Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 6 do not meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for Gateway 1 as they appropriately focus on the major work of the grade but did not always demonstrate coherence within the grade and across other grades. The instructional materials do not meet the expectations for Gateway 2 as they do not appropriately address rigor within the grade-level standards, and there are missed opportunities in the materials when it comes to attending to the full meaning of the MPs.

See Rating Scale
Understanding Gateways

Alignment

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Does Not Meet Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
10
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
8
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Grade 6 Everyday Mathematics partially meet the expectations for Gateway 1. Future grade level standards are not assessed, and the materials devote a majority of the time to the major work of the grade. At times the instructional materials connect supporting work with the major work of the grade, but often the materials do not. Although the materials provide a full program of student that is viable for a school year, students are not given extensive work with grade-level problems. Connections between grade levels and domains are missing. Overall, the instructional materials meet the expectations for focusing on the major work of the grade, but the materials are not always consistent and coherent with 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 Grade 6 Everyday Mathematics materials meet the expectations for not assessing topics before the grade level in which they should be introduced. All items on Unit assessments are focused on Grade 6 standards.

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 Grade 6 meet the expectations for focus within assessment. Overall, the instructional material does not assess content from future grades within the summative assessment sections of each unit.

The program allows for a Beginning-of-Year, Mid-year, End-of-Year Assessment, and Unit Assessments which assess the Grade 6 standards. There are also eight unit assessments/progress checks. The unit assessments/progress checks have portions for Self Assessment, Unit Assessment, Open Response Assessment (odd numbered units), Cumulative Assessment (even numbered units), and a Challenge. These assessments can be found in the Assessment Handbook. The Individual Profile of Progress for tracking and class progress are present in both paper (pages 110-121 in the Assessment Handbook) and digital formats. Most lessons have an Assessment Check-in that can be used as either formative or summative assessment as stated in the implementation guide.

Assessment Check-Ins are part of most lessons and mostly assess grade level content. For example, in the teacher guide, page 168, lesson 2-8, the Assessment Check-In focuses on 6.NS.1, dividing fractions.

All unit assessment items are on Grade 6 level. There are no scoring rubrics provided for the educators; however, all assessments do provide answer keys. Assessments 1-3 include problems involving mode, which is not specifically required by 6.SP.5.C.

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 Grade 6 Everyday Mathematics materials do meet expectations for devoting the large majority of class time to the major work of the grade level. The Sixth Grade Everyday Mathematics engages students in the major work of the grade about 73 percent of the time.

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 Grade 6 meet the expectations for focus by spending the majority of the time on the major clusters of the grade. This includes all the clusters in 6.RP and 6.EE and clusters 6.NS.A and 6.NS.C.

The Grade 6 materials do spend the majority of class time on the major clusters of the grade. Work was not calculated by units since the units spiral and are not clustered by groups of standards. There are eight units with approximately 11-14 lessons per unit. Assessment days were not included in these calculations. Additionally, each unit has a 2-day open response lesson; the Open Response Lessons were counted as one lesson. At the lesson level, the lessons are divided into Warm Up, Focus, and Practice. Each day consists of approximately 5 minutes on Warm Up, 30-45 minutes of a Focus, and 15-25 minutes of practice. To determine the amount of time on major work, the standards covered in the focus lessons were considered since that is where direct instruction takes place and the majority of the lesson takes place during this time.

  • Approximately seventy-three lessons out of the 99 are focused on the major work. This represents approximately 73 percent of the lessons.
  • In Unit 1, five out of fourteen lessons focus on major work.
  • In Unit 3, four out of fourteen lessons focus on major work.
  • In Unit 5, five out of twelve lessons focus on major work.
  • All other units are focused on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
4/8
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Criterion Rating Details

The instructional materials reviewed for Grade 6 do not meet the expectations for coherence. At times the instructional materials use supporting content as a way to continue working with the major work of the grade, but often the materials do not. For example, connections between statistics and probability and major work of the grade are missed. The materials include a full program of study that is viable content for a school year, including approximately 30-31 weeks of lessons and assessment. All students are not given extensive work on grade-level problems. Prior grade-level content is not consistently identified, and materials do not explicitly connect grade level concepts to prior knowledge from earlier grades. These instructional materials are shaped by the cluster headings in the standards; however, only surface level connections are made between domains. Overall, the Grade 6 materials do not support coherence and are not consistent with the progressions in the standards.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. In some cases, the supporting work enhances and supports the major work of the grade level, and in others, it does not.

Units 6-8 are focused entirely on major work, so no specific opportunities to use supporting content to enhance focus and coherence by engaging students in the major work of the grade are found.

At times supporting content does enhance focus and coherence by engaging students in the major work of the grade. Examples of the connections between supporting work and major work include the following:

  • Lesson 4-1 connects supporting standard 6.NS.4 with 6.EE.1 and 6.EE.6, both major work of the grade.
  • Lesson 5-1 connects supporting standard 6.G.3 and 6.NS.6, 6.NS.6.B, 6.NS.6.C, and 6.NS.8, major work of the grade.
  • Lesson 5-4 connects supporting standards 6.NS.3 and 6.G.1 with 6.EE.2 and 6.EE.2.C, major work of the grade.

Supporting work is found in Units 1-5. At times standards listed at the beginning of each unit are logically connected to each other; however, when the specific work of the unit and lessons is examined, some connections are missed or not specifically noted for teacher or students. Also, many lessons address supporting work in isolation from major work of the grade. Examples of lessons without connections between supporting and major work include the following:

  • Many of the lessons in Unit 1 focus on statistics and probability. These lessons are not truly connected to major work of the grade. Although some lesson activities do include both major and supporting standards, there are missed connections between the listed standards. For example, in Lesson 1-7 the Math Masters worksheet “Exploring Bar Graphs and Histograms” is aligned to 6.EE.5, 6.SP.4, 6.SP.5, and 6.SP.5.B. Although both major and supporting work are addressed, the major work is the focus of the last three problems of the worksheet disconnected from the supporting work.
  • Lesson 3-6 is focused on long division with decimals. The Math Masters worksheet “Decimal Division” is aligned to 6.NS.3, 6.NS.4, and 6.EE.7. Although the worksheet claims to connect the supporting work to major work of writing and solving equations of the form x+p=q or px=q, the worksheet does not require students to write and solve equations of this type. The provided sample answers do not show equations of this type.
  • Lessons 3-12, 3-13, and 3-14 focus on box plots and data representations. These lessons are not truly connected to major work of the grade. Although some lesson activities do include both major and supporting standards, there are missed connections between the listed standards. For example, in lesson 3-12 the Math Masters worksheet “Box Plots” is aligned to 6.RP.3, 6.RP.3.C, 6.SP.5, and 6.SP.5.C. Although both major and supporting work are addressed, the major work is the focus of the last three problems of the worksheet disconnected from the supporting work.

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 Grade 6 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 suggested pacing includes 107 days of lessons (99 lessons total) and another 16 days allowed for assessment, making 123 days of materials. According to the Teacher Guide on page xxxvi, each lesson is expected to last between 60-75 minutes. The online curriculum states to use Fridays as a Flex Day for games and intervention work. With Fridays being included as Flex Days, this curriculum allows for approximately 30 to 31 weeks of instruction.

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.
0/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 are not consistent with the progressions in the standards. Content from prior grades is not clearly identified or connected to grade-level work, and students are not given extensive work with grade-level problems.

Material related to prior grade level content is not clearly identified or related to grade level work. The Grade 6 materials have two instances where prior grade-level content is present and not identified as such. The lessons are taught as if this is the first introduction to the content. Lesson 1-11, identified as 6.NS, focuses on equivalent fractions at the Grade 4 level, 4.NF.A.1. Lesson 1-12, identified as 6.NS, focuses on equivalent fractions at the Grade 5 level, 5.NF.A.1.

The content does not always meet the full depth of standards. This mainly occurs because of a lack of lessons addressing the full depth of standards. For example, there are eight lessons listed for 6.SP.A.2; however, only three lessons actually align to the full depth of the standard, lessons 1-8, 3-12, and 3-13. The other cited lessons only have students finding central measures in a very procedural manner without looking at the overall shape to bring context. There are 27 lessons listed for 6.RP.A.3; however, only eight lessons align to the full depth of the standard. There are nine lessons listed for 6.NS.B.3; however, only six lessons align to the standard.

Everyday Mathematics Grade 6 materials do not provide extensive work with grade level standards. For example, the instructional materials do not provide extensive work with the following standards:

  • 6.NS.A.1: Only four lessons align to this standard, one of which is multiplication.
  • 6.NS.C.5: Only seven lessons align to this standard.
  • 6.NS.C.6.B: While there are four lessons aligned to this standard, none of the lessons use reflection across one or both axes.

In lessons where prior knowledge is needed, the instructional materials do not state that prior knowledge is being used. When future grade level concepts are introduced, there is no mention that the concept will be used in future grades. If the teacher uses the spiral trace at the beginning of the lesson or unit, the teacher will know where prior knowledge is used and when the student will use the skill/concept again in the future. The spiral tracker is listed by lessons and not connecting standards. At the beginning of each unit the spiral trace provides an explanation of what will occur by the end of the unit, but the spiral trace does not explain any further and does not connect to the next standard.

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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings, but missed opportunities to provide problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.

Instructional materials shaped by cluster headings include the following examples:

  • Lesson 1-11, "Building a Number Line Using Fraction Strips," is shaped by 6.NS.C.
  • Lesson 3-10, "Percents as Ratios," is shaped by 6.RP.A.
  • Lesson 5-12, "Area versus Volume," is shaped by 6.G.A.
  • The "Solving Problems with Substitution" portion of the Focus of Lesson 6-1 is shaped by 6.EE.B.

While the materials have many instances where two or more domains are connected, often the connections are only surface level connections. For example, Lesson 2-2 shows connections between 6.NS.3, 6.NS.4, 6.SP.1, 6.SP.2, 6.SP.5, 6.SP.5.B and 6.SP.5.C, and 5.NF.1 However, the lesson is divided into parts, and the parts only truly address one standard at a time.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Grade 6 do not meet the expectations for rigor and MPs. The instructional materials do not meet the expectations for the indicators on rigor and balance, nor do they meet the expectations of the indicators on practice-content connections. Overall, the instructional materials are stronger in regards to procedural skill and fluency and identifying MPs, although improvements are still needed to for those to fully meet the standards as well.

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.
4/8
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-
Criterion Rating Details

The instructional materials reviewed for Grade 6 do not meet expectations for rigor and balance. The instructional materials do not give appropriate attention to conceptual understanding or application. The materials do a better job of giving attention to procedural skill and fluency; however, the full meaning of procedural skill and fluency is still not met. Overall, because of not fully meeting expectations for procedural skill and fluency, application, and conceptual understanding, the instructional materials do not reflect the balances in the CCSSM, which help students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.

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.
1/2
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-
Indicator Rating Details

Materials partially meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Frequently opportunities are missed. Opportunities for students to work with standards that specifically call for conceptual understanding occur by use of pictures, manipulatives and strategies but frequently fall short by not providing higher order thinking questions to truly determine students' understandings.

Cluster 6.RP.A calls for understanding ratio concepts and using ratio reasoning to solve problems.

  • There are 13 Focus lessons on 6.RP.1 and eight focus lessons on 6.RP.2. Many of the lessons are doing "dual duty" as many lessons are marked for both standards. The directed and explicit structure of the lessons reduces students' opportunities to struggle with the understanding of the mathematics. There is one Open Response lesson on ratios in the year.

Standard 6.EE.5 focuses on understanding solving an equation or inequality as a process of answering a question.

  • In the following lessons, problems that are part of the practice sections are incorrectly aligned to 6.EE.5, which reduces opportunities to develop conceptual understanding: 1.11, 2.11, 2.14, 3.4, 5.6, 6.3, 7.4 (Math Box Problem 1) and 8.4. The misaligned problems in these lessons have students evaluating numerical expressions as opposed to demonstrating an understanding of solving an equation or an inequality as a process of answering a question.

Some attention to Conceptual Understanding is found in the Professional Development boxes throughout the Teacher Edition.

  • On page 80 of the Teacher Edition, the Professional Development box explains that fractions can serve as area models or as number line strips and provides an example.
  • On page 286 of the Teacher Edition, the Professional Development box explains that working with grids can help "students reason about percents conceptually before they use an algorithm to convert fractions to decimal equivalents and percents."

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.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials lack activities to build fluency computing with multi-digit numbers, 6.NS.2 and 6.NS.3. Standards 6.NS.2 and 6.NS.3 have a total of 215 exposures in the instructional materials. Exposures could include problems in the Math Boxes, problems in the Math Journal, direct instruction during the Focus lesson, problems during the online or hands-on game, and/or homework problems.

Standard 6.NS.2 has 61 exposures within the curriculum and is listed as the focus of three lessons.

  • There is only one focus lesson that explicitly teaches students the standard algorithm for division. Lesson 3.5 is the only lesson where there is focused instruction on the standard algorithm.
  • In Lesson 1.3 "Finding Equal Shares with the Mean," 6.NS.2 is not the focus. Standard 6.NS.2 is only included because division is used to find the mean, and the standard algorithm is not specifically addressed.
  • In Lesson 1.5 about comparing measures of center, 6.NS.2 is not the focus. Standard 6.NS.2 is only included because division is used to find the mean, and the standard algorithm is not specifically addressed.
  • There are 44 exposures for practice aligned to 6.NS.2, but only about half of those opportunities occur after the standard algorithm is discussed in Lesson 3.5.

Standard 6.NS.3 has 154 exposures within the curriculum and is listed as the focus of nine lessons.

  • Lesson 3.3 focuses on the standard algorithm for addition and subtraction of multi-digit decimals.
  • Lesson 3.4 focuses on the standard algorithm for multiplication of multi-digit decimals.
  • Lesson 3.6 focuses on the standard algorithm for division of multi-digit decimals.
  • Lesson 3.7 includes an application problem that involves all operations with multi-digit decimals.
  • There are 93 exposures for practice aligned to 6.NS.3, but only a few more than half of those opportunities occur after the standard algorithms are discussed in Lessons 3.3, 3.4, 3.6 and 3.7.

Math Boxes are used during each lesson. These problems, typically 5-6 problems, do not connect to each other but are pulled from several different clusters and/or domains and are designed for student practice and maintenance of previous skills. Most lessons in the materials have a "Mental Math and Fluency" section which allows students to practice fluencies required in grade 5. However, often lessons develop a specific procedure and reinforce that procedure. The teacher often guides students thinking with direct instruction and procedural guided questioning.

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
1/2
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Indicator Rating Details

The materials partially meet the expectation for being 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.

Most problems are presented in the same way throughout the entire curriculum. There is little variety of problems or types of problems. Problems are presented as short, one correct answer problems. Some of the problems are tied together through concepts and ideas, but many times lessons are completely disjointed from one anther.

Standard 6.NS.1 has 77 exposures within the curriculum and is listed as the focus of four days of Focus lessons.

  • The Focus portions of Lessons 2.5, 2.6, 2.7 and 2.8 are aligned to 6.NS.1.
  • About half of these exposures, including lessons 2.13, 3.1, 3.3, 3.5, 4.4 and 4.13, only involve computing quotients of fractions free from interpreting or being part of a word problem. The practice listed for lesson 3.4 does not actually align to 6.NS.1 as problem 4 in the Math Boxes only has students writing the reciprocal of a number. The practice listed for lessons 2.14, 3.2 and 3.8 are good examples of properly addressing the interpret and compute aspects of 6.NS.1.
  • Only two lessons, 2.6 and 2.7, truly focus on the standard.
  • Lessons 2.5 and 2.8 are also listed as focus lessons for this standard. However, in lesson 2.5, there are no quotients of fractions interpreted or computed, and in lesson 2.8, students are actually comparing when the divisor is a whole number to multiplying by the reciprocal of that divisor. The divisors in lesson 2.8 are whole numbers.

Standard 6.EE.9 has 50 exposures in the curriculum and is listed as the focus of 10 days of Focus lessons.

  • There are 10 focus lessons, 4.3, 7.3, 7.4, 7.6, 7.8 to 7.11, 8.7 and 8.8, that are listed as aligning to 6.EE.9, but only seven of the lessons actually align to the standard.
  • Lesson 4.3 does not have students use any variables, and lessons 7.3 and 7.4 have students write the expression in electronic spreadsheets which detracts from using two variables in one equation.

Standard 6.EE.7 has 58 exposures in the curriculum and is listed as the focus of 11 days of Focus lessons.

  • The Focus portions of Lessons 2.6, 3.3, 3.6, 5.9, 6.3, 6.4, 6.5, 6.8, 7.8, 7.9 and 8.6 are aligned to 6.EE.7.
  • Many of the exposures/lessons overlap with the previous standard.
  • In lessons 2.6, 3.3, 3.6 and 5.9, students do not have the opportunity to write equations with variables and proceed to solve those equations. In these lessons, students write numerical expressions and evaluate those numerical expressions.
  • In lessons 6.3, 6.8 and 7.8, almost all of the equations that are written are of the form px + q = r, which means the lessons more closely align to 7.EE.4.A instead of 6.EE.7. Also, in lesson 6.8, students do not get to solve some of the equations that are written, and in lesson 7.8, the equations that are written are used to complete tables of data and create graphs, not solving real-world or mathematical problems.
  • In lessons 6.4 and 6.5, students compare bar models and pan balances to develop a conceptual understanding of solving an equation, but these lessons do not provide students with opportunities to solve real-world or mathematical problems by writing equations and solving them.
  • In lesson 7.9, students are expected to perform computations with quantities from a real-world context, but there is no direct connection to students writing equations to model the context of the problems before solving them.
  • In lesson 8.6, students are expected to find the mean of a set of data by thinking about the mean as a balancing point, but, as in lesson 7.9, there is no direct connection to writing equations and using those equations to find the mean.

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.
1/2
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Indicator Rating Details

The Grade 6 Everyday Mathematics instructional materials partially meet the expectations for balance. Overall, the three aspects of rigor are treated separately within the materials, and the lack of lessons on conceptual understanding and application do not allow for a balance of the three aspects.

Despite efforts to include conceptual understanding and application, problems are all too often presented in a formulaic way. Questions give away the answers or prompt specific thought patterns. The order of questions often lead students to a specific procedure. Contexts are frequently routine and problems are posed in a way in which students can solve them by relying on the procedural skill. All aspects of rigor are almost always treated separately within the curriculum including within and during lessons and practice.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
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Criterion Rating Details

The instructional materials reviewed for Grade 6 did not meet the expectations for practice-content connections. The materials only partially meet the expectations for attending to all the indicators 2e- 2g, except for 2f which did not meet expectations. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of every practice standard, especially MP3 in regards to students critiquing the reasoning of other students and the use of correct vocabulary throughout the materials.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for identifying the MPs and using them to enrich the Mathematics content.

The MPs are identified in the Grade 6 materials for each unit and the focus part of each lesson.

  • For Unit 3, page 229 discusses how MP1 and MP2 unfold within the unit and lessons.
  • For Unit 5, page 461 identifies which MPs are in the focus parts of the lessons within the unit.
  • For Unit 7, page 655 explains the development of MP5 and MP6 in this unit.
  • Within the lessons are spots where the MPs are identified.

However, within the lessons limited teacher guidance on how to help students with the MPs is given. Because there is limited guidance on implementation, it is difficult to determine how meaningful connections are made. Additionally, it is difficult to determine if the MPs have meaningful connections since the materials break them into small parts and never address the MPs as a whole. The broken apart MPs can be seen on pages EM8-EM11.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
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Indicator Rating Details

The Grade 6 Everyday Mathematics instructional materials do not treat each MP in a complete, accurate, and meaningful way. The lessons give teachers limited guidance on how to implement the standards. Some lessons are attached to standards without having students actually attending to them.

Below are examples of where the full intent of the Standards for Mathematical Practice is not met.

  • MP1: Lesson 5-9 cites MP1; asking students to simply discuss with a partner how they solved the problem does not ensure they are persevering in problem solving. Lesson 6-1 cites MP1; however, the materials are simply asking students to complete the equation. Lesson 6-7 cites MP1; however, the problem is simply asking students to identify which equations are equivalent.
  • MP4: Lesson 2-3 cites MP4; they are using fraction strips and number lines to visualize fraction multiplication. In the math journal on pages 62 and 63, students are using a number line for fraction multiplication when working with real world problems such as eating parts of a granola bar. This illustrates a lack of full intention of MP4 as it highlights the use of a model (noun) instead of modeling (verb). Lesson 5-6 cites MP4; the teacher tells the students how to make a model, so this lesson does not meet the intent of the standard. Lesson 5-7 and 5-10 (MP4) gives students the model that they are supposed to use, thus not allowing them to create a mathematical model to use.
  • MP5: Lesson 5-4 cites MP5; telling the students to use the formula as a tool does not give students the opportunity to select an appropriate tool. Lesson 6-5 cites MP5; but tells them to use a calculator, again not giving students an opportunity to choose the appropriate tool. In Lesson 6-10, students are told to use a pan balance to model the problem when MP5 is cited.
  • MP7: Lesson 5-1 cites MP7. The teacher explains that polygons have at least 3 sides, and they are all line segments so students are not looking for and making use of structure. Lesson 5-12 cites MP7; and again the teacher explains the patterns and relationships. Lesson 6-2 cites MP7; Students are asked how solution sets for inequalities differ from solution sets for equations; however, then the students are only given one example of each. There is no guidance for the teacher on how to help the students see the differences, and in order to look for and make use of structure students would need more than one example of each.

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.
1/2
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Indicator Rating Details

The materials partially meet the expectation for prompting students to construct viable arguments and analyze the evidence of others. MP3 is not explicitly called out in the student material. Although the materials at times prompt students to construct viable arguments, the materials miss opportunities for students to analyze the arguments of others, and the materials rarely have students do both occur together.

There are some questions that do ask students to explain their thinking on assessments and in the materials. Sometimes there are questions asking them to look at other's work and tell whether the student is correct or incorrect and explain. Little direction is provided to make sure students are showing their critical thinking, process or procedure, or explaining their results. Many questions that prompt students to critique the reasoning of others tell the student if the reasoning was originally correct and incorrect. It should be noted though that student materials never explicitly call out entire MPs at once; MP3 is broken into GMP 3.1 and GMP 3.2 in the materials.

The open response lessons could be opportunities for students to construct arguments for or against a mathematical question. However, besides just working in groups, there is little prompting from the teacher for students to discuss the answers of other groups or students

The following are some examples of where the materials indicate that students are being asked to engage in MP3 (Unit 1 and 6 claim MP3 to be a focus):

  • For Unit 1, about half of the 14 lessons have opportunities for students to construct viable arguments, but some of those opportunities, such as in lessons 1-4 and 1-5, are only for students that volunteer and are chosen by the teacher.
  • For Unit 1, there are only two lessons where students are expected to analyze the arguments of others. Both of these lessons also have students construct viable arguments. Neither of them prompt students to use critiques of their arguments to improve their arguments.
  • Math Boxes, page 24, question 5 asks students to explain their reasoning for selecting an answer.
  • Math Boxes, page 48, question 5 asks students to explain how they solved problem 2.
  • Math Boxes, page 79, question 5 asks students to explain how the found the balance point in problem 3.
  • For Unit 6, less than half of the 11 lessons identify opportunities for students to construct viable arguments. Lesson 6-6 has an opportunity for students to construct an argument that includes multiple parts. However, there is no opportunity for students to have their arguments critiqued so that the arguments might be improved.
  • For Unit 6, there are only two lessons where students are expected to analyze the arguments of others. Neither of these lessons also identify opportunities for students to construct viable arguments.

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.
1/2
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-
Indicator Rating Details

The materials partially meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. The Grade 6 materials sometimes give teachers questions to ask students to have them form arguments or analyze the arguments of others, but typically the materials do not give both at the same time.

In the teacher's guide and lessons, the teachers have very specific, almost scripted, directions for students. Most, if not all, of the Math Master worksheets are presented in a step-by-step directive that does not allow for students to evaluate, justify, or explain their thinking. Usually only one right answer is available to the posed problem, and there is not a lot of teacher guidance on how to lead the discussion given besides a question to ask. There are many missed opportunities to guide students in analyzing the arguments of others. Students spend time explaining their thinking but not always justifying their reasoning and creating an argument.

The following are examples of lessons aligned to MP3 that have missed opportunities to assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others:

  • Lesson 1-2 states, "Have students share how they matched a dot plot to each statistical question." The missed opportunity here is for teachers to guide students in a rich discussion about how they used the dot plot.
  • Lesson 1-4 states, "Have the students pose arguments for why the two sides are not balanced," but teachers are not given guidance to help students pose the arguments.
  • Lesson 1-9 is the open response lesson. It tells the teacher to ask “which histogram better supports your view” and "which features of the graph helped you to make your argument,” but does not provide guidance to the teacher to guide students in a rich discussion.
  • Lesson 2-5 cites MP3; however, the questions posed have right and wrong answers and do not have students engaging in constructing viable arguments or analyzing the arguments of others. There is no direct guidance to help the teacher engage students in MP3.
  • Lesson 2-8 has students explain whose strategy is correct. Again, there is not instruction or guidance for the teacher to help the students explore the explanations of others.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 6 partially meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics; however, often the correct vocabulary is not used.

  • Each unit includes a list of important vocabulary in the unit organizer which can be found at the beginning of each unit.
  • Vocabulary terms are bolded in the teacher guide as they are introduced and defined but are not bolded or stressed again in discussions where students might use the term in discussions or writing.
  • Each regular lesson includes an online tool, "Differentiating Lesson Activities." This tool includes a component, "Meeting Language Demands," that includes vocabulary, general and specialized, as well as strategies for supporting beginning, intermediate, and advanced ELLs. An example of this, from Lesson 7-4, includes "For Beginning ELLs, use visuals, restatements, role play, and read-clouds to help students understand task directions and written statements."
  • Everyday Math comes with a reference book that uses words, graphics and symbols to support students in developing language.
  • Some units have a heavy load of required mathematical vocabulary. In unit 5, there are 28 vocabulary words needed for students in Grade 6 to understand the unit. Some of these words include compose, cubic units, decompose, net, scale drawing, surface area and others. In contrast, Unit 8 only has 12 vocabulary words for the unit which is a much more manageable number for students in Grade 6.
  • Correct vocabulary is often not used. For example, name-collection box instead of equivalent equations or equivalent expressions, nested parenthesis instead of brackets, number model instead of expression, responding variable instead of dependent, and manipulated variable instead of independent variable.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

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

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
0/2

Indicator 3b

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

Indicator 3c

There is variety in 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.
0/2

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

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

Indicator 3f

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

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
0/2

Indicator 3h

Materials contain a teacher's edition (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.
0/2

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.
0/2

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 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 3l

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

Criterion 3m - 3q

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

Indicator 3m

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

Indicator 3n

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

Indicator 3o

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

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

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.
0/2

Indicator 3q

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

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

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

Indicator 3s

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

Indicator 3t

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

Indicator 3u

Materials 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 3v

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

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

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

Indicator 3y

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

Criterion 3aa - 3z

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

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0

Indicator 3ab

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

Indicator 3ac

Materials can be easily customized for individual learners. 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 3ad

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

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Mon Apr 11 00:00:00 UTC 2016

Report Edition: 2016

Title ISBN Edition Publisher Year
null 978-0-02-130763-0 null null null
null 978-0-02-135252-4 null null null
null 978-0-02-135277-7 null null null
null 978-0-02-137663-6 null null null
null 978-0-02-138360-3 null null null
null 978-0-02-143073-4 null null null
null 978-0-02-143074-1 null null null
null 978-0-02-143104-5 null null null

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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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