Alignment to College and Career Ready Standards: Overall Summary

The instructional materials for the Discovering series partially meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strengths in the following areas: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites (WAPs), engaging students at a level of sophistication appropriate to high school, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. For rigor and the mathematical practices, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, opportunities for students to develop procedural skills, utilizing mathematical concepts and skills in engaging applications, displaying a balance among the three aspects of rigor, supporting the intentional development of reasoning and explaining, and supporting the intentional development of seeing structure and generalizing.

See Rating Scale
Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
13/18
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Criterion Rating Details

The instructional materials reviewed for the Discovering series partially meet the expectations for Focus and Coherence. The instructional materials meet the expectations for: attending to the full intent of the mathematical content contained in the High School Standards, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs), engaging students in mathematics at a level of sophistication appropriate to high school, and explicitly identifying and building on knowledge from grades 6-8 to the High School Standards. The instructional materials partially meet the expectations for letting students fully learn each non-plus standard and making meaningful connections in a single course and throughout the series. The instructional materials do not meet expectations for attending to 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.
4/4
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Indicator Rating Details

The instructional materials reviewed for the Discovering series meet the expectations for attending to the full intent of the mathematical content contained in the High School Standards for all students. Overall, the instructional materials address most of the non-plus standards, however, there are a few instances where all aspects of the non-plus standards are not addressed across the courses of the series.

The following are examples of standards that are fully addressed:

  • The standards from F-BF are developed starting in the Discovering Algebra course with a study of recursive sequences and writing explicit expressions to represent the sequences. Work with recursive sequences is then expanded to working with exponential equations. In Discovering Algebra, the work in this domain concludes with students identifying and exploring the various function transformations. Work with the F-BF domain continues in the Discovering Advanced Algebra course with a further study of recursive sequences and transformations and a study of building inverse functions.
  • F-IF.7: The materials introduce time-distance graphs in Discovering Algebra Lesson 3.4 by discussing the intercept, periods of non-movement, and speeding up and slowing down. The standard is further addressed through Discovering Advanced Algebra as students examine maximum, minimum, and zero values of quadratic and polynomial functions as well asymptotes and end behavior of rational functions.
  • A-CED.3: In Discovering Advanced Algebra Lesson 2.5, students determine appropriate and reasonable constraints for application problems involving profit from two types of birdbaths. Students also determine if solutions are reasonable in various problems.
  • G-CO.7: In Discovering Geometry Lesson 4.4, students create various triangles using constructions and GeoGebra when given select criteria (such as, one side and two angles must be the same) to generate congruence “shortcuts” for triangles such as ASA, AAS, SAS, and SSS. Students also reason and investigate as to why the shortcut “SSA” does not exist.

The following standards are partially addressed:

  • G-SRT.1a: In Discovering Geometry, Coordinate Geometry 7, students are questioned if “...the corresponding sides are parallel? Explain.” when examining a dilated set of triangles. However, the materials do not address whether a line passing through the center of dilation remains unchanged in either Coordinate Geometry 7 or Discovering Geometry Lesson 7.1.
  • G-GPE.5: In Discovering Geometry, Coordinate Geometry 5, Example A, students are directed to find the equation of a perpendicular line through a point to find perpendicular bisectors. In Discovering Geometry, Coordinate Geometry 11, students are provided with the parallel slope property and perpendicular slope property and are given problems in which to use them in proofs. However, the materials do not contain a proof of these two properties.
  • S-IC.5: This standard is not identified in the Discovering Algebra, Discovering Geometry, or the Discovering Advanced Algebra correlation documents. However, examination of the materials reveal that students compare treatments in Discovering Advanced Algebra Lesson 9.1, but at no time do the materials contain simulations to decide if differences between parameters are significant.

Standard S-IC.6 is not addressed within the three courses of the series. The correlation document for Discovering Advanced Algebra suggests this standard is addressed in Lesson 9.4. Upon examination of the materials, no indication can be found where reports that were either publisher-created or student- generated based on data are to be evaluated.

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 Discovering series do not meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. Throughout the series, there are a number of lessons and activities that contain a variety of components of the modeling process described in the CCSSM. However, throughout the series, students do not have an opportunity to engage in the full modeling process. Notably, the “formulate” part of the modeling process described in the CCSSM is consistently lacking in the materials provided. According to the CCSSM, students should be “formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables.” There is no evidence that students formulate a process for solving problems or work through the modeling process on their own.

Examples of how components of the modeling process are omitted include:

  • In Discovering Algebra, Lesson 2.4, One Step, students “use a graph, a rate, an equation, and a calculator table to fill in the numbers missing from the Ship Canals table.” Students have the opportunity to calculate as part of the modeling cycle, but with the problem’s directions, students do not have the opportunity to formulate on their own within the modeling process.
  • In Discovering Algebra, Lesson 4.10, Activity Day, Data Collection and Modeling, students complete a “bungee jump” activity to predict how many rubber bands are necessary to allow a jumper to safely bungee jump. Step 6 states: “Define variables and make a scatter plot of the information from your table,” but the variables are provided on the table in Step 3. Step 7 directs students to find an equation to fit their data, however, students are told how to model the problem using a table and a graph with equation by the chapter title, “Functions and Linear Modeling.” Thus, students are not determining what model to use on their own. Students justify why their equation is a reasonable fit (interpret), test their results (validate), and write a group report for the activity (report).
  • In Discovering Algebra, Lesson 7.8, Activity Day, Using Transformations to Model Data, students determine a model for a given scenario and test their model. In Experiment 1: The Rolling Marble, students graph their data, but they are given the variables required for the problem. The problem also directs students to model the data using a parabola, as well as provides students with the general equation in Step 5. Students test their equation by catching the marble on the path described by their equations (validate). Students are expected to report their findings to the class (report).
  • In Discovering Algebra, Lesson 7.8, Activity Day, Using Transformations to Model Data, Experiment 3: Calculating, students calculate various sums on the calculator and report the time needed to do so. In Step 3, students record their answers as coordinates on the form (number of numbers to add, time), which provides students with predefined variables. Step 4 directs students to write an equation to model the data (directing students to a certain type of model), and in Step 6, students test their results (validate) through the following questions: “What is the y-intercept of your model? Does this value have any real-world meaning? If so, what is the meaning? If not, why not?” Experiment 3 enables students to interpret their findings and report their results to the class.
  • In Discovering Geometry, Coordinate Geometry 9, students compute and validate, but they don't formulate, interpret, or report. "In a rectangular room, measuring 30 ft by 12 ft by 12 ft, a spider is at point A on the middle of one of the end walls, 1 foot from the ceiling. A fly is at point B on the center of the opposite wall, 1 foot from the floor. What is the shortest distance that the spider must crawl to reach the fly, which remains stationary? The spider never drops or uses its web, but crawls fairly." A diagram is also provided.
  • In Discovering Geometry, Lesson 12.2, One Step, students find the height of a kite when given the angle of elevation and length of kite string. Since this problem is embedded within Problem Solving with Right Triangles, the type of model needed is provided to the students, and students do not get the opportunity to create and select a model on their own (formulate).
  • In Discovering Advanced Algebra, Lesson 4.6, One Step, students determine when the national debt will pass $1 trillion. However, students are provided with a model (equation) and the variables are defined within the problem, so students do not get the opportunity to create and select a model on their own (formulate).
  • In Discovering Advanced Algebra, Lesson 5.5, Exercise 12, students solve the following word problem: “Taoufik has climbed to the top of an apple tree. Finding a good apple, he tosses it up into the air with an initial upward velocity of 60 feet per second. Its height, in feet, is given by the equation h = −16t2 + 60t + 16. a. How high up in the tree was Taoufik when he threw the apple? b. At what time(s) is the apple 52 feet in the air? c. At what time does the apple hit the ground?” In this problem, students are provided with predefined variables and the equation (model) in which to solve the problem. Students are expected to calculate without formulating, validating, interpreting, or reporting.

In Discovering Advanced Algebra and Discovering Geometry, there are additional materials called Projects. While these projects present an opportunity for students to practice components of the modeling process, they fail to allow students to formulate a model. For example:

  • In Discovering Advanced Algebra, “The Cost of Living,” students are told the type of equation to construct (exponential). This same issue of telling the student what type of equation to construct is repeated consistently throughout the materials.
  • In Discovering Advanced Algebra, “Talkin’ Trash,” students collect data on the population of the United States and on recycling, and they are directed to fit a linear model to the data set. Students are not given the opportunity to determine the type of function to use on their own or to test which type of function would be the best fit for the data collected.

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 Discovering series, when used as designed, meet expectations for spending the majority of time on the CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

In Discovering Algebra, students spend a majority of their time working with WAPs from the Number and Quantity, Algebra, Functions, and Statistics and Probability conceptual categories. For example:

  • In Lesson 8.4, students factor quadratic equations to determine zeros using the Zero Product Property (A-SSE.3a). Students also factor quadratic equations from general form to vertex and/or factored form. Students check their work by confirming the locations of zeros as a result of factoring via the graphing calculator.
  • In Lesson 4.1, students use "secret codes" in which each input of the code has only one output to introduce functions and vocabulary such as domain and range (F-IF.1). In Lesson 7.1, students encounter function notation and its relationship to the graph.

The Discovering Geometry course focuses on the widely acceptable prerequisites in the Geometry conceptual category. For example:

  • In Lesson 12.2, students solve word problems using trigonometric functions (G-SRT.8). In Example 1 of the lesson, students use the angle of elevation to determine the distance a sailboat is located from a lighthouse.
  • In Lessons 1.1, 1.2, and 1.3, students learn and use precise definitions for the terms such as line segment, angle, parallel lines, and perpendicular lines (G-CO.1). Students practice labeling each of these and answer questions about each of them.

During Discovering Advanced Algebra, students spend a majority of their time working with widely acceptable prerequisites from Number and Quantity, Statistics and Probability, Algebra, and Functions:

  • In Lesson 4.6, students graph logarithmic functions by looking at how different transformations change each function (F-IF.7e). In Lesson 7.5, students graph trigonometric functions by looking at how different transformations change the period, midline, and amplitude.
  • In Lesson 9.1, students compare and contrast various types of studies such as experimental, observational, and surveys. Students also make predictions based on sample data from a population in Exercise 7 (S-IC.1).

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 Discovering series, when used as designed, partially meet expectations for letting students fully learn each non-plus standard. Overall, the series addresses many, yet not all, of the standards in a way that would allow students to fully learn the standards. However, in cases where the standards expect students to prove, derive, or develop a concept, the materials often provide students with the proofs, derivations, and concept developments.

For the following standards, the materials partially meet the expectation for allowing students to fully learn each standard. These examples represent standards which are present but did not allow students to fully learn the standard:

  • A-SSE.4: In Discovering Advanced Algebra, Lesson 4.8, students are guided through a series of steps to derive the formula for the sum of a finite geometric series. Students are not deriving the formula themselves, which is the expectation of the standard.
  • A-APR.1: In Discovering Algebra, Chapter 8 and Discovering Advanced Algebra, Chapter 6, students add, subtract, and multiply polynomials. However, students have limited opportunities to develop understanding that polynomials are “closed” under these operations.
  • A-REI.5: In Discovering Advanced Algebra, Lesson 2.2, students solve systems of equations using elimination and verify results with a calculator. However, students do not prove that replacing one equation with the sum of that equation and a multiple of the other equation produces a system with the same solutions.
  • F-IF.3: In Discovering Advanced Algebra, Lesson 1.1, students work with sequences. However, the materials do not refer to sequences as functions, whose domain is a subset of the integers.
  • F-IF.7b: In Discovering Advanced Algebra, Lesson 4.3, Exercise 6b, students graph cube root functions. The materials provide a limited number of problems for students to graph cube root functions.
  • F-IF.9: In Discovering Algebra, Lesson 3.3, Exercise #4, students compare properties of two functions represented in different ways (tables and graphs). Beyond Exercise #4, there is a limited number of opportunities for students to compare properties of two functions.
  • F-TF.2: In Discovering Advanced Algebra, Lessons 7.3 and 7.5, students interpret radian measures of angles using the unit circle. However, students do not explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers.
  • G-C.5: In Discovering Geometry, Lessons 8.4 and 9.6, students solve problems by finding the area of a sector or the length of an arc. While students derive the formula for arc length in Lesson 9.6, students do not derive the formula for the area of a sector in either lesson.

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 Discovering series, when used as designed, meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials provide students with opportunities to engage in real-world problems throughout the series. Students engage in problems that use number values that represent real-life values--fractions, decimals, and integers. The context of most of the scenarios are relevant to high school students.

Examples of where the materials require students to engage in mathematics at a level of sophistication appropriate to high school include:

  • In Discovering Algebra, Lesson 4.1, students apply ratios and proportions from middle school to finding the rate of change of a function. Students write the rate of change in terms of unit rates that use compound units.
  • In Discovering Algebra, Lesson 8.1, students solve quadratic equations that have various types of real numbers including terminating decimals, irrational numbers, and integers. Students also work with age-appropriate contexts including the height of a falling baseball, the height of a model rocket, and the height of an arrow being shot from ground level.
  • In Discovering Advanced Algebra, Lesson 4.1, students use exponential equations that model both growth and decay. Students use various types of real numbers including decimals and integers and age-appropriate context such as population growth, growth of plants, and the price of a used automobile.
  • In Discovering Advanced Algebra, Lesson 8.2, students apply key takeaways of basic statistics and probability from middle school to find the probability of compound events such as the probability that two students will be successful, and the probability of getting a number of questions correct in a row on a true/false test when just guessing.
  • In Discovering Geometry, Lesson 11.4, students use rational numbers in fraction and decimal form. There are also operations with radicals and numerical manipulations where students leave “pi” in the answer.
  • In Discovering Algebra, each chapter begins with a “Refreshing Your Skills” section which often allows for practice with varying number types. Discovering Algebra Lesson 4.0, Exercise 2 includes repeating decimals and radicals. In Lesson 6.0, students convert decimals to percents, and students review scientific notation in Lesson 6.4, which is reviewed throughout the exercises thereafter. Negative exponents are presented in Lesson 6.6 and used thereafter.
  • In Discovering Advanced Algebra, students encounter the same variety of number types with the addition of complex number operations in Lesson 5.4. Complex numbers are then used in later work.

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 Discovering series partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series, where appropriate and where required by the standards. Overall, mathematical connections are made within courses, but connections between courses are not made.

The following are examples of connections not being made between courses:

  • In Discovering Algebra, Lessons 8.6 and 8.7, the materials address completing the square and the quadratic formula (A-REI.4). The materials revisit completing the square and the quadratic formula in Discovering Advanced Algebra Lessons 5.2 and 5.3 without connection to Discovering Algebra Lessons 8.6 and 8.7.
  • In Discovering Geometry, Lesson 8.2, students calculate the area of different shapes in different contexts. There is no indication in the materials that writing and solving equations in one variable (A-CED.1) and using units to understand problems and guide the solutions (N-Q.3) could be used to solve the problems on area. A-CED.1 is addressed in Discovering Algebra Lesson 2.8, and N-Q.3 is addressed in Discovering Algebra Lesson 2.3.
  • In Discovering Geometry, Lesson 1.9, the teacher notes state, "This lesson introduces the three rigid transformations (isometries) of the plane: translations, rotations, and reflections." There is no connection to how transformations were addressed in Discovering Algebra Lessons 7.5 (Translating Graphs) and 7.6 (Reflecting Points and Graphs). The standards' correlation document indicates G-CO.2 is addressed in Discovering Algebra, but the connection is not made in the Discovering Geometry materials.
  • Discovering Advanced Algebra, Chapter 1, Linear Modeling addresses and extends many of the concepts addressed in Discovering Algebra, Chapter 3, Linear Equations. The teacher notes at the beginning of Discovering Advanced Algebra, Chapter 1 state, “Much of this chapter reviews basic algebra concepts but is presented from a fresh perspective. Rather than skipping a topic, you may be able to spend less time on some lessons than on others. Many of the Investigations will allow you to assess prior understanding of familiar topics. In the later lessons of the chapter, students are exposed to the analysis of models that they will need throughout the course.” While there are references to content taught previously and subsequently, there are no clear indications of the connections between concepts or standards.

The following are examples of connections made within courses:

  • In Discovering Advanced Algebra, Lesson 8.2, students calculate probabilities of independent events. In Discovering Advanced Algebra, Lesson 8.3, students use that knowledge to calculate the probability of mutually exclusive events. The opening paragraph of Lesson 8.3 describes to students which content they will be using from the previous lesson to apply to the new concept.
  • In the opening of Discovering Algebra, Chapter 3, the teacher notes discuss how the work in Lesson 3.1 with recursive sequences will connect to Chapter 6 when students develop exponential functions. The notes also discuss how the work in Lesson 3.7 connects to the interpretation of fitting a linear function to a set of data.

Indicator 1e

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

The instructional materials reviewed for the Discovering series meet expectations for explicitly identifying and building on knowledge from grades 6-8 to the High School Standards.

In Discovering Algebra, standards from grades 6-8 are explicitly identified in the teacher assistance portal on the left side of the page in the online teacher manual. Standards from Grades 6-8 are listed and aligned to lessons in the Discovering Geometry Correlation Guide. There are no standards from Grades 6-8 listed or aligned to lessons in the Discovering Advanced Algebra Correlation Guide nor in the lessons.

Some examples where the materials explicitly identify content from Grades 6-8, make connections between Grades 6-8 and high school concepts, and allow students to extend their previous knowledge include:

  • Discovering Algebra, Chapter 0, Lesson 0.4 explicitly identifies 6.NS, 7.NS, 7.EE.1, 8.EE, and 8.F.1 and builds upon them to introduce F-BF.1a. Through the context of operations with signed numbers, students look for patterns in order to determine an explicit expression, a recursive process, or steps for calculation.
  • In Discovering Algebra, Lesson 4.1, 8.F.1 is explicitly identified and built upon to address F-IF.1. Students examine functions through the use of “secret codes” and determine that a function is a rule (8.F.1) in order to understand that one element in the domain of a function corresponds to exactly one element of the range (F-IF.1).
  • In Discovering Geometry, Lesson 7.3, students solve problems using scale drawings of geometric figures (7.G.1) while simultaneously solving problems using similar triangles (G-SRT.4).
  • In Discovering Geometry, Lesson 2.5, students use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve problems (7.G.5). This knowledge is extended as students prove that vertical angles are congruent (G-CO.9) in Investigation 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.
0/0
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Indicator Rating Details

The instructional materials reviewed for the Discovering series explicitly identify the plus standards when included and use the plus standards to coherently support the mathematics which all students should study in order to to be college and career ready.

The materials address the following plus standards: N-CN.3, A-APR.7, F-IF.7d, F-TF.3, F-TF.4, F-TF.7, F-TF.9, G-SRT.9, G-SRT.10, G-SRT.11, G-C.4, G-GMD.2, S-CP.8, and S-MD.6. In general, the materials include these standards as additional content that extends or enriches topics within a unit, and their inclusion does not interrupt the flow of the course. No plus standards are located in Discovering Algebra.

The following are examples of the materials addressing the full intent of plus standards:

  • In Discovering Advanced Algebra, Lessons 6.5 and 6.6, students graph rational functions while identifying asymptotes and end behavior. (F-IF.7d)
  • In Discovering Advanced Algebra, Lesson 7.7, students prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (F-TF.9)
  • In Discovering Geometry, Lesson 12.3, students derive the area formula for a triangle by drawing an auxiliary line perpendicular to the base of the triangle. (G-SRT.9)
  • In Discovering Geometry, Lessons 12.3, 12.4, and 12.5, students apply the Law of Sines and Law of Cosines to solve typical problems involving non-right triangles. (G-SRT.11)

The following are examples of the materials not addressing the full intent of plus standards:

  • N-CN.3: In Discovering Advanced Algebra, Lesson 5.4, students find the conjugate of complex numbers and use the conjugates in addition, subtraction, and multiplication. However, students do not find the quotient or modulus of complex numbers.
  • A-APR.7: In Discovering Advanced Algebra, Lessons 6.7 and 6.8, students add, subtract, multiply, and divide rational expressions. However, the materials do not address rational expressions forming a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
  • F-TF.4: In Discovering Advanced Algebra, Lesson 7.3, students use the unit circle to define the periodicity of trigonometric functions. However, the materials do not address how the unit circle relates to symmetry of the functions (even or odd).
  • F-TF.7: In Discovering Advanced Algebra, Lesson 7.1, students use inverse trigonometric functions to solve word problems, but not within a modeling context.
  • G-SRT.10: In Discovering Geometry, Lessons 12.3 and 12.4, students use the Law of Sines and Law of Cosines to solve problems. Students prove the Law of Sines in Lesson 12.3, but the proof of the Law of Cosines is provided for them by the materials.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.
8/8

Indicator 2a

Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.
2/2
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Indicator Rating Details

The instructional materials for the Discovering series meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Throughout the series, the instructional materials develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding.

The instructional materials develop conceptual understanding throughout the series. For example:

  • N-RN.1: In Discovering Advanced Algebra, Lesson 4.3 Investigation, students “describe what it means to raise a number to a rational exponent.” In the Investigation, students create a table and a graph for y = x^(½) in order to state a conclusion about raising a number to the power of ½. Students explain how they would evaluate numerical expressions involving a rational exponent, and they conclude the Investigation by generalizing “a procedure for simplifying a^(m/n)."
  • F-IF.A: Across the series, students develop an understanding of functions. In Discovering Geometry, Lesson 6.2, functions are developed through the algebraic nature of geometric transformations. In Discovering Advanced Algebra, functions are further developed in Chapter 3. Students learn about function notation and evaluate functions. They use real world situations to sketch and interpret graphs of functions. Students talk about reasonable domains and evaluate functions that are representing different situations. Students continue to develop their understanding of functions of different types in Chapters 4, 5, 6, and 7.
  • A-APR.B: In Discovering Algebra, Lessons 8.4 and 8.6, the materials initially address the relationship between zeros and factors of polynomials as students find the zeros of quadratic equations by factoring and completing the square. In Discovering Advanced Algebra, Lessons 6.2, 6.3, and 6.4, students further develop their conceptual understanding of the relationship between zeros and factors of polynomials through polynomial equations of degree 3 and higher. In both courses, students determine factors of polynomial equations from graphs in addition to finding the zeros for given polynomial equations.

The instructional materials provide opportunities for students to independently demonstrate conceptual understanding throughout the series. For example:

  • G-SRT.2: In Discovering Geometry, Lesson 7.1, students determine why two figures are similar. They are expected to answer that the angles are congruent and that the sides are proportional. On Chapter 7, Quiz 1 Form A, students explain why or why not two triangles are similar in Problems 3 and 4. On Chapter 7, Constructive Assessment Options, Problem 3, students extend the sides of a trapezoid to create similar triangles. Students explain why the triangles constructed are similar and determine the ratio of the corresponding sides. In Chapter 11, Constructive Assessment Options, Problem 7, students find the ratio between surface area and volume of two similar triangular pyramids and explain why their cross sections are similar.
  • G-SRT.6: In Discovering Geometry, Lesson 12.1, students explore right triangles with acute angle measures of 20 and 70 degrees. As students draw similar triangles with these angle measures, students develop an understanding that side ratios in right triangles are properties of the angles in the triangle, which leads to definitions of trigonometric ratios for acute angles.
  • S-ID.7: In Discovering Algebra, Lesson 3.3, students interpret the slope of a graph (speed) and starting location (intercept) in order to provide walking directions to another student. In Chapter 3, Quiz 1 Form A, students complete similar problems.

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.
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Indicator Rating Details

The instructional materials for the Discovering series meet expectations that the materials provide intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. The materials routinely address procedural skills and start each chapter with “refreshing your skills.” The materials include an Exercise section so students can independently practice skills and concepts addressed in the lesson.

The instructional materials develop procedural skills throughout the series. For example:

  • F-BF.3: In Discovering Algebra, Lesson 7.5, Problems 4 and 5, students describe the graph of an equation based on the graph of the parent function. Students also write an equation given the description of the transformation and the graph of the parent function. In Chapter 7, Quiz 3, students describe the transformation and write the equation given a parent function.
  • A-APR.6: In Discovering Advanced Algebra, Lesson 6.8, students multiply and divide rational numbers without context to develop procedural skill. Students solve these stand-alone problems during the lessons in Example A and B as well as during the Exercise portion. In Quiz 3, students solve four problems involving rational equations without context to further develop procedural skill regarding rational expressions.
  • G-GPE.7: In Discovering Geometry, Coordinate Geometry 9, students use the distance formula to determine the perimeters and areas of quadrilaterals and triangles.

The instructional materials provide opportunities to independently demonstrate procedural skills throughout the series in the following examples:

  • A-SSE.2: In Discovering Advanced Algebra, Lesson 6.2, students complete guided examples of how a cubic expression for volume can be converted from one form to another (i.e., standard to factored). The materials include methods for using each form to find information about the behavior of the function (the graphed path of the volume expression). Students solve similar problems individually during Exercise 6.2.
  • F-BF.3: In Discovering Algebra, Lesson 7.5, students individually practice transforming absolute value, quadratic, and exponential functions. In Discovering Advanced Algebra, Lesson 3.5, students individually practice transforming square root functions, in Lesson 3.7, circles, in Lesson 6.6, rational functions, and in Lesson 7.5, trigonometric functions.
  • G-GPE.4: In Discovering Geometry, Coordinate Geometry 11, students individually use coordinates to prove the definitions of polygons, such as specific quadrilaterals and triangles, by completing the distance formula or slope.

Indicator 2c

Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The instructional materials for the Discovering series meet expectations that the materials support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. Overall, the instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematics and independently demonstrate the use of mathematics flexibly in a variety of contexts.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematics throughout the series. For example:

  • N-Q.2: In Discovering Algebra, Lesson 2.3, students use conversion rates within contextualized problems. In Exercise 11, students find the conversion factor from a table and use it to solve multiple problems. This problem is multi-step and non-routine.
  • S-IC.1: In Discovering Advanced Algebra, Lesson 9.1, students use statistics as a process for making inferences about population parameters based on a random sample from that population within contextualized problems.
  • Chapter 6 of Discovering Geometry addresses applications of transformations. Students explore transformations through activities such as "Finding A Minimal Path" and "Exploring Tessellations."

The instructional materials include opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. For example:

  • F-IF.4: In Discovering Algebra, Lesson 4.3, Graphs of Real World Situation, students are provided with four problem contexts and need to match them to their corresponding graphs (six are given).
  • A-SSE.3: In Discovering Advanced Algebra, Lesson 5.1, students construct a function from a table and answer questions using their function related to the problem context.
  • G-SRT.8: In Discovering Geometry, Lesson 12.2, students use trigonometric functions to solve single and multi-step contextualized problems.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.
2/2
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Indicator Rating Details

The instructional materials for the Discovering series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The materials represent each aspect of rigor both independently and together.

The materials frequently prompt students to explain their reasoning to demonstrate conceptual understanding, and students complete at least one investigation in each lesson to better understand the concept in the lesson. The lessons also provide opportunities for students to practice problems to increase procedural skills with certain topics. The materials frequently use application/contextualized problems to relate concepts to real-world scenarios. Problems oftentimes address conceptual understanding with procedural skill or conceptual understanding with application.

All three aspects of rigor are present independently throughout the program materials in the following examples:

  • Functions and transformations are addressed in Discovering Algebra and Discovering Geometry. The “rules” related to different transformations, presented in Discovering Algebra, represent the procedural skills for this topic. The use of transformations with functions and combinations of transformations in Discovering Geometry represent conceptual understanding of this topic.
  • In Discovering Algebra, Lesson 5.1, students solve systems of linear equations. Most of the problems in this lesson do not have contexts, so students develop procedural skills in relation to A-REI.6.
  • In Discovering Geometry, Lesson 4.6, students complete several proofs. Students develop conceptual understanding of the triangle congruence criteria in regards to G-CO.8 and G-SRT.5 through the completion of the proofs.
  • In Discovering Advanced Algebra, Lesson 7.6, Exercise 14, students apply trigonometric functions to model a person’s distance from the ground at different places on a double ferris wheel and at different points of the ferris wheel's rotation.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a topic throughout the materials in the following examples:

  • In Discovering Advanced Algebra, Lesson 6.1, students write a function to model the height of a falling object due to gravity (application). Students graph the function and write a description of the graph in the context of the problem (conceptual understanding) for S-ID.6a.
  • In Discovering Algebra, Lesson 6.1, students compare adding the same amount to an account each year with earning interest on the amount each year (application). From this, students compare linear growth to exponential growth (conceptual understanding). In Example C, students divide consecutive terms to find the constant multiplier of a sequence of numbers (procedural skill).

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/8

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.
1/2
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Indicator Rating Details

The instructional materials for the Discovering series partially meet expectations that the materials support the intentional development of overarching mathematical practices (MP1 and MP6) in connection to the High School Content Standards. Overall, MP1 and MP6 are used to enrich the mathematical content, and there is intentional development of MP1 and MP6. However, for all of the MPs across the series, there are many examples of misleading identifications as evidenced in the EdReports.org Criterion Summary for the MPs.

Some examples where MP1 (Make Sense of Problems and Persevere) is used to enrich the mathematical content include:

  • In Discovering Algebra, Lesson 3.4, Investigation the Teacher Notes state: “In Steps 1-5, students are making sense of the problem and looking at correspondences between representations of the situation.” Students use MP1 as they make connections between recursive rules and linear equations.
  • In Discovering Advanced Algebra, Lesson 4.3, Teacher Notes, students persevere (MP1) in determining that any point on the graph can serve as a starting place for solving the problem.

Some examples where MP6 (Attend to Precision) is used to enrich the mathematical content include:

  • In Discovering Algebra, Lesson 5.2, the Teacher Notes state that students attend to precision (MP6) by “using complete sentences and appropriate mathematics as evidence in stating and supporting their conjectures” about the slopes of parallel and perpendicular lines.
  • In Discovering Geometry, Lesson 6.2, Teacher Notes, students use precise mathematical language (MP6) as they write conjectures about the results of composing two reflections.

Examples of the misidentifications for MPs 1 and 6 include:

  • In Discovering Algebra, Lesson 6.2, the teacher’s notes for the Investigation state: “Step 1. Students who did not do Chapter 0 may need help in seeing how to generate one stage from another. Have them write a rule.” MP1 is identified for this lesson, but students do not have to make sense of the problem or persevere in solving it as they can reference Lesson 0.3 to see further stages of the pattern.
  • In Discovering Advanced Algebra, Lesson 1.1, MP6 is identified, and the Teacher’s Edition prompts the teachers to ask: “What’s behind the pattern?” An explanation for the teacher states: “Mathematics isn’t only about seeing patterns but also about explaining them.” However, students do not need to provide precise explanations in this lesson.

Indicator 2f

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

The instructional materials for the Discovering series meet the expectation that the materials support the intentional development of reasoning and explaining (MP2 and MP3), in connection to the High School Content Standards. The majority of the time, MP2 and MP3 are used to enrich the mathematical content and are not treated separately from the content standards. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others.

Some examples where MP2 (Reason Abstractly and Quantitatively) is used to enrich the mathematical content include:

  • In Discovering Algebra, Lesson 4.2, Investigation Step 1, students examine a series of tables, determine which relations are functions (MP2), and explain their reasons for their answers.
  • In Discovering Geometry, Lesson 8.1, Investigation 1, students transform a parallelogram and a triangle labeled with dimensions expressed as variables to derive the formulas for the area of a parallelogram and triangle, respectively. Students reason abstractly by transforming general figures and manipulating variable dimensions, and they can reason quantitatively by contextualizing the general figures and calculating numerical areas to verify the derived formulas are valid (MP2).
  • In Discovering Advanced Algebra, Lesson 3.1, students examine a graph of the speed and time two cars traveled. Students determine which car will be in the lead after 1 minute (MP2) and explain their reasoning.
  • In Discovering Advanced Algebra, Lesson 2.7, students reason abstractly and quantitatively (MP2) by adding and subtracting rational numbers. Students add fractions using fraction bars, and they add and subtract rational expressions in an abstract manner.

Some examples where MP3 (Construct Viable Arguments and Critique the Reasoning of Others) is used to enrich the mathematical content include:

  • In Discovering Algebra, Lesson 2.1, students examine the work of three different students and answer the following questions: “There are many ways to solve proportions. Here are three student papers, each answering the question ‘13 is 65% of what number?’ What steps did each student follow? What other methods can you use to solve proportions?” Students analyze the different solutions to determine what steps were taken.
  • In Discovering Algebra, Lesson 5.2, "The Slopes Investigation," students plot separate rectangles and find the slopes of the four sides to conclude that opposite sides have equal slopes and adjacent sides have slopes that are opposite reciprocals. They move from the concrete shape to the abstract slopes and construct an argument to support their findings (MP2 and MP3).
  • In Discovering Geometry, Chapter 4, Constructive Assessment Options, Problem 2, students agree or disagree with "Chloe" as to whether her triangle on her quiz has enough information to solve the problem. Students provide reasoning to support their answer.
  • Discovering Advanced Algebra, Lesson 2.2, Exercise 12 contains a system of equations. Three fictitious students in the problem recommend different ways to solve the system by substitution, elimination, or graphing. Students determine which method works the best for this particular problem and why.

An example of the misidentifications for MPs 2 and 3 is in Discovering Geometry, Lesson 7.2. The teacher’s notes for summarizing the lesson include: “Return to the list of all potential shortcuts: AA, SSS, SAS, SAA, ASA, and SSA. 'You’ve considered the first three as similarity shortcuts in this lesson; what about the last three?' Ask whether it would help to consider cases in which SSA failed as a congruence shortcut [SMP 1,3,6].” Students do not construct a viable argument or critique the reasoning of others (MP3).

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.
1/2
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Indicator Rating Details

The instructional materials for the Discovering series partially meet expectations that the materials support the intentional development of modeling and using tools (MP4 and MP5), in connection to the High School Content Standards.

For MP4, throughout the Discovering series, students routinely complete portions of model with mathematics.

  • In Discovering Algebra, Lesson 4.6, Exercise 10, students compute the number of calories burned while walking. Students use the data in the table to write an equation and determine the real-world meaning of the equation. Students are also asked if a certain equation can model the situation.
  • In Discovering Algebra, Lesson 1.4, "The Hand Spans Investigation," students collect hand span measurements for the classroom and model the data in a histogram and a stem and leaf plot. Then, they assess which representation would be most appropriate to use under certain circumstances.
  • In Discovering Advanced Algebra, Lesson 7.6, Example B, students build a mathematical model which will find the vertical height of a seat on a ferris wheel at any time during the rotation.
  • In Discovering Geometry, Lesson 6.2, "Finding a Minimal Path Exploration," students use a protractor and straightedge on patty paper to model shots on a pool table.

For MP5, throughout the Discovering series, students do not have opportunities to choose an appropriate tool to use to solve a problem because the materials include directions which specify which tool(s) to use.

  • In Discovering Algebra, Lesson 4.6, the teacher notes state: “Step 3 uses technology to allow students to focus on how the tables and graphs are the same.” However, in Step 3, students are directed to: “Enter both your point-slope equation and your intercept equation into your calculator.” Thus, students are not choosing their own tools.
  • In Discovering Geometry, Lesson 4.2, MP5 is referenced multiple times in the teacher notes, but students do not choose their own tools in the investigations. In Investigation 1, students are directed to use patty paper and a protractor to construct a triangle and measure the angles in it. In Investigation 2, students are directed to use a compass to copy an angle during the construction of a triangle.
  • In Discovering Advanced Algebra, Lesson 4.2, the teacher notes provide the following: “Ask students to check the answers on their calculators. [SMP 5]” There is no indication that students are choosing their own tools, but they are directed to use the calculator.

Indicator 2h

The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.
2/2
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Indicator Rating Details

The instructional materials for the Discovering series meet expectations that the materials support the intentional development of seeing structure and generalizing (MP7 and MP8) in connection to the High School Content Standards. The majority of the time, MP7 and MP8 are used to enrich the mathematical content and are not treated separately from the content standards. Throughout the materials, support is present for the intentional development of seeing structure and generalizing.

Some examples where MP7 (Look for and Make Use of Structure) is used to enrich the mathematical content include:

  • In Discovering Algebra, Lesson 3.7, students examine the graph of two lines and use the structure of the graphed lines to determine how the lines and their equations are similar.
  • In Discovering Algebra, Lesson 6.1, students look for and describe patterns in the data they have collected. They look for structure when they analyze the pattern to see if it is linear. By examining data and determining that linear data grows at equal amounts over equal intervals, students look for and make use of structure.
  • In Discovering Geometry, Lesson 6.4, Congruence Shortcuts, students complete a series of compositions to see if certain compositions of transformations can be combined into a single transformation.
  • In Discovering Advanced Algebra, Lesson 5.2, Investigation, students expand a binomial raised to the second power resulting in a perfect-square trinomial. Students use the structure of the perfect-square trinomial to rewrite other expressions as perfect-square trinomials (completing the square) which develops the vertex form of a quadratic equation. Students also use the structure of completing the square to determine how to find the x-coordinate of a vertex given the general form of a quadratic equation. MP7 is not identified in the teacher materials for this lesson, though students use structure to proceed through the investigation.

Some examples where MP8 (Look for and Express Regularity in Repeated Reasoning) is used to enrich the mathematical content include:

  • In Discovering Advanced Algebra, Lesson 6.7 Investigate Structure, students graph rational functions. Students determine the slant asymptote equation for a general rational function in terms of variables by recognizing patterns from the graphs of the provided functions.
  • In Discovering Algebra, Lesson 3.1 The Toothpick Patterns Investigation, students complete a series of repeated steps to determine a recursive formula for finding the number of toothpicks in subsequent terms.
  • In Discovering Geometry, Lesson 5.1, students examine different angle sums in polygons and look for a pattern to determine the polygon interior angle sum formula.

An example of the misidentifications for MPs 7 and 8 is in Discovering Geometry, Lesson 2.3. Students draw a model of handshakes using points and line segments and, after completing a table, are told, “Notice that the pattern does not have a constant difference. That is, the rule is not a linear function. So we need to look for a different kind of rule.” The teacher’s note states: “Step 3. Students may be drawing points rather randomly. “How could you arrange the points to be sure that every pair is connected by a line segment?” [Using vertices of a convex polygon is a good arrangement.] [SMP 1,2,4,7,8]" Duplicating a representation given in the investigation does not engage students in MP4. Furthermore, students do not use MP7 or MP8 as students are told that the pattern does not have a constant difference. Students do not engage in MP7 or MP8 on their own due to the steps that are provided for the investigation.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

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.
0/2

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

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

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

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.
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.
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.
0/2

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

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

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
0/2

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/10

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

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).
0/2

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/0

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

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.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

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

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
0/0

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.
0/0

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.).
0/0

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.
0/0

Additional Publication Details

Report Published Date: Thu Apr 19 00:00:00 UTC 2018

Report Edition: 2014

Title ISBN Edition Publisher Year
Discovering Algebra 978-1465239051 Student eBook Third Edition Kendall Hunt 2014
Discovering Algebra 978-1465239068 Teacher eBook Third Edition Kendall Hunt 2014
Discovering Geometry 978-1465255051 Teacher eBook Fifth Edition Kendall Hunt 2015
Discovering Advanced Algebra 978-1465290434 Teacher eBook Third Edition Kendall Hunt 2017
Discovering Geometry 978−1465255020 Student eBook Fifth Edition Kendall Hunt 2015

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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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