The instructional materials reviewed for the Mathematics Vision Project Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. There are some standards for which the instructional materials attend to parts of the standard and some standards for which the instructional materials do not attend to the standard.

The following are examples for which the materials attend to the full intent of the standard:

• A-SSE.3: In Algebra II, Module 3, Task 7, students verify different forms of a quadratic expression to solve a given equation. Students explain how the factored form helps to reveal the zeros and what that means in the context of the Curbside Rivalry question. In Algebra I, Module 2, Task 6, students are guided through an exploration of how expressions with different rational exponents are equivalent, yet highlight different mathematical properties.
• G-MG.1: In Geometry, Module 7, Ready, Set, Go! Problem 3, students use a model to find the total surface area and volume of the Washington Monument. In Geometry, Module 7, Task 4, students model how they would determine the volume of a nail.
• S-IC.2: In Algebra II, Module 9, Task 7, students analyze a model created by a “slacker” student for a true/false quiz. Within this task, students complete an analysis of his model and, at the same time, test their analysis using coin flips.

The materials attend to some aspects, but not all, of the following standards:

• F-IF.6: In Algebra I, Module 8, Task 2, students calculate the average rate of change from piecewise functions. In the majority of the examples, students calculate a constant rate of change from linear, piecewise functions. The materials do not include estimating the rate of change from a graph, only equations or functions.
• F-IF.7b: Cube root functions or graphs are not present in the materials.
• G-CO.1: The definitions are present within Geometry Module 1, Task 4, but the definitions are not based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
• N-Q.3: Students do not choose a level of accuracy. In Geometry, Module 7, Task 8, students are directed to round to the nearest centimeter, but students do not choose the level of accuracy for themselves.

The following standards are not attended to by the materials:

• A-SSE.4: The materials do not have a derivation of the formula for the sum of a finite geometric series. This standard was not identified in the materials.
• S-IC.4: Students do not use data from a sample survey to estimate a population mean or develop margins of error. This standard was not identified in the materials.
• S-IC.5: There is a discussion of how students could randomly assign participants in an experiment in Algebra II, Module 9, Task 5, but there is no use of simulations. This standard was not identified in the materials.
• S-IC.6: Students do not evaluate reports based on data. This standard was not identified in the materials.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation for attending to the full intent of the modeling process when applied to the modeling standards. The materials provide opportunities for students to engage in the modeling process. Tasks that involve modeling include a graphic of the modeling process in the teacher notes. Additionally, the modeling standards are addressed in the materials.

Examples of modeling tasks include: 

• In Algebra I, Module 8, Task 3, students interpret a graph detailing Michelle’s bike ride to and from a lake. Students are asked to create a function to model the situation. 
• In Algebra I, Module 3, Task 1, students sketch a graph given steps that Sylvia used to clean and refill her pool (F-IF.4). Students answer provided questions to complete the problem. 
• In Geometry, Module 4, Tasks 10 and 11, students complete real-world problems with angles of elevation, angles of depression, and right angles (G-SRT.8).
• In Geometry, Module 5, Task 11 is designed to “deepen their understanding of volume formulas” (G-GMD.3). Students discuss why the formula for the volume of a cone is one-third the volume of a prism. Students compare the two volumes. 
• In Algebra II, Module 1, Task 2 details mathematical modeling completed by police departments and insurance companies to determine how far a car goes once it begins to break (in order to solidify the topic of an inverse function, F-BF.1). 
• In Algebra II, Module 9, Task 2, students analyze and determine a “good” score on the ACT given information about the mean and standard deviation (S-ID.1). Students answer analysis questions that are provided.

While there are many examples of modeling problems throughout these materials, there are some problems labeled as “modeling” problems that provide scaffolding which inhibits students from engaging in the full modeling process.

The instructional materials reviewed for the Mathematics Vision Project Traditional series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers. There was a large focus on WAPs in the Algebra I course with a decreasing amount of tasks in the subsequent courses. Throughout all three courses, the majority of the tasks spend time developing student understanding of the WAPs. Throughout the materials, there are a limited number of times that students spend too much time on prerequisite skills or distracting material. 

Within the WAPs, the largest focus was on the Algebra and Function standards. The Geometry WAPs were cited only in the Geometry course. The Number and Quantity and Statistics WAPs were addressed the least by the materials. 

The WAPs from Number and Quantity are included in all three courses. Evidence is found in Algebra I, Modules 1, 2, 3, 4, 5 ; Geometry, Module 7; and Algebra II, Module 3.  

 The WAPs from Functions are included in Algebra I and Algebra II. Evidence is found in Algebra I, Modules 1, 2, 3, 4, 5, 6, 7 and Algebra II, Modules 3, 4, 5.  

The WAPs from Algebra are included in Algebra I and Algebra II. Evidence is found in Algebra I, Modules 1, 2, 3, 5, 6, 7, 8 and Algebra II, Modules 1, 2, 3, 4, 5, 6, 7, 8.

The WAPs from Geometry are included in Geometry. Evidence is found in Geometry, Modules 1, 2, 3, 4, 7.

The WAPs from Statistics and Probability are included in Algebra I and Algebra II. Evidence is found in Algebra I, Module 9 and Algebra II, Module 9.

The instructional materials reviewed for the Mathematics Vision Project Traditional series partially meet the expectation for, when used as designed, allowing students to fully learn each standard. The instructional materials address many standards in a way that would allow students to fully learn them. There are some standards, however, that are not fully addressed, or the instructional materials do not provide enough opportunities for students to practice and learn the standards fully. 

The following are examples where the instructional materials partially meet the expectations for allowing students to fully learn a standard:

• N-CN.1: Students name the complex conjugate (Algebra II, Module 3, Ready, Set Go 6), but there is not enough practice for students to fully use the complex conjugate.
• N-CN.2: Students use the relation $$i^2=-1$$ and multiply the imaginary parts of complex numbers (Algebra II, Module 3, Ready, Set, Go! Problemm 5), but there is not enough practice for students with the commutative, associative, and distributive properties of complex numbers.
• A-APR.1: Students practice this standard in Algebra II, Module 3, Task 1, and do not practice it after this introductory task. The materials develop how the polynomials are analogous under the operation of division, but they do not develop how they are analogous under the operations of addition, subtraction, and multiplication.
• A-APR.4: In Algebra I, Module 7, Ready, Set, Go! Problem 10, students verify the factored form of a quadratic is the same as standard form. In Geometry, Module 6, Ready, Set, Go! Problem 4, students verify Pythagorean Triples, and in Algebra II, Module 4, students factor sums and differences of cubes. These are all aspects of this standard, but students do not prove the polynomial identities to use them to describe relationships.
• A-APR.6: In Algebra II, Module 5, Ready, Set, Go!, students complete Problems 15-18 and the related task to determine the simplified form of a rational expression. Three of these problems result in an improper rational expression which enables the students to rewrite the expression. This is not enough practice to fully learn this standard.
• F-IF.9: Throughout the materials, students often have to compare two or more representations of functions, but they do not compare different types of functions through different representations.
• F-BF.1b: Students do not combine various types of functions until Algebra II, Module 3, Task 6 when combining trigonometric functions with other functions.
• F-TF.8: Students are not provided opportunities to practice finding the measure of an angle in any quadrant.
• S-ID.1: In Algebra I, Module 9, Ready, Set, Go! Problem 2, students are provided a recommendation to use a dot plot, but there are no mention of dot plots in the instructional materials beforehand. There is not enough practice of all the types of plots for students to fully learn this standard.

The instructional materials reviewed for the Mathematics Vision Project 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 where the materials use age appropriate contexts include:

• In Geometry, Module 7, Task 3, students find the volume of a frustum (created by rotating a trapezoid around the y-axis) and approximate the volume of a vase by replacing the curved edges of the vase diagram with segments. Teachers have students share several different strategies for approximating the volume. (G-GMD.1,4) 
• In Algebra 2, Module 7, Task 1, students use the information from Ferris Wheel tasks in previous modules to develop strategies for transforming the functions to represent different initial starting positions for the rider. Students focus on horizontal translations and may recognize that either sine or cosine functions can be used with an appropriate horizontal shift. (F-TF.5, F-BF.3)
• In Algebra 2, Module 8, Task 2, students sketch the shape of given graphs and give reasoning for their sketches. These functions combine linear, quadratic, absolute value, and trigonometric functions. While doing this, students design plans for a new amusement park ride. (F-BF.1b)

Examples where the materials use various types of real numbers include:

• In Algebra I, Module 2, Task 6, students verify that the properties of integer exponents also apply to rational exponents. Students use exponent rules to write equivalent forms of expressions involving rational exponents and rational bases. Expressions include rational numbers in the base, as well as in exponents. (N-RN.1,2, A-SSE.3)
• In Algebra 2, Module 3, Task 4, students write the equation of given graphs of parabolas in vertex, standard, and factored forms. Students use irrational numbers and the radical form of i to write the factored form of the equations. Task 5 introduces i, and students write equations for given parabolas using complex and imaginary roots.

Examples where the materials provide opportunities for students to apply key takeaways from grades 6-8 include:

• In Algebra I, Module 3, Task 4, students use a given graph of two functions to answer questions regarding key features of the graph, and students interpret some of the key features. This is an application of a key takeaway from Grades 6-8 in applying basic function concepts to develop/solidify new understanding in this module. (A-APR.1, A-CED.3, A-REI.11, F-IF.7)
• In Geometry, Module 4, Task 1, students are presented a scenario where an employee at a copy center is enlarging a photo for a customer and makes a mistake. Students answer questions to determine what the mistake was and how the employee should have enlarged the photo. Students apply a key takeaway from Grades 6-8 regarding similar figures. (G-SRT.1)

The instructional materials reviewed for the Mathematics Vision Project Traditional series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Overall, the materials provide tasks in similar contexts throughout the series, so students can make connections to previous and future learning. The practice problems in Ready, Set, Go! revisit topics in a spiral manner for students to maintain skills throughout the series. 

Examples of the instructional materials fostering coherence through meaningful mathematical connections in a single course include:

• In Algebra 1, Module 6, Task 1, students describe a growing pattern which represents a quadratic function. They build upon interpreting expressions and writing recursive and explicit equations from Module 1 (A-SSE.1 and F-BF.1) to develop the idea that quadratic functions show linear rates of change. In Module 6, this is also connected to A-CED.2 as students write equations to represent quadratic relationships. 
• In Geometry, Module 4, Tasks 8-11 address trigonometric ratios and using trigonometric ratios to solve right triangles in mathematical and applied problems (G-SRT.6-8). Task 8 builds upon students’ previous understanding of similar triangles to define trigonometric ratios. Tasks 9 and 10 use those understandings to develop relationships between sine and cosine of complementary angles. G-SRT is also connected to F-TF.8 in Task 9 as students justify whether given conjectures are true or false, and three of the questions presented are based on the Pythagorean identity. In Task 11, students solve applied and mathematical problems using all concepts and skills from the previous tasks. 

Examples of the instructional materials fostering coherence through meaningful mathematical connections between courses include:

• In Algebra I, Module 1, Task 4, students analyze the pattern of push-ups Scott will include in his workout. Students examine tables, graphs, and recursive and explicit formulas that show how the constant difference is represented in different ways and define the function as an arithmetic sequence. In Algebra II, Module 4, Task 1, students revisit Scott’s workout and develop understanding related to the degree of a polynomial function and the overall rate of change. Students use multiple representations to arrive at this understanding (F-BF.1; F-LE.1-3,5; F-IF.4,5; A-CED.1,2).
• In Geometry, Module 6, Tasks 7 and 8 (G-GPE.2), students define a parabola geometrically using the focus and directrix. In Task 8, students connect this to quadratic functions and parabolas, which were addressed in Algebra I, Modules 6 and 7 (Functions and Algebra conceptual categories). The concepts are further connected in Algebra II, Module 3, Tasks 4 and 5 (A-REI.4, N-RN.3, and N-CN), where students discover a need for complex solutions to quadratic equations and define the imaginary unit.
  

The instructional materials reviewed for the Mathematics Vision Project Traditional series partially meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. In Launch, teachers “review”, “remind”, or “connect” students to work from previous math classes or prior years, but there is no explicit indication of standards from Grades 6-8. Examples where the materials do not explicitly identify standards from Grades 6-8 include, but are not limited to:

• In Algebra I, Module 2, Task 6, students use their understanding of positive whole number exponents to rewrite expressions using the properties of exponents, but there is no mention that this is connected to or building upon 8.EE.1.
• In Algebra I, Module 9, Task 1, the materials state that students will use “prior knowledge” to interpret data presented in a histogram and represent the same data with a box plot. Students previously displayed data in histograms and box plots with 6.SP.4, but this is not identified within the materials. 
• In Geometry, Module 4, Task 3, the materials state, “The definition of similarity that students have been introduced to prior to this task is: Two figures are similar if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations”, and students extend this understanding to develop a new definition of similarity for polygons. The stated definition is established in 8.G.4, but is not identified within the materials. 
• In Geometry, Module 4, Task 5, students apply the Pythagorean theorem to find missing side lengths and, conversely, determine whether given side lengths represent a right triangle. This builds upon 8.G.6 and 8.G.7, but these are not identified in the materials.
• In Algebra II, Module 3, Task 3, the materials build upon students’ understanding of division of whole numbers to support the development of polynomial long division without any identification that students would have developed that fluency in 6.NS.1.
• In Algebra II, Module 4, Task 5 indicates that students have compared and analyzed growth rates of functions but does not identify 8.F.2.

The instructional materials reviewed for Mathematics Vision Project Traditional series do not consistently identify the plus standards, when included. The instructional materials use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready. There are inconsistencies with the identification of the plus standards. 

• N-CN.8 is identified in Algebra II, Module 3, Tasks 4 and 5, Module 4, Tasks 4 and 6, Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. In Module 3, Task 4, students use the quadratic formula to find non-real roots and write the equation of the parabola in factored form, and in Task 5, students extend this understanding to include imaginary roots. In Module 4, students find suitable factorizations of quadratic, cubic, and quartic polynomials, and some of these have imaginary roots and develop understanding that imaginary roots occur in conjugate pairs.
• N-CN.9 is identified in Algebra II, Module 3, Tasks 4 and 5, Module 4, Tasks 3, 4, and 6, Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. In Module 3, Task 4, Question 10, and Task 5, Question 15 address the Fundamental Theorem of Algebra. In Module 4, Tasks 3 and 4, students determine if their responses are consistent with the Fundamental Theorem of Algebra.
• A-APR.5 is identified in Algebra II, Module 3, Task 2, Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. The task starts with a review of multiplying polynomials and ends with eight questions that have students using Pascal’s Triangle to expand binomials.
• A-APR.7 is identified in Algebra 2, Module 5, Task 5, Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. In this task, students perform operations with rational expressions.
• A-REI.8 is identified in Algebra I, Module 5 of the “non-honors” curriculum. The Table of Contents lists tasks 11H and 12H as addressing this standard, but those tasks are not included in the Module 5 materials for the “non-honors”.
• F-IF.7d is identified in Algebra 2, Module 5, Tasks 1, 2, 3, and 6, Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. Each of these tasks address graphing rational functions.
• F-BF.1c is identified in Algebra II, Module 8, Tasks 4, 5, and 6 and Table of Contents, and it is identified as a plus standard in the Teacher Notes. It is not included in the Core Correlation. Students compose functions in the Go practice sections of Algebra II, Module 1, Tasks 2, 3, 4, and 5 before there is formal instruction of composition in Module 8.
• F-BF.4b is identified in Algebra II, Module 1, Tasks 4 and 5, Teacher Notes as a plus standard, but is not identified as a plus standard in Table of Contents. The standard is not listed in Core Correlation. Students verify inverse functions with an alternate use of composition (The function g is the inverse of function f if and only if f(a) = b and g(b) = a). Students use composition in the Go section of the practice set at the end of the task, but no connection is made between the composition of functions and verifying that the functions are inverses of each other. Task 5 is designed to give students additional practice with finding inverses.
• F-BF.4c is identified in Algebra I, Module 8, Tasks 5 and 6, and the Teacher Notes but not in the Table of Contents or Core Correlation. In the Teacher Notes, it is identified as a plus standard. Students create multiple representations, including graphs and tables, of given functions and determine if there is a relationship between the functions, which develops into recognizing inverse functions. The standard is also identified in Algebra II, Module 1, Tasks 2, 3, and 5 and the Teacher Notes and marked as a plus standard. It is also identified in the Table of Contents, but not as a plus standard, and it is not identified in Core Correlation. Task 2 extends inverse functions to quadratic and square root functions, and Task 3 extends inverse functions to exponential functions. Task 5 provides students additional practice with finding inverses. 
• F-BF.4d is identified in Algebra I, Module 8, Task 6 as a plus standard in the Teacher Notes, but it is not identified in the Table of Contents or Core Correlation. Students write inverse functions for linear and quadratic functions, which results in restricting the domain to create an inverse function. This standard is also identified in Algebra II, Module 1, Tasks 2, 3, and 5 in the Teacher Notes as a plus standard. It is identified in the Table of Contents, but not as a plus standard, and it is not identified in Core Correlation. Task 5 provides students additional practice with finding inverses.
• F-BF.5 is identified in Algebra II, Module 1, Task 3, and Module 2, Tasks 1 and 2. In Module 1, the standard is identified as a plus standard in the Teacher Notes, but it is not identified in the Table of Contents. In Module 2, the standard is not identified as a plus standard in the Table of Contents, but it is identified as a plus standard in the Teacher Notes. The standard is in Core Correlation and identified as a plus standard, but the tasks listed in Core Correlation are from Module 2. Module 1 introduces the term, logarithm, and a logarithm is formalized in Module 2. In both tasks in Module 2, there is little to no connection made to the inverse relationship between exponentials and logarithms.
• F-TF.3 and 4 are identified in Algebra II, Module 7, Tasks 4 and 5, and the Table of Contents without being identified as a plus standard. They are identified as plus standards in the Teacher Notes, but they are not included in Core Correlation. Task 4 extends previous learning about the unit circle to the tangent function, and Task 5 uses the unit circle as a foundation for F-TF.8. 
• F-TF.7 is identified in Algebra II, Module 7, Task 6 in the Table of Contents without being identified as a plus standard. It is identified as a plus standard in the Teacher Notes, but it is not included in Core Correlation. In this task, students solve trigonometric equations through an application of the trigonometric identities learned in previous tasks.
• G-SRT.9,10, and 11 are identified in Geometry, Module 7, Tasks 5 through 8 in the Table of Contents with no indication of being plus standards. In the Teacher Notes and Core Correlation, the standards have the plus sign (+). Task 5 addresses special right triangles (45-45-90 and 30-60-90) and does not include the Laws of Sines and Cosines. Task 6 addresses finding missing sides and angles of non-right triangles using right triangle trigonometry after drawing ancillary lines. Task 6 does not use the Laws of Sines or Cosines, so it does not address the standards listed. Task 7 derives the Laws of Sines and Cosines, and in Task 8, an alternate formula for the area of a triangle using sine (G-SRT.9) is derived.
• G-C.4 is identified in Geometry, Module 5, Task 3 in the Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. Constructing a tangent line from a point outside a given circle is addressed in question 8.
• G-GMD.2 is identified in Geometry, Module 5, Task 12 in the Table of Contents, Teacher Notes, and Core Correlation, but is never identified as a plus standard. This task addresses giving an informal argument using Cavalieri’s principle for the formulas for the volumes of solid figures.
• S-MD.7 is identified in Geometry, Module 8, Task 1 in the Table of Contents and the Teacher Notes. In both locations, the standard is identified as a plus standard, but it is not listed in Core Correlation for Geometry. Students analyze the accuracy of a tuberculosis skin test using conditional probability.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Every three tasks in each module follow the develop/solidify/practice sequence. This allows students to develop conceptual understanding across many tasks. For example, in Algebra I, Module 4, each task builds upon the previous to reinforce concepts:

• Task 1 Develop - Explaining each step in the process of solving an equation (A-REI.1).
• Task 2 Solidify - Rearranging formulas to solve for a variable (N-Q.1,2; A-REI.3; A-CED.4).
• Task 3 Practice - Solving literal equations (A-REI.1,3; A-CED.4).

Within this progression, students develop their conceptual understanding of what it means to solve an equation in each task. The materials develop the understandings through each task, so students can build on the previous days’ learnings.

• F-IF.7: In Algebra I, Module 7, Task 1, students develop an understanding of transformations on a graph and how it relates to a corresponding equation. Students explore the changes of a graph in relationship to the area of a square. By the end of this task, students identify the key features of the graph and how changes to a corresponding equation will change the graph. This development is continued in Task 2.
• G-CO.10: In Geometry, Module 3, Task 1, students explore why the interior angles of a triangle add up to 180 degrees. Their understandings of the sum of angles along a straight line and transformations are expanded as they prove relationships about triangles. Students also use the key mathematical concepts of transformations and congruence to prove other theorems about triangles.
• N-RN.3: In Algebra II, Module 3, Tasks 5 and 6 develop the concept of irrational numbers. The tasks begins with plotting real numbers on a number line and moves to plotting irrational numbers on the number line. This activity helps students understand how irrational numbers behave in similar and different ways to the rational numbers. Once students establish this understanding in Task 5, the students develop their understanding of the properties of irrational numbers in Task 6. The materials address irrational numbers and their properties over two tasks, so students can develop a more thorough understanding of the mathematical concept.

The instructional materials for Mathematics Vision Project Traditional series partially meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. Within Ready, Set, Go!, students practice various skills from across the series, however, some standards/clusters do not have enough practice problems. Examples of the materials not containing enough practice problems for students to independently demonstrate procedural skills include, but are not limited to:

• In Algebra I, Module 7, Task 1, students complete scaffolded questions about the effect on the graph of f(x) by replacing it with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) (F-BF.3). In Set, students complete five problems to develop and demonstrate their procedural skill.
• In Geometry, Module 4, Task 6, students determine the midpoint of multiple line segments (G-GPE.6) by answering scaffolded questions. One question within the introduction is based on finding a point on a line segment beyond a 1:1 ratio. In Ready, students work ten problems related to the concept, with four of those addressing a ratio other than 1:1.
• In Algebra II, Module 3, Ready, Set, Go!, five of the quadratic equations have complex solutions (Questions 22-25 and 36). This is not enough practice for students to develop procedural skills with complex solutions (N-CN.7).

The instructional materials for Mathematics Vision Project 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. Every task begins with an engaging scenario that is either a direct, real-world application of the content for that day or provides a unique, novel problem for the students to solve. The applications within the series enable students to develop their conceptual understanding of the mathematics and the abstract notation or procedural skills once students have built that understanding. There are also scenarios that recur throughout the series. As a result, students contextualize many different mathematical ideas to the same scenario.

The series includes numerous applications across the series, and examples of select standard(s) that specifically relate to applications include, but are not limited to:

• A-REI.11: In Algebra I, Module 3, Tasks 4-6 use a Water Park scenario where students, in task 4, determine when both pools are the same height using intersection points. In task 5, they compare the graphs of the pools to the sum of both pools. In task 6, students set the two function rules equal to each other to determine the intersection point. The scenario spans the three tasks, so students develop their understanding about the intersection points of two graphs and the different properties of functions.
• G-SRT.8: In Geometry, Module 4, Task 10, students determine the height of a tree using angle of elevation and shadows. Students work within the same scenario to determine unknown angles of depression and elevation. In Ready, students work multiple real-world problems using trigonometric ratios to determine missing lengths and angles.
• F-IF.7: In Algebra II, Module 5, Task 1, students write, graph, and solve rational equations in the context of winning the lottery. Students compare different points on the equation and graph based on different ways of splitting the prize money. In Set, students interpret an equation and graph to determine different ways of paying for a gift among friends.

The instructional materials for Mathematics Vision Project Traditional series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The materials engage students in each of the aspects of rigor in a cycle throughout the materials. Each module contains a Developing Understanding task to build conceptual understanding in students, a Solidifying Understanding task to build on that conceptual knowledge, and a Practicing Understanding task. Within each task there are Ready, Set, Go! activities that spiral procedural skills for students. 

For example, in Geometry, Module 6, Task 4, students develop conceptual understanding of the equation of a circle centered at the origin. Students practice procedural skills with the equations of circles in Ready, Set, Go!, Questions 10-15. In Task 5, students solidify their understanding with a sprinkler application problem and determine the equation of a circle when it is not centered at the origin. Students practice this concept in Ready, Set, Go!, Questions 11-19. In Task 6, students continue working with equations of circles with different challenges in the task and the Ready, Set, Go! questions.

The instructional materials for Mathematics Vision Project Traditional series meet expectations that the materials support the intentional development of making sense of problems and persevere in solving them, as well as attending to precision (MP1 and MP6) in connection to the high school content standards.

Examples of MP1 include, but are not limited to:

• In Geometry, Module 2, Task 1, students construct two shapes, a rhombus and a square. Within the materials, teachers are prompted for students to get enough time to explore the constructions fully. Within this task, students make sense of the constructions and persevere through the process of making the construction.
• In Algebra II, Module 1, Task 1, students recall previous information about functions and their graphs to make sense of inverse functions. Through the task, students notice how a function and its inverse are related and make sense of the relationship. Students determine what makes two functions inverses from their observations about the Pet Sitter situation.  
• In Algebra II, Module 5, Task 5, students identify and record errors in the Rational Expression and Functions activity. Students provide strategies to help others avoid these errors in the future. Through this, students make sense of the problems they are completing by determining where the errors might occur.

Examples of MP6 include, but are not limited to:

• In Algebra I, Module 2, Task 2, students identify the domains of two sequences in the Please Be Discrete task. Students determine that one is arithmetic and the other geometric. Students discuss how discrete and continuous functions are related, specifically around their domains. In order to discuss the difference between these two functions, students must be precise to show the differences between the two functions.
• In Geometry, Module 1, Task 1, students use precision in their language for transformations. Students use precise definitions for each of the transformations so the final image is a “unique figure, rather than an ill-defined sketch”. The materials prompt students to see how precision is needed when defining geometric relationships to make sure that images are well defined. 
• In Algebra 2, Module 8, Task 3, students attend to precision as they determine different parameters of their equations. The Bungee Simulator is a sophisticated graph that combines a sinusoid and exponential decay. In order to match a function to the graph provided, students utilize precision with their parameters to create a function that models the situation.

The instructional materials for Mathematics Vision Project Traditional series meet expectations that the materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. Throughout the materials, there are many opportunities for students to critique the reasoning of others and to reason abstractly.

Examples of MP2 include, but are not limited to:

• In Algebra I, Module 4, Task 4, students are given a statement and determine which of the two expressions represent a larger value. In the Which is Greater task, students reason abstractly about an expression, compare it to another expression, and explain their reasoning.
• In Algebra I, Module 7, Task 1, students reason abstractly by relating the numeric results in a table to the graphs and explain the way the graph is transformed. Students examine the abstract relationships between the different representations (table, graph, and function) and how a change in one form impacts a change in the other.
• In Geometry, Module 5, Task 5, students engage in reasoning that considers how an infinite process might converge on a unique value. In Polygons to Circles, students examine the case of how an inscribed regular polygon with more and more sides converges on the shape of a circle. This limiting process provides an informal proof for the circumference and area of a circle.

Examples of MP3 include, but are not limited to:

• In Algebra 1, Module 3, Task 2, students interpret two representations (a table and a graph) and determine if Sierra’s statements are correct. During the task, students analyze the situations, justify their reasoning, and communicate their conclusions to others.
• In Geometry, Module 4, Task 8, the whole-class discussion begins by sharing several examples of triangles, so equivalent ratios can be observed. From this, students hypothesize the trigonometric relationships for all right triangles. Students determine how the ratios are related and construct an argument for what they believe about the trigonometric ratios. The materials promote a discussion for why these ratios are equivalent in all right triangles.
• In Algebra II, Module 4, Task 5, students use prior knowledge about polynomials and function behavior to construct an argument for the end behavior of various polynomial and exponential functions. They compare the functions and defend their conclusions.

The instructional materials for Mathematics Vision Project Traditional series meet expectations that the materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. 

Examples of MP4 include, but are not limited to:

• In Algebra 1, Module 5, Task 3, students manipulate a system of equations to model the constraints of setting up a pet-sitting business. They determine the best use of space to provide maximum profit. Students also have to understand what terms in their expressions are related to the different constraints. From this, they derive various forms of the equations to determine maximum profit.
• In Geometry Module 5, Task 4, students analyze a plan to build a regular, hexagonal gazebo. In the plan, there are several statements students have to agree or disagree with and then design their own gazebo.
• In Algebra II, Module 8, Task 3, students model a bungee jump simulation and use calculator technology to create their model.

Examples of MP5 include, but are not limited to:

• In Algebra I, Module 2, Task 8, students compare linear and exponential growth related to two small companies. They are encouraged to use a calculator or spreadsheet to determine if this growth is continuous or discrete.
• In Geometry, Module 2, Task 2, students use the circle as a tool to create congruent line segments. Students also consider transformations as tools to think about congruence when creating mappings.
• In Algebra II, Module 2, Task 5 notes that students should use various tools, such as tables, graphs, and technology, to compare functions and their end behavior.

The instructional materials for Mathematics Vision Project Traditional series meet expectations that the materials support the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards.

Examples of MP7 include, but are not limited to: 

• In Algebra I, Module 8, Task 3, students use their understanding of absolute value to help solidify their understanding of piecewise functions. They develop the graph for an absolute value function using their understanding of piecewise functions. 
• In Geometry, Module 1, Task 6, students uncover the structure of regular polygons through the ideas of rotational and line symmetry. They notice the relationship between the number of sides in a regular polygon and the shape’s rotational and line symmetry. 
• In Algebra II, Module 3, Task 5, students use their knowledge of the quadratic formula to predict the nature of the roots of a parabola. Students relate their understanding of the different forms of the quadratic equation to the graph of a parabola to make predictions about roots. 

Examples of MP8 include, but are not limited to:

• In Algebra I, Module 8, Task 6, students are prompted to see when finding an inverse you can sometimes just “undo” the operations in the opposite order of the original function. Students also build an understanding of how to restrict the domain of the inverse based on this process.
• In Geometry, Module 5, Task 10, students determine the relationship between the area and perimeter of similar figures. Through the task, students develop the pattern for the relationship of properties between these scaled figures.
• In Algebra II, Module 4, Task 1, students explore how to determine the degree of a polynomial function. Students look at different rates of change to determine the type of function. For example, students understand that a cubic has a “first difference that is quadratic, a second difference that is linear, and a third difference that is constant”. Students are prompted to understand this pattern in all polynomial functions.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation that the underlying design of the materials distinguish between problems and exercises. Problems are included in “tasks”, which attend to specific standard(s) or aspect of a standard(s). There are three different kinds of tasks: Develop Understanding, Solidify Understanding, and Practice Understanding. Develop Understanding tasks introduce concepts and build on previous knowledge by providing discovery problems. Solidify Understanding tasks focus on the concepts being developed in the unit and provide students opportunities to practice what they have learned so far in the unit. Practice Understanding tasks extend learning by adding small extensions to the concepts covered in the unit. Ready, Set, Go! Exercises are designated as “homework”. Ready exercises are intended to prepare students for the upcoming work in class, Set exercises reinforce the work done in class that day, and Go exercises review concepts and skills that students learned previously.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet expectations that the design of the assignments is not haphazard and are given in intentional sequences. The materials create connections as tasks begin by re-examining mathematical content so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the material is designed to spiral concepts throughout the entire series.

Structure of the Materials states that Ready and Go exercises provide a spiraling sequence of content to help maintain skills. However, these spiraled exercises often contain concepts that are unrelated to the content of the new lesson and/or have not yet been learned in the sequence of the course or series. Examples of these exercises affecting the overall sequence of the materials include:

• In Algebra I, Module 5, Ready, Set, Go! Problem 8, students identify transformations in Ready, but this concept is not addressed until Geometry even though the concept is addressed in Grade 8 standards. The main topic of the module is systems of equations, and this practice does not provide practice that connects to the work being done in the Module or the course. 
• In Algebra 1, Module 9, Ready, Set, Go! Problem 8, students create geometric constructions after learning about residuals. These topics are not related, and the materials do not address constructions until Geometry.
• In Geometry, Module 2 addresses geometric constructions and connects those to congruence of figures. In Go for Task 1, students solve systems of equations. In Go for Task 2, students write recursive and explicit formulas for sequences. While this is connected to content from Algebra I, it is not connected to new content in Module 2.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet expectations for having variety in how students are asked to present the mathematics. For example, students provide numerical answers, produce graphs, compile charts, draw pictures, find equations and functions, create models, describe patterns, articulate arguments, write critiques, and analyze work and possible solutions. In almost every task, students present mathematics in multiple ways. For example, in Algebra I, Module 5, Task 5, students write inequalities and create graphs. In Geometry, Module 7, Task 1, students draw three-dimensional solids and their two-dimensional cross sections. In Algebra II, Module 3, Task 2, students create area models to solve binomial multiplication.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet expectations that manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials occasionally instruct students to use manipulatives within the materials (for example: Algebra 2, Module 6, Task 8). On the main webpage, under the Resources header, there are links that are connected to a set of ten GeoGebra Interactive Applets (i.e. Leaping Lizards, Triangle Dilation). Directions for the interactive applets can be found within the applets and the teacher notes. A few examples of suggested physical manipulatives include dice to model a data set, and an area model for multiplying binomials, completing the square, and factoring.

The instructional materials reviewed for Mathematics Vision Project Traditional series have a visual design that is not distracting or chaotic. The materials are digital versions of print books. The e-book does not have any enhancement features such as embedded media, interactivity, narration, etc. There are no places for students to enter answers that are then compiled for teachers. The index at the beginning of each module doesn’t have bookmark links to the lessons within that module, and there are no page numbers when it is a printed resource.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation for supporting teachers by providing quality questions to guide students’ mathematical development. The Teacher Notes provide suggested questions to use during the Teaching Cycle (Launch, Explore, Discuss) that aid in students’ developing understanding of the content. For example, Algebra I, Module 1, Task 6, Launch: “Then, wonder out loud whether or not it would be an arithmetic sequence if a number is subtracted to get the next term. Don’t answer the question or solicit responses.” There is also an Essential Question provided as part of the Enhanced Teacher Notes for each task, and the tasks contain questions designed to elicit discovery and exploration.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation that the teacher edition contains ample and useful annotations. Teacher Notes are provided for each module, and the notes contain structured guidance on how the lessons should proceed. The notes may include some or all of the following sections:

1. Special Note to Teachers: highlights an aspect of the task and how it fits in the overall sequence of the three course materials.
2. Purpose: describes the previous development of concepts needed for the lesson and where to place emphasis for the lesson.
3. New Vocabulary: lists new vocabulary introduced in the lesson.
4. CCSSM Standards focus and related Standards: lists those addressed in the lesson.
5. Standards for Mathematical Practice: lists those addressed in the lesson.
6. The Teaching Cycle: Launch, Explore, Discuss, provides a detailed discussion on lesson delivery. 

There is also reference made to the use of technology within the teaching cycle, but there is no discussion of how to use the technology. In Algebra I, Module 9, Task 5, the introduction states, “Most graphing calculators will work well. Free computer apps would be very helpful and easy to use on this task as well (GeoGebra and Desmos, etc.).”

 The MVP Enhanced Teacher Notes include the basic Teacher Notes, Essential Questions for each task, articulation of Standards of Math Practices of Focus, exit ticket ideas, instructional supports, instructional adaptations, intervention ideas, challenge activities, answer keys to in class tasks, and answer keys to Ready, Set, Go!.

The instructional materials reviewed for Mathematics Vision Project Traditional series do not meet the expectation for containing adult-level discussions of the mathematics. The Teacher Notes do not contain explanations of advanced mathematical topics that advance the knowledge of the teacher. For example, in Geometry Module 5, Task 4, the purpose states, “In this task students will develop a strategy for finding the perimeter and area of regular polygons. This work will lead to informal arguments for the formulas of the circumference and area of a circle in the next task.” Teachers are not provided with further instructions within the task to advance the learning of the concept for the teacher.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that the Teacher edition addresses the standards in the context of the overall series. An overview of each module and associated tasks is provided in the Introduction to the Materials document on the course page. An overview of each task is also provided in the Teacher Notes. The materials make occasional references to previous and future standards related to the current task. Also, occasional references are made to a course, but rarely to the module or the task. For example, in Geometry, Module 6, Task 2 states, “The purpose of this task is to prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. Students have used these theorems previously.” No precise reference about how current content fits into the vertical progression of learning is provided.

The instructional materials reviewed for Mathematics Vision Project Traditional series contain Teacher Notes that include an index of Tasks within each Module with related standards. A Core Correlations document is included in the materials, which serves as a reference for standards addressed in the materials. A pacing guide for the materials was not provided, but the materials state to "usually" use/teach a task a day.

The instructional materials reviewed for Mathematics Vision Project Traditional series provide a link on the main webpage for parents that contains a general, course-wide letter. If support is needed for homework, the materials suggest, “If there are areas in the Ready, Set, Go! homework assignments, where your student feels uncertain and needs guidance, please access the online help videos hosted at rsgsupport.org. For a very small subscription fee you can provide your student with help that is directly connected to his/her homework assignment. There are also print resources that can be obtained for reference.” The videos provided on rsgsuppport.org are currently available for the Integrated series. Helps, Hints and Explanations is a resource available for purchase and was developed for students and parents to assist them as they work on Ready, Set, Go! homework. This resource has explanations and examples intended to remind students of what they learned in class and provide them with support as they work on their homework. 

The instructional materials reviewed for Mathematics Vision Project Traditional series provide a link for professional development on the main webpage. This webpage contains past presentations, via powerpoint, on the Comprehensive Mathematics Framework, the basis of the design of MVP. Professional development options are also available for purchase about the approaches, strategies, and research.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing materials for gathering information about student’s prior knowledge within and across grade levels/courses. The Ready exercises within a task are intended to help students review and prepare for the skills and concepts that will be needed for the task. However, there is no guidance for the teacher as to how to interpret these exercises, nor is there any discussion of possible strategies for remediation.

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation for providing support for teachers to identify and address common student errors and misconceptions. The materials often include a comment related to common errors or misconceptions, but they do not always identify what these might be. For example, in Algebra I, Module 8, Task 2 Explore, the teacher notes state: “As you monitor, look for common student misconceptions to discuss during the whole group discussion. For example, some students may not realize…” and the notes go on to explain a misconception. In the same module, Task 7 Explore states: “Look for common errors among students so that you can discuss these more thoroughly during the whole group discussion”, but no indication is included of what these might be or how to address them in the whole group discussion.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing opportunities for ongoing review and practice of both skills and concepts. The structure of the tasks within a module, and across modules, provides for review of concepts. However, besides the Ready, Set, Go! exercises within each task, there is no ongoing practice of skills, and there is no discussion of how to provide feedback. The Ready, Set, Go! exercises do provide students the opportunity to show proficiency on certain topics, but few resources are provided for teachers to provide feedback. 

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that standards are clearly denoted for assessments. Assessments do indicate course, module, and task, but specific standards are not identified on the assessments. Algebra II, Module 2 Quiz, states, “Logarithmic Functions 2.1-2.4”, but it does not indicate for each question which standards are addressed. Assessments are based on modules, which include the standards of focus. Although quizzes and tests do not specifically provide standards, performance-based assessments include the standards.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

Assessments typically have multiple parts including a mixture of the following types of problems: Multiple Choice, Matching, Building Tables, Short Answer, and Short Essay. Occasionally students are asked to demonstrate different methods to solve similar problems. There were few of the short answer and short essay problems, and the majority of the assessments were comprised of multiple choice/matching type problems.  

Scoring rubrics for the short answer and short essay questions were not available, and grading expectations for weighted value of the assessments. Sample assessments include rubrics for the performance-based assessments which offer limited guidance, but do not provide guided feedback.

Self assessments are included within the materials and allow students to monitor their progress. Students are expected to document evidence of their personal rating. The students have three choices for assessing, "I can do this without mistakes", "I understand most of the time…," and "I don't understand." Students are asked to give evidence of their response. No teacher materials were provided to explain what this "evidence" should or could look like or to explain how the teacher should use the "evidence".

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. Teacher materials provide a prescribed Teaching Cycle. Each task has an Explore (Small Group) component for developing student understanding. If the students do not meet the expectations in small group, strategies are not consistently provided for how the teacher can scaffold the content of the task. An example: Algebra I, Module 5, under Explore Small Group, “watch and listen and encourage connections.”

The Enhanced Teacher Notes offer “Instructional Supports” that sometimes contain a scaffolding/intervention section, such as in Algebra I, Module 2, Task 10 which provides a graphic organizer to help students classify forms of linear equations. 

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners. Enhanced Teacher Notes offer “Instructional Supports”, “Instructional Adaptations”, and “Challenge Activities” as resources to differentiate instruction. These, however, are not comprehensive. The note in Geometry, Module 1, Task 5, under Instructional Adaptations states, “The use of the cutouts described in the Instructional Supports section should be sufficient intervention for this task, and provide adequate support for all students.” However, no other strategies or suggestions were given.

The Enhanced Teacher Notes list “Instructional Supports” and “Instructional Adaptations” at the end of each task. For example, Geometry, Module 1, Task 3, has these instructional supports listed:

• Relatable Context - summarizes why this context will engage students.
• Visualization - addresses the misconception that could result if students mistakenly think of this as a three-dimensional action instead of a two-dimensional action of reflecting.

And these Instructional Adaptations:

• Intervention Activity - use of tracing paper.
• Challenge Activity - “Ask students to consider this question: Is it possible to find a sequence of transformations that will carry every image to every other image in the diagram if the first transformation in the sequence is always to translate the tip of the middle fingers of the left hand of the first image to the corresponding point on the second image? What are the implications of this?”.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. Most tasks do not provide multiple entry-points. 

Some tasks do provide multiple entry points. For example, in Geometry, Module 7, Task 1, students explore two-dimensional cross sections of three-dimensional objects. The materials offer many different ways for students to engage in this visualization - drawing “slices” of a cube on a two-dimensional drawing, partially filling a cylinder with water and tilting and turning it different ways while watching what the surface of the water does, and finally, observing the possible shapes of shadows that can be cast by different objects.

The tasks set for the students can often be approached from many perspectives, using different strategies and representations. In some cases this is encouraged; however, in most cases the teacher is instructed to guide the students to the “desired” method of solution so as to address the standard in question.

The instructional materials reviewed for Mathematics Vision Project Traditional series do not meet the expectation for providing 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). No accommodations for English Language Learners or other special populations are available.   

The instructional materials reviewed for Mathematics Vision Project Traditional series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. The Enhanced Teacher Notes offer “Challenge Activities” as resources for advanced students. For example, in Algebra I, Module 9, Task 5 the teacher is prompted to “have students find data in two way tables on the internet, then have them write a story, using relative frequency statements.”

The instructional materials reviewed rarely contain images of people. The names included in the problems are diverse.  

The instructional materials provide some suggestions for teachers to use a variety of grouping strategies. The Enhanced Teacher’s Notes have suggestions for grouping listed next to each activity. Group work is embedded in every task; MVP strongly suggests all teachers take their inservice training. No implementation guide was made available to teachers related to the pedagogy of collaborative learning, how to form and manage groups, or effective techniques that could be used. 

The instructional materials did not provide references for teachers to draw upon home language and culture to facilitate learning.

The instructional materials for the Mathematics Vision Project Traditional series are accessible within any browser. Each module is presented as a Portable Document File (pdf), which can be viewed online or printed. These files can be viewed on tablets and mobile devices.

In the instructional materials for the Mathematics Vision Project Traditional series, students demonstrate knowledge and understanding through the virtual manipulatives, but other than those, there are few opportunities to show knowledge and understanding by using technology. The enhanced teacher materials provide teachers with suggestions on how technology can help students develop an understanding of concepts, but they do not provide specific instructions on the use of technology to assess understanding and procedural skills for each task.

The instructional materials reviewed for the Mathematics Vision Project Traditional series do not allow personalization. 

The instructional materials reviewed for the Mathematics Vision Project Traditional series do not offer a wide range of lessons on each topic. Each lesson involves a central task or problem. Teachers are encouraged to seek additional resources in order to give students a deeper understanding of certain topics. Teachers and individuals that have purchased the print version of Ready, Set, Go! Answer Keys and Sample Assessments can also receive Word Document files containing the sample assessment items. These sample assessment items could be easily customizable for local use.

The instructional materials for the Mathematics Vision Project Traditional series do not offer opportunities for students to collaborate with each other using technology. 

Mathematics Vision Project has a current Facebook page with over 1,035 likes and can be followed on Twitter at @MVPmath. Teachers can also register to receive updates related to instructional supports and materials from the MVP team.

Although the instructional materials for the Mathematics Vision Project Traditional series are presented in a digital format, few opportunities are provided for students to use technology in effective ways for the purpose of engaging in the Mathematical Practices. A few virtual manipulatives are listed on the course home page (via Geogebra), but they are aligned to the courses of the integrated series. The activities are not linked to, nor referenced in, the teacher or student materials. The interactive activities give instructions for students to complete the tasks. These tasks are provided for a few lessons throughout the entire series (approximately 10 activities posted).