## Alignment: Overall Summary

The instructional materials reviewed for the Discovery Integrated series meet expectations for alignment to the CCSSM for high school. The materials meet the expectations for focus and coherence and attend to the full intent of the mathematical content standards. The materials also attend fully to the modeling process when applied to the modeling standards. The materials 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.

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## Gateway 1:

### Focus & Coherence

0
9
14
18
15
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

|

## Gateway 3:

### Usability

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

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

### 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).
15/18
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Integrated series meet the expectation for focusing on the non-plus standards of the CCSSM. The Concepts and Units across the series are structured in a consistent logical structure of mathematics. However, Geometry standards are taught in isolation and do not always make meaningful connections to previous or future content. Overall, the instructional series does not attend to the full intent of the non-plus standards. The series does attend to the full intent of 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 Education Integrated series meet the expectation that materials attend to the full intent of the mathematical content contained in the high school standards for all students. Overall, the majority of non-plus standards are addressed throughout the series, though some aspects of the non-plus standards were not completely addressed or were omitted from the instructional materials of the series.

The following are some examples of standards that were fully addressed in the materials:

• F-IF.4: Students are presented with various functions throughout the instructional materials and provided the opportunity to “interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.”
• In Math I Concept 9.1 Practice students analyze a function and determine what price of a sweatshirt would produce the greatest income.
• Math II Concept 5.1 Investigation 2 provides students the opportunity to explore how key features of equations help when graphing functions.
• Math III Concept 6.2 Investigation 2 requires students to identify key features of tables and graphs in context with temperatures.
• G-CO.10: Throughout the Math II materials, students are developing proofs of triangle theorems.
• In Math II Concept 4 Investigation 1 students develop the Triangle Sum Theorem and Exterior Angle Theorem proofs. In Investigation 3 students prove base angles of isosceles triangles are congruent and equilateral triangle angles are congruent.

The following standards were partially addressed in the materials:

• G-CO.2: Math I Concept 3.1 provides students opportunities to “represent transformations in the plane” using software and to “describe transformations as functions that take points in the plane as inputs and give other points as outputs.” No evidence was found where students were expected to “compare transformations that preserve distance and angle to those that do not.”
• A-SSE.3b: While students solve equations by completing the square in Math II Concept 4.1 Investigation 4, no instruction was found wherein students complete the square for the purposes of revealing the maximum or minimum value of the function it defines.

### 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 Education Integrated series meet the expectation that the materials attend to the full intent of the modeling process when applied to the modeling standards. Opportunities to implement the modeling process are integrated throughout all the instructional materials. The materials provide students with intentional development of the modeling process throughout the courses in the series. Overall the modeling process is used to reach the full depth of the modeling standards.

In the beginning of the series, the materials are presented in a way that intentionally develops the modeling process. A few examples include:

• Math I Concept 1.1 Apply 3, Which Cell Phone Plan Should You Choose?, addresses standards N-Q.1 and 2 as well as A-SSE.1a and provides students exposure to the beginning stages of the modeling process, scaffolding by providing initial variables while allowing students to compute and validate their results.
• Math I Concept 1.2 Apply 1, How Long Will The Kayak Trip Take?, addresses standards A-SSE.1a and contains more aspects of the modeling process. In the Teacher’s Notes, students are encouraged to discuss why it is important that the kayakers’ speed in still water be greater than the speed of the current. Teachers are also encouraged to ask students how they might validate whether their answer for the time needed to complete the trip is reasonable.

Students have opportunities to experience the entire modeling process with increasing complexity. Here are some examples:

• Math I Concept 6.2 Apply 3, How Much Solar Power Should Your Community Purchase?, incorporates the modeling process in its entirety. Students define variables, formulate a system of inequalities to model all constraints, write and compute a function to model greenhouse gas emissions, determine how many megawatts of power to purchase, justify decisions, and report their rationale.
• In Math I Concept 4.3 Apply 2, How Can You Make The Most of $1,500?, students research and compare different financial institutions and their various types of accounts for investing. Students are expected to compare their investment options, validate accuracy using technology, interpret their analysis to make an informed decision and then report out by presenting their findings to the class. • In Math II Concept 7.1 Apply 2, How Can You Design A Trail That Challenges Hikers With Different Skill Levels?, students research the type of information needed to build a hiking trail and design one with minimal prescribed constraints, computing at least two angles of elevation and two angles of depression. Students interpret those angles in terms of the context. • In Math III Concept 8.2 Apply 1, Is it Normal?, students “(c)reate an event that is binomial, such as the coin flipping example or rolling a pair of number cubes and getting a 3 or not.” After students choose their event, they define and execute their experiment, including measures of central tendency. Results of the experiment are validated by comparing the actual results with the predicted result. Students interpret whether their data is normal and then report their findings by explaining their experiment and stating their conclusions. ### 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 Education Integrated series meet the expectation that the materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs, and careers. The majority of concepts throughout each course focus on the WAPs. Examples of students engaging with the WAPs include: • The majority of the concepts in Math I focus on the WAPs. • Standards within Quantities are addressed throughout Unit 1, and Concepts 2.2 and 6.2. • Standards within Algebra are addressed throughout Units 1 and 6, and Concepts 2.1, 2.2, 5.1, and 8.2. • Standards within Functions are addressed throughout Units 4, 5, 8, and 9. • G-CO.1 is addressed in Concept 2.3, and G-CO.9 is addressed is in Concept 3.3. • S.ID.2 is addressed in Concept 7.1 and S.ID.7 is addressed in Concept 7.2. • The majority of the concepts in Math II focus on the WAPs. • Standards within The Real Number System are addressed throughout Concepts 3.1, 3.2, and Unit 4. • Standards within Algebra are addressed throughout Units 3, 4, and 11, and Concept 5.1. • Standards within Functions are addressed throughout Units 4, 6, and 11, and Concepts 5.1, and 7.3. • G-CO.1 is addressed in Concepts 1.1 and 1.2. G-CO.9 is addressed in Concepts 1.1 and 1.3. G-CO.10 is addressed in Concepts 2.2 and 9.1. • G-SRT.B standards are addressed in Concepts 1.4 and 2.3, and G-SRT.C standards are addressed in Concepts 7.1 and 7.2. • The majority of the concepts in Math III focus on the WAPs. • Standards within The Real Number System are addressed throughout Concept 2.2. • Standards within Quantities are addressed throughout Concept 7.2. • Standards within Algebra are addressed throughout Units 1, 3, 5, 9, 10, and 11, and Concept 2.2. • Standards within Functions are addressed throughout Units 2, 3, 4, 6, and 11, and Concepts 7.1, 9.3, and 12.4. • S-IC.1 is addressed in Concept 8.2. While there are additional and prerequisite topics found throughout the series, they do not distract from the work of the WAPs and other standards. • In Math II Concept 3.1 problem 4 within Coach goes beyond the intent of the standard (N-RN.1) with fractions that have terms with rational exponents in the numerator and in the denominator with nested exponents and the expectation that students will “rationalize” the denominator. The unit test requires students to “order the steps” to rationalize a denominator. • In Math II Concept 9.1 Investigations 1-4 coherently connect the structure and key features of polynomials with quadratics including factoring powers of four and cases where higher powers factor out as monomials. Investigation 4 then leads students through a visualization for the formulas of differences and sums of cubes which is beyond the stated intent of the standard (A-SSE.2). Investigation 5 contains explorations of Pascal’s triangle and binomial expansion. ### Indicator 1b.ii The materials, when used as designed, allow students to fully learn each standard. 2/4 + - Indicator Rating Details The materials, when used as designed, partially meet the expectation that students are provided with opportunities to fully learn each non-plus standard. Overall, the Concepts and Units throughout the series are structured in a way that allows students to fully engage with the majority of the non-plus standards without distracting students with prerequisite or additional topics. 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. • A-SSE.1,2: Students are provided multiple opportunities across the series to develop these standards. Students begin in Math I Concepts 1.1 and 1.2 analyzing and reasoning with basic expressions within context. In Math I Concept 8.2 students begin looking at structure of expression in situations of growth and decay. In Math II Concept 3.2 students extend their thinking when introduced to polynomial relationships and explore factoring polynomials and polynomial operations. In Math 3 Concept 9.1 again revisits polynomial operations, and in Concept 10.1 students move their thinking to develop rational expressions. • F-IF.4: The materials provide students multiple opportunities across the series to explore the function relationships and interpret key features of graphs and tables. Beginning in Math I Unit 5 students analyze and compare graphs of linear and exponential functions. In Concept 8.1 “Students expand their understanding of exponential functions to model real‐world scenarios.” Students extend their thinking further when presented with a new function family, quadratics, in Concept 9.1. In Math II students are expected to analyze and compare key features of additional function relationships. Concept 5.1 revisits quadratic functions, Concept 6.1 addresses power and inverse functions, and Concept 7.3 provides students the opportunity to investigate and interpret circle equations. In Math III Concept 2.1 the Course Overview states “Students extend their knowledge of rational and irrational numbers to square and cube root functions.” In Concept 6.2 students explore and represent trigonometric functions. Lastly, Concept 9.3 requires students to analyze polynomial functions. However, there are a number of places where students have limited opportunities to fully learn all aspects of the standard. • A-APR.4: Polynomial identities are provided in the teacher materials in Math III Concept 9.1; however, no evidence was found of students being provided the opportunity to “prove polynomial identities” or to “use them to describe numerical relationships.” • A-APR.2: The standard requires students to know and apply the Remainder Theorem. The Remainder Theorem is incorporated into two problems throughout the series. Within Math III Concept 9.2 the Remainder Theorem is applied in problem 4 of the fifteen Play problems as well as the Extension activity. • A-REI.5: While Investigation 3 in Math I Concept 6.1 provides students with a hands-on activity to justify their work, the activity does not require students to prove that “given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.” • F-IF.7b: There are many opportunities for students to graph square root, cube root, and piecewise defined functions, including step functions, throughout Math II and Math III. However, no opportunities were found for students to graph absolute value functions. There is one question in the Math III Concept 5.1 practice problems that requires students to solve a system including an absolute value expression; however, the solution can be found without graphing. • G-SRT.6: In Math I Concept 7.1 the Investigations develop connections between right triangles and trigonometric ratios; however, no connection was found as to similarity being the basis for those ratios. ### 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 Education Integrated series meet the expectation that materials require students to engage in mathematics at a level of sophistication appropriate to high school. Investigations and Apply problems provide students with tasks that are age-appropriate and of interest. The sophistication of numbers is lacking in the Investigations and Practice problems but appropriate in the Apply problems. Throughout Math I, II, and III, students are presented problems with contexts that are age-appropriate with a level of complexity expected for high school. • In Math I Concept 9.1 Investigation 2 students use the quadratic parent function to model the path of a basketball. • In Math II Concept 5.1 Introduction presents students with the concept of world population size and growth rate. • In Math III Concept 2.2 Investigation 2 students analyze radical functions through the medical context of BSA (Body Surface Area). Throughout the materials, students are expected to apply key takeaways from middle school. • Math 1 Unit 1 Assessment 1 extends and connects 7th and 8th grade understanding of integer expressions, distribution, and area (7.EE.1, 7.G.6, 8.EE.7.b) by having students associate the product of a binomial and a monomial with the area of a floor mat. Students interpret a part of a term with respect to its physical value. These extensions are strategically built from the Introduction of Math I Concept 1.1 wherein students make a conjecture for an expression, reflect on it, and then describe it in terms of constant, coefficient, variable, factor, and term. • In the Math I Concept 2.2 Introduction students recall and extend their understanding of solving equations from 8.EE.7b by exploring numerical relationships in variable contexts. In Investigation 1, students explain the process of solving equations to extend the process to more complicated cases with multiple distributions with fractions. • Math II Concept 8.3 Play problem 14 extends the middle grades focus on ratios and proportions when asking students to determine how many fish a tank can support given the following: “No more than 10% of the volume of the tank can be reserved for eels, rays and leopard sharks. The ratios for each of these marine animals are as follows: • 1 eel per 150 gallons • 1 ray per 180 gallons • 1 leopard shark per 400 gallons.” Within Apply problems, and some Investigations problems, students work with more complex, age-appropriate numbers while Play problems are typically presented with simple numbers and do not vary the types of real numbers being used. • In Math I Concept 7.1 Investigation 3 students analyze levels of protein in various breakfast cereals. The initial grams of protein consist of all whole numbers ranging from 1 to 6. As students begin to find the mean, deviation from the mean, and square of deviation, the students are now interpreting and analyzing more complex numbers ranging from -1.4 and 12.96. • In Math II Concept 11.1 Apply 2 students create and analyze piecewise functions to determine “How Many T-Shirts Should You Purchase for a Fundraiser?”. Students are provided with a table from two different companies displaying the cost per shirt when purchasing various range of quantities. Best Tees company offers prices that are more simplistic while T-Shirts D-Luxe prices- such as$3.72, $4.08, and$4.64- are more complex.
• In Math III Concept 3.1 Apply 3 students explore how math can help them learn to play the guitar. Students are first asked, “What are the common ratios for the sequences for the string length and frequency?” The string length common ratio ends up being 0.9438, and the frequency common ratio is 1.0594. Students then use this information to predict the string length and frequency of the 13th fret.
• Math I Concept 2.1 provides 15 play problems, and all but two problems result in answers involving integers. One of these two problems results in a fraction, and the other one results in a decimal.

### 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
+
-
Indicator Rating Details

The instructional materials reviewed for the High School Discovery Education Integrated series partially meet the expectation that materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

Teacher materials identify where coherence and connections are to be made. In each unit, the Progressions and Standards tab lists “Reach Back” standards, “Standards Covered,” and “Reach Ahead” standards. Connecting concepts are outlined below:

• During Previous Instruction
• The Investigations in This Concept
• During Subsequent Instruction

Examples of coherence both within and across courses include:

• Throughout the series, the materials make strong connections between many of the standards in the domains A-SSE, A-CED, F-IF, and F-LE. Math I focuses mainly on Algebra and Functions as students explore, interpret, graph, and analyze linear functions as well as transfer understanding to exponential and quadratic functions. In Math II students continue this work with the Algebra and Function Conceptual Categories with revisiting quadratic functions and then moving on to power, inverse functions and piecewise functions. Math III builds onto the function families by adding trigonometric functions, logarithmic functions, and rational functions.
• In Math I Concept 1.2 students construct expressions (A-SSE.A) and create equations (A-CED.A). The focus of Reason with Expressions and Equations in Concept 1.2 extends the work of Concept 1.1 where students Analyze Expressions and Equations and dovetails with Concept 1.3 Apply and Evaluate Expressions and Equations. Altogether, these Concept sections keep a focus for the unit on A-SSE and A-CED standards. Later units, for example, Unit 2 Equations and Inequalities and Unit 6 Linear Systems, tie back into this focus. The materials continue to intertwine work around A-SSE and A-CED throughout the series, notably with work around quadratic and polynomial functions (e.g. Math II Units 3-5).
• In Math I Concept 1.1 as students explore A-SSE.1a, Play problem 15 requires students to square an integer to simplify an expression. In Investigation 2 Concept 1.2 students evaluate expressions with exponents as they explore A-CED.1, A-SSE.1, 1a, and 1b. While the standards in Math I do not explicitly address exponents, the concept is incorporated throughout in preparation for Math II where students extend their knowledge of exponents. In Math II Concept 3.1 is entirely dedicated to rational exponents (N-RN.1-3) with Investigation 3 explicitly connecting rational exponents with roots as students translate their equation containing rational exponents into an equation in radical form in order to obtain the product property of radicals.

Although the materials connect various standards, the Geometry standards do not always make meaningful connections to previous or future content. At times, units are unconnected from the preceding and proceeding units.

• Math I Unit 1 focuses on expressions (A-SSE.1) and equations (A-CED.1, 3, 4, A-REI.1, 3, 11). Math I Unit 2 Concept 2.3 addresses four isolated Geometry standards (G-CO.1, G-GPE.4, 6, 7) yet lacks a coherent connection with the concepts from the previous Unit. Concept 2.3 makes minimal connections to Unit 3 which focuses on geometric Transformations and Constructions. Unit 3 focuses on Geometry but does not connect coherently with previous Units or with subsequent Units.
• The Math II techbook begins with two Geometry units, Transformations and Congruence and Similarity. The next four units focus on standards from the Numbers and Quantities, Algebra, and Functions Conceptual Categories (N-RN, N-CN, A-SSE, A-APR, A-CED, A-REI, F-IF, F-BF, and F-LE) with some attention to G-C0.5 and G-CO.6 in the last part of Unit 6. Unit 7 Concept 7.1 (G-SRT.6-9(+)) builds off of Similarity from Unit 2. Concept 7.2 focuses on Circles (G-C.1, 2, 4(+)). Concept 7.3 does connect to Concepts 7.1 and 7.2 by requiring students to “use special right triangles to determine geometrically the values of sine and cosine to develop the unit circle and prove the Pythagorean Theorem.” As such, the geometry standards handled in Units 1, 2, and 7 stand disconnected from the non-geometry standards of the four intermediate units. Furthermore, in Units 8 and 9 students are again focused on the Geometry Conceptual Category as they explore Area, Volume and Polygons. Unit 10 begins a new focus on Probability (S-CP.1-9(+)). Conditional Probability standards are isolated to this one Unit for the entire series. Math II wraps up with a unit of Piecewise Functions where students “will depend on their previous work with writing linear equations to write and define piecewise functions.”

### 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 Integrated series meet the expectations that the materials explicitly identify and build on knowledge from Grades 6-8 to the High School Standards. Connections between Grades 6-8 and High School concepts are identified for teachers in the Model Lesson tab as well as the During Previous Instruction section of the Progressions and Standards tab.

In each unit, the Progressions and Standards tab in the teachers materials provides teachers with lists of standards linking previous grade standards as Reach Back, within the current unit, as Standards Covered and future targets as Reach Ahead.

• In Math III Concept 1.1 a graphic is used to link Reach Back Standards to the Standards Covered and Reach Ahead Standards. These are listed as “7.EE.B.3, 8.EE.C.7a, 8.EE.C.7b, 7.EE.B.4a, and 7.EE.B.4b” leading to “HSA-REI.B.3 and HSA-CED.A.3” and then to “HSA-REI.D.11 and HSF-IF.C.7b.”

Session Notes to Teachers call out prior knowledge to be used when appropriate.

• In Math I Concept 1.1 Session 1 the Introduction notes state “Students apply prior knowledge and understanding of variables and algebraic equations to model an observed behavior.”
• In Math I Concept 1.3 Session 2 Investigation notes state “Students are bringing prior experience with interest from Grade 7, but the video that introduces the investigation and the sequence of activities in the investigation provide solid support for students who may not have understood these concepts in prior grades.”

### 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 instructional materials reviewed for the High School Discovery Integrated series address 19 of the plus standards. Included plus standards are identified by a (+) symbol within the Course Overview document as well as within the Progressions and Standards tab for each unit in the teacher materials. Session Instructional Notes, however, do not identify content specific to plus standards.

The plus standards that are identified in the Course Overview document and addressed to reach the full intent of the standard are listed below:

• Math I: F-BF.1c (Concept 5.1)
• Math II: F-BF.1c (Concept 6.2), F-BF.4c (Concept 6.2), F-TF.3 (Concept 7.3), G-SRT.9 (Concept 7.1), G-C.4 (Concept 7.2), G-GMD.2 (Concept 8.3), S-CP.8 (Concept 10.2), S-CP.9 (Concept 10.3), S-MD.6 (Concept 10.2), S-MD.7 (Concept 10.2)
• Math III: N-CN.3 (Concept 9.2), N-CN.4 (Concept 9.1), A-APR.5 (Concept 9.1), A-APR.7 (Concept. 10.1), F-IF.7d (Concept 11.1), F-BF.4c (Concept 4.1), F-BF.5 (Concepts 4.1 and 4.2), F-TF.3 (Concept 6.2), G-SRT.10 (Concept 7.2), G-SRT.11 (Concept 7.2), G-GPE.3 (Concepts, 12.1, 12.2, and 12.4), S-MD.6 (Concept 8.2), S-MD.7 (Concept 8.2)

Included plus standards coherently support the mathematics which all students should study in order to be college- and career-ready. Work with those plus standards does not deter from the work with the non-plus standards.

• In Math III Concept 9.1 Investigation 1 students graph complex numbers in a coordinate plane which supports their understanding of the real and imaginary parts of a complex number introduced with complex addition N-CN.2. The plus standard N-CN.4 supports non-plus standards.
• In Math III Concept 9.1 Session 6 students review properties of exponents and practice binomial multiplication while extending toward A-APR.5.

However, particular standards, plus or non plus, are not mentioned in the “Discover” tab of the tech book. Materials do not identify standards addressed in the Introduction or in each Investigation.

• Math III Concept 9.1 Investigation 1 “Representing Imaginary Numbers” addresses N-CN.4. Students begin Investigation 1 with properties and operations of complex numbers, adding and subtracting them, and then graphing. No notation was found identifying that a plus standard is being addressed in the Investigation.

## Rigor & Mathematical Practices

### 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 Integrated 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 Education Integrated series meet the expectation that materials support the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters. This series is constructed in such a way that each Concept contains Discover, Practice, and Apply tabs. The Introduction, Investigations, Summary, and Extension tabs within the Discover tab are predominantly where students’ conceptual understanding of key mathematical concepts is developed.

Each Concept within each Unit contains a list of Conceptual Understandings to be found in that section. This list is located within the Progressions and Standards tab in the Teacher edition. For example, Math III Concept 2.2 includes the following list of Conceptual Understandings:

• "Explain why the inverses of quadratic and cubic functions are square root and cube root functions and may require restricted domains."
• "Recognize how the effects of changing parameters within the radical equation will affect the translation of the function’s graph."
• "Compare and contrast methods for solving radical equations of square roots and cube roots while realizing that some of these equations have extraneous solutions."

Included throughout teacher materials within the Session tabs are “Questions to promote development of conceptual understanding.” Within Math I Concept 5.1 the materials provide questions in the Session 1 and 2 Instructional Notes. “Questions to promote development of conceptual understanding” include the following:

• “Which attributes were more challenging to assign to the figures? What made them more challenging?"
• "Which attribute assignments did you and your partner disagree on? How did you resolve the dissenting analysis?"
• "How can you use the responses you made for these problems to compare and contrast linear and exponential functions?”

Examples of select cluster(s) or standard(s) that specifically relate to conceptual understanding include, but are not limited to, the following:

• F-LE.1: In Math I Concept 8.2 Investigation 1 students use equations and graphs to model how the amounts in three different accounts grow over time. Students use technology to analyze and verify how changes in parameters affect the graphs of the equations. Students identify which options involve adding a fixed quantity to the previous year’s amount and which options involve multiplying a fixed quantity by the previous year’s amount.
• G-SRT.6: In Math II Concept 7.1 Investigation 2 students use an online interactive to explore the relationship between the angle measures and the ratios of the sides of a right triangle to develop conceptual understanding of trigonometric ratios. Students look for any relationships that might help the team determine how far they are from the checkpoint. Students are asked to articulate their observations in writing.
• S-ID.7: In Math I Concept 7.2 Investigation 3 students collect measurements of their forearms and right feet to determine if there is a relationship between forearm length and foot length. After students examine results and write an equation of a line of best fit they are asked: “What does the slope of the line of best fit represent in this context? What does the y-intercept of the line of best fit represent in this context? Explain why the y-intercept is or is not realistic in this context.”

### 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 Education Integrated series meet the expectation that materials provide intentional opportunities for students to develop procedural skills and fluency, especially where called for in specific content standards or clusters. The instructional materials build fluency practice into multiple sections of concepts.

Each concept contains a Fluency box within the Progressions and Standards tab of the teacher materials where specific skills are identified for focused fluency development. For example, in Math III Concept 6.1 the Fluency box include the following:

• “Identify the radian measure for angles within a unit circle.”
• “Measure angles using radians by finding the measure of an angle as the length of the arc on the unit circle subtended by the angle.”
• “Convert between radians and degrees.”

Students are provided opportunities to develop procedural skills and fluencies in the Intro, Investigations, Play, and Check for Understanding tabs.

• The Play tab, which consists of a Coach and Play section, is designed to address procedural skill and fluency. The Play tab includes practice problems placed in a progression of learning that provides students the opportunity to build procedural fluency from conceptual development.
• Every Investigation contains a Check for Understanding where students determine their “current level of understanding”. Problems within the Check for Understanding are often focused on procedural skills and fluency. For example, Math III Concept 1.1 Check for Understanding includes:
• "Hurricane strength is classified using the Saffir-Simpson scale. Category 3 hurricanes have wind speed greater than 110 miles per hour but at most 130 miles per hour. Which of these show possible wind speeds, w, in this category? Select all that apply."
• "Which compound inequality is shown by the number line graphed?"

Examples of select cluster(s) or standard(s) that specifically relate to procedural skill and fluency include, but are not limited to:

• G-GPE.4: In Math I Concept 2.3 students are asked to use the Pythagorean Theorem to find locations of a statue in the Investigations as well as Check your Understanding. In Investigation I of Math II Concept 7.3 students are asked to write an equation that represents all the points on a circle when given the center and a point on the circle.
• A-SSE.1b: In Math I Concept 1.2 Investigation 3 students explore card tricks and write and simplify algebraic expressions to express the number of cards in a pile. In Trick 2 students ultimately write equations, based on expressions they wrote, to describe the results of the card trick. Investigation 3 also offers four questions providing students the opportunity to interpret expressions. In the Play tab students are given multiple scenarios and asked to write an expression/equation that represents the scenario or given options and asked to choose all that apply. In the Play tab of Math II Concept 3.2 students are again asked to simplify or write equivalent expressions and/or polynomials. In the Play tab of Math III Concept 9.1 students are given the opportunity to expand binomials, factor expressions, provide missing factors for expressions, and identify “Which of the following is the factored form of 16x^4+32x^3y+24x^2y^2+8xy^3+y^4?” and “Which of the following expressions show the difference of two perfect squares. Select all that apply.”

### 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that materials support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. The third tab in each Unit is titled Apply. The Apply tab consists of one or more open-ended problems aimed at the development of students’ ability to utilize mathematical concepts and skills in engaging applications.

Each Concept has an Apply section where students are able to apply what they have learned in the investigation.

• In Math I Concept 5.1 Apply Problem 1, How Can You Use Functions to Make an Image?, students are expected to draw a recognizable figure using graphs of linear and/or exponential functions, vertical lines, and at least one pair of non-vertical parallel or perpendicular lines. This application task requires students to identify the domains of the functions they use, explain the relationship between the slopes of parallel or perpendicular lines, and identify and describe transformations of linear and exponential functions. The materials explains that architects, fashion designers, and engineers draw using technology. (F.IF.4)
• In Math II Concept 5.1 Apply Problem 1, How Can Math Help You Create a Successful Business?, students analyze the relationship of a demand function and a revenue function. They interpret the key features of the graphs and determine the price of the item that will maximize revenue. (F-IF.7)
• In Math III Concept 3.1 Apply Problem 1, How Many Digits Are Needed in a Telephone Number?, students watch a video about the history of telephone numbers and are posed with the question of whether or not “10 digits will be enough to ensure that everyone has a unique phone number.” After some guided questions to get students thinking, they are told “the world will continue to increase by 25 million every month.” Then they are asked, “How many digits are needed right now to accommodate all phones? When would more digits be needed for phone numbers so each user has one unique number?” (F-LE.2)

### 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 reviewed for the High School Discovery Education Integrated series meet the expectation that 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. As described in indicators 2a, 2b, and 2c, there is evidence that all three aspects of rigor are present in the materials. Overall, the series provides a balance of the three aspects of rigor throughout the materials.

Each Concept includes Discover, Practice, and Apply sections:

• Discover includes Introduction, 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.

Some examples that demonstrate this balance include:

• In Math 1 Concept 4.1 students "engage with real-world phenomena that involves a dependent relationship, constraints in data, and different mathematical representations of the data." The Concept progresses to students using "function notation to represent, interpret, and evaluate functions." (F-LE.5, F-IF.1, 2, and 9)
• In Math II Concept 5.2 students explain complex numbers and extend the commutative, associative, and distributive properties to operations with complex numbers. They explain the relationship between the discriminant and complex quadratic solutions and show procedural skills by comparing quadratics having both real and complex roots. Students then "apply the real-world implications of complex quadratics solutions to word problems." (N-CN.1, 2, and 7)
• Math III Concept 6.1 balances conceptual understandings, procedural fluencies, and applications as students explore angle measures and define radian measures for angles throughout the unit circle. In the Intro, students utilize Geometry software to discover patterns between central angle measure, radius length, and arc length. Throughout the Investigations, students explore angles within the coordinate plane, derive radian measure, and begin converting between degree and radian measures. The use of interactive software provides students the opportunity to discover relationships and develop conceptual understanding of radian measure. Each Investigation contains a Check for Understanding where students practice more procedural skills such as identifying “Which of the following angle measures given in radians is greater than 28.5°?” and completing a table of equivalent radian and degree measures. Students then apply their new understandings of radian measure when posed with two application problems where they are asked “How Would you Design Your Own Ferris Wheel?” and “How Can You Create a New Protractor?”. (F-TF.1)

### Criterion 2e - 2h

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

The instructional materials reviewed for the High School Discovery Integrated 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that 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 Standards for Mathematical Practice. Within each Unit Concept, the Standards for Mathematical Practice are identified under the Progressions and Standards tab. Additionally, the materials provide information regarding the Standards for Mathematical Practice within the Teacher Model Lesson under the Standards tab as well as within the Teacher Notes.

Examples of MP1 are as follows:

• In the Math I Concept 8.3 Intro students analyze geometric patterns, making sense of the algebraic relationship between the quantities. In Investigation 2, students are asked to confirm their solutions through graphic analysis. In Investigation 4 MP1 is evident as students analyze relationships between an initial investment and changes to an account. (F-IF.7e, 9, A-REI.11, F-LE.5, F-BF.2)
• In the Math II Concept 9.1 Intro students analyze givens, constraints, relationships, and goals as they explore and discuss different meanings for the center of a triangle. In Investigation 1 students start each exploration by explaining to themselves the meaning of the problem, analyzing goals, and looking for entry points to its solution. (G-C.3, C-CO.10)
• In Math III Concept 3.2 Apply 1 students collect data and select an appropriate time period when they would most likely see a wolf when visiting Yellowstone National park and provide strong support from graphical and algebraic analysis. Students then make predictions from their models. (A-CED.1, A-REI.11, F-BF.1b, F-IF.8,8b, F-LE.1c, 2, 5)
• In Math III Concept 5.1 Apply 2 students use data tables showing the number of transistors in various processors over the years. Students make predictions based on data of when processors will hit 10 billion transistors. Students must research their conclusions to confirm accuracy. (A-REI.7, 11)
• In Math III Concept 4.1 Investigation 4 MP1 is explicitly noted in the Instructional Notes for teachers to “encourage students to consider different methods of solving, including both algebraic and graphic approaches.”

Examples of MP6 are as follows:

• In the Math I Concept 1.1. Intro students are led to discuss precise vocabulary for parts of expressions. The rubric for Apply I requires students to identify all variables, explain what the expression represents, and include units. (N-Q.1, 2, A-SSE.1a)
• In the Math II Concept 3.2 Intro, the Teacher Notes state that students “will communicate clear definitions and state the meaning of the symbols they use (MP.6).” Later in the intro exercise, students “Discuss with a partner: What distinguishes a polynomial from an expression that is not a polynomial?” The Teacher Notes suggest referring students back to the initial class list of definitions for a polynomial. Students are expected to refine the definition based on the examples and nonexamples of polynomials. (A-APR.1, A-SSE.1a, 1b, N-RN.2)
• In Math III Concept 9.1 Investigation 2 students use MP6 as they attend to precision when describing characteristics of polynomial equations and their relationship to the graphs of the related functions. (A-APR.1, 2, 3, 4, 5(+), A-SSE.1b, 2, N-CN.2, 4(+))

### 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 reviewed for the High School Discovery Education Integrated series meet the expectation that 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 Standards for Mathematical Practice. Within each Unit Concept, Standards for Mathematical Practice are identified under the Progressions and Standards tab. Additionally, the materials provide information regarding the Standards for Mathematical Practice within the Teacher Model Lesson under the Standards tab as well as within Teacher Notes.

Examples of MP2 are as follows:

• In the Math I Concept 5.1 Investigation 1, Teacher Notes state “MP.2 will also be evident as students decontextualize information to create a graph and analyze it to draw conclusions regarding the domain and range. They will use the graph to compare the density of different substances, such as water.” (A-REI.10, G-GPE.5, F-BF.1a, 1b, 1c(+), F-IF.1, 2, 4, 5, 6, 7a, 7e)
• In Math 1 Concept 8.3 Investigation 2 students formulate a process for solving exponential equations by analysis of quantitative relationships, identifying common structure to the base values. (F-IF.7e, 9, A-REI.11, F-LE.5, F-BF.2)
• In Math II Concept 10.1 Investigation 1 students contextualize and de-contextualize different scenarios to construct mathematical models and interpret the likelihood of winning. (S-CP.1 - 5)
• In Math II Concept 8.2 Investigation 1 students analyze and evaluate the distribution of cookie weight data. They analyze the variability in the data and explain what the variability means in the context provided. (S-ID.4, S-MD.6(+), 7(+))

Examples of MP3 are as follows:

• In the Math I Concept 2.3 Intro students relate dimensions and units to a coordinate plane. In Investigation I a variety of dimensions are presented that may or may not satisfy given constraints. Students are asked to justify their conclusions. (G-CO.1, G-GPE.4, 6, 7)
• The Math I Concept 5.1 Introduction to the Investigations states the following: “MP.3 will be evident as students compare characteristics among the figures, justifying their reasoning for similarities and differences. Allow students to discuss with a partner before reconvening the class to share their reflections. Questions to promote discussion: How did you know whether each figure on the image was exponential or linear? Under what conditions could an interval of an exponential function behave like a linear function?” (A-REI.10, G-GPE.5, F-BF.1a, 1b, 1c(+), F-IF.1, 2, 4, 5, 6, 7a, 7e)
• In the Math I Concept 6.2 Intro students debate options for buying economy versus quality brushes. (A-CED.3, N-Q.3)
• In Math II Concept 1.3 Investigation 2 students analyze givens and diagrams and develop proofs with classmates and on their own. Students choose and arrange the statements and reasons for the Corresponding Angles Theorem and Alternate Interior and Exterior Angles Theorems (paragraph, two-column, and flowchart proofs). Though the student and teacher view of the Techbook does not specifically invite students to critique the reasoning of others, the Instruction Notes in the Model Lesson tab suggests teachers “invite pairs of students to share different proof formats… During critiquing, make sure students can ascertain the validity of each proof.” Investigation 3 Instruction Notes suggest that teachers “invite students to present their proof of the Converse of the Consecutive Angles Theorem and have students critique selected proofs in pairs or small groups.” (G-CO.9, G-GPE.4, 5)
• In Math II Concept 8.1 Investigation 2 students use properties of dilation to justify the area of a circle. Within Investigation 3 students explore the concept of sampling variability and the margin of error. Students justify their conclusions and communicate them to others. (G-C.5, G-GMD.1)
• In Math III Concept 11.2 Apply 1 students extend their ability to analyze dimensions by finding ways of reducing the amount of aluminum used for soup cans, presenting advantages and disadvantages for sizing options. (A-CED.1, 2, A-REI.11, F-BF.4a, F-IF.5)

### 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 Education Integrated series meet the expectation that 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 Standards for Mathematical Practice. Within each Unit Concept, Standards for Mathematical Practice are identified under the Progressions and Standards tab. Additionally, the materials provide information regarding the Standards for Mathematical Practice within the Teacher Model Lesson under the Standards tab as well as within Teacher Notes. Students have access to a wide range of tools throughout the series, and although the tools are prescribed in some cases, students are given the opportunity to choose appropriate tools strategically in many of the Apply problems.

Examples of MP4 are as follows:

• In Math I Concept 2.1 Investigation 4 students model and analyze the use of tickets at an amusement park. In Investigation 5 students extend their understanding of equations and inequalities to model a real-world scenario, analyzing the relationship between two options to determine when the options are equivalent or when one is more reasonable. (A-CED 1, 3, A-REI.1, 3, 11)
• In Math 1 Concept 7.1 Apply 1 students create a graphical display to represent data. Students justify their choice in data display. (S-ID.1-3)
• In the Math II Concept 5.1 Intro students model with mathematics by representing the data with different equations and graphs. In Investigation 1 students model a real-world situation by using both the equation and graph of a quadratic function and analyze this function quantitatively. (A-CED.1, F-IF.4, 5, 7a, 7c, 8a, 9, F-BF.1, 3, F-LE.3)
• In Math III Concept 3.2 Apply 1 students collect data and select an appropriate time period with strong support from graphical and algebraic analysis. Students then make predictions from their models. (A-CED.1, A-REI.11, F-BF.1b, F-IF.8, 8b, F-LE.1c, 2, 5)

When working through Investigations, students are often prescribed the appropriate tool(s) to utilize, providing students with guided practice using each tool. As students reach the Apply problems, the choice of tool becomes the decision of the student. Examples of MP5 are as follows:

• Math I Concept 3.1 Apply 2 students “determine the shortest path the [Mars] rover can take to visit all three rocks and then travel to its ending point. Your job is to determine this shortest path, and then model it by using transformations.” The materials provide students with a Mars map as well as an image of the Mars Rover and a rock on Mars. Students must utilize these provided tools and determine what additional tools they would need to accomplish this task. (G-CO.2, 3, 4, 5)
• In Math II Concept 2.1 Apply 1 students consider the question “How Would You Set Up a Projector to Show an Outdoor Movie?” Students experiment with their classroom projector and the concept of aspect ratio to determine the location of an outdoor movie projector for optimal size and clarity of the movie. Selection of appropriate tools for this task is left up to the student. (S-SRT.1, 1a, 1b, 2)
• In Math III Concept 3.2 Apply 3 students determine how much each person in the country would have to contribute to pay off the national debt within four years. Students conduct their own research and use technology (specific technology is not provided) to make calculations and display their data. The Teacher’s Note in the materials states, “Encourage students to use 21st-century publishing tools to present their responses. You may wish to have students use the Board Builder or a particular software tool or leave the choice of tools open.” (A-CED.1, A-REI.11, F-BF.1b, F-IF.8, 8b, F-LE.1c, 2, 5)

### 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 Education Integrated series meet the expectation that 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 Standards for Mathematical Practice. Within each Unit Concept, Standards for Mathematical Practice are identified under the Progressions and Standards tab. Additionally, the series materials provide information regarding the Standards for Mathematical Practice within the Teacher’s Model Lesson under the Standards tab as well as within Teacher Notes.

Examples of MP7 are as follows:

• In Math I Concept 2.1 Apply 3 students consider a sales pattern and write a system of linear inequalities that would assist in identifying all possible solutions. (A-CED.1, 3, A-REI.1, 3, 11)
• In Math 1 Concept 9.2 Investigation 1 students use the structure of functions to determine which function will eventually have the greatest value. In Investigation 2 students make use of the structure of linear, exponential, and quadratic functions in order to compare them. (F-IF.9, F-LE.3)
• In Math II Concept 8.1 Investigation 1 students look for and make use of structure to determine the trend in the data and develop the understanding that the area of the circle will approach π as the grid size decreases. (G-C.5, G-GMD.1)
• In Math III Concept 12.1 Investigation 1 students look for patterns in determining the radius of the circle, based on repeated applications. In Investigation 3 students look for patterns in determining the foci and major and minor axes of the ellipse. (G-GPE.1, 2, 3(+))

Examples of MP8 are as follows:

• In Math I Concept 6.1 Investigation 1 students use repeated reasoning to create single equations by applying the substitution method. (A-CED.2, 3, 4, A-REI.5, 6, 11, 12)
• In Math II Concept 8.1 Investigation 5 students look for and express regularity in repeated reasoning as they examine the ratio of the arc length to the circumference for arcs of different measures and the ratio of the arc length to the radius for arc with the same measure. (G-C.5, G-GMD.1)
• In Math III Concept 4.1 Investigation 3 students analyze patterns of inputs and outputs of logarithmic and exponential function compositions and then use these patterns to discern structure relative to the properties and justify the inverse relationship algebraically. (F-BF.3, 4a, 4c(+), 5(+), F-IF.4, 7e)

## Usability

### Criterion 3a - 3e

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

The instructional materials reviewed for the High School Discovery Integrated 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson.

As the online materials organize learning in a particular order, the structure delineates between problems and exercises. This order includes the following:

• A Discover Tab which has an Intro problem followed by multiple Investigations and a Summary and Extensions. This is where problems for learning new mathematics are found.
• A Practice Tab consisting of Coach and Play sections which contain exercises.
• An Apply Tab which has one or more open-ended exercises. Exercises which build mastery and student capacity for a given skill with application are found mainly in the Practice and Apply Tabs.

This structure is repeated throughout the series.

### Indicator 3b

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

The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that the design of assignments is not haphazard and that exercises are given in intentional sequences.

The basic structure of each concept includes interactive core mathematical content and concurrent formative assessment. Modeling investigations intentionally build on and extend from the core content concepts, and the Coach and Play sections assess and reinforce procedural skills.

### 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 Education Integrated series meet the expectation that students are asked to produce a variety of products throughout the Concepts in each Unit to demonstrate their learning of the mathematics.

The materials ask students to engage in mathematics in a variety of ways. For example, students are asked to make predictions based on a set of data, estimate measurements and use geometric tools, and compare/contrast information from a diagram.

• In Math II Concept 1.2, students are asked to make conjectures, explain their reasoning orally and through writing, and collect data.
• In Math I Concept 2.3 Apply 2 students design a chairlift by making a graph of the lift and spacing towers to adequately support the lift using ratio reasoning. Students research lifts from existing ski resorts and defend their decisions using citations. They calculate coordinates on their graphs to correspond to the towers they recommend.

### 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Education Integrated series meet the expectation that manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The series makes use of a range of virtual manipulatives including, but not limited to, calculators, a geometry sketchpad, a geometry construction app, a unit converter, a data analysis app, a matrix solver, and a virtual whiteboard. General manipulatives and tools are listed in the Teacher Preparation sections. A few examples of these include, but are not limited to, paper towel tube, meter stick, measuring tape, straws, and pins. Throughout the series, students are exposed to a wide variety of manipulatives and virtual tools and are expected to utilize them as necessary.

• In Math I Concept 3.1 students explore transformations using a flip-book cut from a printable template.
• In the Math I Concept 3.3 Intro students use a construction app to reconstruct the flower of life.
• In Math II Concept 2.3 students use straws and pins.
• In Math II Concept 1.2 Investigation 1 students use the dynamic geometry tool to explore parallel and perpendicular lines and are also asked to verbalize their findings. In Investigation 2 they are asked to use patty paper and paper folding to construct different types of lines.

### 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 Education Integrated series meet the expectation that the visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The layout of the materials is identical for every course, Unit, and Concept. Teachers can easily toggle between the “teacher view” and the “student view.” A Glossary tab and Math Tools tab are also easily accessible. Pictures and models used throughout the series support student learning as they are connected directly to an Investigation or problems being solved. The figures and models used 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
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Criterion Rating Details

The instructional materials reviewed for the High School Discovery Integrated 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each course contains a Course Overview which is divided into Unit Overviews and Concept Overviews explaining what students will be doing in each section. Within the Model Lesson tab of each Concept, there are tabs which contain Objectives (Lesson Objectives, Essential Questions, and Enduring Understandings), Progressions and Standards, Teacher Preparation (materials list, common misconceptions, and key vocabulary), Sessions (introduction and instructional notes), Extensions, and Apply. Throughout each lesson, additional instructional notes and guiding questions are also included in the materials. For example:

• Math II Concept 4.2 Sessions 1 and 2 Instructional Notes include the following questions:
• "How do you know that it is not possible for the graph of a quadratic function to have three x-intercepts?"
• "If the graph of a quadratic function has exactly one x-intercept, what can you conclude about the location of its vertex?"
• "If the graph of a quadratic function has no x-intercepts and a minimum point, does its vertex lie above or below the x-axis? How do you know?”
• In Math II Concept 4.2 Investigation 3 a Teacher Note states: “Have students share their reasoning for each answer and critique one another’s arguments. Analyze the graph and discuss what all of the parts mean in the context of the problem.” Though questions are provided for teachers to use, no explanation of possible answers is included.

### 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series meet the expectation that 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.

Teachers are able to easily toggle a “teacher view” on or off. When the toggle is on, teacher notes and answers to all problems are visible. Throughout the teacher materials there are instructional notes for each Investigation in addition to the thorough instructional notes located in the Model Lesson tab of each Session. These notes tie directly to the Investigations found in the Discovery tab.

A dynamic geometry tool and construction tool which is referenced extensively and is freely available to the students in and out of class time is embedded within the instructional materials. It is employed in all three courses. There are “?” icons next to embedded technology where students can see explanations of how to use the technology. Additional technology support is provided in the Help menu.

### 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 Integrated series partially meet the expectation that materials contain a teacher’s edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

The Progressions and Standards tab provides teachers information of the standards as well as a description of mathematics in During Previous Instruction, Through the Investigations in This Concept, and During Subsequent Instruction. The Teacher Preparation tab also provides teachers with common misconceptions. Teacher materials are written in appropriate mathematical language. This provides adult-level information specific to the course and does not provide more advanced mathematical concepts for the teachers.

The materials lack explanations for answers. Answers are either provided with no accompanying explanation or are simply listed as “answers may vary” without providing examples of acceptable answers.

### 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 Integrated series meet the expectation that materials contain a teachers edition that explains the role of the specific mathematics standards in the context of the overall series.

The Progressions and Standard tab in the Model Lesson provided in each concept provides teachers with an explanation of the role of specific math standards within that concept. Materials provide teachers an overview of the progression of the content standards by listing Reach Back Standards, Standards Covered, and Reach Ahead Standards. In addition, for each Concept the materials provide a narrative of mathematics learned “During Previous Instruction,” “Through the Investigations in this Concept,” and “During Subsequent Instruction.”

### 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 Integrated series provide a list of lessons in the teacher’s edition, cross-referencing the standards addressed and providing an estimated instructional time for each Unit, Concept, and Session.

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 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 Investigations, the user must navigate to the specific Concept page and view the Investigations individually.

Standard alignment is available for each 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, Math I Concept 1.2 includes four Investigations. To determine the pacing for this Concept, a teacher would take note of the times suggested by clicking five different session tabs within the Model Lesson tab. 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, Session 5 (Investigation 4) 50 min. A teacher would then need to compile this information in order to determine suggested pacing of their instruction.

### 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated 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 the student share how they used a specified interactive in the investigations to discover the mathematics, and having the student 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
+
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Criterion Rating Details

The instructional materials reviewed for the High School Discovery Integrated 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
+
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Indicator Rating Details

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

In the 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 Introduction 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 Introduction 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
+
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series partially meet the expectation that materials provide support for teachers to identify and address common student errors and misconceptions. 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
+
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Indicator Rating Details

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

In each concept, the Coach and Play sections 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
+
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series partially meet the expectation that assessments clearly denote which standards are being emphasized.

The instructional materials include a pre-made unit assessment. The standards are identified for the unit, and therefore it is clear, as a whole, what standards are being emphasized on the unit assessment. However, there is not a standards alignment item by item, and therefore, 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. The Math Assessment Builder does clearly denote standards by allowing teachers to select questions for their assessment based on specific standards.

### Indicator 3p.ii

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

The instructional materials reviewed for the High School Discovery Integrated series partially meet the expectation that assessments provide sufficient guidance 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, based on a 0, 1, or 2 point scale that shows the criteria needed to receive that score. Each Apply question includes a rubric where the scores range 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 Integrated 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 have a dashboard on their Math Techbook home screen to keep track of their answers to questions and points given to responses throughout the Discover, Practice, and Apply cycle. A student would have to be directed by the teacher to look in the dashboard or self direct. 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 Integrated 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 Integrated series partially meet the expectation that the materials provide teachers with strategies to help 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 Integrated 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, students are provided with online, tutorial websites for instructional assistance when needed in the Summary section. 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 Integrated 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, Math I Concept 6.1 introduces students to the lesson using a Car Rental task. This tasks presents students with the question,”How can you use math to compare rates at two car rental companies?” Students explore the question in their own way and then through the lens of equations. Following the equation exploration, students are posed with the question, “What other solution strategies could you use to help you make decisions?” Questions such as these provide students the opportunity to expand their thinking based on their entry point and represent the solution in another way.

### 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 Integrated series do not meet the expectation that the materials suggest 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 Integrated 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series provide a balanced portrayal of various demographic and personal characteristics. The activities are diverse, meeting the interests of a demographically diverse student population. Images presented display a balanced portrayal of various demographic and personal characteristics.

### Indicator 3x

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

The instructional materials reviewed for the High School Discovery Integrated series provide opportunities for teachers to use a variety of grouping strategies.

Instructional notes in the Session tabs provide teachers with suggestions on grouping for each activity; suggestions are made whether work should be done individually, in pairs, or in small groups. For example, the Math III Concept 6.2 Instructional Notes for Session 1 direct the teacher to “Prompt individual students to consider ways to remember the coordinates of the ordered pairs, and then have them discuss their strategies with their partner. Then, ask pairs to jointly make a list of similarities and differences between the values for the special right triangles they already knew and the values on the unit circle. Reconvene the class and ask pairs to share their lists. Finally, ask pairs to share their strategies for remembering the numbers.”

### Indicator 3y

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

The instructional materials reviewed for the High School Discovery Integrated 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 a parent of the content their student will be learning and ways in which they may help their student.

### 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
+
-
Criterion Rating Details

The instructional materials reviewed for the High School Discovery Integrated 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 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
+
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series are compatible with multiple internet browsers and devices. The Discovery Integrated Series is compatible with the following most recently updated browsers: Chrome, Safari (version 9.0 and above), Firefox (version 44 and above), Explorer (version 11 and above), and Edge (version 24 and above) as well as tablets and mobile devices with ChromeOS, Android, or iOS operating systems.

### Indicator 3ab

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

The instructional materials reviewed for the High School Discovery Integrated series include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Each unit contains an online Unit Assessment that can be assigned for students to complete electronically. Materials also provide teachers with technology-enhanced assessment items to build their own Standards Based Assessments. Additionally, materials include electronic Check for Understandings, as do the Coach and Play tabs within each concept.

### 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
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated 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.

Innovative tools are embedded throughout the instructional materials. These innovations include Highlight, Speak Text, and Take Notes. Materials also provide a “My Notebook” tab which enables printing of notes for every Concept in each Unit.

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

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
+
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Indicator Rating Details

The instructional materials reviewed for the High School Discovery Integrated series incorporate technology that provides opportunities for teachers and/or students to collaborate with each other. 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.

### 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 Integrated 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.

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Report Published Date: 2017/05/04

Report Edition: 2017

## Math High School Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria 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 review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria 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.

## Math High School

Evidence Guide Review Criteria

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. 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).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, 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.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, 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.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.