Alignment: Overall Summary

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

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Partially Meets Expectations

Not Rated

Gateway 3:

Usability

0
21
30
36
27
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
16/18
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series 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. Overall, the instructional series attends to the full intent of the non-plus standards and the modeling process, spends a majority of time on the widely applicable prerequisites from the CCSSM, and requires students to engage at a level of sophistication appropriate to high school.

Indicator 1a

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

Indicator 1a.i

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for attending to the full intent of the mathematical content in the high school standards for all students. Overall, all of the standards are addressed during the course of this high school series.

All aspects of non-plus standards are addressed by the instructional materials and assessments. The following examples demonstrate the development of the aspects of the standards leading to the full intent:

  • N-RN.1 (concerned with rational exponents and radicals) is developed in Algebra I Concept 7.3 and Algebra II Concept 3.1, moving from guided investigation of rewriting expressions with rational exponents and performing operations with rational exponents to solving equations with radicals and using properties of exponents.
  • A-CED.2 (creating equations to solve problems) is a component of numerous lessons, including Algebra I Concepts 1.1, 1.2, 1.3 (simple expressions and equations); 2.1 (linear equations and expressions); and 11.1 (quadratics) and Algebra II Concepts 2.2 (exponential growth and decay); 6.3 (polynomials); 7.2 and 8.2 (rational equations).
  • F-IF.2 (using function notation) is directly addressed in two lessons, Algebra I Concepts 3.1 and 4.1 and then built upon throughout the series in lessons that include functions.

Indicator 1a.ii

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that they attend to the full intent of the modeling process when applied to the modeling standards. Overall, all modeling standards are addressed with the full intent of the modeling process in the series.

Modeling tasks are included regularly and frequently throughout the series. Apply tasks are included for every Concept and generally require students to engage in the full modeling process. These tasks typically involve real-world applications and require students gather, integrate, apply data in context, analyze, consider and validate results, and draw conclusions.

  • Algebra I Concept 2.1 Apply 2 asks students to use a map and a limited amount of information on the speed and time spent driving each day for two drivers, one starting on the east coast and one starting on the west coast, to find when and where they might meet (A-CED.1, A-REI.3). Students are given information needed to understand the problem context but must develop and formulate the modeling process to complete the task.
  • Geometry Concept 10.2 Apply 1 is a task about designing a parade balloon. Students conduct research to determine what information is important to find the amount of helium it would take to fill the balloon they design and the number of handlers it would require to control it. Students choose appropriate units and level of accuracy for calculations and must make sense of their calculations along the way. (G-GMD.7, G-MG.1)
  • Algebra II Concept 2.2 Apply 1 asks students to research the Yellowstone National Park Wolf Project. Students review data about the number of wolves in the park since the beginning of the program in 1995, analyze the data to find a time period that can be modeled by an exponential growth or decay function, and write a paragraph to explain their analysis and give a comparison of the populations for one year before and one year after the time period selected. (F-IF.8b, F-LE.2, F-CED.1, F-LE.1b, F-LE.5)
  • Algebra II Concept 7.2 Apply 3 requires students to use an app and workout information to explain how to change the next workout so that the average burn rate of calories increases eases by 5% over the average burn rate for the previous workout. (A-CED.1, A-CED.2, A-REI.2)

In addition, lessons consistently include application tasks that address modeling but provide students guidance in working through the modeling cycle.

  • Algebra I Concept 2.1 Investigation 5 includes a task having students use equations to find the best deal for printing posters. Students are given costs by setup fees and the charge per poster printed for two companies and then asked to write equations modeling the cost of each company. They complete a table of costs for given numbers of posters and provide justification for which deal is best. (A-REI.11)
  • Algebra I Concept 1.2 Investigation 4 asks students to make a conjecture about the relationship between the number of vertices in the polygon and the total number of diagonals. They attempt to write a mathematical model and share their ideas before being prompted to analyze data that will help them revise their original conjectures. To make sense of their models, this investigation guides them to organize their information in a table. Students share their results and discuss the validity of their expressions as well as how they might modify them. (A-SSE.1, A-SSE.1a)
  • Geometry 1.1 Apply 2 asks students to choose a photograph that includes at least seven given geometric objects. They explain why the objects in the photo are the geometric objects identified, including the use mathematical definitions (G-CO.1, G-MG.1). Students must make decisions, provide evidence, and support the conclusions.
  • Algebra II Lesson 9.3 Apply 2 asks students to research biorhythms; calculate their own physical, emotional, and intellectual biorhythm cycles; write and graph a function to represent each cycle; and interpret the points of intersection in the context. (F-TF.5)

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that students spend the majority of their time on the content from CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, post-secondary programs, and careers.

The following examples show that the standards/clusters specified in the Publisher’s Criteria as WAPs are addressed across the entire series:

  • N-RN and N-Q: Algebra I Units 7, 9, 10 and Algebra II Unit 3
  • A-SSE, A-REI, A-APR, A-CED: Algebra I Units 1, 2, 4, 5, 7-11 and Algebra II Units 2-8
  • F-IF, F-BF.1, and F-LE.1: Algebra I Units 3, 4, 7, 8, 10, and 11, Geometry Unit 7, and Algebra II Units 1-4, 6, and 9
  • G-CO.1, G-CO.9, G-CO.10, G-SRT.B, and G-SRT.C: Geometry Units 1, 3, 4, 5, 6, and 8
  • S-ID.2, S-ID.7, and S-IC.1: Algebra I Units 6, 11

The tasks aligned to WAPs from Grades 6-8 were included as a way to support student learning. For example, Algebra I Unit 5 begins with tasks that map to 8.EE.8 (solving pairs of linear equations) before moving on to the related high school content. This example is repeated across the Algebra 1 and Algebra 2 courses as students work with increasingly complex applications of systems for various parent functions.

Indicator 1b.ii

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

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that students are provided with opportunities to fully learn each non-plus standard.

Throughout the series there are tasks that provide students the opportunity to fully engage with all aspects of the standards addressed in the tasks and do not distract students with prerequisite or additional topics. Examples include:

  • F-IF.A: This series allows students to fully develop the use of function notation. Function notation is introduced in Algebra I Concept 3.1, emerging at the beginning of Investigation 4 when students examine a table of information to make sense of function notation. After making sense of the notation, the Algebra I materials continue to embed the notation in subsequent tasks and continue to use the notation in Algebra II.
  • S-ID.5: In Algebra I Chapter 6 Unit 3, students make claims and associations about frequency tables; summarize the tables in percents and raw numbers; and apply joint, marginal and conditional frequencies. In addition, students create, interpret, and recommend solutions using conditional relative frequencies.

However, there are a number of places where students have limited opportunities to make connections and fully learn all aspects of the standard.

  • N-Q.1 (using units in problems, formulas, graphs, and data displays) is related to the topics of Algebra I Unit 1, Foundations of Algebra, and Concept 2.1, Solve Equations and Inequalities. These tasks include applications for which understanding the units can help with problem solving, but using units to understand problems and guide solutions is not addressed explicitly.
  • N-Q.3: Students are not provided sufficient opportunities to choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Examples of choosing a level of accuracy appropriate to limitations on measurement are limited to linear programming (Algebra I Concept 5.2), Laws of Sines and Cosines (Geometry Concept 6.2), and linear systems (Algebra II Concept 5.1). This issue could be addressed in Apply tasks, though neither the tasks nor the accompanying Teacher Notes mention choosing levels of accuracy.
    • In Algebra I Concept 5.2, N-Q.A did not truly emerge in the investigations, practice, and applications for this task, although it is referenced in the teacher notes: “They interpret each of these solutions in terms of the real-world situation (HSA.CED.A.3, HSN.Q.A.3).”
    • In Algebra II Concept 2.2 Apply 2, students are asked to research carbon-14 dating. The video included in the task mentions the approximate nature of these results, but the answer key gives a result to the nearest year rather than something more appropriate such as the nearest thousands of years.
  • N-RN.3 (explanations about the sum and product of rational and irrational numbers) was not addressed, though the publisher indicates that it is included in Algebra I Concept 10.1, Solve Quadratics, and Concept 10.2, Analyze Quadratic Equations. These tasks include adding and multiplying rational and irrational numbers but do not ask students for explanations (e.g., why the sum of a rational and irrational number is irrational). Students are limited to identifying relationships in relation to the roots and whether they are rational or irrational in Algebra I Concept 10.1 Investigation 5.
  • G-GPE.5: In Geometry Concept 3.1, Explore Parallel and Perpendicular Lines, students are presented with many opportunities to investigate properties, discuss the definitions, and use the slope criteria of parallel and perpendicular lines. However, students are not given the opportunity to prove the slope criteria for parallel and perpendicular lines, as stated in the standard. In Session 1 of Concept 3.1, there is a possible extension in the Instructional Notes for Investigation 1, “Ask the class how they might approach a proof that lines are parallel or perpendicular", but the students are not asked to formally prove the slope criteria for parallel and perpendicular lines in the Concept.

Indicator 1c

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school.

Tasks are frequently presented in engaging contexts and vary in the types of numbers used.

  • The tasks in Algebra I Unit 3.1 (addressing F-IF.1, F-IF.2, and F-IF.9) focus on understanding and interpreting functions. In Investigation 1, students use a telescope to determine the relationship between the distance of an object and the diameter of the field of view so that they can see advantages of representing a relationship between two variables algebraically. In Investigation 3, students determine whether or not different relations are functions (e.g., a planetary orbit and the area of a circle). In Investigation 4, students work with partners to view different functions and determine whether or not they are functions they know. Through extensions and applications students research the dietary intake of astronauts to determine the effects of space travel on the human body as well as daily caloric intake to find the basal metabolic rate, the weight of a million dollars, and the basics needed to calculate wind chill.
  • In Geometry Unit 4.2, students research Da Vinci’s “Flower of Life” to find common structures and how to recreate their own versions of similar patterns. They further analyze abstract art to justify their own construction of triangles and angles with respect to midpoints and angle bisectors. As an extension, students construct a Wheel of Theodorus where they broaden their knowledge of angles and bisectors as well as the Pythagorean Theorem. Students also have three application tasks where they learn to copy an image using only a straightedge and a compass, create geometric figures in harmony, and use the geometry tool to explore “bank shots” with respect to the layout of a basketball court.
  • In Algebra II Unit 5.1, students must research gas mileage, retail prices, and gas mileage to find the better deal, thereby allowing students to work with values that are real and appropriate for high school.

In addition, topics from grades 6-8 are included in a way that supports meeting high school expectations. For example, Algebra I Unit 2.1 (equations and inequalities) includes problems aligned with 8.EE.7.b (solving linear equations with rational number coefficients) but spends the bulk of the tasks on high school standards (including A-CED.3, A-CED.1, and A-REI.11).

Indicator 1d

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for fostering coherence and making meaningful connections in a single course and throughout the series.

All Concepts include a progressions and standards section for teachers. “Reach Back Standards” describe the groundwork needed to be prepared for concepts in the Standards Covered while “Reach Ahead Standards” identify connections to future mathematics.

The materials feature coherency within a course.

  • In Geometry, there are connections among similarity, right triangle trigonometry, transformations, and circles. Students begin developing ideas of similarity in Unit 5 of the Geometry course. In Unit 6, students use similarity to develop an understanding that the ratios of sides in similar right triangles allows them to define the trigonometric ratios of angles. In Unit 7, students prove why all circles are similar using similarity transformations. The instructional materials make the connection clear to students by stating, “Recall that any two figures are similar if there is a combined transformation of a dilation and a rigid transformation that maps one to the other.” Students are prompted to use an exploration tool that allows them to determine that all circles are similar using their understanding of similarity transformations.
  • In Algebra II, connections are made between inverse functions and the relationship between exponential and logarithmic functions. The concepts of inverse functions are learned in Concept 1.2, then in Unit 2 Concept 2.3 students connect to their prior learning of inverses to develop understanding of logarithms. The connection is pointed out to the teachers through instructional notes, “Before students start the activity, have them discuss what they recall about a function and its inverse—numerically, graphically, and algebraically,” and to the students by instructing them to “Use the Hands-On Activity: Exponential to Logarithmic to explore the relationship between an exponential function and its inverse.”
  • In Algebra I Concept 3.2, linear functions and arithmetic sequences receive extensive development, including recursive and explicit aspects of sequences, along with exponential functions and geometric sequences. These concepts reappear in Algebra II when students model situations with either arithmetic or geometric sequences and extend their understanding of sequences to attend to deriving and using the formula for the sum of a finite geometric series.

In addition, the materials feature coherency throughout the series.

  • Connections are made for quadratics among the Algebra I and Algebra II courses. Students learn to solve quadratics in Algebra I, and then Algebra II Concept 3.2 connects that learning to the idea of non-real solutions and imaginary numbers. The student materials make the connection clear to students in Investigation 2, “Remember when you solved the equation x^2+25=0? You realized that there was no real number solution because the square root of –25 is not defined in the real number set. Now that you know the complex number set, try solving it again to find all the possible solutions.”
  • In Geometry, in Unit 2 students connect to their use of function notation (F-IF.1, F-IF.2) and utilize the notation to represent transformations as functions.
  • In Algebra II, in Unit 9 connections are made to students’ prior learning about units of measure, circles, similarity, and right triangle trigonometry in the Geometry Course. In Concept 9.1 Investigations 1-3, connections are made for students between the degree measure of the angle, the circumference of the circle, arc length, the radius, and radian measure. Then, in Investigation 4, Converting between Degrees and Radians, the instructional materials specifically connect the idea of converting between degrees and radians as a way of converting between units as students have done before. The investigation begins with the statement, “Think about how you convert between familiar units, such as feet to miles or days to hours. You can convert radians and degrees in a similar manner.” Connections continue to be made to students’ prior learning in Geometry as the unit progresses into further study of the unit circle and trigonometric functions. Students connect special right triangles and the Pythagorean Theorem to make sense of the structure of the unit circle, which leads to connections within the Algebra II course itself when students connect the unit circle to the graphs of the sine and cosine functions in Concept 9.

Indicator 1e

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for explicitly identifying and building on knowledge from grades 6-8 to the high school standards.

Content from grades 6-8 is clearly identified in each Concept’s instructional notes, called “Progressions and Standards,” in this series. Standards from grades 6-8 are identified for the teacher in the “Reach Back Standards” section. This section provides a detailed progression of student learning from their 6-8 experiences.

The grades 6-8 standards are consistently integrated into the tasks in a way that supports learning the high school standards.

  • In Geometry Unit 2, Geometric Transformations, the instructional materials identify how Concept 1 connects to 7.G.2 (geometric figures) and 8.G.1 (rotations, reflections, and translation), building off these concepts to address G-CO.2, G-CO.3, G-CO.4, and G-CO.5 (transformations in the Euclidean and coordinate planes).
  • Algebra I Concept 3.1, Understand and Interpret Functions, integrates a review of related grade 8 standards (8.F.1-4) about functions and then builds on that work to address high school standards F-IF.1 and 2.
  • Geometry Concept 2.2 connects earlier exploration of congruence in terms of rigid motion and use of coordinates to describe the effect of a rigid motion (8.G.2, 8.G.3) to express congruence in terms of rigid motion (G-CO.6) and use rigid motions to show triangles are congruent and establish the SSS, SAS, and ASA triangle congruence criteria (G-CO.7, G-CO.8).
  • Algebra II Unit 10 builds upon students’ previous understanding of using random samples to draw inferences about a population (7.SP.1, 2) and prior experience with determining probabilities (7.SP.5, 6, 7, 8) to develop ways to describe their sample spaces (S-CP.1) and to understand ideas of independence (including two-way frequency tables) and conditional probabilities (S-CP.2-5).

In addition, the materials frequently include brief references to previous grades 6-8 and high school work that help students connect their learning.

  • Algebra I Concept 6.1 Investigation 1 has a note reminding teachers that “students created histograms, dot plots, and box plots and used terms such as cluster, peak, gap, symmetry, and skew to describe displays” in middle school (6.SP.4) and gives a brief task to check students’ understanding of these topics.
  • Geometry Concept 4.1 includes a brief reference to earlier work about the sum of the angles in a triangle (8.G.5, though it is not explicitly identified in the materials) before leading students through a formal proof of the triangle sum theorem (G-CO.10).

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
+
-
Indicator Rating Details

The plus standards are clearly identified in the teacher resource materials. For each Concept, the teacher notes include a “Progressions and Standards” section indicating to the teacher which plus standards are included in the current Concepts and describing how they connect to the nonplus standards in that Concept. The teacher notes, however, do not indicate which standards are addressed by a particular Investigation. Instead, teachers are provided only a broader description of the standards that the entire Concept develops.

Work with plus standards is integrated into Concepts.

  • Geometry Concept 7.1, Investigate Circles and Parts of Circles, focuses on G-C.2 (inscribed angles, radii, and chords) but includes one task (Investigation 4) addressing plus standard G-C.4 (constructing tangent lines).
  • Algebra II Concept 4.1, Analyze Graphs and Equations of Circles and Ellipses, has students derive the equation of a circle (A-APR.6). Algebra II Concepts 4.2 and 4.3 have students use a similar process to derive the equations of an ellipse and hyperbola.

Of the 46 plus standards in the CCSSM, 14 are included across the traditional series, all having meaningful connections to the content of the Concept in which they are placed. The plus standards addressed in the series are listed below:

  • A-APR.5: Algebra II 6.1
  • A-APR.7: Algebra II 7.1
  • F-IF.7d: Algebra II 8.1
  • F-BF.1c: Algebra I 4.1, 11.1; Algebra II 1.1, 1.2
  • F-BF.4c: Algebra II 1.2, 1.3
  • F-BF.5: Algebra II 2.3, 2.4
  • F-TF.3: Algebra II 9.2
  • G-SRT.11: Geometry 6.2
  • G-C.4: Geometry 7.1
  • G-GPE.3: Algebra II 4.1, 4.2, 4.4
  • G-GMD.2: Geometry 10.2
  • S-CP.8: Algebra II 10.2
  • S-CP.6: Algebra II 10.2
  • S-CP.7: Algebra II 10.2

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
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, all three elements of rigor are thoroughly attended to and interwoven in a way that focuses on the needs of a specific standard as well as balancing procedural skill and fluency, application and conceptual understanding.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for supporting the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

Each Concept promotes student thinking with an introduction activity that is relevant and accessible to all students, preparing students for a more in-depth exploration of mathematical concepts in the investigations.

  • Algebra I Concept 7.2 Intro asks students to estimate the area of a square with a given side length and the side length of a square with a given area, then explore both ideas using a dynamic geometry tool.

Tasks are designed so students develop understanding of the mathematics through an investigation.

  • Algebra I Unit 3, Functions, has students engage with real-world phenomena involving dependent relationships to understand the “input/output” nature of mathematical relationships, classify data as representing functions or non-functions, and develop their own definitions of function. (F-IF.1, F-IF.2, F-IF.3, F-LE.1a, F-IF.1b)
  • Geometry Concept 2.2 Investigation 2 has students make a conjecture and use a dynamic geometry tool to explore and then follow a scaffolded process to test their conjecture, write a general rule, and summarize their results. (G-CO.6, G-CO.7, G-CO.8)
  • Algebra II Concept 5.2 Investigation 1 has students explore the possibilities for the intersection of some nonlinear equations and a line, then follows up with questions and tasks to formalize student understanding. (A-REI.7, A-REI.11)

Indicator 2b

Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for providing intentional opportunities for students to develop procedural skills and fluencies.

Each Concept includes a Practice tab with:

  • A Coach section that focuses on procedures and leads students through solving a problem. This section provides support and immediate feedback.
  • A Play section that focuses on procedures without scaffolded support.
  • A Check Your Understanding section focused primarily on procedural tasks.

The following are examples of items found in Practice:

  • In Algebra II Concept 2.4 Investigation 1, students investigate rewriting logarithmic equations as exponential equations to solve logarithms (F-LE.4, F-LE.5). After exploring the inverse property of inverse exponents and logarithms to rewrite equations, students are given the opportunity to reach procedural fluency with the “Check Your Understanding. “
  • In Geometry Concept 6.1, students work through right triangle trigonometry by solving problems around mapping out a race course and finding checkpoints along the way. The Coach section has the students practice the procedural skills of solving trigonometric ratios.

Procedural items are also embedded into Concepts and Investigations.

  • In Algebra II Concept 7.1 students write rational numbers in different forms and connect this to writing rational expressions in different forms (A-APR.6). They apply their understanding of factoring to identify and generate equivalent rational expressions (A-SSE.2).
  • Throughout the investigations in Algebra II Concept 6.1, students write polynomials in different forms, perform operations with polynomials, and interpret parts of the expressions helping them reach further procedural fluency with A-SSE.1b, A-SSE.2, and A-APR.1.

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 reviewed for the High School Discovery Traditional series meet expectations that they support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially (but not limited to) where called for in specific content standards or clusters. The curriculum is written with an investigative, context-based approach that allows multiple opportunities for students to apply what they discover in each lesson.

Every Concept includes multiple Apply tasks that provide students meaningful opportunities to apply the mathematics they have learned.

  • Algebra I Concept 6.2 Apply 1 and 2 provide opportunities for students to apply their abilities to represent and analyze data for population growth and building height. Students’ apply their knowledge of correlation and residuals to the contexts as well as model the data with a regression line and make predictions from it (S-ID.6a-c; S-ID.8). Apply 3 asks students to reason and to justify their understandings of correlation in the context of sports data. (S-ID.8)
  • Geometry Concept 10.2 Apply 2 provides students with an opportunity to use volume formulas to solve problems (G-GMD.3) and apply geometric concepts in a modeling situation (G-MG.A).
  • Algebra II Concept 11.2 Apply 3 has students determine a strategy for winning a contest involving cell phone data by making an estimate based on random sampling of the populations’ text message usage during a certain time period. (S-IC.1)

In addition, application tasks are typically included in Investigations.

  • Algebra I Concept 6.1 Investigation 4 has students compare data about cereals’ nutrition. They apply their knowledge of measures of center and spread by determining which measure, center or spread, is most appropriate to use to make comparisons of the cereals’ nutritional data. Students then write an argument to justify the most healthy cereal based on these comparisons. (S-ID.2)
  • Geometry Concept 7.2 Investigation 4 looks at circles inscribed in regular polygons, leading to informal justification of the formula for the circumference of a circle, and then has students apply what they’ve learned to a task about lights on a ferris wheel. (G-GMD.1)
  • Algebra II Unit 8 has students interpret rational functions in a variety of applications. In the Introduction, students determine the function necessary to give a child of specific ages doses of medication. The application of medicine doses continues in Investigation 3 where students look at different medications and what different parts of the function mean in relationship to the medication. (F-IF.B)

The entire series is designed with application problems embedded within the lessons, as well as an Apply section at the conclusion of the lesson.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately and that the three aspects of rigor are balanced with respect to the standards being addressed.

Each Concept includes Discover, Practice, and Apply sections:

  • Discover includes Intro, Investigation, Summary, and Extension sections that give students the opportunity to build conceptual understanding of the mathematics and practice procedural skills, typically in the context of a real-world example;
  • Practice focuses on procedural skills with a Coach section that provides student support to develop fluency- for example, leading students through solving an algorithmic problem and giving immediate feedback- as well as a Play section where students demonstrate procedural fluency without support; and
  • Apply includes extended tasks based on real-world applications.

In the Model Lesson section of the teacher materials, Progressions and Standards includes a diagram that identifies for teachers the balance of conceptual understandings, procedural fluencies, and applications that should emerge from each Concept in a Unit.

The following are examples of balancing the three aspects of rigor in the instructional materials:

  • Algebra I Concept 8.2 asks student to examine data in a table to see what type of function it matches, to analyze the data in the table to identify key features, to write an equation to model the data, and to evaluate the equation for a given value. (A-SSE.3c, F-IF.7e, F-IF.8b, F-LE.1c, F-LE.2)
  • Geometry Concept 6.1 gives students an opportunity to explore right triangle trigonometry first by developing the concepts within the context of racers finding distances on a map to determine shortest distances, as well as finding how to get back on course. Students then practice skills they have learned in the Coach and Play sections within the Practice tab. Finally, students apply what they have learned by designing a wheelchair ramp and hiking trails in the Apply tab. (G-SRT.7, G-SRT.8)
  • Algebra II Concept 6.1 has students explore polynomials in different forms and develop an understanding of the meaning for writing the different forms of polynomials. Throughout the investigations, they use contextual situations, connections to prior knowledge about the different forms of quadratics, and peer interactions to conceptually develop their ability to write equivalent forms of polynomials, perform operations with them, identify zeros, and interpret different parts. Students practice these skills in the Coach and Play sections within the Practice tab. In the Apply tab, there are two application problems available for students to apply what they have learned using polynomial models that represent a lizard population and the design of a roller coaster. (A-SSE.1b, A-SSE.2, A-APR.1, A-APR.2,3 A-APR.4)

Criterion 2e - 2h

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that materials support the intentional development of all eight MPs, in connection to the high school content standards. Overall, many of the lessons in the series deliberately incorporate the MPs as an integral part of the learning. The teacher's notes list the specific MPs that are a focus for each Concept, and the MPs are embedded in notes to teachers for individual Investigations. The instructional materials reviewed meet the expectations for making sense of problems and persevering in solving them as well as attending to precision; reasoning and explaining; modeling and using tools; and seeing structure and generalizing.

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for supporting the intentional development of making sense of problems and persevering in solving them as well as attending to precision (MP1 and MP6).

The course lists the Standards of Mathematical Practice in each section of the model lesson for the teacher. The teacher can see which Mathematical Practices are being addressed and in what way. Examples of the use of MP 1 and 6 to enrich the mathematical content include:

  • Algebra I Concept 10.1 asks students to use precise language and clear definitions when discussing quadratic functions and their related equations; explain the correspondence among equations, graphs, and verbal descriptions to make sense of the given problems; use repeated reasoning as they persevere in creating the necessary adjustments to the model with algebra tiles representing values that will complete the square; and estimate solutions from graphs when calculating the exact roots of quadratic equations.
  • Geometry Concept 1.2 Session 1 directs students to analyze given information and constraints while using a grid system to identify possible strategies for locating a statue.
  • Algebra II Concept 9.2 Investigation 6 has students determine which trigonometric sine function gives the best prediction of temperature, which includes analyzing the preciseness of each model to find the most accurate model for predicting temperature.

In addition, each Concept includes multi-part, extended Apply tasks where students develop perseverance and precision in their work. For example, Geometry Concept 5.1 Apply 1 asks students to set up a projector to provide the best image; to do so, they must meet given constraints, experiment with the projector, and give a mathematical justification for their choice.

The materials clearly identify these mathematical practices, both in unit-level teacher notes and embedded in individual Investigations. For example, Algebra II Concept 3.2 Investigation 1 includes a teacher note to guide application of MP 1 and 6. Teachers are advised to have students discuss moving to the use of imaginary numbers. Key terminology, common mistakes and misconceptions are given as well.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for supporting the intentional development of reasoning and explaining (MP2 and MP3). MP2 and MP3 are used to enrich the mathematical content and are not treated separately from the mathematical content.

Examples of the use of MP 2 and 3 to enrich the mathematical content include:

  • Algebra I Concept 2.1 Investigation 5 has students decontextualize a given real-world situation by representing it symbolically with equations and inequalities and then re-contextualize the algebraic solution sets of the inequalities in terms of the original real-world situation.
  • Geometry Unit 1 Concept 1.2 Investigation 2 asks students to reason abstractly and quantitatively to derive an expression for the midpoint of a segment and to develop a formula for partitioning a segment in the coordinate plane in a given ratio.
  • Algebra II Concept 9.2 Investigation 6 has students work to determine which trigonometric function gives the best prediction of temperature, justifying the reasonableness of their algebraic results to their original conjectures.
  • Geometry Concept 5.1 Investigation 2 has students reason abstractly and quantitatively (MP 2) as they describe dilations as functions. In Investigations 1 and 3, MP3 is embedded as students make conjectures about dilations and then explore and justify their conclusions. They culminate their explorations in Investigation 3 by constructing arguments for the properties of similarity transformations.
  • The Algebra II course demonstrates MP2 in Concept 5.1 Investigation 2 where students analyze how inequalities and graphs can be used to solve a real-world problem. MP3 is evident in Concept 11.2 Investigation 2 when students evaluate their model to determine whether it creates a realistic representation of the game and justify their reasoning to others.

The materials clearly identify these mathematical practices, both in unit-level teacher notes and embedded in notes to teachers for individual Investigations. For example, Algebra I Concept 4.1 Investigation 1 includes a teacher note to guide application of MP 2 and 3. The Investigation gives students tables of data about the density of two candies and asks them to graph, analyze, and discuss the condition under which each floats. The teacher note describes key points to address in the discussion with students to identify key features of the graphs.

Indicator 2g

The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for supporting the intentional development of modeling and using tools (MP4 and MP5). MP4 and MP5 are used to enrich the mathematical content and are not treated separately from the mathematical content.

Examples of the use of MP 4 and 5 to enrich the mathematical content include:

  • In Algebra I Concept 4.1 Investigation 4 students are asked to use a graphing tool to draw parallel and perpendicular lines by changing slope and y-intercept in the context of locating fences and then analyze how changes in equations’ features affect their graphs using a graphing calculator tool.
  • In Geometry Concept 4.2 Investigation 1 students examine art designs and try to construct their own version. Students choose and use geometric tools in order to recreate the design and write detailed descriptions of how to do it.
  • In Algebra II Concept 4.1 students explore and make sense of the equations for circles and ellipses. Interactive tools such as Conic Section Interactive, Circle Interactive, Ellipse Interactive, Dynamic Geometry Tool, and Graphing Calculator Tool are embedded in the investigations and available for student use. In addition, students build a model of conic sections through these investigations and apply the graphing form of an ellipse to the orbital path of Pluto.

The materials clearly identify these mathematical practices, both in unit-level teacher notes and at the beginning of individual Investigations. For example, Geometry Concept 8.1 Intro includes a teacher note to guide application of MP 4 and 5 by reminding teachers of the possible tools students could use to explore locations within a triangle and different geometric models that could be used to represent a real-world problem. These teacher notes at the Concept level provide general guidance for teachers to emphasize MP 4 and 5, but there is limited support at the Investigation level for these math practices.

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 reviewed for the High School Discovery Traditional series meet the expectation for supporting the intentional development of seeing structure and generalizing (MP7 and MP8). MP7 and MP8 are used to enrich the mathematical content and are not treated separately from the mathematical content.

Examples of the use of MP 7 and 8 to enrich the mathematical content include:

  • Algebra I Concept 10.2 Investigation 1 asks student to use completing the square to develop the quadratic formula and look at how values in the quadratic formula provide information about the roots of the equation.
  • In Geometry Concept 6.2 Investigation 3 students use geometric software to explore the relationship between the Pythagorean Theorem and the law of cosines. They analyze the structure of the triangle and understand the role of an auxiliary line in the development of the formula, determine which calculations are repeated, and look for other methods.
  • In Algebra II Concept 1.1 students explore recursive functions. In Investigation 3, students use a hands-on paper tearing activity to record the outcomes of tearing their paper in half repeatedly. They observe the structure and pattern of the results (a geometric sequence) and use their observations to generalize their results into both recursive and explicit formulas. Repeated reasoning appears throughout other Investigations in Concept 1.1 as students use similar processes to develop understanding of geometric sequences, as they did to develop arithmetic sequences. In addition, students use the regularity in the reasoning associated with the arithmetic and geometric patterns to generalize to formulas, including Sierpinski’s Triangle.

The materials clearly identify these mathematical practices, both in unit-level teacher notes and embedded in individual Investigations. For example, Algebra II Concept 9.1 Investigation 5 (Angle Measure) includes a reminder that MP 8 (generalizing) is met when students see a proportional relationship among arc lengths with the same central angle and gives a recommendation for discussing this relationship and relating it to radians.

Gateway Three

Usability

Partially Meets Expectations

Criterion 3a - 3e

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for having a use and design to facilitate student learning. Overall, the materials are designed well and take into account effective lesson structure and pacing. The design and layout of the materials are easy to use and not distracting and support students in engaging thoughtfully with the content.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the underlying design of the materials distinguishes between lesson problems and student exercises for each lesson. It is clear when the students are solving problems to learn and when they are applying their skills to build mastery.

  • Throughout the Investigations of each Concept, students explore and solve problems to learn new mathematics. The design of the instructional materials allow multiple opportunities for students to build mastery.
  • Each Investigation has a Check Your Understanding for student and teachers to assess what students understood from the investigation. Each Concept has a Practice tab with a Coach and Play section. These sections include a variety of exercises that allow students to develop procedural skills.
  • Each Concept also has an Apply tab which contains real-world problems with various contexts, embedding aspects of the modeling standards, for students to apply their understanding of the mathematical concepts and demonstrate their mastery of mathematical concepts.

Indicator 3b

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the materials in this series are designed and presented in intentional sequences. The series uses a consistent lesson structure throughout the courses. Each Concept is built around this lesson structure that engages students in multiple lesson sections where they Discover, Practice, and Apply what they are learning. The consistent lesson structure demonstrates an intentional sequence within a Concept, across a course, and throughout the series.

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that students are asked to produce a variety of products during each Concept in a unit to demonstrate their learning.

The series consistently asks students to share their understanding of mathematics in a variety of ways. Students produce models, make conjectures, create arguments, justify their reasoning, and make real-world connections throughout the materials. Opportunities are provided throughout the investigations for students to present their work using digital tools. The Model Lesson notes for teachers describe instructional strategies that ensure students produce this variety of work to demonstrate their learning.

Indicator 3d

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives.

Virtual manipulatives and tools are embedded throughout the series. Some are available on every page of the Techbook and include calculators,a dynamic geometry tool, construction tool, unit convertor tool, data analysis tool, whiteboard tool, and a matrix solver tool. In some Investigations, the manipulatives embedded are specific to the lesson. Examples of this include but are not limited to:

  • In Investigation 1 of Algebra I Concept 2.1 virtual algebra tiles are embedded to help students build understanding of the properties of equality.
  • In Investigation 1 of Geometry Concept 7.1 the Dynamic Geometry Tool is embedded with two circles that students can manipulate to explore the possible number of intersections.
  • In the Introduction to Concept 4.1 in Algebra II a technology enhanced item, Conic Section Explorer, is embedded in the lesson to allow students to determine how the cut of the plane through the cone affects the related graph of the curve to determine the relationship that results in a point, line, circle, or ellipse.

In addition to these virtual manipulatives, students use a wide collection of manipulatives when completing the hands-on activities throughout the series. These include, but are not limited to, modeling clay, straws, coffee stirrers, paper towel tubes, tools for measurement, scissors, tape, cardboard, string, a variety of sports balls, and various circular objects. Each of the manipulatives provides a representation that allows students to explore the related mathematics and connects them to procedures and written methods.

Indicator 3e

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

The instructional materials reviewed for the High School Discovery Traditional series have a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the content. The digital Techbook materials have a consistent layout of Units, Concepts, and Investigations. Pictures, videos, technology enhanced items, and models used throughout the series support student learning as they are connected directly to the mathematics in an Investigation and are not distracting from the mathematical content.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for teacher planning and learning for success with the CCSS. Overall, the materials support teacher learning and understanding of the Standards. The materials provide the teacher necessary supports through quality questions to help guide students' mathematical development, annotations and suggestions on how to present the content, and strategies for informing students, parents, or caregivers about the mathematics program.

Indicator 3f

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that teachers are provided quality questions to guide students' mathematical development.

The materials include a Model Lesson section and Teacher View that can be enabled as teachers navigate through the Investigation pages. Tabs, labeled as Sessions, include instructional notes for each Investigation. For example, in Algebra I Concept 7.2 Session 2 the teaching notes include questions that prompt discussion: “Why is the square root of a negative number not a real number, but the cube root is? What are some examples you can use to justify your reasoning?”

In addition, with the teacher view enabled, as teachers progress through the Investigations, blue boxes with quality questions and their connections to the mathematical practice they will enrich are included. The instructional reminders in this view are provided in a timely, and helpful way, just before the part of the Investigation to which it applies. This design supports teachers in both planning and implementing an effective lesson.

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the teacher edition contains ample and useful annotations.

The Model Lesson section of the digital curriculum includes in-depth instructional notes and suggestions for both presenting and discussing the mathematical content of each Investigation, as well as use of the technology enhanced items and manipulatives embedded in the materials. For example, in the Introduction of Concept 4.1 in Algebra II a technology enhanced item, titled Conic Section Explorer, is included. In the Model Lesson Session 1 tab, teachers are provided detailed instructional notes on how to launch this technology tool, facilitate and implement it with students in a way that guides the learning, and bring closure to the exploration associated with this tool.

With the teacher view enabled, teachers have access to timely instructional notes that include useful suggestions to make sure the essential understandings are captured and the mathematical practices of focus are used to enrich the mathematics content on the Investigation pages.

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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that the teacher edition contains adult-level discussion of the mathematics.

Instructional notes in the Model Lesson section of the Techbook provide teachers with in-depth guidance on how to present the information in the Investigations to assist in full understanding of the standards developed in the students’ Investigations. The notes include detailed explanations of the essential and enduring understandings from the standards and any student misconceptions that may emerge.

Explanations of the responses to questions and tasks in the student Investigations are provided when the teacher view is enabled. At the end of the Concept, there is a summary tab. This tab includes a summary of the essential understandings and a link to additional assistance. The additional assistance provides video explanations and tutorials of the related mathematics. The Summary and Additional Assistance are available to both teachers and students. All explanations, however, focus on the mathematics of the Investigations without specific connections to mathematics outside of the instructional materials.

Indicator 3i

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that the materials explain the role of the specific mathematics standards in the context of the overall series.

The Model Lesson section of each Concept contains a tab titled Progressions and Standards. This tab provides an overview that explains the progression of the standards including identification and detailed descriptions of Reach Back Standards (content from previous courses), standards covered in the Concept of the current course, and the Reach Ahead standards (links to future lessons and courses). Occasionally the information will include a reference to courses in higher mathematics beyond the scope of the series. For example, in Concept 1.1 of Algebra II, it is noted that, “Students will further apply their knowledge of sequences and series in calculus, analyzing both ordinary differential equations and partial differential equations, as well as integral calculus, when analyzing area under a curve (F-LE.2, F-BF.1a, F-BF.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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series 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.

The Table of Contents page and the Course Overview PDF both provide a list of the Units for each course in the series. The Units are divided into lessons, which the publisher identifies as Concepts, and these are also listed on both of these resources. Each Concept is then broken into Investigations. These are not provided as a list. In order to identify the different Investigations, the user must navigate to the specific Concept page and view the Investigations individually.

Standard alignment is available for the Unit in the Unit Overview and in a variety of places for the Concepts. The standards aligned to each Concept can be found in the Progression and Standards Tab of the Model Lesson section, the Course Overview PDF, a drop down menu for each Concept on the Table of Contents page, and the Standards section on the homepage of each course. Alignment is not provided at the Investigation level. Therefore, it cannot be determined which standard, specified for the Concept, students are developing in each Investigation without reading or working the Investigation.

The instructional materials reviewed did not include a pacing document. The publisher provides suggested pacing for each investigation in the Model Lesson section of the techbook. To determine how many instructional days should be planned to complete a Concept, teachers must find the timing for each Investigation and determine how these times would align to their instructional time. For example, Algebra I Concept 1.2 contains four Investigations. To determine the pacing for this Concept, a teacher would take note of the times suggested by clicking five different session tabs. The following times are suggested per the session tabs: Session 1 (Introduction) 20 min, Session 2 (Investigation 1) 40 min, Session 3 (Investigation 2) 40 min, Session 4 (Investigation 3) 75 min, and Session 5 (Investigation 4) 50 min. A teacher must access the five different tabs to collect this information and then determine how to pace this for their instructional time.

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 Rating Details

The instructional materials reviewed for the High School Discovery Traditional series contain strategies for informing students and parents or caregivers about the mathematics program. Each unit has a parent letter, available in both English and Spanish. These letters have three sections that 1) identify the learning goals for the unit, 2) explain how the teaching may differ from how the parents learned the concepts, and 3) provide specific suggestions for supporting students in the unit. Specific examples of suggested support include discussing the interactive glossary terms together, having students share how they used a specified interactive in the Investigations to discover the mathematics, and having students explain their understanding or connections they have made from specific examples from the Investigations.

Indicator 3l

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

The Discovery Education Teacher portal includes professional development academies, white papers, case studies, and virtual tours to build understanding of the instructional approaches and provide a research-based framework for the design of the program.

The teacher edition provides a white paper entitled Meeting the Mathematics Needs of 21st-Century Students with Math Techbook which “relates the guiding principles of Discovery Education philosophy about learning in math, explains each principle using supporting research and reports on accepted best practices, and demonstrates how Math Techbook is specifically designed to help students meet the expectations of the CCSS and its vision for increased mathematics proficiency.”

Teachers can also select the picture of the home next to “My DE Services,” and on the left side of the page is a “Try a Strategy” tab which states “Discovery Education’s Spotlight on Strategies are creative, research-based instructional strategies, presented by teachers for teachers. These simple instructional strategies incorporate digital media in meaningful, effective, and practical ways.”

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation for assessment and offering teachers resources and tools to collect ongoing data about student progress on the standards. The materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills, but the materials partially meet the expectations for the rest of the indicators in assessment. The materials do offer students opportunities to monitor their own progress.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that they provide materials for gathering information about student’s prior knowledge within and across grade levels/courses.

In Progressions and Standards for each Concept, the materials provide teachers with Reach Back Standards from prior grade levels/courses to which the standards of the current Concept connect. The activities found within the Intro at the beginning of each Concept are designed to activate prior knowledge that students would have of the Reach Back Standards. Although the identification of the Reach Back Standards and their inclusion in the Intro activities could provide teachers a way to indirectly assess students’ prior knowledge, the materials do not supply specific or direct strategies for assessing students’ prior knowledge.

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation of providing support for teachers to identify student errors. The instructional materials provide a suggested list of common student misconceptions in the teacher preparation section of each Concept within the Unit. There is no specific support available to assist teachers in addressing those specific misconceptions.

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials include a Coach and Play section in each Concept that provide opportunities for review and practice of both concepts and skills. In the Coach section, the materials offer feedback when an answer is incorrect and allow the student to try again. After a third incorrect answer, the Coach section shows the student how to answer the problem correctly. The Play section allows the student to earn badges for correct answers when completed online. The Play section can also be completed offline, and if the offline version is completed, an answer key is provided. At the end of each Investigation, there is a Check for Understanding. The Check for Understanding contains problems that could be in the format of short answer, short answer with explanations, or multiple-choice questions. The materials offer feedback on review and practice in the form of instant, digital feedback or teacher-provided feedback throughout each Concept.

The teacher also has opportunities to provide the students feedback within the Dashboard, and a teacher can create an assignment in the Assignment Builder feature.

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation of clearly denoting standards on the assessments. The instructional materials include a pre-made unit assessment. The standards are identified for the unit; therefore, it is clear, as a whole, which standards are being emphasized on the unit assessment. However, there is not a standards alignment for these pre-made tests item by item, so it could be challenging to determine which standards are assessed by each question. Check for Understandings and Apply problems also do not denote which standards are being emphasized. There is a Math Assessment Builder tool for teachers that will allow teachers to create their own standards-based assessment.

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that sufficient guidance is given to teachers for interpreting student performance and suggestions for follow-up.

The Unit Assessments include very specific and clear Evaluation Criteria for each constructed response question, and the criteria are based on a 0, 1, or 2 point scale that shows the specific criteria needed to receive each score. Also, each Apply question includes a rubric with scores ranging from 0 to 4, and there are clear descriptions of what a student must do in order to earn each score. However, there are no suggestions for follow-up based on the students’ scores provided to the teachers.

There is also a dashboard that allows teachers to monitor the progress students are making as they navigate through the Discover, Practice, and Apply cycle. The dashboard indicates to a teacher where the student is performing based on a color indication as well as with points. The teacher can track scores and visually determine if a student is being successful, but there is no clear guidance given for interpreting student performance. The Teacher Notes, which are included in the Investigations before the Check for Understanding, provide some suggestions for follow-up, but these suggestions are not consistently placed throughout the materials.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series offer opportunities for students to monitor their own progress.

Each Concept has a Summary section that includes examples of mathematical concepts that were examined during the Investigations. Directly connected to the Summary is an Additional Assistance section that includes videos and math explanations related to the current learning which students are able to review on their own as needed. The Coach section allows students to monitor their own progress by giving direct feedback after a question which a student can use to gather further understanding on a skill they have not yet mastered. Scoring rubrics provided for Apply and constructed response questions can also be given to students to reference as they complete those tasks.

The students also have a dashboard on their Math Techbook home screen that gives them the opportunity to keep track of their answers to questions and points given to responses throughout the Discover, Practice, and Apply cycle. Students get immediate feedback during the Coaching cycle that allows them to determine their progress as they navigate through the Concept.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
6/10
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation for differentiated instruction for diverse learners within and across grades. The materials do embed tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations, and they provide strategies to help teachers sequence or scaffold lessons. The materials do not always provide teachers with strategies for meeting the needs of a range of learners or provide opportunities for advanced students to investigate mathematics content at greater depth.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Each Concept’s Discovery, Practice, and Apply sections are broken up into Sessions in which activities are sequenced for the teacher. Included in all Sessions are Instructional Notes that provide teachers with key math concepts to develop, sample questions to ask, ways to share student answers, and other similar instructional supports. Also, each Investigation includes Teacher Notes that assist a teacher in making the content accessible to all learners with supports similar to those found in the Instructional Notes for the Sessions.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
+
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that the materials provide teachers with strategies for meeting the needs of a range of learners.

Different strategies are recommended throughout the instructional materials, but the strategies are typically intended to be used with all students and not necessarily geared toward a range of learners. For students excelling, the materials provide extension problems. For struggling learners, in the Summary section students are provided with online tutorial websites for instructional assistance when needed. This section provides step-by-step instruction on material taught throughout the Investigations.

Indicator 3t

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

The instructional materials reviewed for the High School Discovery Traditional series meet the expectation that materials embed tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations. Application tasks—particularly Apply tasks— allow for multiple solution strategies or representations, and applications are available to assign in each Concept. For example, Algebra I Concept 1.2 Apply 2 asks students to create a card trick and model the trick algebraically, following an example from an earlier task.

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 Rating Details

The instructional materials reviewed for the High School Discovery Traditional series do not meet the expectation that the materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. Neither the teacher notes nor the tasks directly address support for students with a disability, students from different cultural backgrounds, or English Language Learners. A text-to-speech tool, however, is available and could be used for ELL students, and parent letters included with each unit are available in Spanish.

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. Neither the Teacher Notes nor the tasks directly address support for advanced students. Each Concept includes an Extension task that could be used for advanced students, though the materials do not indicate that they are designed for a particular audience.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series provide a balanced portrayal of various demographic and personal characteristics. The names, situations, videos, and pictures demonstrate diversity.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series provide opportunities and directions for teachers to use a variety of grouping strategies. Group work is frequently embedded in tasks, and teacher notes provide guidance on how to structure and use groups. For example, Algebra II Concept 1.2 Investigation 4 suggests that teachers use think-pair-share to have students consider features of a function’s inverse.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series do not consistently encourage teachers to draw upon home language and culture to facilitate learning. Parent letters are evidence of the materials drawing upon home language and culture to facilitate learning. Parent letters are provided as Word documents, so they can edited to meet a teacher’s needs. Letters are provided in English and Spanish. The letter informs parents of the content their students will be learning and ways in which they may help their students.

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.
0/0
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Traditional series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials integrate technology in ways that engage students in the MPs, include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology, and incorporate technology that provides opportunities for teachers and/or students to collaborate.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the MPs. The math tools and virtual manipulatives/objects are available to students within the Investigations, when appropriate, as well as in the home screen under math tools. In addition to the online and interactive format of the Techbook, Graphing Calculator and Dynamic Geometry Tool are incorporated directly into Investigations in order to engage students in the MPs.

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 Rating Details

Discovery Education works on multiple devices including tablets and mobile devices with ChromeOS, Android, or iOS operating systems and with a wide range of browsers. While platform neutral, it is recommended you use the following browsers to ensure the best experience.

  • Google Chrome
  • Mozilla Firefox 44 and above
  • Safari 9.0 and above
  • Internet Explorer 11 and above
  • Microsoft Edge 24 and above

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Traditional series include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. All assessments and practice questions within the Coach and Play tabs are done via the online platform. The Check Your Understanding tasks that are found within the Unit Concepts are to be printed. The Coach section assesses students and provides feedback to the student instantly as they navigate through the problems. The assessments included for each Unit are designed to be taken online, but there is an option for an offline version that can be printed and scored.

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 Rating Details

The instructional materials reviewed for the High School Discovery Traditional series include opportunities for teachers to personalize learning for all students. The online platform allows for teachers to create additional assignments and assessments for students under the tab labeled Builder Tools at the top of the Techbook home screen. The Assignment Builder gives teachers the opportunity to upload materials and add media from Discovery Education and then assign the new item to the entire class. The Assessment Builder lets the teacher create additional assessments by standard. These assessments can be assigned to individual students. The assessments are not adaptive but are taken online.

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 Rating Details

The instructional materials reviewed for the High School Discovery Traditional series are not customizable for local use. The digital materials include Builder Tools that provide for some customization. However, the structure of the materials within Concepts- Discover, Practice, and Apply- does not provide teachers the opportunity to teach Concepts and/or Investigations out of order without missing important information.

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 Rating Details

The instructional materials reviewed for the High School Discovery Traditional series incorporate technology that provides opportunities for teachers and/or students to collaborate. The teachers are given an opportunity to share files under the My Content tab on the Math Techbook homepage. There are spaces for teachers to share files within their school site or within the district. Students can collaborate in the Bulletin Board. They can post small notes after the teacher creates a Bulletin in the Bulletin Builder under Builder Tools.

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Additional Publication Details

Report Published Date: 05/04/2017

Report Edition: 2017

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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