Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 8 Discovery Education meet the expectations for alignment and usability at each grade. The materials spend the majority of the time on the major work of the grade, and the assessments are focused on grade-level standards. Content is aligned to the standards and progresses coherently across the grades and within each grade. The lessons include conceptual understanding, fluency and procedures, and application. There is a balance of these aspects for rigor. The Standards for Mathematical Practice (MPs) are used to enrich the learning.

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
18
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Partially Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
29
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for being focused on and coherent with the Common Core State Standards in Mathematics. The Unit Assessments do not assess above grade-level topics, and the instructional materials devote over 65 percent of class time to major work. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and will foster coherence between the grades. The materials explicitly relate grade-level concepts to prior knowledge from earlier grades, and the materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
+
-
Criterion Rating Details

The instructional materials reviewed meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials did not include any assessment questions that were above grade-level.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
+
-
Indicator Rating Details

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for assessing grade‐level content and, if applicable, content from earlier grades. The Unit Assessments that are included in the Teacher View were reviewed for Discovery Education Math Techbook Grade 8 Mathematics. Overall, there were no assessment questions addressing standards from above Grade 8.

Examples of grade-level assessment items include the following:

  • Unit 1 question #11- Students show their knowledge of 8.EE.1 by dragging and dropping tiles into an equation to create equivalent expressions.
  • Unit 4 question #7- Students demonstrate their knowledge of 8.G.7 by trying to informally prove the converse of the Pythagorean Theorem by producing supporting evidence.
  • Unit 5 question #14- Students demonstrate their knowledge of 8.EE.A by applying their understanding of scientific notation to solve a real-world application problem to determine the approximate number of liters of water that go over the Horseshoe Falls in the Niagara River in 1 year and explain how they found their solution.

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
+
-
Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meets the expectations for having students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. Overall, the materials devote approximately 80 percent of class time to major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
+
-
Indicator Rating Details

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 80 percent of the instructional time is spent on major work of 8th grade.

To determine this, three perspectives were evaluated: 1) the number of units devoted to major work, 2) the number of instructional periods/sessions devoted to major work, and 3) the time devoted to major work. Time devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts.

Evidence was collected from the Content Pages, Scope and Sequence, Table of Contents, and the Course Overview.

  • Units – Approximately 9 complete units out of 11 units, which is approximately 82 percent, is spent on major work.
  • Sessions (Excluding Extensions)– Approximately 99 sessions out of 117, which is approximately 85 percent, is spent on major work.
  • Time (Excluding Extensions)– Approximately 5,350 minutes out of 6,650 minutes, which is approximately 80 percent, is spent on major work.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
+
-
Criterion Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for being coherent and consistent with the standards. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior or future grades is clearly identified, and the materials explicitly relate grade-level concepts to prior knowledge from earlier grades. The objectives for the materials are shaped by the CCSSM cluster headings, and they also incorporate natural connections that will prepare a student for upcoming grades.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Overall, many Concepts that address supporting work integrate it with major work so that students are given more opportunities to engage with the major work of the grade.

Some examples of how the Concepts that address supporting standards integrate them with major work are:

  • In Concept 2.3 students have the opportunity to identify irrational numbers and compare their sizes and locations on a number line, supporting standards 8.NS.1,2 by evaluating square roots of small perfect squares and cube roots of small perfect cubes, major standard 8.EE.2.
  • In Concept 10.2 students have the opportunity to model a bivariate relationship with a linear model and use the linear model to answer questions in the context of the bivariate data set, supporting standards 8.SP.2,3. Modeling a bivariate relationship with a linear model and using the model to answer questions in terms of a context enhances students' opportunities to construct a function to model a linear relationship between two variables and interpret the rate of change and initial value of the function in relationship to the situation being modeled, major standard 8.F.4.
  • In Concept 11.1 students have the opportunity to work with and solve problems using the formulas for the volumes of cones, cylinders, and spheres, supporting standard 8.G.9. Since the formulas for the volumes of cones, cylinders, and spheres involve squared and cubed terms, these problems enhance students' opportunities to use and evaluate square and cube roots, major standard 8.EE.2.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades.

The Scope and Sequence document states that one period is equivalent to approximately 50 instructional minutes. According to the times given in each of the Units, there are approximately 133 50-minute class periods without Extension Lessons. Since there are eleven Unit Assessments, the total number of days would increase to approximately 144 days if one day is allotted for each Unit Assessment. The Scope and Sequence document also states that “the instructional time does not include in-class time for the extensive, independent student work available in the Practice and Apply sections that many teachers may wish to incorporate as part of their daily instruction.”

There are 26 Practice and 26 Apply sections in the materials as each of the 26 Concepts in the materials has a Practice and Apply section. Adding one day to complete the Practice and Apply sections for each Concept brings the total number of instructional days to approximately 170 50-minute class periods. Overall, with 170 50-minute class periods, the instructional materials meet the expectations for this indicator.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for the material being consistent with the progressions in the Standards. The materials develop according to the grade-by-grade progressions in the Standards, and the content from prior or future grades is clearly identified and related to grade-level work.

At the beginning of each Concept, there is a section called Progressions and Standards, and in this section, there are three parts titled During Previous Instruction, Through The Investigations In This Concept, and During Subsequent Instruction.

  • During Previous Instruction identifies content from previous grades and explains how previous content is related to grade-level work. For example, Concept 9.1 includes the following: "During Previous Instruction, students have learned how to use variables to represent unknown quantities in equations (6.EE.6), and have represented and solved real-world situations using equations (6.EE.5,7). Students also have worked with independent and dependent variables (6.EE.9). In Grade 7, students extended these understandings to proportional relationships and solve equations algebraically and graphically (7.EE.4a, 7.RP.2a–d)."
  • Through The Investigations In This Concept discusses grade-level content. For example, Concept 9.1 includes the following: "Through The Investigations In This Concept, students learn how to represent situations with two variables using a system of equations (8.EE.8). Students explore methods for solving a system of equations algebraically (through substitution and elimination), graphically, and by inspection (8.EE.8c). Students develop an understanding that a system of equations can have one solution, infinite solutions, or no solution, and they can understand the meaning of the solution in context (8.EE.8a)."
  • During Subsequent Instruction describes how the grade-level content relates to content later in the current grade-level and future grade-levels. For example, Concept 1.2 includes the following: "During Subsequent Instruction, students will apply the properties of exponents when using scientific notation and solving rational and radical equations (8.EE.4, A-REI.2). Students will extend the properties of integer exponents to ... leading to logarithmic functions (N-RN.1,2). They will recognize and graph exponential and logarithmic functions (A-REI.11) and use the properties of exponents to transform expressions for exponential functions (A-SSE.3c)."

The instructional materials give all students extensive work with grade-level problems. Each Concept has three sections- Discover, Practice, and Apply- which contain grade-level problems. The following are included in the three sections:

  • In the Discover section, there are at least two Investigations that enable all students to work with grade-level problems. There are Extension Lessons that take grade-level work and enhance it by utilizing new contexts or different tools. For example the Unit 4 Concept 4.2 Extension has students extending their grade-level standards into working with a Dynamic Geometry Tool to create triangles and observe what happens under given restraints. There is Additional Assistance in the Summary, and in the Additional Assistance, there are math explanations, extra videos, and blackline masters that provide more instruction for students who need it. For example, the Unit 8 Concept 8.2 Summary has definitions to assist in solving linear equations, videos to deepen understanding, and View Math Explanations that are on grade-level and offer extra practice.
  • In the Practice section, there are the Coach and Play sections, and each of these include grade-level problems. The Coach section offers grade-level work that gives students guided practice and hints when needed. For example, the Unit 10 Concept 10.3 Practice Coach has ten grade-level questions with supports and feedback available as students work through creating and analyzing two-way tables.
  • In the Apply section, there are two or three grade-level problems that offer real-world contexts in which students apply the content that has been learned in the current Concept. For example, Concept 6.2 has the following two problems in the Apply section: How Are Parallel Lines and Transversals Used in Stage Sets, which has students identify and explain the relationships between angles created when parallel lines are cut by a transversal in a real-world context, and How Do Intersecting Lines Make Such Beautiful Designs, which offers students opportunities to explore lines and angle relationships in art and architecture.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings and problems and activities that serve to connect two or more clusters in a domain or two or more domains in the grade.

Examples of how the learning objectives are visibly shaped by the CCSSM cluster headings include:

  • In Concept 3.2 one objective is "describe a sequence of transformation(s) needed to generate a similar image from a given pre-image," which is shaped by the cluster heading for 8.G.A, "Understand congruence and similarity using physical models, transparencies, or geometry software."
  • In Concept 7.2 one objective is "represent and compare functions in multiple ways," which is shaped by the cluster heading for 8.F.A, "Define, evaluate, and compare functions."
  • In Concept 9.1, one objective is "match a system of linear equations with one solution, no solution, and infinite solutions to graphs and to real-world contexts," which is shaped by the cluster heading for 8.EE.C, "Analyze and solve linear equations and pairs of simultaneous linear equations."

Examples of problems and activities that serve to connect two or more clusters in a domain or two or more domains in the grade include:

  • Unit 4 Concept 4.1 connects 8.EE.A with 8.G.B as students solve equations of the type x^2 = p while investigating and solving problems with the Pythagorean Theorem.
  • Unit 7, Concept 7.1 connects 8.EE.B with 8.F.A as students graph proportional relationships, explain the slope of a graph using similar triangles, and interpret the equation y = mx + b as defining a linear function.
  • Unit 7, Concept 7.2 connects 8.F.A with 8.F.B as students explore characteristics of functions, determine when a table of values displays a linear relationship, and construct a function that models a linear relationship between two quantities.
  • Unit 8, Concept 8.1 connects 8.EE.C with 8.F.B as students solve linear equations and analyze graphs to describe functional relationships.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for rigor and mathematical practices. The materials meet the expectations for rigor as they balance and help students develop conceptual understanding and procedural skill and fluency. The materials meet the expectations for mathematical practices as they attend to the full meaning of each of the MPs and support the Standards' emphasis on mathematical reasoning.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
+
-
Criterion Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance in all three aspects of rigor.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Multiple opportunities exist for students to work with standards that specifically call for conceptual understanding and include the use of visual representations, interactive examples, and different strategies.

Cluster 8.EE.B explores the connections between proportional relationships, lines, and linear equations to build conceptual understanding.

  • In Concept 7.1 students work with proportional relationships that are represented by tables, graphs, equations, and verbal descriptions (8.EE.5). Through these multiple representations, students develop their understanding of the connections between proportional relationships, lines, and linear equations. Concept 7.1 also includes investigations that offer students the opportunity to make connections between similar triangles, constant of proportionality, rate of change, and slope. Students develop their understanding of these connections through discussions with their classmates and by completing multiple hands-on activities (8.EE.6).
  • In Concept 7.3 students continue to develop their understanding of the connections between proportional relationships, lines, and linear equations as they work with non-proportional relationships that include a constant rate of change and are represented by equations, graphs, tables, and verbal descriptions (8.EE.5). Students complete investigations that help them make the connections between the different representations, and they also work with situations that result in graphs of horizontal and vertical lines. As they work with the various representations, students are asked to create new ones both manually and with technology.

Standard 8.F.1 develops understanding that a function is a rule that assigns to each input exactly one output. Opportunities to develop key mathematical concepts of functions are found in the following examples:

  • In Concept 7.2 students begin to understand functions by examining situations represented with tables of data to see if they can write a rule that uses one column of data as input and produces the corresponding values in the second column of data as output. At this time, students are also presented with tables of data for which a consistent rule cannot be written. As the Concept progresses, understanding of a function as a rule that assigns exactly one output to each input is further developed as students investigate functions represented by graphs and equations, and this Concept concludes by having students match three different representations of a function (verbal, graphical, and tabular) together (8.F.1).
  • In Concept 7.4 the understanding of a function is expanded as students are presented with non-linear functions represented by tables, graphs, and verbal descriptions (8.F.3).

Cluster 8.G.A builds over several Concepts an understanding of congruence and similarity through different representations and tools.

  • In Concept 3.1 students have opportunities to verify the properties of rotations, reflections, and translations as they transform real-world figures, such as stop signs, and geometric figures, such as triangles and line segments, with and without coordinates. They perform these transformations with different tools, such as transparencies and a dynamic Geometry tool.
  • In Concept 3.2 students continue to use various tools both on and off a coordinate plane as they develop understanding of congruence by experimenting with different combinations of rigid transformations. Students either create a new figure given an initial figure and a sequence of rigid transformations or create a sequence of rigid transformations that maps a preimage onto its image.
  • In Concept 3.3 the materials include dilations as a possible transformation, and students get the opportunity to develop their understanding of similarity using similar tools and activities used when developing congruence in Concept 3.2.
  • In Concept 6.1 students use transformations, along with manual and virtual tools, to develop an understanding of the relationships between interior and exterior angles within a triangle.
  • In Concept 6.2 students use transformations and different tools to understand relationships between pairs of angles that are formed when parallel lines are intersected by a transversal, and students also examine relationships between pairs of angles that are formed when lines that are not parallel are intersected by a transversal.
  • In Concept 6.2 students develop an understanding of the angle-angle criterion for similarity of triangles using their understanding of angle pairs formed by parallel lines and a transversal along with the relationship of interior and exterior angles within a triangle.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, the Practice section is designed to give students opportunities to develop procedural skills and fluency in each Concept, and the Practice section has Coach and Play sections that allow the students to choose in which they want to work. The Coach section provides ten guided practice questions, and the Play section is independent practice with at least 15 questions.

Standard 8.EE.7 addresses solving linear equations in one variable.

  • In Concept 8.2 Practice, the Coach and Play sections present students with opportunities to solve linear equations in one variable. The Coach section offers scaffolded feedback to students if they incorrectly answer a question for two incorrect answers, and on the third incorrect answer, the feedback shows students how to solve the equations. The Play section allows students to earn rewards for correctly answering questions that involve solving linear equations in one variable.

Standard 8.G.9 addresses using formulas for the volume of cylinders, cones, and spheres.

  • In Concept 11.1 students explore the formulas for the volumes of cylinders, cones, and spheres. Students develop procedural skills with them by completing numerous problems where they are asked to find the volume of objects with given dimensions or find a missing dimension given the volume and other dimensions.
  • In Concept 11.1 Extension students are provided with more opportunities to develop procedural skill with the formulas for volumes of special shapes that are either composed of cylinders, cones and spheres or created by modifying a cone.
  • In Concept 11.1 Apply students continue to use the three formulas as they use them to solve real-world problems involving the volumes of cylinders, cones, and spheres.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for teachers and students spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade. The materials have Extension and Apply questions with each Concept, and many of these allow students the opportunity to apply procedural skills and understandings in non-routine ways or within unique contexts. The Introduction section for most Concepts establishes real-world contexts in which students apply the skills and understandings of the Concept.

Cluster 8.F.B addresses students using functions to model relationships between quantities.

  • In Concept 7.3 Apply 1 students choose a country and research the country’s average monthly temperatures over a six-month period. Students create two separate tables of data to help them determine if Celsius is a function of Fahrenheit, Fahrenheit is a function of Celsius, both tables represent functions, or neither table represents a function. Students create graphs for the tables of data and write equations to model the data in each of the graphs.
  • In Concept 7.3 Apply 2 students use functions to determine which package would be the best choice when throwing a party for 8 guests and themselves.
  • In Concept 8.1 Apply 1 students use functions to model the relationship between the length of the humerus bone and either a male’s or female’s height, and they also test the functions created against their own measurements and the measurements of three classmates.

Standard 8.EE.8c addresses students solving real-world and mathematical problems leading to two linear equations in two variables.

  • In Concept 9.1 Extension students solve a real-world problem that leads to three equations in three unknowns. Students are presented with a scenario where a person invests three different amounts of money in three different types of accounts, and the students determine how much money was invested by the person in each account.
  • In Concept 9.1 Apply 1 students use a system of two equations with two unknowns to answer various questions about flight plans that include finding the speed of the wind, the length of the flight in miles, and the length of the flight in minutes. In Apply 2 students use a system of two equations with two unknowns to determine which of two pets would be cheaper to own.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for balance. Overall, the three aspects of rigor are not always treated together and are not always treated separately.

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.
  • 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. For example, Concept 5.2 includes the following:

  • Conceptual understanding includes “discover and understand the rules and methods for adding and subtracting numbers in scientific notation”, “discover and understand the rules and methods for multiplying and dividing numbers in scientific notation”, and “discover and understand how the properties of exponents can make operations with scientific notation more quick and efficient”;
  • Fluency includes “add and subtract numbers in scientific notation with both like and unlike degrees with precision and efficiency”, “multiply and divide numbers in scientific notation with precision and efficiency”, and “rewrite the sum, difference, product, or quotient in scientific notation”; and
  • Application includes “apply the rules for performing operations with scientific notation to solve a variety of real-world problems.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
10/10
+
-
Criterion Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for practice–content connections. The materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialized language of mathematics. Overall, the materials attend to the full meaning of each MP.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for identifying and using the Standards for Mathematical Practice (MPs) to enrich the mathematics content within and throughout the grade. Overall, the MPs are identified in different places throughout the materials, and the MPs enrich the content as students make sense of problems, reason about the mathematics, and use different models and tools to complete the problems.

The MPs that are a focus for each Unit are identified under each Concept on a tab marked Progressions and Standards, and the MPs that are a focus for each Session appear on the session tab in a part labeled Standards for Mathematical Practice. For example, in Unit 3 MPs 3, 5, and 7 are identified as the focus MPs on the Progressions and Standards tab in Concepts 3.1, 3.2, and 3.3. In Concept 3.3 there are four sessions, and the following MPs are addressed in each of the four sessions respectively: MPs 3, 5, and 8 (Sessions 1 and 2); MPs 3 and 5; and MPs 3, 5, and 7.

Some examples of how the MPs are used to enrich the mathematics content include:

  • MPs 1 and 2: In Concept 10.1 Investigation 1 students make sense of a problem to determine if there is any relationship between their height and the length of their hand span. Students determine that they need to create a scatter plot of the data for the students in their class, and they persevere in solving the problem by collecting the data, graphing it, and analyzing it to see if they can identify the existence of a relationship. Students engage in reasoning abstractly and quantitatively as they consider what labels, ranges, and scales to use for each axis in the scatter plot.
  • MP4: In Concept 7.4 Apply 4 students research gravity on the moon, cite evidence that explains any data, graph the data, discuss their findings, compare and contrast linear and nonlinear functions, identify rates of change and y-intercepts, and explain if they would rather play baseball on Earth or the moon and justify their answer with the information that has been gathered.
  • MP5: In Concept 3.2 Investigation 5 students are presented with pairs of congruent figures to determine a rigid transformation or sequence of rigid transformations that maps one image onto the other. To complete this Investigation, the materials include a dynamic geometry tool, but students still get to engage with using appropriate tools strategically as they have to determine which rigid transformations to use within the dynamic tool in order to map one image onto the other.
  • MP7: In Concept 5.1 Investigation 1 students look for and make use of structure as they identify compact ways to write large numbers using scientific notation.
  • MP8: In Concept 1.1 Investigations 1 through 4, students look for and express regularity in repeated reasoning as they develop and use rules for simplifying expressions with integer exponents based on completing various hands-on and virtual activities.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials, as a whole, address the full meaning of each of the Standards for Mathematical Practice (MPs).

Some examples of where the materials attend to the full meaning of the MPs include:

  • MP1: In Concept 4.3 Investigation 4 students make sense of a problem as they try to determine if two planes are within one nautical mile of each other on radar, realizing that they can use the Pythagorean theorem to determine the distance between the planes. Students first analyze the paths of the planes two-dimensionally, and they persevere in solving the problem as they have to complete their analysis in three-dimensional space after correctly completing it in two-dimensional space.
  • MP2: In Concept 9.1 Investigation 2 students reason abstractly and quantitatively as they answer questions about different race scenarios. The students reason abstractly as they create different mathematical representations of the race scenarios in order to perform various computations, and they reason quantitatively as they re-contextualize what they see in the abstract representations in order to determine the outcomes of the race scenarios and how those outcomes unfolded.
  • MPs 4 and 5: In Concept 7.1 Investigation 4 students model with mathematics as they try to put together a triathlon team that can break the world record. Students use data for different athletes swimming, biking, and running times- represented in various ways- and examine many different combinations of athletes to determine which combination is the fastest. As students examine the times of the athletes, they can choose to represent data from the athletes with an equation, table, or graph, and they can choose to create these representations manually or with technology.
  • MPs 7 and 8: In Concept 2.2 Investigation 1 students look for and make use of structure while completing Using a Spreadsheet as they examine the prime factorizations of the denominators of fractions to determine whether or not the fraction has a decimal expansion that terminates or repeats. In the same Investigation while completing Converting Fractions to Decimals, students look for and express regularity in repeated reasoning as they create the decimal expansions for two sets of fractions and compare the sets of fractions based on the decimal expansions created using the standard algorithm for division.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for prompting students to construct viable arguments and analyze the arguments of others. Overall, the materials provide multiple opportunities for students to explain their reasoning and to conduct error analysis of work.

Some examples of students being prompted to construct viable arguments and/or analyze the arguments of others include:

  • In Concept 1.1 Investigation 6 students analyze the work of a fictitious student for possible errors because two different expressions simplify to the same value. Students determine which expressions are correct and explain their reasoning.
  • In Concept 4.3 Investigation 1 students construct an argument as they estimate the distance between two locations on a grid. They also assess their own estimate by analyzing the reasoning and estimate of a fictitious student.
  • In Concept 6.1 Introduction students discuss their conjectures about relationships among angles with another student. Through the discussions, students are expected to refine their original conjectures based on the critiques given to them by others.
  • Unit 6 Assessment Problem 12 asks students to use their knowledge of rigid transformations to justify their answers in one part of the problem. Then, they explain a relationship among the measures of the three angles of a triangle.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, teachers are given questions to ask during the Investigations that assist students in constructing viable arguments and analyzing the arguments of others.

The following are some examples of the materials assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others:

  • The Concept 1.1 Investigation 3 Instructional Notes state, "Have students work in small groups to make a conjecture for this activity. Students should explain their conjecture using examples to their group members. Group members are asked to challenge any conjectures and/or examples that they believe are incorrect or only partially correct."
  • In Concept 3.1 Introduction students determine if the conclusions of two fictitious students are correct or incorrect. The Instructional Notes and the Teacher Note for the Introduction both alert teachers that this activity is a place where teachers can assist students in constructing viable arguments and analyzing the arguments of others.
  • In Concept 6.2 Investigation 1 the Teacher Note guides teachers to "facilitate a discussion about the relationships between the different pairs of angles in the diagram and help students come to the conclusion that every pair is either congruent or supplementary." The Teacher Note includes the following questions to assist teachers in facilitating the discussion: “How many angles are formed by a transversal intersecting a pair of parallel lines, and how could you describe the angles formed when the transversal is perpendicular to the parallel lines?”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The materials reviewed for Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for attending to the specialized language of mathematics. Overall, the specialized language of mathematics is appropriately introduced and reinforced throughout the materials.

Some examples of attending to the specialized language of mathematics include:

  • In Concept 1.1 Session 1 Introduction the Instructional Notes state that teachers should "model precise mathematical language and then ask students to explain their thinking in a similar way." In the Concept 1.1 Investigation 4 Instructional Notes, teachers are reminded "as students engage in these example problems, continue to review the vocabulary associated with the expressions (expansion or expanded form, exponential form, standard form)."
  • The Concept 2.1 Session 3 Instructional Notes state that "after students complete Another Number Riddle, have them discuss their results with a partner. Listen to student responses as they justify their answers and provide ideas to help refine their mathematical communication."
  • The Concept 3.1 Session 4 Instructional Notes state, "you may want to have students make a table in their notes, such as the one below, to help them remember the vocabulary introduced in this concept." The column headings for the table given in the Instructional Notes are "Vocabulary Term," "Formal Definition," "Description in Your Own Words," and "Example Image."

The following are some examples of how the specialized language of mathematics is regularly addressed throughout the materials.

  • The vocabulary terms for each unit are given in the Teacher Preparation for each Concept, and new vocabulary terms are often italicized or mentioned in a sentence.
  • There is an Interactive Glossary that provides students with the definition of a word, an animation, and a video that uses the word in a real-world context. The glossary can be searched alphabetically or by Concept, and during lessons, students could be asked to refer to the Interactive Glossary for assistance with the vocabulary.
  • When there is a new vocabulary term, it is regularly used throughout the remainder of the unit to reinforce comprehension.
  • In Common Misconceptions, the materials will state that "Students may have difficulty with the vocabulary" when appropriate.

Gateway Three

Usability

Partially Meets Expectations

Criterion 3a - 3e

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

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for use and design. Materials are well-designed, and lessons are intentionally sequenced. Students learn new mathematics in the Apply section of each Concept as they apply the mathematics and work toward mastery. Students produce a variety of types of answers including both verbal and written answers. The Discover sections introduces the mathematical concepts, and the Practice highlights connections within and between the concepts of the Concept. Manipulatives are used throughout the instructional materials as mathematical representations and to build conceptual understanding.

Indicator 3a

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. It is clear when the students are solving problems to learn, and when they are applying their skills to build mastery.

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

Indicator 3b

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for not being haphazard with exercises given in intentional sequences.

The sequencing of Units, and Concepts within the Units, develops in a way that helps to build students’ mathematical foundations.

  • The Units are comprised of related content. For example, Unit 7, Introduction to Functions, includes Concept 7.1, Represent Proportional Relationships; Concept 7.2, Investigate Properties of Functions; Concept 7.3, Understand Linear Functions; and Concept 7.4, Graph, Describe and Analyze Functions.
  • Within each Concept, Session development is sequential. Each Concept has numbered Sessions that include Investigations. The Investigations include different activities that build upon each other and help students develop understanding of the mathematical concepts being addressed.
  • After working through the Investigations, the student has Practice (Coach and Play) and Apply sections that help students continue to sequentially build their understanding of the mathematical topics addressed in the Concept. Each Concept ends with the Apply section allowing students to consolidate and apply their new learning with a real-world problem.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for having variety in what students are asked to produce.

Throughout the materials, students are asked to produce answers and solutions as well as to justify their answers and solutions, discuss ideas, make conjectures, make sketches and diagrams, and connect mathematical topics to the real world. Students are often asked to show all of their work, which includes drawing visual representations in the form of figures, tables, graphs, writing equations, and explaining steps and reasoning. At times, this work is presented using technologically-enhanced tools. The Model Lesson notes for teachers describe instructional strategies that ensure students produce this variety of work to demonstrate their learning.

Indicator 3d

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives.

Virtual manipulatives and tools are embedded throughout the series. Some are available on every page of the techbook and include calculators,a dynamic geometry tool, construction tool, unit convertor tool, data analysis tool, and whiteboard tool. Number tiles and Algebra tiles are the primary physical manipulatives used, and there are blackline masters of these that can be copied and used during the Investigations. Each Concept has a Teacher Preparation section that lists the materials needed for all of the Sessions in the Concept. Manipulatives accurately represent the related mathematics; for example, in Unit 4 Concept 4.1 students use triangles to determine the relationship between the lengths of the sides.

Indicator 3e

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

The visual design is not distracting or chaotic in Discovery Education Math Techbook Grade 8 Mathematics and supports students in engaging thoughtfully with the subject. The digital Techbook materials keep a consistent layout for their Units, Concepts, and Investigations.

The student materials are written at grade-level and have numerous videos and real-world pictures that are aligned to the mathematics being taught in the Concepts.

For the students, the Discover, Practice, and Apply sections are clearly labeled, and each section includes clear links to the pieces that are embedded in them making it easy for students to maneuver through the materials. Concepts and Investigations have a consistent numbering system which helps students to know where they are in the materials and what should come next. At the end of each Concept, there is at least one Apply problem that supports students in engaging thoughtfully with the mathematical content in a real-world setting.

Criterion 3f - 3l

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

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics meet expectations to support teachers’ learning and understanding of the standards; however, they do not attend to learning at an adult level. The instructional materials provide Essential Questions that support teachers in delivering quality instruction. The teacher’s edition is easy to use and consistently organized and annotated. The teacher’s edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.

Indicator 3f

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each Concept offers essential questions to guide the teacher and students through the Concept., An example of an essential question is, "How do you represent functions in mathematics?" from Concept 7.2. In addition, with the teacher view enabled as teachers progress through the Investigations blue boxes with quality questions, and their connections to the MPs, are included. The blue boxes are provided with the part of the Investigation to which they apply. This design supports teachers in both planning and implementing an effective lesson.

Indicator 3g

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for containing 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. Also, where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The Concepts have an Objectives tab with Lesson Objectives, Essential Questions, and Enduring Understandings. Also, there is a Progressions and Standards tab that includes Reach Back Standards, Standards Covered, and Reach Ahead Standards, Standards for Mathematical Practice, During previous instruction, Through the investigations, During subsequent instruction, and a graphic that shows what Conceptual Understanding, Procedural Fluency, and Application will take place in the concept. Finally, there is a Teacher Preparation tab that includes a Materials List, Common Misconceptions, and Key Vocabulary.

The Model Lesson section of the materials includes in-depth instructional notes and suggestions for both presenting and discussing the mathematical content of each Investigation, as well as how to use the technology-enhanced items and manipulatives embedded in the materials. For example, in Concept 3.1 Investigation 2 the Instructional Notes remind teachers to, “Direct students to Part I of the section titled Transforming a Line Segment. Have them open the Dynamic Geometry Tool. Because this may be the first time many students have worked with this tool, give them a few minutes to explore how it works. When you are ready for the class to continue, students can click the Reset button within the tool to clear any marks they have made.”

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectation for the teacher’s edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

Instructional notes in the Model Lesson section of the techbook provide teachers with in-depth guidance on how to present the information in the Investigations to assist students in a full understanding of the standards developed. The notes include detailed explanations of the essential and enduring understandings from the standards and any student misconceptions that may emerge. There is also a Professional Learning section within the materials, but neither the Instructional Notes nor Professional Learning section explain or give examples that a teacher could use to improve their content knowledge of the grade-level standards or of advanced mathematics concepts that are connected to future grades or courses. Solutions to problems are provided for teachers, but these solutions do not always have explanations as to why an answer would be acceptable or alternate ways to solve the problem that would give support to teachers’ own understanding.

At the end of each Concept, there is a Summary, and it includes a summary of the essential understandings in the Concept and a link to Additional Assistance. The Additional Assistance provides video explanations and tutorials of the related mathematics. The Summary and Additional Assistance are available to both teachers and students, but these are not designed specifically to assist teachers in further developing their own understanding of the grade-level standards or of advanced mathematics concepts that are connected to in future grades or courses.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

The Model Lesson section of each Concept contains a tab titled Progressions and Standards that connects to standards from previous grade-levels and discusses standards that will be connected to in future grades. For example, Unit 10, Concept 10.2 makes connections to standards from 6th grade (6.RP.3a and 6.EE.9) through the 8th grade (8.SP.2,3) and to standards in Grades 9-12(S-ID.3,6a,7). The Progressions and Standards section also includes, in paragraph form, sections that give more information on the listed connections. These sections are During Previous Instruction, which describes how prior standards connect to current standards, and During Subsequent Instruction, which describes how current standards will connect to future standards.

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics provide a list of Concepts in the teacher’s edition that cross-references the standards addressed and provides an estimated instructional time for each Unit and Session.

In the Table of Contents for each course, there is a drop-down menu for each Concept that shows which standards a Concept addresses, and there is a separate section entitled CC Standards which allows users to select a standard in order to see which Concepts address it. The standards aligned to each Concept can also be found in Progression and Standards of the Model Lesson section and the Course Overview PDF provided with the materials. The alignment to standards for each Unit is available in the Unit Overview, but there is no documentation that aligns individual Investigations to standards.

There is a Scope and Sequence document that provides an approximate number of instructional periods for each Unit, and in this document, an instructional period is defined to be approximately 50 minutes. There is no specific documentation provided that states an approximate number of instructional periods for each Concept, but within the Sessions of each Concept, specific times are given in minutes in the Model Lesson section for the Intro, Investigations, and Extension that are parts of the Concept.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. 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 logging into the Math Techbook together and 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics contain explanations of the program's instructional approaches and identification of the research-based strategies.

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

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

Criterion 3m - 3q

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

The instructional materials for Discovery Education Math Techbook Grade 8 Mathematics partially meet expectations for providing teachers resources and tools to collect ongoing data about student progress. There are no assessments that purposely identify prior knowledge within and across grade levels. The Teacher Preparation section identifies common misconceptions and errors, but there are no specific strategies strategies to address these when they arise. Opportunities for ongoing review, practice, and feedback occur in various forms. Standards are identified that align to the Concept; however, there is no mapping of Standards to items. Students have opportunities to monitor their own progress.

Indicator 3m

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

In Progressions and Standards for each Concept, the materials provide teachers with Reach Back Standards from prior grade levels/courses to which the standards of the current Concept connect. The activities found within the Intro at the beginning of each Concept are designed to activate prior knowledge that students would have of the Reach Back Standards. Although the identification of the Reach Back Standards and their inclusion in the 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 strategies for teachers to identify and address common student errors and misconceptions.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions. Within each Concept in the the Teacher Preparation section, there is a bulleted list of common misconceptions about the mathematical material being taught in that Concept. During the lesson itself, there are no specific strategies provided for teachers to identify and address those common student errors and misconceptions.

Indicator 3o

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials include a Coach and Play section in each Concept that provides 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 formative and summative assessments:
0/0

Indicator 3p.i

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectation for assessments clearly denoting which standards are being emphasized.

The materials clearly denote which assessments are intended to be formative and which are intended to be summative. The summative Unit assessments are located on the Unit-level page, and there is a tab for accessing the Unit Assessment. The formative assessments are located at the Concept level and are included in each Investigation as a Check for Understanding. The questions on the summative and formative assessments are not clearly denoted as assessing a particular standard. Each Unit has a set of standards being addressed, and each Concept has a set of standards addressed. However, the assessment questions themselves are not aligned to standards making it difficult to determine which standards are being emphasized by the assessments.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectation for assessments including aligned rubrics and scoring guidelines that 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, and the criteria are based on a 0, 1, or 2 point scale that shows the specific 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics offer opportunities for students to monitor their own progress.

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

The students also have a dashboard on their Math Techbook home screen that gives them the opportunity to keep track of their answers to questions and points given to responses throughout the Discover, Practice, and Apply cycle. 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.
8/12
+
-
Criterion Rating Details

The instructional materials for Discovery Educations Math Techbook Grade 8 Mathematics partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. Activities provide student with multiple entry points and a variety of solution strategies and representations. However, the materials provide few strategies for ELL, special populations, or to challenge advanced students to deepen their understanding of the mathematics. Grouping strategies are designed to ensure roles for each group member.

Indicator 3r

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Each Concept’s Discovery, Practice, and Apply sections are broken up into Sessions in which activities are sequenced for the teacher. Included in all Sessions are Instructional Notes that provide teachers with key math concepts to develop, sample questions to ask, ways in which 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics partially meet the expectation for providing 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 needing enrichment, 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 Discovery Education Math Techbook Grade 8 Mathematics 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.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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 opportunities for advanced students to investigate mathematics content at greater depth.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. The activities are diverse, meeting the interests of a demographically, diverse student population. The names, situations, videos, and 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics provide opportunities for teachers to use a variety of grouping strategies. Instructional Notes for the Sessions provide teachers with suggestions regarding groupings for each activity; suggestions are made whether work should be done individually, in pairs, or in small groups. For example, the Concept 2.1 Sessions 1 and 2 Instructional Notes state, “In the next part of this Session, direct students’ attention to the Cell Phone Calculator image. Have students work in pairs or small groups to answer the on-screen questions.”

Indicator 3y

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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 be edited to meet a teacher’s needs. Letters are provided in English and Spanish. The letter informs a parent of the content their child will be learning and ways in which they may help their child.

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 for Discovery Education Math Techbook Grade 8 Mathematics support effective use of technology to enhance student learning. The materials are web-based and platform neutral. The materials embed technology enhanced, interactive virtual tools, and dynamic software that engages students with the mathematics. Opportunities to assess students through technology are embedded. The technology provides opportunities to personalize instruction; however, these are limited to the assignment of problems and exercises and cannot be customized for local use. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.

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 Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics are web-based and compatible with multiple internet browsers. In addition, the materials are “platform neutral” and allow the use of tablets and mobile devices. The materials are 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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 to students to complete electronically. Teachers are provided with technology-enhanced assessment items to build their own standards-based assessments. Each Concept contains Check for Understandings, Coach, and Play tabs are completed within the Techbook.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. 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 Discovery Education Math Techbook Grade 8 Mathematics 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 instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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 a concept out of order without missing important information.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 8 Mathematics 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 Board 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 Discovery Education Math Techbook Grade 8 Mathematics 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.

Additional Publication Details

Report Published Date: Thu May 04 00:00:00 UTC 2017

Report Edition: 2017

About Publishers Responses

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

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

Educator-Led Review Teams

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

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

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

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

X