Alignment

Focus & Coherence

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Rigor & Mathematical Practices

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Meets Expectations
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Usability

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Alignment

The instructional materials reviewed for the Mathematics Vision Project Integrated series meet expectations for alignment to the CCSSM for high school. The materials meet the expectations for focus and coherence and attend to the full intent of the mathematical content standards. The materials also attend fully to the modeling process when applied to the modeling standards. The materials meet the expectations for rigor and the Mathematical Practices as they reflect the balances in the Standards and help students meet the Standards’ rigorous expectations and meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

For this report, the complete student materials for Secondary Mathematics One, Two, and Three were considered. The Enhanced Teacher Notes for Secondary Mathematics One and Two were reviewed, but the Enhanced Teacher Notes for Secondary Mathematics Three was not reviewed as it was not complete at the time this report was released. This report will be updated upon completion of the Enhanced Teacher Notes for Secondary Mathematics Three.

GATEWAY ONE

Focus & Coherence

MEETS EXPECTATIONS

Criterion 1a-1f

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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).

The instructional materials reviewed for the Mathematics Vision Project Integrated series meet the expectation for focusing on the non-plus standards of the CCSSM. The Modules and Tasks across the series are organized in a consistent logical structure of mathematics. Overall, the instructional materials attend to the full intent of the non-plus standards, attend to the full intent of the modeling process, spend a majority of time on the widely applicable prerequisites from the CCSSM, require students to engage at a level of sophistication appropriate to high school, and make meaningful connections within each course and throughout the series.

Indicator 1a

The materials focus on the high school standards.*

4/4
Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The instructional materials reviewed for the Mathematics Vision Project Integrated series meet the expectation that the materials attend to the full intent of the mathematical content contained in the high school standards for all students. Overall, the materials fully addressed the mathematical content of the standards, but there were a few instances where the materials failed to meet the full intent of the standard.

The following are examples of standards that are attended to fully by the materials:

  • F-IF.3: In Secondary Math One, Module 2, Task 1 students work with arithmetic and geometric sequences including discrete and continuous linear and exponential situations. In Secondary Math One, Module 2, Task 2 students connect context with domain and distinguish between discrete and continuous functions, and in Secondary Math One, Module 3, Task 7 students identify whether or not a relation is a function given various representations.
  • F-IF.7: This standard is addressed across multiple lessons and courses and incorporates a variety of functions in a variety of ways. For example, the standard is addressed in Secondary Math Two (2.2.1, 2.4.1-4) and Secondary Math Three (3.3.3,6,7,8).
  • A-APR.1-5: These standards are addressed in Secondary Math Three, Module 3, Tasks 4-8. In task 4, students add, subtract, and multiply polynomials while looking for patterns and paying attention to end behavior. In task 5, students develop an understanding of multiplicity to gain a deeper understanding of the relationship between the degree and the number of roots of a polynomial. In task 6, students identify the degree of the polynomial, determine end behavior, use the Fundamental Theorem of Algebra, determine the multiplicity of a given root, and recognize graphs, including those with imaginary roots. In task 7, students apply the Remainder Theorem. In task 8, students factor, solve, and graph polynomials and find roots, determine multiplicity, and predict end behavior.
  • N-RN and N-CN.1, N-CN.2, and N-CN.7: In Secondary Math Two, Module 3, Tasks 1-4, the introduction of rational exponents is done in context (i.e. bacteria population growth rates and interest on a savings account). Students choose their quantities and scale and explain why they are being used. When graphing, the students often begin with a blank grid and must supply the scale and labels they will use. In Secondary Math Two, Module 3, Task 9 students extend the real and complex number systems, and in Task 10 students examine the arithmetic of real and complex number systems, engaging students in the use of with rational and irrational numbers.
  • S-CP.A: The materials address conditional probability in Module 9, Task 3 (using samples to estimate probabilities), Task 5 (examining independence of events using two-way tables), and Task 6 (using data in various representations to determine independence).

There are instances where the materials attend to part of the standard but do not attend to every aspect of the standard:

  • G-GPE.7: Secondary Math One, Module 8, Tasks 1 and 3 address perimeter, but the materials do not address area. There are no tasks where students find area by using the coordinates.
  • S-IC.4: The materials have students engage in the use of a random sample in the Ice Cream Task in Secondary Math Three, Module 9, Task 2, but population “mean” or “proportion” and “margin of error” are not mentioned. Also, the sample the task is analyzing is not truly “random,” because the participants in the survey are voluntary and not randomly selected.
  • N-Q.3: Students are not required to choose a level of accuracy appropriate to limitations on measurement when reporting quantities. The standard is not listed in the “Core Alignment Document.” There are instances in the materials where students would need to choose a level of accuracy appropriate to the limitations on measurement when reporting quantities, such as Secondary Math Three, Module 6, when students are using Trigonometric functions to analyze the periodic rotation of the ferris wheel. Some of the answers will be irrational and require students to round and decide what place value would be best to round to. The materials do not appear to instruct students on how to make this decision.

These standards are not attended to by the materials:

  • A-SSE.4: Students are not required to derive the formula for the sum of a finite geometric series (when the common ratio is not 1) and then use the formula to solve problems such as calculating mortgage payments. The standard was listed in the “Core Alignment Document,” yet the reviewers did not find it addressed by any specific tasks.
  • S-IC.5: The use of simulation as stated in the standard is not included in the series. The standard is listed in the “Core Alignment Document,” yet the reviewers did not find it addressed by any specific tasks.
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Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.

The instructional materials reviewed for Mathematics Vision Project Integrated 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 every step of the modeling process. Tasks that involve modeling include a graphic of the modeling process in the teacher notes. Additionally, all the modeling standards are addressed in the materials.

Examples of modeling tasks include:

  • Secondary Math One, Module 1, Task 2, “Growing Dots” addresses standards F-BF.1 and F-LE.1, 2, and 5. The students are presented with a visual pattern of dots and are asked to describe that pattern and to predict how the pattern would look after 3 minutes, 100 minutes, and "n" minutes. The teacher notes prompt the teacher to ask students to share out specific strategies and solution paths. While the teacher notes are scripted and prompt the teacher to seek out specific strategies, the problem leaves students open to any approach they find logical. The teacher notes place equal value on any of the possible student strategies and encourage students to analyze and discuss the variable strategies.
  • Secondary Math One, Module 2, Task 5, “Making My Point” addresses standards A-SSE.1, A-SSE.2, A-CED.2, and F-LE.5. The focus is on understanding and using various notations for linear functions. Students are guided to create two different but equivalent equations that are a mathematical model of the context: quilt blocks in a quilting pattern. By constructing tables, drawing graphs, and completing patterns they investigate both equations in order to identify that they are in fact equivalent.
  • Secondary Math Two, Module 1, Task 3, “Scott’s Macho March” addresses standards F-BF.1, F-LE.A, A-CED.1 and 2, and F-IF.4 and 5. Details about the number of push-ups Scott completes a day are provided, and students are left to interpret the information, formulate a strategy, and compute their answers. Students solve by extrapolating how the pattern will continue into the future as they are looking at the sum of the number of push-ups that Scott has completed on a particular day. The teacher notes provide instructions for teachers to have students share out their answers, interpret what their answers mean in context, and evaluate each other’s answers and strategies.
  • Secondary Math Two, Module 7, Task 10, “Sand Castles” addresses standards G-GMD.1 and G-GMD.3. Students pretend they are entering a sand castle competition. Equipped with key parameters and details (like shape and size), this task has them analyze the area of the base and the volume of sand necessary for their three sand castles.
  • Secondary Math Three, Module 5, “Modeling with Geometry,” and Task 4, “Hard as Nails” engage students in the modeling process. This task addresses standards G-MG.1, 2, and 3. In this task, the students are given a detailed drawing of a nail on a coordinate plane and are then asked to find the volume of an individual nail and then use that information to calculate how many nails would be necessary for a particular building project.
  • Secondary Math Three, Module 6, Task 12, “Getting on the Right Wavelength” addresses standards F-TF.5 and F-BF.3 and 4. Students are given a picture of a Ferris wheel, along with a few details, and are then asked to write equations to model the height of the rider at any given time and make predictions about how the wheel will behave in the future.

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.

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.

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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.

The instructional materials reviewed for Mathematics Vision Project Integrated series, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, post-secondary programs, and careers. All of the WAP standards were addressed. Overall, the majority of the tasks addressed WAP standards. The percentage of tasks that addressed WAPs was the greatest in Secondary Math One and the least in Secondary Math Three. The Algebra and Function WAPs are emphasized to the greatest degree, followed by the Number and Quantity standards, while the Geometry and Statistics WAPs are given the least attention.

The WAPs from the Function Conceptual Category are included throughout the series. Evidence is found in Secondary Math One, Modules 1, 2, 3, 8; Secondary Math Two, Modules 1, 2, 4; and Secondary Math Three, Modules 1, 2, 3, 4, 6, 7.

The Algebra Conceptual Category standards are included throughout the series. Evidence is found in Secondary Math One, Modules 4, 5; Secondary Math Two, Module 1; and Secondary Math Three, Module 4.

The WAPs from the Geometry Conceptual Category are largely addressed in the Secondary Math One, Modules 6, 7, 8; Secondary Math Two, Modules 5, 6, 7, 8; and Secondary Math Three, Module 5.

The WAPs from the Statistics Conceptual Category are largely addressed in the Secondary Math One, Module 9; Secondary Math Two, Module 9; and Secondary Math Three, Module 8.

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Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.

The instructional materials reviewed for the Mathematics Vision Project Integrated series partially meet the expectation to provide opportunities to work with all high school standards and not distract with prerequisites or additional topics. In general, the series addresses many of the standards in a way that would allow students to learn the standards fully. However, there are cases where the standards are not fully addressed or where the instructional materials do not provide enough opportunities for students to practice and to learn the standards fully.

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

  • F-IF.7b: Students are given limited opportunities to graph cubic or piecewise-defined functions by hand or using technology throughout the series, but they are provided opportunities to interpret given graphs. For example, in Secondary Math Two, Module 4 students are occasionally asked to graph.
  • S-ID.2: In Secondary Math One, Module 9, Task 8, Ready problems 1 and 2 students are given one opportunity to compare the interquartile range of a data set. Students typically work with standard deviation when discussing spread in these materials.
  • S-ID.4: In Secondary Math Three, Module 8, Task 1-4 students are given limited opportunities to manipulate real data to recognize that there are data sets for which such a procedure is not appropriate. Opportunities for students to organize and make sense of raw data are limited. Within the teacher notes page 9, students are asked for examples of what might be normal but not what types may not be normal.
  • S-ID.9: In Secondary Math One, Module 9, Task 5, Problems 7-9 students discuss the difference between causation and correlation. The next time students encounter problems regarding causation and correlation is in Secondary Math Three, Module 8, Task 5, Ready problems 1-4. Students decide whether they think the variables explain each other or if they think one variable would cause the other to change. Note: S-ID.9 is explicitly identified by the teacher notes but not identified in the table of contents in Secondary Math One, Module 9.
  • S.IC.2: In Secondary Math Three, Module 8, Task 6 students are presented with one data-generating process: a simulation of coin tossing.
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Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school. Students engage in investigations throughout each task that ground the standards in real-world context appropriate for high school use.

Some examples from various Modules and Tasks that highlight high school sophistication include, but are not limited to:

  • Secondary Math One, Module 2, Task 6 “Form Follows Function”: This task builds fluency with linear and exponential functions by recognizing and efficiently using the information given in a problem. Students work with linear and exponential functions represented by a variety of tables, graphs, equations, and story contexts. This variety of representation, context and the numbers incorporated (annual rate of 2.4%, height in cm to the nearest tenth) make them appropriate for high school. (F-LE.2, F-LE.5, F-IF.7, A-SSE.6)
  • Secondary Math One, Module 9, Task 7 “Getting Schooled”: Students are presented with the opportunity to analyze the Census Bureau’s income data to understand more about the differences in women’s and men’s salaries. Based on the data in this task and in Module 9, Task 6, “Making More $,” students make a case to support whether the difference in income may be explained by differences in education or discrimination and consider what other data would be useful. (S-ID.6, S-ID.7, S-ID.8)
  • Secondary Math Two, Module 1, Task 5 “How Does It Grow?”: Students distinguish between relationships that are quadratic, linear, exponential, or neither. The materials include relationships presented with tables, graphs, equations, visuals, and story context. Students are asked to create a second representation for the relationships given. Graphing technology is recommended for this task. (F-LE.1, F-LE.2, F-LE.3)
  • Secondary Math Two, Module 3, Task 5 “Throwing an Interception”: In this task, the quadratic formula is developed from the perspective of visualizing the distance the x-intercepts are away from the axis of symmetry, by engaging students in a scenario most high school students find relevant. Question 7 provides an alternative algebraic approach for deriving the quadratic formula that does not include completing the square. Instead, students make use of the idea that the x-intercepts are d units from the axis of symmetry x=h, and therefore are located at h-d and h+d. (A-REI.4, A-CED.4)
  • Secondary Math Three, Module 5, Task 3 “Taking Another Spin”: Students approximate the volume of solids of revolutions whose cross section include curved edges, by replacing them with line segments. Teachers are encouraged to share students' multiple strategies, starting with simple decomposition and ending with a sophisticated one, such as slicing the solid into a stack of circular disks, every ½ unit along the horizontal axis. (G.MG.1, G.GMD.4)
  • Secondary Math Three, Module 6, Task 5 “Moving Shadows”: Students continue to use the ideas, strategies, and representations discovered when completing the Ferris wheel tasks from the previous lessons. Students are asked to describe the periodic motion of the rider’s shadow on the Ferris wheel as the shadow moves back and forth across the ground when the sun is directly overhead. Students apply the cosine function to determine the distance horizontally from the center of the wheel and derive the function horizontal position of the shadow = 25cos(18t). Discussions include defining cos(18t) when 18t is not located within the first quadrant. (F-TF.5, F-TF.2, G-SRT.8)
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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.

The materials reviewed for Mathematics Vision Project Integrated series meet the expectations for being coherent and making meaningful connections within each course and throughout the series. Overall, the materials include connections as the tasks are reexamined so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the materials is designed to spiral concepts throughout the entire series.

  • Secondary Math One, Module 1, Task 4, “Scott’s Push-Ups” addresses F-BF.1, F-LE.1, F-LE.2, and F-LE.5. Students analyze the pattern of push-ups Scott will include in his workout. This task elicits tables, graphs, and recursive and explicit formulas that focus on how the constant difference shows up in each of the representations and defines the function as an arithmetic sequence. In Secondary Math Two, Module 1, Task 3, “Scott’s Macho March” addresses standards F-BF.1, F-LE.A, A-CED.1 and 2, and F-IF.4 and 5. Students revisit Scott’s workout, but this time his push-up pattern creates a quadratic model. Again, students have the opportunity to use algebraic, numeric, and graphical representation to represent a story with a visual model. In Secondary Math Three, Module 3, Task 1, “Scott’s Macho March Madness” addresses F-BF.1, F-LE.3, and A-CED.2. The purpose of this task is to develop student understanding of how the degree of a polynomial determines the overall rate of change.
  • Secondary Math Three, Module 6, Task 6, “Diggin’ It” addresses standards F-TF.1 and F-TF.2. The purpose of this task is to discover alternative ways of measuring a central angle of a circle: in degrees, as a fraction of a complete rotation, or in radians. Students practice using right triangle trigonometry to find the coordinates of points on a circle and use the relationship between arc length measurements and radian angle measurements all within the context of an archeological dig. This task builds upon what students did in Secondary Math Two, showing the length of an arc intercepted by an angle is proportional to the radius and defining the radian measure of the angle as the constant of proportionality (G-C.5). This is followed by Task 7, “Staking It” that addresses standards F-TF.1 and F-TF.2. This task solidifies students’ previous understanding of radians as the ratio of the length of an intercepted arc to the radius of the circle on which that arc lies and uses radian measurement as a proportionality constant in computations.

The materials demonstrate their coherence by revisiting the same contexts and increasing the level of sophistication of the mathematics students engage in.

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Indicator 1e

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

The instructional materials reviewed for the Mathematics Vision Project Integrated series partially meet the expectations that the materials explicitly identify and build on knowledge from Grades 6-8 to the high school standards. Overall, the materials include Grade 6-8 standards that sometimes allow students to review and build on the middle school standards.

Prior standards are used to support the progression into high school standards; however, the materials do not consistently identify the standards on which they are building. Within the Core Alignment documents for Secondary Math Two and Three, there are several times when concepts that were introduced “in the middle grades” are mentioned. However, standards are not cited (Secondary Math Two, Core Alignment, page 6), and concepts done “in earlier grades” are mentioned but not cited (Secondary Math Three, Core Alignment, page 2).

Below are examples of where the materials do not reference standards from Grades 6-8 for the purpose of building on students’ prior knowledge:

  • In Secondary Math One, Module 1, Task 1 the materials do reference building on prior knowledge, but the middle school standards are not cited. “The focus of this task is on the generation of multiple expressions that connect with the visuals provided for the checkerboard borders. These expressions will also provide opportunity to discuss equivalent expressions and review the skills students have previously learned about simplifying expression and using variables.”.
  • In Secondary Math One, Module 3, Task 1, “Getting Ready for a Pool Party” focuses on F-IF.4 by developing the features of functions using a real-life context. The water level of a pool over a period of time provides opportunities for students to make connections to these key features. For example, the sketch of the graph is decreasing as the water is being emptied from the pool and increasing as it is being filled. The sketch is continuous when the hose is used (for filling or emptying) and stepped when buckets are used. When friends are assisting it is reflected in the rate of change. Students recognize that this is a functional situation by connecting every input of time with exactly one output representing the depth of water at that moment. The materials do not reference that they are building on Grade 8 standards (8.F.A,B).
  • Secondary Math One, Module 4, Task 1: The materials do reference building on prior knowledge, but the middle school standards are not cited. “In this task students will develop insights into how to extend the process of solving equations--which they have previously examined for one- or two-step equations--so that the process works with multi-step equations.”.
  • In Secondary Math One, the Module 5.3 Go exercises provide no reference for the eight problems covering Grade 5 content on adding and multiplying fractions. (5.NF.1 and 5.NF,4a)
  • In Secondary Math One, the Module 5.7 Ready exercises review the Pythagorean Theorem and have students identify which lengths make a right triangle with no reference to 8.G.B.
  • In Secondary Math One, Module 9, the Go exercises on page 10 provide no reference that the percent problems are a review of 6.RP.3c.
  • In Secondary Math Two, Module 9, Task 1 the materials do reference building on prior knowledge, but the middle school standards are not cited. “Students will connect their prior understandings of tree diagrams (from earlier grades) and frequency tables (from Secondary Mathematics I) to analyze a tree diagram and explain the results to others.”
  • In Secondary Math Two, Module 9, the Go exercises on page 11 provide no reference that the percent and fraction problems are a review of 6.RP.3c and 6.NS.1.
  • In Secondary Math Three, Module 4, Task 1, the Ready exercises on page 4 provide no reference that the generating equivalent fractions problems are a review of 4.NF.1.
  • In Secondary Math Three, Module 4, Task 2, the Ready exercises cover Grade 5 and Grade 6 content on adding, multiplying, and dividing fractions (5.NF.1, 5.NF,4a and 6.NS.1).
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series do not consistently identify the plus standards, when included, and although they do coherently support the mathematics which all students should study in order to be college and career ready, the plus standards could not be easily omitted from the materials without disrupting the sequencing of the materials.

Within the reviewed material, the plus standards are cited mostly in Secondary Math Three.

In the Table of Contents, there is an inconsistency in indicating the presence of plus standards.

When a plus standard is addressed in Secondary Math Three, it is not always noted with a “+”. For example, in the table of contents for the students it is never marked, but it is marked in the teacher notes. In Module 6.9, F-TF.3 is not listed in the Table of Contents as a focus standard but is listed in the teacher notes. In Module 6.13, F-TF.3 and F-TF.4 are listed without a + notation in the Table of Contents but are marked in the teacher notes (page 118). There is also a note in the Core Alignment document for this course which states F-TF.4 is a plus standard in Utah, but there is no such note for F-TF.3 (page 5).

In Secondary Math Three, Module 1, Task 2, “Flipping Ferraris” addresses F-BF.4, which the materials recognize as a plus standard in the teacher notes. Students apply an equation that relates the speed of a car to its braking distance as well as the inverse equation: how the braking distance relates to the speed of the car. Students begin by calculating the braking distance when given the speed, and then later the driver slams on the brakes to avoid hitting a cat. Students use the resulting skidmark to determine the original speed of the car. Students analyze both the original equation and the inverse, using the equations, charts, and a graph. This task could be skipped if a teacher does not want to cover plus standards.

Secondary Math Two, Module 3, Tasks 8 and 9 address N-CN.8 and N-CN.9 and do not indicate that they are plus standards in the core alignment document, the table of contents, or the teacher notes (pages 70 and 81). Module 7, Task 3 addresses standard G-C.4 but does not label it as a plus standard in the table of contents or the teacher notes (page 24). The Secondary Math Two, Task 9 would be difficult to adjust to while avoiding the plus standards. This task addresses N-RN.3, N-CN.1, N-CN.2, and N-CN.7 (non-plus standards) in addition to N-CN.8 and N-CN.9 (plus standards). In order to not teach the “plus-standard” math in this task while still teaching the “non-plus standard” math, the entire task would need to be rewritten.

GATEWAY TWO

Rigor And Mathematical Practices

MEETS EXPECTATIONS

Rigor and Balance
MEETS EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, conceptual understanding and application are thoroughly attended to, but students are provided limited opportunities to develop procedural skills and fluencies.

Criterion 2a-2d

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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.

2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectations of intentionally developing students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

Most of the lessons across the series are exploratory in nature and encourage students to develop understanding through questioning and through various activities. Concepts build over many lessons within and between courses in the series. Examples highlighting specific clusters include:

  • A-REI.A and B: Secondary Math One, Module 4 builds students’ conceptual knowledge by first introducing multivariable linear equations and then having students express given relationships in equivalent forms. Students engage with inequalities as they encounter the contextual need for inequalities. Students consider the differences and similarities between solving inequalities and solving equations, including that inequalities produce a range of solutions, the inequality symbol must be changed when multiplying or dividing by a negative number, and the reflexive property is true only for equations.
  • N-RN.A: In Secondary Math Two, Module 3 a contextual situation offers students the opportunity to understand how values of a dependent variable can exist on the intervals between the whole number values of the independent variable for a continuously increasing exponential function. Next, students examine the role of positive and negative integer exponents and begin to understand the need for rational exponents. Students further develop their conceptual understanding by verifying that the properties of integer exponents remain true for rational exponents.
  • A-APR.B: In Secondary Mathematics Three, Module 3 students develop an understanding of multiplicity and a deeper understanding of the relationship between the degree and the number of roots of a polynomial. Then, students use their background knowledge of quadratic functions and end behavior to extend their understanding to higher-order polynomials. The polynomials in this module are factorable and allow students opportunities to solidify their understanding of end behavior, the Fundamental Theorem of Algebra, the multiplicity of a given root, and what the multiplicity would look like graphically. Finally, students extend their understanding of the Fundamental Theorem of Algebra and the nature of roots by applying the Remainder Theorem.
  • G-GPE.5: In Secondary Math One, Module 8, Task 2 students prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. The proofs use the ideas of slope triangles, rotations, and translations and are preceded by a specific case that demonstrates the idea before students are asked to follow the logic using variables.
  • G-GPE.6: In Secondary Math Two, Module 6, Task 6 students use similar triangles and proportionality to find the point on a line segment that partitions the segment in a given ratio. Students are first asked to find the midpoint of a segment using two possible strategies and use similar triangles to find segments in ratios other than 1:1. The formula for finding the midpoint of a segment is formalized during the discussion. The discussion can also be extended to derive a formula for finding the midpoint that partitions a segment in any given ratio.
  • G-GPE.1, 2: In Secondary Math Two, Module 8, Task 1 students cut out triangles and pin them to a coordinate plane to build a unit circle, effectively developing their understanding of the relationship between the Pythagorean Theorem and the equation of a circle at the origin. Students connect their geometric understanding of circles as the set of all points equidistant from a center to the equation of a circle. This task focuses on a circle (constructed of right triangles) with a radius of 6 inches in order to focus on the Pythagorean theorem and use it to generate the equation of a circle centered at the origin. After constructing a circle at the origin, students consider how the equation would change if the center of the circle is translated.
1/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series partially meet the expectation that the materials provide intentional opportunities for students to develop procedural skill and fluencies, especially where called for in specific content standards or clusters.

The limited number of problems provided to students as practice limit the number of intentional opportunities to develop procedural skill and fluencies. Overall, there is a general lack of problems that provide students the opportunity to practice procedural skill. The Ready, Set, Go practice sets are intended to support learning, but students needing to practice course level skills in order to have access to more complex concepts and procedures must seek out other materials and resources in some instances. For example, A-REI.2 Secondary Math Three, Module 4, Task 3 does not provide enough opportunity for solving equations (two radical equations, two radical inequalities, and five rational equations) that lead to extraneous solutions (A-REI.2).

2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation to support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications. The materials use real-world situations in which students can apply mathematical concepts, and in situations where a real-world context is not immediately appropriate, the materials begin with abstract situations (graphs, dot models, etc.) and build to the application of the concept in a real-world situation in a later task. Every lesson involves a task, and every task is a real-world situation or a mathematical model that will build to a real-world situation.

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-CED.3: In Secondary Math One, Module 5, Task 1 the pet-sitting problem uses systems of equations and inequalities to build a business model, minimize costs, and maximize profit.
  • F-IF.4,5: In Secondary Math One, Module 3, Task 2 students use tables and graphs to interpret key features of functions (domain and range, where function is increasing/decreasing, x- and y- intercepts, rates of change, discrete vs. continuous) while analyzing the characteristics of a float moving down a river. Students interpret water depth, river speed, and distance traveled using the function skills they are developing.
  • F-BF.1: In Secondary Math Two, Module 1, Task 2 students develop a mathematical model for the number of squares in the logo for size n. Students are encouraged to use as many representations as possible for their mathematical model.
  • F-TF.5: In Secondary Math Three, Module 6.2 students use the Ferris wheel to determine how high someone will be after 2 seconds, after observing that the Ferris wheel makes one complete rotation counterclockwise every 20 seconds. Students are continuing the work from a previous task in 6.1. Students then determine elapsed time since passing a specific position. Students generate a general formula for finding the height of a rider during a specific time interval and are then asked how they might find the height of the rider for other time intervals.
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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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, the three aspects are balanced with respect to the standards being addressed. 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, developing procedural skill and fluency, and providing engaging applications.

The materials engage students in each of the aspects of rigor in a pattern that repeats itself throughout that materials. Each module contains Developing Understanding (conceptual understanding), Solidifying Understanding, Practicing Understanding, and the Ready Set Go (procedural skill) activities.

For example, in Secondary Math One, Module 2, Task 1, a Developing Understanding Task focuses on conceptual understanding as students build upon their experiences with exponential and geometric sequences and extend to the broader class of linear and exponential functions with continuous domains. Students compare this variety of functions using various representations (table, graph, and equation). In Task 2, a Solidifying Understanding Task, students discern when it is appropriate to represent a situation with a discrete or continuous model, thus deepening conceptual understanding. This task also has students practice modeling with mathematics by connecting the type of change (linear or exponential) with the nature of that change (discrete or continuous) which develops students’ procedural skill and fluency. Throughout both tasks, problems are presented to students within real-world contexts (medicine metabolized within a dog’s bloodstream, library reshelving efficiency, e-book download rate, savings accounts, pool filling, pool draining, etc), so students are learning the mathematical concepts and procedures while understanding the application of the mathematics.

Mathematical Practice-Content Connections
MEETS EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series meet the expectation that materials support the intentional development of all eight MPs, in connection to the high school content standards. Overall, the materials deliberately incorporate the MPs as an integral part of the learning. The instructional materials reviewed meet the expectations for making sense of problems and persevering in solving them as well as attending to precision, reasoning and explaining, modeling and using tools, and seeing structure and generalizing.

Criterion 2e-2h

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Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

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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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that materials support the intentional development of making sense of problems and persevering in solving them, as well as attending to precision (MP1 and MP6) in connection to the high school content standards. Overall, MP1 and MP6 are used to enrich the mathematical content. Throughout the materials, students are expected to make sense of problems and persevere in solving them while attending to precision. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Some examples of MP1 are as follows:

  • In Secondary Math One, Module 3, Task 1 students are able to make sense of creating graphs, given a situation. Students are already familiar with graphing rate of change and continuous and non-continuous situations. This task addresses domain and step functions. Students persevere in creating graphs by analyzing what is happening during each interval of time on their graph.
  • In Secondary Math Two, Module 3, Task 10 students practice with the arithmetic of irrational and complex numbers and make conjectures as to which of the sets of integers, rational numbers, irrational numbers, real numbers, or complex numbers are closed under the operations of addition, subtraction, and multiplication. Students also experiment with the closure of the set of polynomial functions under the operations of addition, subtraction, and multiplication. Students work with 15 incomplete conjectures and are asked to: “1. Choose the best word to complete each conjecture. 2. After you have made a conjecture, create at least four examples to show why your conjecture is true. 3. If you find a counter-example, change your conjecture to fit your work.” Students creating their own examples and correcting themselves when they find they had initially made the wrong choice provides them the opportunity to persevere.
  • In Secondary Math Three, Module 7, Task 2 students make conjectures about how the features of individual functions will show up in the graph of the combined functions when asked to sketch a graph of the path of a rider on a proposed thrill ride at a local theme park. Students then compare their predictions to the actual graphs. Students change the viewing window on their graphing calculator to obtain the information they need to reveal as many of the features of the graphs as possible.

Some examples of MP6 are as follows:

  • In Secondary Math One, Module 5, Task 4 students represent constraints with equations or inequalities and with systems of equations and/or inequalities. Students must interpret the solutions as viable or not depending on the context. Students must attend to the language in the constraints. Students convert between units of time and use fractional coefficients within the inequalities, thus also attending to precision of numbers.
  • In Secondary Math Two, Module 7, Task 1 students use correct mathematical vocabulary when describing and illustrating their process for finding the center of rotation of a figure consisting of several image/pre-image pairs of points.
  • In Secondary Math Three, Module 5, Task 4 students decompose a geometric solid of revolution into familiar three-dimensional objects whose volumes can be calculated. Students calculate the weight of 16d nails, use density information of steel, and complete conversions from ounces to pounds. Students must be precise with their conversions to perform their calculations.
2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that materials support the intentional development of reasoning and explaining (MP2 and MP3) in connection to the high school content standards, as required by the MPs. Overall, MP2 and MP3 are used to enrich the mathematical content found in the materials, and these practices are not treated as isolated experiences for the students. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Some examples of MP2 are as follows:

  • In Secondary Math One, Module 5, Task 7, “Get to the Point," students reason abstractly and quantitatively which window cleaning company to hire, by using a table, a graph, and/or algebra.
  • In Secondary Math Two, Module 2, Task 1, “Transformers: Shifty y’s,” students reason abstractly and quantitatively, relating the numeric results in the tables to the graphs to explain why the graphs are transformed as they are.
  • In Secondary Math Three, Module 3, Task 2, “Which is Greater?” students reason abstractly and quantitatively about the rates of change and end behavior when comparing various one-variable expressions, by examining how the order changes, arranging either least to greatest or greatest to least depending on the values of x close to negative infinity, zero, and positive infinity. Students reason quantitatively by substituting in values and reasoning abstractly, by making assumptions based on their knowledge of exponents, comparing polynomial to exponential functions, and comparing what happens when the degree of the polynomial is even or odd when values of x approach −∞.

Some examples of MP3 are as follows:

  • In Secondary Math One, Module 3, Task 2, “Floating Down the River,” students explain why they either agree or disagree with each observation Sierra made. Some of Sierra’s observations include: “a) The depth of the water increases and decreases throughout the 120 minutes of floating down the river, b) The distance traveled is always increasing, or c) The distance traveled is a function of time.”
  • In Secondary Math Two, Module 6, Task 3, “Similar Triangles and Other Figures,” students read through Mia and Mason’s conjectures about similar polygons and decide which they believe are true. Students are also presented “explanations” from either Mia or Mason and must write an argument deciding whether they agree.
  • In Secondary Math Three, Module 4, Task 5, “Watching your Behavior,” students work with partners to try to come up with various rational functions that create different end behaviors. For each rational function they create, they state the end behavior and come up with an equation that models the end behavior asymptotes. With examples, they provide evidence that their end behavior is correct and begin to identify generalizations to find the end behavior asymptotes for various rational functions.
2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that materials support the intentional development of addressing mathematical modeling and using tools (MP4 and MP5), in connection to the high school content standards, as required by the MP. Overall, MP4 and MP5 are used to enrich the mathematical content, and these practices are not treated as isolated experiences for the students. Throughout the materials, students model with mathematics and use tools strategically. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

Some examples of MP4 are as follows:

  • In Secondary Math One, Module 5, Task 3 students use systems of equations, tables and graphs to model the start-up costs of a new business and use the information to minimize costs and maximize profit.
  • In Secondary Math Two, Module 9, Task 3 students use Venn diagrams to model the situation, analyze the data, write various probability statements (unions, intersections, and complements), and then apply the Addition Rule and interpret the answer in terms of the model.
  • In Secondary Math Three, Module 5, Task 3 students examine a solid of revolution and a frustum to create a strategy for finding volume. Students use a variety of strategies to decompose a figure that consists of curved edges into cylinders, frustums, and cones in order to generate a sequence of better approximations of the actual volume of the solid.

Some examples of MP5 are as follows:

  • In Secondary Math One, Module 9, Task 5 students use technology such as the graphing calculator, GeoGebra, or Desmos to compute and interpret the correlation coefficient of a linear fit.
  • In Secondary Math Two, Module 2, Task 1 students use technology to explore the results of various changes to the function they are investigating. Students choose the technology.
  • In Secondary Math Three, Module 2, Task 5 students choose to use calculators or other technology with base 10 logarithmic and exponential functions to complete the problems.
2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that materials support the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards, as required by the MP. Overall, MP7 and MP8 are used to enrich the mathematical content, and these practices are not treated as isolated experiences for the students. There is an increasing expectation that these practices will lead students to experience the full intent of the standards.

The materials frequently take a task from a previous course and add a new contextual layer to the mathematics, such as the Pet Sitter Task and Bruno Bites Task. Students are constantly extending the structures used when solving problems that build on one another and, as a result, are able to solve increasingly complex problems. In the instructional materials, repeated reasoning based on similar structures allows for increasingly complex mathematical concepts to be developed from simpler ones.

Some examples of MP7 are as follows:

  • In Secondary Math One, Module 2, Task 1 builds upon students’ previous experiences with arithmetic and geometric sequences to extend to the broader class of linear and exponential functions with continuous domains. Students use tables, graphs, and equations to create mathematical models for contextual situations. Students continue to define linear and exponential functions by their patterns of growth. Students are repeatedly asked to identify similarities and differences between problems in an effort for them to identify the structure present.
  • In Secondary Math Two, Module 4, Task 3 students learn how to graph, write, and create linear absolute value functions by looking at structure and making sense of piecewise-defined functions. They connect prior understandings of transformations, domain, linear functions, and piecewise functions and share strategies for how to go from one representation to another to graph and write equations for absolute value piecewise functions.
  • In Secondary Mathematics Three, Module 3, Task 6, “Seeing Structure,” students use their background knowledge of quadratic functions and end behavior to extend their understanding of polynomials in general. The polynomials in this task are easily factorable and allow students opportunities to solidify their understanding of end behavior, the Fundamental Theorem of Algebra, and the multiplicity of a given root (and what that would look like graphically).

Some examples of MP8 are as follows:

  • In Secondary Math One, Module 5, Task 6, students practice solving systems of linear inequalities by identifying the overlapping region of the half-planes that form the solution sets of each of the two-variable inequalities in the system. Students recognize the difference between a strict inequality and one that includes the points on the boundary line as part of the solution set. Through repeated practice students develop a procedure for solving a system of linear inequalities.
  • In Secondary Math Two, Module 3, Task 5, students use what they already know about quadratic functions to generalize a process for finding x-intercepts for any quadratic function that has them. Students use the method of completing the square to rearrange the formula to highlight a quantity of interest, using the same reasoning as in solving equations.
  • In Secondary Math Three, Module 6, Task 7, students calculate the x- and y- coordinates for stakes placed on a circle, as well as the arc length on concentric circles placed around an archeological site. Repeating the same calculations, students recognize they can just double or triple the coordinates or arc length given on the 10-meter circle to get the coordinates or arc length on the 20-meter or 30-meter circles.

GATEWAY THREE

Usability

PARTIALLY MEETS EXPECTATIONS

Use and design facilitate student learning
MEETS EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series meet expectations that the materials are well designed and take into account effective lesson structure and pacing. Overall, the materials distinguish between problems and exercises and have a design that is not haphazard with tasks being intentionally sequenced. Students produce a variety of types of answers including both verbal and written answers, and manipulatives are used throughout the instructional materials as mathematical representations and to build conceptual understanding.

Criterion 3a-3e

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Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

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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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the underlying design of the materials distinguish between problems and exercises.

Problems within the Mathematics Vision Project materials are designated as “tasks.” Every task included attends to specific standard(s) or aspect of a standard(s) and builds upon prior knowledge. There are three different kinds of tasks: Develop Understanding, Solidify Understanding, and Practice Understanding tasks. The Develop Understanding tasks introduce concepts and build on previous knowledge by providing discovery problems. The Solidify Understanding tasks focus on the concepts being developed in the unit. They provide students opportunities to practice what they learned so far in the unit. The Practice Understanding problems extend the learning by adding small extensions to the concepts covered in the unit. The Ready, Set, Go exercises within the Mathematics Vision Project are designated as “homework.” The Ready exercises are intended to prepare students for the upcoming work in class, the Set exercises reinforce the work done in class that day, and the Go exercises review concepts and skills that students learned previously.

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Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the design of the assignments is not haphazard, and they are given in intentional sequences. The materials include connections as the tasks are reexamined so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the materials is designed to spiral concepts throughout the entire series. The Ready, Set, Go exercises are designated as “homework.” The Ready exercises prepare students for the upcoming work in class, the Set exercises reinforce the work done in class that day, and the Go exercises review concepts and skills that students learned previously.

2/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that there is variety in how students are asked to present the mathematics. For example, the series asks students to 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 the mathematics in multiple ways. For example, in Secondary Math One, Module 8, Task 5 students complete tables, write equations, and draw graphs, and in Secondary Math Two, Module 5, Task 1 students draw a sequence of rotated triangles and then use their drawings to write a mathematical proof.

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Indicator 3d

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

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation 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 do occasionally instruct students to use manipulatives within the materials (for example: Secondary Math 2, Module 8, Task 1, Unit Circle Task). The materials do not provide directions for the use of virtual manipulatives. On the main webpage, under the Resources header, there are links that connect to a set of ten GeoGebra Interactive Applets (i.e., Leaping Lizards, Triangle Dilation). 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.

Indicator 3e

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

The instructional materials reviewed for Mathematics Vision Project Integrated series have a visual design that is not distracting or chaotic. The materials are flat digital versions of print books.

Teacher Planning and Learning for Success with CCSS
DOES NOT MEET EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series do not meet expectations that materials support teacher learning and understanding of the standards. The instructional materials provide questions that support teachers in delivering quality instruction, and the teacher’s edition is easy to use and consistently organized and annotated. However, the teacher edition for the instructional materials does not contain adult-level discussions of the mathematics, and the teacher edition does not explain the role of the specific mathematics standards in the context of the overall series.

Criterion 3f-3l

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Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

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Indicator 3f

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

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that teachers are provided quality questions to guide students’ mathematical development.

The Teacher’s Notes provide suggested questions to use during the Teaching Cycle (see #6 under indicator 3g); these aid in students’ development of the concepts. The following example is found within the Secondary Math One, Module 1, Task 6, Launch section: “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. The tasks themselves contain questions designed to elicit discovery and exploration.

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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.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the teacher edition contains ample and useful annotations. The materials provide documents for each module under the Teacher’s Notes. These notes contain structured guidance on how the lessons should proceed. The notes may be included in some or all of the sections. For example:

  • Special Note to Teachers: highlights an aspect of the task and how it fits in the overall sequence of the three-course materials.
  • Purpose: describes the previous development of concepts needed for the lesson and where to place emphasis for the lesson.
  • New Vocabulary: lists new vocabulary introduced in the lesson.
  • CCSSM Standards focus and related standards: lists those standards addressed in the lesson.
  • Standards for Mathematical Practice: lists those standards in the lesson.
  • 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. For example: Secondary Math Two, Module 4, Task 1, page 4 states, “If this is the first time they are using CBR’s, you may wish to model how to use this before sending them out in groups. If you are not using a CBR for Ball Bounce 2, you will want to find a way to model quadratic data using a different method.” Secondary Math One, Module 9, Task 5, page 37 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 the Ready, Set, Go!

0/2
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.

The instructional materials reviewed for Mathematics Vision Project Integrated series do not meet the expectation that the teacher edition contains adult-level discussion of the mathematics.

The Teacher Notes do not contain any explanations of advanced mathematical topics that advance the knowledge of the teacher. For example, the Teacher Notes for Secondary Math One, Module 9, Task 5, page 37 state, “They will order the graphs and create new data sets to develop the idea that the correlation coefficient indicates the strength and direction of a linear relationship in the data. Students also consider situations in which two variables are highly correlated, but the relationship is not necessarily causal.” There is no discussion of, or information links for, the correlation coefficient or causation that help prepare the teacher for questions that may arise related to this advanced topic.

0/2
Indicator 3i

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

The instructional materials reviewed for Mathematics Vision Project Integrated series do not meet the expectation that the teacher’s edition addresses the standards in the context of the overall series.

An overview by module or course is not provided. An overview of each task within the module is provided. Within the materials an occasional reference is made to previous standards related to the current task and to future standards related to the current task. Also, an occasional reference is made to a course- Secondary Math One, Two, or Three- but rarely to the module or the task. An example from Secondary Math One, Module 8, Task 2, page 16 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, such as related to Secondary Math One, Module 6, Task 1.

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).

The instructional materials reviewed for Mathematics Vision Project Integrated series contained Teacher Notes that included an index of tasks within each module with related standards. However, neither a pacing guide nor a cross-referencing guide for the standards was provided. The intent would be to "usually" use a task a day.

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.

The instructional materials reviewed for Mathematics Vision Project Integrated series provide a link on the main webpage for parents that contain a general course-wide letter. If support is needed for homework, the materials suggest searching by “examples of“ the topic on the internet for additional resources. The materials state that there are many math sites that contain print instructions for the many topics that students will be studying. Helps, Hints and Explanations is a resource available for purchase. It 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 to provide them with support as they work on their homework.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.

The instructional materials reviewed for Mathematics Vision Project Integrated series provide a link for professional development on the main webpage. This webpage contains past presentations via powerpoint found 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.

Assessment
PARTIALLY MEETS EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series partially meet expectations that materials offer teachers resources and tools to collect ongoing data about students progress on the Standards. The materials provide support for teachers to identify and address common student errors and misconceptions, but the materials partially meet the expectations for the rest of the indicators in assessment. The materials do offer students opportunities to monitor their own progress.

Criterion 3m-3q

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Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

1/2
Indicator 3m

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

The instructional materials reviewed for Mathematics Vision Project Integrated series partially meet the expectation that they provide 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 discussion of possible strategies for remediation.

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Indicator 3n

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

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that support is provided 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 Secondary Math Two, Module 4, page 13, 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….” The notes go on to explain a misconception. In the same module, page 51 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.

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Indicator 3o

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

The instructional materials reviewed for Mathematics Vision Project Integrated 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 provide 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.

Indicator 3p

Materials offer ongoing assessments:

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Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for Mathematics Vision Project Integrated 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. Secondary Math Three, 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.

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Indicator 3p.ii

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

The instructional materials reviewed for Mathematics Vision Project Integrated 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 provided. There are no suggested answers or example answers for the short answer/short essay questions. Sample assessments include rubrics for the performance-based assessments, which offer limited guidance but do not provide guided feedback.

Indicator 3q

Materials encourage students to monitor their own progress.

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."

Differentiated Instruction
DOES NOT MEET EXPECTATIONS

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The instructional materials reviewed for the Mathematics Vision Project Integrated series do not meet the expectation for differentiated instruction for diverse learners within and across courses. The instructional materials do provide opportunities for advanced students to investigate mathematics content at greater depth. However, the materials do not always provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners, provide strategies for meeting the needs of a range of learners, or embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Criterion 3r-3y

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Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

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Indicator 3r

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

The instructional materials reviewed for Mathematics Vision Project Integrated 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. For example, Secondary Math One, Module 5, Explore (Small Group) states, “watch and listen and encourage connections.”

The Enhanced Teacher Notes do offer “Instructional Supports” that at times contain a scaffolding/intervention section, such as in Secondary Math One, Module 2, Task 6, which provides a graphic organizer to help students classify forms of linear equations.

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Indicator 3s

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

The instructional materials reviewed for Mathematics Vision Project Integrated series partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners.

The series states, “Students who need additional help with the Ready, Set, Go assignments should do a search by the topic for the problem set in a popular search engine or follow the internet links when available. Most search engines return quality resources in a reliable fashion.”

The Enhanced Teacher Notes offer “Instructional Supports,” “Instructional Adaptations,” and “Challenge Activities” as resources to differentiate instruction. These, however, are not comprehensive. The note in Secondary Math One, Module 6, 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 of all students.” No other strategies or suggestions were given.

The Enhanced Teacher Notes list “Instructional Supports” and “Instructional Adaptations” at the end of each task.

  • Secondary Math One, Module 6, 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.
  • Secondary Math One, Module 6, Task 3 has 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 implication of this?”
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Indicator 3t

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

The instructional materials reviewed for Mathematics Vision Project Integrated 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. One example, Secondary Math Two, Module 3, Task 1, provides partially completed tables for the students.

However, some tasks do provide multiple entry points. For example, in Secondary Math Three, Module 5, 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.

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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).

The instructional materials reviewed for Mathematics Vision Project Integrated 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). Although Spanish materials are provided for Secondary Math One Modules 2-6, no accommodations for English Language Learners or other special populations are available.

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Indicator 3v

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

The instructional materials reviewed for Mathematics Vision Project Integrated 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 Secondary Math One, Module 9, Task 5 the teacher is told to “have students find data in two-way tables on the internet, then have them write a story, using relative frequency statements.”

Indicator 3w

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

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

Indicator 3x

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

The instructional materials did not provide suggestions for teachers to use a variety of grouping strategies. Group work is embedded in every task; Mathematics Vision Project 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.

Indicator 3y

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

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

Effective Technology Use

The instructional materials reviewed for the Mathematics Vision Project Integrated series inconsistently support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide few opportunities for students to use technology in effective ways for the purpose of engaging in the Mathematical Practices and few opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. The instructional materials do provide choices for teachers and/or students to collaborate with each other, and sample assessments items could be purchased and easily customized for local use.

Criterion 3z-3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Although the course series is 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 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 curriculum series. (Approximately 10 activities are posted.)

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.

The materials 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.

Indicator 3ab

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

Except for the virtual manipulatives, students are given 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.

Indicator 3ac

Materials can be easily customized for individual learners.

Indicator 3ac.i

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

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

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.

The instructional materials reviewed for the Mathematics Vision Project Integrated 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 copy of Ready, Set, Go Answer Keys and Sample Assessments also have rights to receive the Word Document files containing the sample assessment items. These sample assessments items could be easily customizable for local use.

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.).

The website for the Mathematics Vision Project Integrated series offers a “Collaboration Community” that features one teacher who uses the resources extensively. The teacher uses modules from the curriculum series for Math One and Math Two classrooms. Currently, there is low participation in the Collaboration Community.

Mathematics Vision Project has a current Facebook page with over 680 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.