Alignment: Overall Summary

The instructional materials reviewed for the Saxon Traditional Series do not meet expectations for alignment to the CCSSM for high school. Since the copyright for this series is 2009, these materials were created before the release of the CCSS. The instructional materials spend a majority of time on the widely applicable prerequisites from the CCSSM and engage students in mathematics at a level of sophistication appropriate to high school. However, the instructional materials partially attend to allowing students to fully learn each non-plus standard, making connections within courses and across the series, and explicitly identifying standards from Grades 6-8 and building on them to the High School Standards. Since the materials do not meet the expectations for focus and coherence, evidence for rigor and the mathematical practices in Gateway 2 was not collected.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
8
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
21
30
36
N/A
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Does Not Meet Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
8/18
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Criterion Rating Details

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

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
0/4
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Indicator Rating Details

The instructional materials reviewed for the Saxon Traditional Series do not meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The instructional materials include many instances where all aspects of the non-plus standards are not addressed and omit many non-plus standards across the series.

The standards where at least one aspect of the standard is not addressed across the series include:

  • N-Q.1: In Algebra 1, Lesson 8, students convert a variety of units. In Problem 21 students convert from feet to square inches; however, there is no evidence of choosing and interpreting units.
  • A-APR.1: Students apply operations to polynomials in Algebra 1, Lessons 53 and 58 and in Algebra 2, Lesson 19. However, there is no evidence for building understanding that polynomials form a system closed under addition, subtraction, and multiplication.
  • A-REI.3: In Algebra 1, Lessons 19, 21, and 26 include solving linear equations. Algebra 1, Lesson 77 includes solving inequalities. However, there is no evidence of solving linear equations or inequalities where coefficients are represented by letters.
  • A-REI.6: In Algebra 1, Lesson 63, students use elimination to solve systems of linear equations. In Lesson 55, students solve systems of equations by graphing; however, there is no evidence for approximating a solution. Graphing calculators are utilized to determine the exact point of intersection.
  • A-REI.11: In Algebra 1, Lesson 55, students explain why the intersection of two linear functions is the solution for a system of linear equations. In Lesson 112, students graph and solve systems of linear and quadratic equations and are directed to approximate first, then utilize the graphing calculator to confirm their solution. In Algebra 2, Lesson 117, students show how to solve nonlinear systems of equations. However, there is no evidence for solving systems of equations using absolute value, exponential, and logarithmic equations.
  • F-IF.4: In Algebra 1, Investigation 11, students learn to find exponential growth and decay by graphing data and creating data tables. They determine increasing and decreasing values, initial amounts, intercepts, and whether or not a graph opens upward or downward. No evidence was found for determining symmetries, end behavior, and periodicity given in a verbal description of the relationship.
  • F-IF.8a: In Algebra 2, Lessons 35 and 78, students factor quadratic equations to determine the roots. Students also solve quadratic equations by factoring. In Algebra 1, Lesson 98 and in Algebra 2, Lesson 58, students complete the square and solve, finding the roots. Included in this lesson is also an extension where students approximate the maximum. There is no evidence found to determine the symmetry.
  • F-BF.3: In Algebra 1, Investigation 6, students use technology to recognize transformations of linear functions. Likewise, in Algebra 1, Investigation 10, students use technology to investigate transformations of quadratic functions. However, there is no evidence for recognizing even and odd functions from graphs or algebraic expressions.
  • F-LE.1a: In Algebra 1, Lesson 119, students compare linear, quadratic, and exponential functions. From a table, students determine and prove a function is linear by proving there is an equal difference over equal intervals; however, there are no opportunities for proving exponential functions grow by equal factors over equal intervals.
  • F-LE.5: In Algebra 2, Lessons 20 and 93, students use linear and exponential functions. In example 5 on page 139, students find the profit from a given function, and in example 4 on page 655, students use exponential functions as they study compound interest. However, there is no evidence for interpreting the parameters of these types of functions.
  • F-TF.8: On page 594 in Geometry, students are shown the proof of the Pythagorean identity; however, there is no evidence for using the proof to find sine, cosine, or tangent of an angle given sine, cosine, or tangent and the quadrant of the angle.
  • G-CO.4: In Geometry, Lesson 67, students measure along the perpendicular line to locate the corresponding points of a reflected image. In Lesson 74, students reflect utilizing the perpendicular line as seen in Example 3. In Lesson 78, students learn more about rotations in terms of angles. There is no evidence for defining translations in terms of parallel lines or line segments.
  • G-CO.5: In Geometry, Lessons 74 and 78, students draw reflections and rotations. There is no evidence for specifying a sequence of transformations that will carry a given figure onto another. In Lesson 67, Problem 14, students identify the transformation but not a sequence of transformations.
  • G-CO.6: In Geometry, Lesson 90, students perform transformations on a rectangle; however, congruence in terms of rigid motions is not found.
  • G-CO.13: Geometry Lab 9 demonstrates how to construct a regular hexagon. Students explore the relationship between circles and inscribed regular polygons. There is no evidence for constructing an equilateral triangle and a square.
  • G-GPE.5: In Geometry, Lesson 37, students find the equation of a line passing through a point parallel to a given line. However, there is no evidence for proving the slope criteria for parallel and perpendicular lines.
  • G-GMD.1: In Geometry, Lesson 62 provides a brief, informal argument for finding the volume of a cylinder. However, informal arguments for the formulas for the circumference of a circle, area of a circle, or volume of a pyramid and cone were not found.
  • S-ID.2: In Algebra 2, Lesson 80, students use statistics as they work with mean and standard deviation of a normal distribution. However, there is no evidence for comparing the statistical findings of two or more different sets of data.
  • S-ID.5: In Algebra 2, Lesson 80, students use a sample space to find the probability of two dependent events both occurring. Data from a table is used to find conditional probabilities. However, there is no evidence for recognizing possible associations and trends in the data or interpreting marginal frequencies in the context of the problem.
  • S-IC.3: In Algebra 1, Investigation 3, students determine what makes a survey question biased and write their own biased and unbiased questions. In Algebra 2, Investigation 7, students investigate how data is collected, displayed, and described. There is no evidence for recognizing the difference between sample surveys, experiments, and observational studies.

In looking through the entire set of instructional materials, there was no evidence found of several non-plus standards. The standards that are omitted across the materials include:

  • A-SSE.1b
  • A-SSE.3b
  • A-SSE.3c
  • A-APR.4
  • F-IF.6
  • F-IF.9
  • F-LE.3
  • G-CO.3
  • G-CO.7
  • G-CO.8
  • G-C.1
  • G-SRT.2
  • G-SRT.3
  • G-SRT.6
  • G-GPE.2
  • G-GPE.6
  • G-MG.2
  • G-MG.3
  • N-RN.3
  • N-Q.2
  • S-ID.6b
  • S-ID.9
  • S-IC.4
  • S-IC.5
  • S-CP.5

Indicator 1a.ii

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

The instructional materials reviewed for the Saxon Traditional Series do not meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials do not include all aspects of the modeling process and do not allow students to engage in parts of the modeling process.

Lessons are scaffolded to such an extent that students do not have an opportunity to work through the entire cycle of the modeling process independently. Students are not given the opportunity to develop their own solution strategies, select the best tools for solving a problem, revise their answers, and report their work. Students are not given an opportunity to question how precise they need to be or what aspects they need to control or optimize.

While aspects of the modeling process are attended to, there are components of the modeling process that are altogether missing from the series. For example:

  • Algebra 1, Lab 8 and Lesson 8 (F-IF.4 and F-IF.7): Students find the highest point a golf ball reaches and how long it takes to reach it. The lesson provides explicit support, including the function, the height of the platform, and the variables to use, so students do not make sense of the problem or formulate a solution process.
  • Algebra 1, Lesson 119 (F-LE.2): Students identify the appropriate model for various situations, such as the height of a balloon, the cost of a tank of gas, and the number of bacterial cells in a laboratory, in Example 4. In each scenario, students are not given the opportunity to validate their answers.
  • Geometry, Lesson 57 (G-GPE.7): Students find perimeter and area with coordinates. In Example 5, students use estimation to determine the amount of seed needed to buy. The example does not have a defined area, but it gives the students a scale of measurement. Students are not given the opportunity to determine their own tools, scaling, or ways to find the dimensions.
  • Geometry, Lesson 73 (G-SRT.8): Students apply trigonometric ratios along with angles of elevation and depression to solve problems. The students are given dimensions and detailed drawings which removes the aspect of formulating and validating their own findings.
  • Algebra 2, Investigation 2, page 143 (A-SSE.1, A-CED.1): Students are given a context about painting a house. However, there is no problem presented to students for a context that lends itself to the modeling process. The students are given equations, instructed to complete a partially filled-out table, and told to graph the equations. The students do not have the opportunity to formulate a solution strategy or make decisions about which models might be useful. They are asked to use the given equations to compute some values and to interpret the meaning of a point on the graph. They are not asked to validate any of their answers or to report on any conclusions.
  • Algebra 2, Lesson 35, practice g (A-SSE.3a): Students are given an equation for the height of a free-falling object. They substitute given numbers into the equation and solve the resulting equation to answer the question of when the object will hit the ground. The parts of the modeling process that are evident in this problem are compute and interpret, but students do not make sense of the problem or formulate a solution process.
  • Algebra 2, Lesson 113, practice f (F-BF.1): Students are given a salary structure that increases exponentially each year and are to find the total amount the employee would earn over 20 years of work. This problem refers students back to an example in the lesson that shows them exactly how to formulate the problem. There is no student choice in the method of problem solving, in the way the model could be formulated, or in what students must compute. They don’t have to validate their result or adjust their original model to make it more precise. Students follow the exact steps that were shown to them in the example on that same page.
  • Algebra 2, Lesson 116 (S-ID.6): Students determine curves of best fit for different data sets. In each case, students are told exactly which regression curve to use. In Example 5, an applications example, every step in the process is completed for the students. The exercises in the lesson practice state which functions to use and how choices can be based on the R2 values. Students do not make sense of the problem or formulate a solution 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.
0/0

Indicator 1b.i

The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Saxon Traditional Series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

The instructional materials for the series spend a majority of time on the content widely applicable as prerequisites (WAPs) and other non-plus standards. There is little evidence of topics that distract from the non-plus standards in the materials. Some examples of how the materials spend a majority of time on the WAPs and other non-plus standards include:

  • In Algebra 1, the majority of the materials addressed non-plus standards from the Algebra, Functions, and Number and Quantity conceptual categories, and this included WAPs from the same three categories. The remainder of the Algebra 1 materials address standards from Grades 6-8 (including integers, distributive property, finding slope, solving percent problems, etc.). There are no plus standards in the Algebra 1 course.
  • In Geometry, the majority of the materials addressed non-plus standards from the Geometry conceptual category, and this included the WAPs from Geometry. The remainder of the Geometry materials address standards from Grades 6-8 (volume and surface area of prisms and solving problems involving similar figures) and plus standards (vectors and matrices).
  • In Algebra 2, the majority of the materials addressed non-plus standards from the Algebra, Functions, and Number and Quantity conceptual categories, and this included WAPs from the same three categories. The remainder of the Algebra 2 materials address standards from Grades 6-8 (properties of real numbers, like terms, rules of exponents, solving two-step equations, converting units of measure, and understanding and applying the Pythagorean theorem) and plus standards (matrices, polar coordinates, vectors, and graphing rational functions).

Indicator 1b.ii

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

The instructional materials reviewed for the Saxon Traditional Series partially meet expectations, when used as designed, for letting students fully learn each non-plus standard.

The instructional materials for the series, when used as designed, do not enable students to fully learn some of the non-plus standards. The non-plus standards that would not be fully learned by students include:

  • G-SRT.4: In Lessons 46 and 60, students use theorems about proportional relationships of triangles. Students prove parallel lines and the Triangle Proportionality Theorem. They are not asked to prove the converse; however, the proof is shown as an example. Students apply the Pythagorean Theorem in Lessons 33 and 53, but there are no opportunities for students to prove the Pythagorean Theorem using triangle similarity.
  • A-APR.3: Students factor and find zeros of polynomials. However, only a few examples were found for students to graph the quadratic function after finding the zeros. For example, in Algebra 2, Lesson 35, Example 3, Lesson Practice 35, Problems D and E and in Algebra 2, Lesson 65, Example 3. There are limited opportunities for students to use the zeros to construct a rough graph of the function defined by the polynomial.
  • A-CED.1: The series provides many opportunities to practice creating and solving linear, quadratic, and exponential equations. However, only a few examples were found where students write a rational function (for example, in Algebra 1, Lesson 90, Example 5 and Practice Problem G and in Algebra 1, Lesson 99, Example 5 and Problem 27).
  • A-CED.2: Students create equations to represent relationships between quantities; however, students have limited opportunities to graph equations on the coordinate axes with labels and scales. For example, in Algebra 1, Lesson 49, Example 4, Practice Problem G and Algebra 2, Lesson 34, Example 6, students create an equation and graph the equation they created.
  • A-REI.4a: Students practice completing the square. However, the materials show the derivation of the quadratic formula in Algebra 1, Lesson 110 and do not provide students an opportunity to practice this.
  • F-IF.2: In Algebra 2, Lesson 4, students identify domain and range and are introduced to function notation. In this lesson, Example 3, students use function notation, but this is the one opportunity for students to demonstrate the concept on their own. In Algebra 1, Lesson 25, students are introduced to the concept of relations and functions, but function notation is not used consistently for students to fully learn the standard.
  • F-BF.4a: In Algebra 1, Lesson 4, students solve equations in the form f(x) = c, and in Algebra 2, Lesson 50, students find inverse functions, mainly for equations of lines and mostly without using function notation. There are limited opportunities for students to solve nonlinear equations of the form f(x) = c that have an inverse and to write an expression for the inverse function.
  • N-CN.1,2: There are limited opportunities for students to know and understand complex numbers. There are two lessons (Algebra 2, Lessons 62 and 69) in the materials that address what a complex number is and operations on complex numbers.
  • N-RN.2: There were six lessons across the series (Algebra 1, Lessons 46 and 61; Geometry Lesson 29; Algebra 2, Lessons 40, 59, and 70) that address rewriting radical and exponential expressions; one of the six involved rational exponents. There are limited opportunities for students to rewrite expressions involving rational exponents using the Properties of Exponents.
  • S-IC.6: In Algebra 2, Lesson 18, students evaluate some reports with a histogram to determine if the graph is misleading. This is an opportunity for students to read a report; however, students do not evaluate reports based on data.
  • S-ID.1: In Algebra 1, Lesson 54, students make box-and-whisker plots and interpret them. In Lesson 62, students display data with histograms and stem and leaf plots. However, students do not have the opportunity to represent data using dot plots.
  • S-ID.3: In Algebra 2, Lesson 25 addresses outliers and their effect on a distribution. In Algebra 2, Lesson 80, students examine a normal distribution and how the mean and standard deviation relate to the normal distribution, but students are not given opportunities to interpret differences in shape, center, and spread in the context of data sets.
  • S-ID.4: In Algebra 2, Lesson 80, Lab 12, students calculate the area under the normal curve using z-scores and the graphing calculator. However, there is no evidence where students utilize spreadsheets.
  • S-ID.6a: There are limited opportunities for students to fit a function to data and use functions fitted to data to solve problems in the context of the data. There is one lesson (Algebra 2, Lesson 116) that addresses fitting a nonlinear function to a set of data, and that function was not used to solve problems.

Indicator 1c

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

The instructional materials reviewed for the Saxon 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.

In every lesson throughout the series, there is one application problem. These problems use contexts relevant for high school students. For example:

  • In Algebra 1, Lesson 78, students graph rational functions in the context of a soccer tournament.
  • In Geometry, Lesson 73, students use the tangent function to find a missing length in a surveying problem.
  • In Algebra 2, Lesson 55, students use probability in the context of meteorology.

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

  • In Algebra 1, Lessons 26, 27, and 28 address solving equations, and practice problems integrate rational coefficients and decimal solutions. In Algebra 2, Lesson 7 has many problems that utilize rational coefficients and solutions. In Algebra 2, Lesson 34, students graph linear equations where the slope and y-intercepts are rational values.
  • In Algebra 1, Lesson 75, Problems 5 and 6 involve radicals. In Problem 14, a steel bar increases or decreases in size as the temperature changes; the given change is 0.12%, which students convert into a decimal. In Problem 22, the times for swimming laps are given in minutes, but the solution to the problem is less than a minute. Students may decide to convert the minutes into seconds in order to give an answer that is easier to understand in the context of the situation. Problem 28 includes rainfall amounts recorded to hundredths.
  • In Geometry, Lesson 46, 2 of the 30 practice problems contain decimals, and the rest use whole numbers. In Lesson 95, there is one problem that uses a fraction and no problems that use decimals. There are some problems that have decimal answers even though the given numbers are all integers. In Lessons 9 and 11, students practice with rational values and solutions using the distance formula and finding midpoints.
  • In Algebra 2, Lesson 19, many practice problems have decimals or fractions. In Problem 11, students identify direct or inverse variation from tables. One table has a mix of integers and decimals, and the other two tables are a mix of integers and fractions. Also, in Problem 22 students write an absolute value equation using realistic information about the temperature of helium, correct to the ten-thousandths place. In Problems 29 and 30, students find the slope of a line given two coordinates whose values are fractions.

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

  • In Algebra 1, Lesson 8, students apply 6.RP.3d by converting units to solve problems involving currencies, units of volume, and units of area. In Algebra 1, Lesson 31, students apply unit rates (6.RP.2) to diving speeds and scaling on a map.
  • In Geometry, Lesson 87, students use areas of polygons (6.G.1) to find relationships between the scale factor, perimeter, and areas of similar figures.
  • In Algebra 2, Lesson 4, students apply their understanding of functions (8.F.1) by identifying functions based on inspecting the domain and range.
  • In Algebra 2, Lesson 45, students apply modeling relationships with a straight line (8.SP.2) as they find the line of best fit given a set of data and use the data to calculate the correlation coefficient, r.

Indicator 1d

The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.
1/2
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Indicator Rating Details

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

There are natural connections throughout the materials, as evidenced in instructional activities, practice problems, and assessments. The materials are designed where groups of lessons for different concepts are separated and placed in different units across the series. For example, in Algebra 1, Unit 4, the lessons are as follows:

  • Lesson 31-Using Rates, Ratios, and Proportions
  • Lesson 32-Simplifying and Evaluating Expressions with Integer and Zero Exponents
  • Lesson 33-Finding the Probability of Independent and Dependent Events
  • Lesson 34-Recognizing and Extending Arithmetic Sequences
  • Lesson 35-Locating and Using Intercepts
  • Lesson 36-Writing and Solving Proportions
  • Lesson 37-Using Scientific Notation
  • Lesson 38-Simplifying Expressions Using the GCF
  • Lesson 39-Using the Distributive Property to Simplify Rational Expressions
  • Lesson 40-Simplifying and Evaluating Expressions Using the Power Rule for Exponents

As seen by the lesson titles in this unit, ratios and proportions are introduced in Lesson 31 and revisited in Lesson 36. The Algebra 1 materials further build upon this concept in Lesson 42, solving percent problems, and in Lesson 44, finding slope using the slope formula.

These natural connections occur in each course. For example, in Algebra 2, Lesson 38, students practice long division of polynomials, and in Lesson 51, students practice synthetic division and the remainder theorem. Then in Lesson 76, students use long division and the remainder theorem to factor and find roots of polynomials.

Examples of where the materials do not foster coherence by omitting appropriate and required connections include:

  • A-REI.4b and F-IF.8a: The Algebra 1 materials address all the different methods of solving quadratic equations; however, the methods are taught in isolation from each other. Factoring is taught in Lesson 98, then graphing in Lesson 100. In Lesson 102, students solve by finding square roots, and in Lesson 110, they learn the quadratic formula. There is no evidence of connecting the different methods of solving quadratic equations, graphing to see that a quadratic equation yields the same answers as factoring, and factoring to help see the x-intercepts of a parabola which yields the same results as the quadratic formula.
  • A-REI.6: The Algebra 1 materials address three different methods for solving systems of equations: graphing (Lesson 55), substitution (Lesson 59), and elimination (Lesson 63). These different methods are taught in separate lessons, and students are not given the opportunity to make connections between the different methods.
  • Geometry: When trigonometric ratios are introduced in Lesson 68, there are no connections made between the definitions of trigonometric ratios and similar triangles.

Much of the mathematics in Algebra 1 is repeated in Algebra 2 without any connections across courses to the way the mathematics was developed in the materials. The following examples highlight where there is no coherence between content taught in one course to content within that course or to other courses in the series. Examples of where the materials do not foster coherence by omitting appropriate and required connections across the courses include:

  • In Algebra 1, Lesson 26, students solve multi-step linear equations. They continue work with linear equations in Algebra 1, Lessons 28, 29, and 31. In Algebra 2, Lesson 7, students again work with multi-step linear equations. The materials do not make connections to this work on multi-step linear equations within the Algebra 1 lessons or between the Algebra 1 and 2 courses.
  • In Algebra 1, Lesson 79, students factor trinomials using greatest common factors. This concept is introduced again in Algebra 2, Lesson 23, without any connections to Algebra 1.

Indicator 1e

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

The instructional materials reviewed for the Saxon Traditional Series partially meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The instructional materials do not explicitly identify content from Grades 6-8. Additionally, the instructional materials make some connections between Grades 6-8 and high school concepts, but the connections do not allow students to extend their previous knowledge.

In each lesson throughout the series, a “Warm Up” is provided to review previously-learned mathematics. In the teacher’s edition, there is a “Math Background” which references skills and concepts previously addressed, but the materials do not explicitly identify the standards from Grades 6-8 which are being referenced. There are no clear connections between standards from Grades 6-8 and high school standards. Some examples of where the materials do not fully build on knowledge from previous understandings include:

  • There is no connection made between N-RN.1 and 8.EE.1. When N-RN.1 is addressed in Algebra 2, Lesson 59, the materials present the definition of rational exponents without any explanation of how it connects to the definition and properties of integer exponents.
  • In Algebra 1, Lesson 23, students solve linear equations (A-REI.3), but the lesson does not refer to standards from Grades 6-8 or to the skills required for solving equations building toward this high school standard.
  • In Geometry, Lesson 35, the formulas for arc length and area of a sector (G-C.5) are introduced but are not connected to the formulas for area and circumference of circles (7.G.4).
  • In Geometry, Lesson 12, students use supplementary, complementary, vertical, and adjacent angles (7.G.5) to prove theorems about lines (G-CO.9). The ideas are presented as a new concept, making no connection to previously-learned standards.
  • In Geometry, Lessons 22 and 62 address 7.G.6. Lessons 12, 29, and 33 address 8.G.5, 8.G.7, and 8.G.6, respectively. There is no acknowledgement that middle school standards are being used or built upon. In addition, the teacher’s materials state that future lessons will address these same skills, but there is no identification where these concepts or skills are being developed to a greater degree.

No connections are contained for Statistics and Probability across the series. Examples include:

  • In Algebra 1, 13 lessons, three labs, and two investigations address standards from Statistics and Probability (S-ID.1,5 and S-CP.2), but there are no connections between these activities and standards from Grades 6-8 (6.SP.B, 8.SP.4, and 7.SP.C).
  • Geometry has one lesson and lab that addresses S-ID.6a (Use a function fitted to data to solve problems.). This standard is not connected to any Functions or Statistics and Probability standards from Grade 8.
  • Algebra 2 has 10 lessons, four labs, and two investigations that deal with standards from Statistics and Probability (S-ID.2,4 and S-CP.2). Of these 16 activities, three deal with middle school content (6.SP.B, 7.SP.B, and 7.SP.C), but there were no connections made between the standards from Grades 6-8 and the high school standards.

Although no explicit references are made to middle school standards, there are some locations where connections between standards from Grades 6-8 and high school standards are made. Examples include:

  • In Algebra 1, Lesson 41 defines the slope of a line as the rate of change of that line (8.EE.5). In later lessons, the materials develop the slope formula, writing linear equations, and graphing linear equations (F-IF.7a). The middle school standard is a focus of these lessons as they build on slope and rate of change in connection to the Functions standards.
  • In Algebra 2, Lesson 2 addresses 6.EE.2c, and Lessons 7 and 8 address 8.EE.7b. The “Math Background” makes connections to the middle school standards of solving equations in one variable. The lesson itself focuses on linear equations making connections to A-CED.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.
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Indicator Rating Details

The instructional materials reviewed for the Saxon Traditional Series do not explicitly identify the plus standards and do not use the plus standards to coherently support the mathematics which all students should study in order to to be college and career ready.

The plus standards are not explicitly identified in the teacher or student editions of the materials. Where plus standards are present, they are not connected in a coherent manner to support the mathematics students need to be college and career ready. There is no evidence of the plus standards enhancing the work of the lessons or courses, and often the inclusion of plus standards in a lesson are a distraction to the work of the course because of the lack of connections to surrounding lessons and what the students are learning.

Omitting a plus standard does not diminish a student's’ opportunity to learn the non-plus standards in the lesson/unit. An example of a plus standard that serves as a purposeful extension is G-SRT.11, which is addressed in Geometry, Lessons 94 and 98. The formulas for Laws of Sines and Cosines are not proven nor derived, but they are used to solve problems. This connects to students' work with solving right triangles using trigonometric functions.

There is no evidence where the following plus standards connect to, build, or support any of the non-plus standards:

  • A.REI.8 and A.REI.9 are addressed in Algebra 2, Lesson 32.
  • A-APR.5 is addressed in Algebra 2, Lesson 49.
  • N-CN.3 and the first part of N-CN.4 (represent complex numbers on the complex plane in rectangular and polar form) are addressed in Algebra 2, Lesson 69.
  • G-C.4 is addressed in Geometry, Lab 8.
  • N-CN.9 is addressed in Algebra 2, Lesson 106.
  • N-VM: In Algebra 2, Lessons 5, 9, 14, 16, 32, and 99 address this domain, but these are not connected to any non-plus standards.

Teachers who omit instructing a plus standard in the materials need to adjust homework assignments, because practice problems in the series incorporate the plus standards.

Gateway Two

Rigor & Mathematical Practices

Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
N/A

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
N/A

Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
N/A

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
N/A

Criterion 2e - 2h

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

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2f

The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
N/A

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

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

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

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

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

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

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

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

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

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

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

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

Indicator 3w

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

Indicator 3x

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

Indicator 3y

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

Criterion 3z - 3ad

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

Indicator 3z

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

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

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

Indicator 3ac

Materials can be easily customized for individual learners.
N/A

Indicator 3ac.i

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

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
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Additional Publication Details

Report Published Date: 02/07/2018

Report Edition: 2009

Title ISBN Edition Publisher Year
Saxon Math: Algebra 1 978-1602773011 Student Edition Houghton Mifflin Harcourt 2009
Saxon Math: Algebra 1 978-1602773028 Teacher Edition Houghton Mifflin Harcourt 2009
Saxon Math: Algebra 2 978-1602773035 Student Edition Houghton Mifflin Harcourt 2009
Saxon Math: Algebra 2 978-1602773042 Teacher Edition Houghton Mifflin Harcourt 2009
Saxon Math: Geometry 978-1602773059 Student Edition Houghton Mifflin Harcourt 2009
Saxon Math: Geometry 978-1602773066 Teacher Edition Houghton Mifflin Harcourt 2009

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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