modifying vocabulary.

Suggestions for supporting other special populations (i.e. struggling students and advanced students) are included in the Teacher’s Implementation Guide in the Facilitation Notes for each activity. Some of these suggestions for other special populations are general, and some are specific to the content of the lessons in which they are found.

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
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Indicator Rating Details

The instructional materials for Carnegie Learning Math Solutions Traditional series partially meet expectations for providing support for advanced students to investigate mathematics content at greater depth. Each assignment includes a Stretch problem. The materials state, “The Stretch section is not necessarily appropriate for all learners. Assign this to students who are ready for more advanced concepts.” The materials do not provide an assignment guide for advanced students, therefore, as designed, advanced students are completing more problems than non-advanced students in the print materials. In MATHia, advanced students complete fewer of the basic problems before they move to more advanced content, which prevents them from having to do more problems than non-advanced students.

Some of the differentiation strategies listed in the Teacher’s Implementation Guide are intended to extend the activity, yet they can benefit all students. For example in Algebra I, Module 3, Topic 2, Lesson 1, the materials state, “To extend the activity, ask students to create posters for classroom display that highlight an increasing linear function in general form, a decreasing linear function in general form, an increasing exponential function in general form, and a decreasing exponential function in general form. Be sure that students emphasize the appropriate forms of each function.”

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series provide a balanced portrayal of various demographic and personal characteristics.

Examples include:

  • No examples of bias were found.
  • Pictures, names, and situations present a variety of ethnicities and interests.
  • The text is black and white with green as the only color. The people are gray with black hair, but appear to represent many ethnicities.
  • Problems include a wide span of international settings, as well as, situations in urban, suburban, and rural settings.
  • There is a wide variety of names in the problems, from James, Ben, and Haley to Keirstin, Miguel, and Miko, representing a variety of cultures.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials for Carnegie Learning Math Solutions Traditional series provide opportunities for teachers to use a variety of grouping strategies. The Blended Learning Model is explained in the Teacher’s Implementation Guide. “Carnegie Learning delivers a different brand of blended learning: it combines collaborative group learning with focused individual learning.” The two components are Learning Together and Learning Individually. Carnegie believes students “learn together” in a collaborative classroom model where they can think critically, reason mathematically, and learn from each other. Consumable textbooks and manipulatives allow students to engage directly with the mathematics as they learn. There are differentiation strategies for grouping students in the Facilitation Notes of each lesson, and individual practice with skills practice and/or MATHia software is to be done as individual learning.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series partially encourage teachers to draw upon home language and culture to facilitate learning. There is no evidence of teachers drawing upon home language and culture to facilitate learning. There is a Family Guide with each topic that explains the mathematics and provides tips to support learning, but it does not utilize aspects of language and culture. Materials are available in Spanish.

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.
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Criterion Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and they include opportunities to assess students' mathematical understandings and knowledge of procedural skills. The instructional materials include opportunities for teachers to personalize learning for all students, and the materials offer opportunities for customized, local use. However, the instructional materials do not include opportunities for teachers and/or students to collaborate with each other.

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.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series integrate technology incorporating Mathematical Practices which include:

  • Explore tools for students to investigate mathematical topics,
  • Animations containing demonstrations of mathematical concepts and providing connections between visual and audio representations,
  • Classification tools to categorize answers and discover patterns,
  • Problem Solving tools adapt instructions to individualize them and allow students to reason, and
  • Worked examples for students “to identify their own misconceptions, make sense of the mathematical concepts, and then ultimately to persevere in problem-solving.”

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.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series, with MATHia software, will run on the following:

  • Windows Computers with operating systems Windows 7 and 10,
  • Apple Computers with operating systems Mac OS X 10.13 or higher,
  • Apple iPads with iOS 11 or higher,
  • Android Tablets with Android 9 and above, and
  • Chromebooks with ChromeOS 74 or higher.

The materials are not recommended for use on phones or small devices.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series include opportunities to assess student mathematical understanding and knowledge of procedural skills using MATHia’s Adaptive Personalized Learning Reports. Mathematical understanding can be displayed in Student View or Class View and is separated into three types of reports. The reports include: a session report informing teachers of work being completed, a standards report designed to assess mastery of a mathematical concept, and a student detailed report providing information about progress and performance. 

Indicator 3ac

Materials can be easily customized for individual learners.
0/0

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. In MATHia, teachers can choose a constructed course, copy modules from a class, or select modules for primary or secondary. The lessons/modules can be arranged in any order; however, the questions cannot be modified. 

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.
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series allow for the implementation of the MATHia software or a skills practice workbook. Within the MATHia software, teachers can manipulate the order of the activities; however, the print textbook does not include options for modifying the sequence or the structure of the lesson.

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.).
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Indicator Rating Details

The instructional materials for the Carnegie Learning Math Solutions Traditional series provide opportunities for teachers to communicate with a community of teachers. The materials state, “You’re part of a collective and have access to special content, events, meetups, book clubs, and more.” Teachers can access the online community through www.longlivemath.com. However, the materials do not allow opportunities for students to collaborate with each other online or through technology-based programs.

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Additional Publication Details

Report Published Date: 10/02/2019

Report Edition: 2018

Title ISBN Edition Publisher Year
Print HSMS SE & MATHia Bundle Algebra 1 978-1-60972-920-2 Carnegie Learning 2018
Print HSMS SE & MATHia Bundle Geometry 978-1-60972-921-9 Carnegie Learning 2018
Print HSMS SE & MATHia Bundle Algebra 2 978-1-60972-922-6 Carnegie Learning 2018

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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