Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 6 Discovery Education meet the expectations for alignment. 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

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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

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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

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Gateway One Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 Mathematics 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 Mathematics meet the expectation for assessing grade‐level content and, if applicable, content from earlier grades. The Unit Assessments included in the Teacher View were reviewed. Overall, there were no assessment questions addressing standards from above Grade 6.

Examples of grade-level assessment items include the following:

  • Unit 1 question #10- Students show their knowledge of 6.RP.3 by finding equivalent ratios on a double number line that express cable modem download speeds.
  • Unit 8 question #4- Students demonstrate their knowledge of 6.EE.7 by writing an equation that models a real-world problem and then explaining the meaning of each part of the equation.
  • Unit 12 question #10- Students demonstrate their knowledge of 6.G.1 by applying their understanding of area and decomposing shapes to solve a real-world application problem based on the flag of Kuwait.

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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 Mathematics meet 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 68 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 Mathematics meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 68 percent of the instructional time is spent on major work of 6th 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 7 complete units out of 13 units, which is approximately 54 percent, is spent on major work.
  • Sessions (excluding Extensions)– Approximately 79 sessions out of 109, which is approximately 72 percent, is spent on major work.
  • Time (excluding Extensions)– Approximately 4,240 minutes out of 6,250 minutes, which is approximately 68 percent, is spent on major work.

Criterion 1c - 1f

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

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 for 6.G.A, a supporting cluster, are integrated with major work of the grade for 6.EE.2 and 6.RP.3 are as follows:

  • In Concept 12.1 students have the opportunity to develop the formulas for the area of and to find the area of parallelograms and triangles, 6.G.1. This supporting work with area also integrates the major work of writing algebraic and numerical expressions, 6.EE.2a, and evaluating expressions for specific values of the variables, 6.EE.2c.
  • In Concept 13.1 students are given the opportunity to create nets for three-dimensional figures and use those nets to calculate the surface area of the figures represented by the nets. By calculating the surface area of the figures, this Concept also provides an opportunity to evaluate numerical and algebraic expressions. This Concept uses supporting work from 6.G.4 to enhance the major work of 6.EE.2c.
  • In Concept 13.2 students explore the effects of changing one or more dimensions of a three-dimensional figure on the volume of that figure. This supporting work of 6.G.2 enhances the major work of 6.RP.3d as students have to manipulate units appropriately as they multiply or divide quantities.

Some examples of how the Concepts for 6.NS.B, a supporting cluster, are integrated with major work of the grade for 6.RP.A and 6.EE.3 are as follows:

  • In the Intro to Concept 2.1 students are asked to determine to which food bank they should make a donation. To make the decision, students have to be able to divide multi-digit numbers, 6.NS.2; use their result to show understanding of unit rates, 6.RP.2; and solve a unit rate problem, 6.RP.3b.
  • In Investigation 4 of Concept 2.2 the materials have opportunities for students to write numerical expressions using the greatest common factor (GCF). Using the GCF connects to applying the properties of operations for generating equivalent expressions, and this Investigation integrates 6.NS.4 with 6.EE.3.

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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 125 50-minute class periods without Extension Lessons. Since there are thirteen Unit Assessments, the total number of days would increase to approximately 138 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 28 Practice and 28 Apply sections in the materials as each of the 28 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 166 50-minute class periods. Overall, with 166 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 7.2 includes the following: "During previous instruction, students learned how to solve multi-step real-world problems with whole numbers using the four operations, and write a number sentence/equation to represent the problem (4.OA.2, 4.OA.3). Grade 5 students worked more formally with expressions. They learned to express calculations written in words as numerical expressions and then evaluated and interpreted expressions (5.OA.2). They also learned to express and examine powers of 10 as whole number exponents and carry out order of operations, including expressions with parentheses, braces, and brackets (5.OA.1, 5.NBT.2). In the previous concept, students read and wrote algebraic expressions from math phrases and real-world contexts. They also learned some algebra vocabulary, such as term, coefficient, and variable in earlier concepts of this unit (6.EE.1, 6.EE.2a, 6.EE.2b, 6.EE.6)."
  • Through The Investigations In This Concept discusses grade-level content. For example, Concept 11.2 includes the following: "Through the investigations in this concept, students will explore measures of variability as they describe data sets. They will learn how to calculate range, interquartile range (IQR), and mean average deviation (MAD), which will assist them in describing the overall shape of the distribution (6.SP.3, 6.SP.5d.). They will use these values to summarize and identify patterns within data sets as they relate to their real-world contexts (6.SP.5, 6.SP.5c). Students extend this understanding of IQR and MAD as they choose which measure of center best describes a data set based on the shape of the data distribution and the context (6.SP.5d)."
  • 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 4.1 includes the following: "During subsequent instruction in this unit, students will discover percents as rates per 100 (6.RP.3c) and will also perform measurement conversions, viewing conversion factors as unit rates (6.RP.3d). ... In Grade 7, students will apply their knowledge of rates to determine unit rates derived from ratios of fractions (7.RP.1). ... In addition, they will apply unit rates to solve problems involving scale drawings (7.G.1)."

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 also Extension Lessons that take grade-level work and enhance it by utilizing new contexts or different tools. For example, the Unit 7 Concept 7.2 Extension 1 has students extend their grade-level work with evaluating expressions by using spreadsheets to evaluate an algebraic expression for any integer value. There is Additional Assistance in the Summary, with grade-level math explanations and extra videos that provide more instruction for students who need it, including blackline masters. For example, the Unit 9 Concept 9.1 Summary has definitions of dependent and independent variables, videos to deepen understanding, and blackline masters for 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 9 Concept 9.1 Practice Coach has ten grade-level questions with supports and feedback available as students work through the problems.
  • 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 8.2 has the following three problems in the Apply section that use inequalities to describe different ranges: Can you Keep Solids Solid and Gases Gaseous, describes the temperature ranges for the three states of different substances; Could You Be a Nutritionist, describes a child's nutritional needs; and How Much Medicine Should You Give This Dog, describes the weight ranges for dogs that correspond to different doses of medicines.

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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 3.1 one objective states that students should "see the relationship between multiplication and division to explain why the standard algorithm for fraction division works." This objective is shaped by the cluster heading for 6.NS.A, "Apply and extend previous understandings of multiplication and division to divide fractions by fractions."
  • In Concept 7.3 the objective is "identify and generate equivalent expressions using properties of operations," which is shaped by the cluster heading for 6.EE.A, "Apply and extend previous understandings of arithmetic to algebraic expressions."
  • In Concept 11.2 one objective is "select appropriate statistics to describe a data set, based on the shape of the distribution and other factors," which is shaped by the cluster heading for 6.SP.B, "Summarize and describe distributions."

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:

  • In Unit 2, the Investigations of Concept 2.1 connect 6.NS.B with 6.RP.A as students learn to divide multi-digit numbers using the standard algorithm and use that to solve unit rate problems.
  • In Unit 6, Concept 6.2 connects 6.G.A with 6.NS.C as students graph polygons in all four quadrants of the coordinate plane and use the graphs to solve problems. In one portion of Investigation 2, students are given sets of coordinate pairs and are asked to match each set of coordinate pairs to the name of a shape.
  • Unit 7 Concept 7.1 connects 6.EE.A with 6.EE.B as students learn to write numerical and algebraic expressions and use variables when solving a real-world or mathematical problem.
  • Unit 10 Concept 10.2 connects 6.SP.A with 6.SP.B as students learn to describe a single distribution by its center, shape, and spread and then to summarize and describe multiple distributions with both graphs and statistical measures.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials for Discovery Education Math Techbook Grade 6 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
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Criterion Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 6.RP.A addresses understanding ratio concepts and using ratio reasoning to solve problems.

  • In Concept 1.2 students begin to develop their understanding of ratio concepts and rate reasonings as they explore different representations of ratios and rates in the context of rabbits and weasels. Students represent ratios with tape diagrams, double number lines, and tables of values. Students also compare ratios using these different representations. (6.RP.1, 6.RP.3a)
  • In Concept 4.1 students continue to develop their understanding of rate reasoning as they identify the unit rate for a given context. Finding the unit rate is coupled with the different representations from Concept 1.2, and students work to solve problems using unit rate and the different representations. Students also discuss how scenarios can have more than one unit rate, and they compare unit rates. (6.RP.2, 6.RP.3b)
  • In Concept 4.2 students enrich their understanding of ratios and rates as they examine converting between units of measurement in contexts such as length, volume, and money. Students also add to their understanding by making complex conversions in order to determine if a person could outrun different animals. (6.RP.3d)
  • In Concept 4.3 students add to their understanding of ratios and rates as they use them to examine percentages and to solve problems finding the percent of a quantity or finding the whole, given a part and the percent. (6.RP.3c)

Cluster 6.NS.C addresses applying and extending previous understandings of numbers to the system of rational numbers.

  • In Concept 5.1 students begin to apply and extend their previous understandings of numbers to rational integers by learning how to plot negative integers on horizontal and vertical number lines. Through the number lines, students also begin to compare rational integers, and the students also begin to understand opposites as they explore an interactive applet that has them place objects on a tray in a position that is opposite of objects already on the tray. Positions on the tray are identified by rational integers along a horizontal number line. (6.NS.C.5)
  • In Concept 5.2 students expand their understandings from Concept 5.1 as they begin to work with all rational numbers and not just integers. Students continue to use horizontal and vertical number lines for the purposes of plotting, comparing, and ordering rational numbers. (6.NS.6c)
  • In Concept 5.3 students further develop their understanding of rational numbers as they build upon the idea of opposites to explore and compare absolute values, and they play an interactive game where they choose numbers for absolute value in order to throw boomerangs and defeat attacking skeletons. Students choose the absolute values based on the skeletons’ positions on a horizontal number line as the boomerang travels through those positions that have the chosen absolute value. (6.NS.6a, 6.NS.7)
  • In Unit 6 students are introduced to the coordinate plane with four quadrants so that they can explore and understand how rational numbers are used to locate points on a coordinate grid and how real-world objects, such as maps, can be identified when superimposed on a coordinate grid. Students also develop an understanding of how rational numbers on a coordinate grid can be used to calculate lengths, perimeters, and areas of geometric shapes whose vertices are identified by coordinate pairs of rational numbers. (6.NS.6b, 6.NS.8)

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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 how 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 6.NS.2 addresses students being able to fluently divide multi-digit numbers using the standard algorithm.

  • In Concept 2.1 students investigate the standard division algorithm with multi-digit numbers during the Discover section of the Concept. In the Coach section of Practice, there are problems that highlight students using division to solve a problem, and there are other problems that highlight students being asked to determine when division is needed to solve a problem.
  • In Concept 2.1 Extension students build procedural fluency in dividing multi-digit numbers using the standard algorithm as they examine division problems for patterns.

Standard 6.NS.3 addresses students being able to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

  • In Concept 3.2 Discover students develop fluency in adding, subtracting, multiplying, and dividing multi-digit decimals in the context of money, using the standard algorithms for each operation. Multiplying decimals is represented by an area model to help students connect and develop procedural skill with the standard algorithm for multiplying decimals and show how dividing by decimals can be related to dividing by whole numbers to help students develop procedural skill in using the standard algorithm for dividing decimals.
  • In Concept 3.2 Practice Coach students further develop their procedural skills with the standard algorithms for multiplying and dividing decimals. In the Coach and Play sections, students use the standard algorithm for adding, subtracting, multiplying, and dividing decimals in order to strengthen their fluency in these operations with multi-digit decimals.

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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 Introduction section for most concepts establishes real-world contexts in which students apply the skills and understandings of the Concept while Extension and Apply questions provide students with the opportunity to apply procedural skills and understandings in non-routine ways in unique contexts.

Standard 6.RP.3 addresses students using ratio and rate reasoning to solve real-world and mathematical problems.

  • In Concept 1.1 students begin to apply ratio and rate reasoning to solve problems as they are presented with videos and pictures of animals and asked to state different comparisons about the pictures. Students then compile survey data gathered from their classmates and write ratios that describe the responses from the survey. Then, students use ratios to design their own strand of lights for a light company.
  • In Concept 1.2 students use different representations of ratios- such as tape diagrams, double number lines, and tables- to solve non-routine or novel real-world problems, such as predators and their prey, animals living in a garden, and mixing paints to produce certain shades of colors.
  • In Unit 4 students apply their knowledge of rates to solve various real-world problems along with converting units of measurement and working with percents.

Standard 6.NS.1 addresses students solving word problems involving division of fractions by fractions.

  • In Concept 3.1 students use division of fractions by fractions to solve real-world problems in various contexts that include adjusting recipes for making food, using ribbon and string to create different objects, and distributing supplies for camping and hiking.

Standards 6.EE.7 and 6.EE.9 addresses students writing and solving linear equations in order to solve real-world and mathematical problems.

  • In Concept 8.1 students write and solve linear equations to solve problems that involve saving money from recycling, determining the number of wolves living in separate packs, determining the amount of money made by collecting rocks, studying volcanoes, and determining the profit made by selling fresh fish.
  • In Concept 9.1 students examine a situation that involves a county fair and roller coasters. Using the roller coasters, students explore the relationship between independent and dependent variables, and the exploration of the relationship leads to writing equations. Then, the story leads into using a problem involving popcorn and another involving the games at a fair to help students create tables and write equations.

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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 problems.
  • 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 6.2 includes the following:

  • Conceptual understanding includes “explain how absolute value can be used to calculate distances on a coordinate plane” and “explain how the coordinate plane relates to attributes of two-dimensional geometric figures.”
  • Fluency includes “use absolute value to find distance between points that lie on the same vertical or same horizontal plane” and “plot vertices of a geometric figure based on a description of attributes.”
  • Application includes “use absolute value of coordinates to determine distance between points on a horizontal line or on a vertical line to determine area and perimeter of rectangles for a real world context” and “use coordinates to describe and identify two-dimensional geometric figures for a real world context.”

Criterion 2e - 2g.iii

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

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 12 MPs 1, 4, and 6 are identified as the focus MPs on the Progressions and Standards tab in both Concepts 12.1 and 12.2. For Sessions 1 and 2 in Concept 12.2, MPs 1 and 3 are listed as being addressed during the sessions.

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

  • MPs 1 and 2: In Concept 8.2 students engage in writing and solving inequalities. MP1 is used to enrich the content across the three Investigations as students make sense of various contexts in order to translate them into an inequality with appropriate constraints. MP2 is used to enrich the content as students reason to represent the symbols of inequalities (abstract) on a number line diagram with units from the context (quantities).
  • MPs 4 and 5: In Concept 1.2 students engage in creating equivalent ratios. MP4 is used to enrich the mathematics content as students learn how to model ratios with tables, tape diagrams, double number lines, and graphs across the four Investigations of the Concept. MP5 enriches the content as students are asked which models they would use to solve different types of problems involving ratios in Investigation 4.
  • MP7: In Concept 6.2 Investigation 1 teachers are reminded that the investigation is a chance for students to use the structure of finding the distance between two points on a number line when trying to find the distance between two points that have the same x-coordinate or the same y-coordinate.
  • MP8: In Concept 3.1 Investigation 2 teachers are reminded to have students discuss how the fraction division they just completed compares to the fraction division students completed in Investigation 1. By looking for and using repeated reasoning across the investigations, the students use MP8 to strengthen their knowledge of dividing fractions.

Indicator 2f

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

The instructional materials reviewed for Discovery Education Math Techbook Grade 6 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 13.2 Apply 2 students are asked to redesign the packaging for a food product so that the new package holds the same amount of food as in the original package but uses less material. The students are also given three constraints for their new, redesigned package. In this problem, the students must first realize that holding the same amount of food refers to the volume of the new container and that using less material refers to the surface area of the package. Students then have to make sense of which dimensions are affected by the three constraints and how those constraints affect the dimensions. Once the students have made sense of the constraints, the students will have to persevere in finding a set of dimensions for their new package that meets all of the criteria given to them.
  • MP2: In Concept 5.1 Investigation 1 students engage with plotting integers on a number line and comparing integer quantities in the contexts of temperatures and climbing heights relative to a fixed position. Students reason quantitatively as they are asked to put different sets of values in order from least to greatest while considering the context. The students reason abstractly by comparing pairs of integers free from context and by graphing sets of integers on horizontal or vertical number lines.
  • MP 5: In Concept 11.2 Investigation 3 students are presented with different types of statistical plots, and they are asked to explain which measure of center and which measure of variability would best describe each plot. In addition to using specific measures of center and variability to strategically describe the plots, students also get to choose which tools they would use to help them calculate the measures of center and variability that they select.
  • MPs 7 and 8: In Concept 4.3 Investigation 1 students explore the relationship between fractions, decimals, and percents through an interactive that uses an area model. As students select regions of the area model to shade in, the interactive model produces a fraction, decimal, and percent for the shaded-in area. Students use the structure of the rectangular area model, which includes 10-by-10 grids, to see the correspondence between the area model and the equivalent fraction, decimal, and percent. By changing the shaded area in the area model and recognizing the repetition in the relationship between the fraction, decimal and percent, students express the regularities of how a decimal is changed to a percent and how a percent is changed to a decimal.

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
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Indicator Rating Details

The materials reviewed for Discovery Education Math Techbook Grade 6 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:

  • Unit 1 Assessment Problem 4 has students explain the difference between ratios and fractions and "describe how the process of making equivalent ratios is similar to the process of making equivalent fractions."
  • Unit 4 Assessment Problem 10 has students analyze the arguments of two people as they calculated different unit rates for a problem, and the students construct a viable argument as they explain how the different unit rates could both be correct.
  • In Concept 5.3 Session 3 students analyze the arguments of others that involve using absolute value to describe amounts of money owed to people, and the students use their analyses to construct a viable argument as to how the actual values of numbers compares to the absolute values of the numbers.
  • In Concept 10.2 Investigation 1 students analyze data so that they can critique the hypothesis of two children playing a game, and after collecting data of their own, students construct their own hypothesis about the game.
  • In Concept 12.2 Investigation 1 students construct an argument for how they found the area of a trapezoid, and they analyze the arguments of others because they are supposed to find a classmate that used a method different from them and compare the strategies that each student used.

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
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Indicator Rating Details

The materials reviewed for Discovery Education Math Techbook Grade 6 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 examples illustrate how the materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others:

  • In Concept 3.2 Session 1 students are asked to complete a problem during Investigation 1 entitled "Multiplying Money," and they are supposed to justify their answer to the multiple-choice problem. In the Instructional Notes for the Investigation, the teacher is given the following questions to ask students: “Why can’t choice A be correct?; What do you think the student who wrote choice B did wrong and why is this a common error?; What do you think the student who wrote choice D did wrong, and why is this a common error?” Each of these questions prompts students to analyze the argument on which each of the incorrect choices is based.
  • In Concept 4.2 Session 2 Investigation 1 students complete "Find the Height in Yards," a problem that utilizes many different methods and models. The students explain how they solved the problem, and in the Instructional Notes for the Session, the teacher is given the following instruction, "After students complete each problem, have them discuss their solutions with a partner or in a class discussion, justifying their own work and critiquing that of fellow students.” This additional information for the teacher assists them in helping to engage the students in constructing a viable argument and analyzing the arguments of others.
  • In Concept 11.1 Session 2 Investigation 1 students complete a task called "Analyze Methods" for finding the mean of a set of data. In the Instructional Notes for the Investigation, the teacher is given the following questions to ask students: “How are Christina’s and Davis’ strategies similar, and how are they different?; What steps did Davis use to find the mean?; How are the numerical expressions that model Davis’ strategy connected to the strategy that Group 3 used, and would this strategy work for any other groups?” Each of these questions prompts students to analyze the argument of another person.

Indicator 2g.iii

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

The materials reviewed for Discovery Education Math Techbook Grade 6 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 5.2 Session 1 students are asked to "define what a rational number is with a partner, and then compare it to the definition in the glossary. Students will most likely be surprised that the definition includes the fact that all rational numbers can be written as fractions (when the denominator is not zero)."
  • Concept 7.1 Investigation 1 states, "Have students complete Analyze. ... As a class, develop a definition of an algebraic expression and compare it to the glossary definition. Ask: How can you define an equation in terms of expressions? (An equation is made up of expressions that are equal to each other.)" In the next part of the Investigation, students work with a partner to determine the characteristics of a term in an expression, when terms are like each other, and when terms are not like each other.

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 may be referred 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 the 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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 10, Data Distributions, includes Concept 10.1, Collect and Represent Data, and Concept 10.2, Describe and Compare Data.
  • 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 at this level, 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 13 Concept 13.1 students use actual rectangular boxes to help them determine how much material is needed to make food containers in the shape of rectangular prisms.

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
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Indicator Rating Details

The visual design is not distracting or chaotic in Discovery Education Math Techbook Grade 6 and supports students in engaging thoughtfully with the content. 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 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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 for Concept 12.1 is, "How can you calculate the areas of trapezoids and other polygons?" 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 instructional reminders in this view are provided in a timely manner with the part of the Investigation to which it applies. This design supports teachers in both planning and implementing an effective lesson.

Indicator 3g

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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. The Progressions and Standards tab 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 1.2 Investigation 3 the Instructional Notes remind teachers to, “Direct students’ attention to the Snail Garden Interactive. The on-screen text will set up the scenario and direct students to look for patterns as they explore the garden. In the first tab, students will use a variety of animals to measure a rectangular garden. Each time they measure the garden, recording the length and the width, they will need to show it as a ratio. In the second tab, students will graph the data from the table using the length and width measurements as ordered pairs.”

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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 in Investigations. 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 in 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 2 Concept 2.2 makes connections to standards from 3rd grade (3.OA.5) through the 5th grade (5.NBT.6 and 5.OA.2) and to standards in 7th Grade(7.RP.1 and 7.EE.1,2). 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics provide a list of Concepts with 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.

The publisher does provide 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 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. There are limited opportunities for students to monitor their own progress.

Indicator 3m

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 Intro activities could provide teachers a way to indirectly assess students’ prior knowledge, the materials do not supply specific or direct strategies for assessing students’ prior knowledge.

Indicator 3n

Materials provide strategies 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 Discovery Education Math Techbook Grade 6 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, though, there is 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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. Also, 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 Discovery Education Math Techbook Grade 6 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
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Criterion Rating Details

The instructional materials for Discovery Educations Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics do not meet the expectation that the materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. Neither the teacher notes nor the tasks directly address support for students with a disability, students from different cultural backgrounds, or English Language Learners. A text-to-speech tool, however, is available and could be used for ELL students, and parent letters included with each unit are available in Spanish.

Indicator 3v

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

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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, in the Instructional Notes for Concept 11.2 Session 3 teachers are told, “Ask students to work in pairs as they view the dot plot, Distances, and discuss the arrows and distances. Reconvene the class, and ask the following questions.”

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 Discovery Education Math Techbook Grade 6 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 student 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
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Criterion Rating Details

The instructional materials for Discovery Education Math Techbook Grade 6 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
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics are 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.
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 Mathematics include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Each Unit consists of 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. 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.
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 6 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.).
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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 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.
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Indicator Rating Details

The instructional materials reviewed for the Discovery Education Math Techbook Grade 6 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.

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