Everyday Math 4
Downloadable Resources
Publisher Response
2015-2016

Everyday Math 4

Publisher
McGraw-Hill Education
Subject
Math
Grades
K-6
Report Release
04/08/2016
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
Downloadable Resources
Publisher Response
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Showing:
5th Grade

About This Report

Report for 5th Grade

Alignment Summary

The instructional materials reviewed for Grade 5 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 do 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 standards for mathematical practice.

5th Grade
Gateway 1

Focus & Coherence
11/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
09/18
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Gateway 3

Usability
Usability (Gateway 3)
Not Rated
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 5 Everyday Mathematics partially meet the expectations for Gateway One. 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 study that is viable for a school year, students are not always 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.

Gateway 1
v1.0
Gateway 1

Focus & Coherence
11/14
0
7
12
14
Criterion 1.1: Focus
02/02
Criterion 1.2: Coherence
04/04
Criterion 1.3: Coherence
05/08
Partially Meets Expectations

Criterion 1.1: Focus
02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The Grade 5 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 5 standards.

Indicator 1A
02/02
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.

The instructional materials reviewed for Grade 5 meet the expectations for focus within assessment. Overall, the instructional materials do 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, and Unit Assessments which assess the Grade 5 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 113-124 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 on page 64, lesson 1-8, the Assessment Check-In focused on 5.MD.3, 5.MD.3.B, and 5.MD.4, volume, and gives additional questions for the students who excel.

All unit assessment items are on Grade 5 level. There are no scoring rubrics provided for the educators; however, all assessments do provide answer keys. 

Criterion 1.1: Focus
02/02
Indicator 1A
02/02

Criterion 1.2: Coherence

04/04
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.

The Grade 5 Everyday Mathematics materials do meet expectations for devoting the large majority of class time to the major work of the grade level. The Grade 5 Everyday Mathematics engages students in the major work of the grade approximately 74 percent of the time.

Indicator 1B
04/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 5 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 5.NBT and 5.NF and cluster 5.MD.C.

The Grade 5 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 between 12-14 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 5 minutes on warm-ups, 35-45 minutes of a focus lesson, 20-30 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.

  • Seventy-eight lessons out of the 105 are focused on the major work. This represents approximately 74 percent of the lessons. Additionally, another nine lessons, or approximately 9 percent are supporting work which truly supported the major work of the grade bringing the time spent on major work to approximately 83 percent.
  • Two lessons out of the 105 are focused on off grade-level work. Lessons 2-13 and 3-3 focus on 4.OA.A.3, interpreting remainders.
Criterion 1.2: Coherence
04/04
Indicator 1B
04/04

Criterion 1.3: Coherence
05/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 5 partially 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 geometry 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 32.5 weeks of lessons and assessment. Content from prior grades is not clearly identified or connected to grade-level work, and students are not always given extensive work with grade-level problems. Material related to prior, grade-level content is not clearly identified or related to grade-level work. These instructional materials are shaped by the cluster headings in the standards; however, only surface-level connections are made between domains. Overall, the Grade 5 materials partially support coherence and are not consistent with the progressions in the standards.

Indicator 1C
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 5 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 3 and 5 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 2-6 connects supporting standards 5.OA.1, 5.OA.2 and 5.MD.1 with 5.NBT.5, major work.
  • Lesson 6-3 connects supporting standard 5.MD.1 with 5.NBT.2, major work.
  • Lessons 6-4 and 6-5 connect supporting standards 5.MD.1 and 5.MD.2 with 5.NF.1, 5.NF.2 and 5.NBT.6, all major work.
  • Lesson 6-13 connects supporting standards 5.OA.1 and 5.MD.2 with 5.NBT.1 and 5.NBT.3, both major work.
  • Lesson 7-9 connects supporting standard 5.MD.2 with 5.NF.1, 5.NF.2 and 5.NF.4, all major work.

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 teachers 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:

  • Lessons 4-6, 4-7, 4-9, and 4-10 focus on plotting points on a coordinate grid, 5.G.1 and 5.G.2. These lessons are not truly connected to major work of the grade. Although lesson 4-9 does connect plotting points to 5.OA.3, this standard is also not 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 4-6, the Math Masters worksheet "Plotting Points to Create an Outline Map" is aligned to 5.G.1, 5.NBT.1, 5.NBT.3 and 5.NBT.3.A. Although both major and supporting work are addressed, the major work is the focus of the last two problems of the worksheet disconnected from the supporting work.
  • Lessons 7-5, 7-6, 7-7 and 7-8 focus on two-dimensional shapes, 5.G.3 and 5.G.4. The focus portions of these lessons are exclusively on these supporting standards, and no connections to any other standards, including major work, is made in the lessons. Although some lesson activities do include both major and supporting standards, there are missed connections between the listed standards. For example, in Lesson 7-6, the Math Masters worksheet, "The Quadrilateral Hierarchy," is aligned to 5.G.3, 5.NF.7 and 5.NF.7.A. Although both major and supporting work are addressed, the major work is the focus of the last four problems of the worksheet disconnected from the supporting work.
  • Lessons 7-10, 7-11 and 7-12 focus on patterns, 5.OA.3. Although patterns are connected to plotting points on a coordinate grid, plotting points is not 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 7-12, the Math Masters worksheet, "Interpreting Tables and Graphs," is aligned to 5.OA.3, 5.G.1, 5.G.2 and 5.NBT.7. Although both major and supporting work are addressed, the major work is the focus of the last two problems of the worksheet disconnected from the supporting work.
Indicator 1D
02/02
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for Grade 5 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 113 days of lessons (105 lessons total) and another 16 days allowed for assessment, making 129 days of materials. According to the Teacher Guide, 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 32.5 weeks of instruction.

Indicator 1E
01/02
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.

The instructional materials reviewed for Grade 5 partially meet the expectation for being 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 always 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 5 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. Lessons 2-13 and 3-3 focus on 4.OA.A.3, interpreting remainders in problems.

The content does not always meet the full depth of standards. This mainly occurs because of a lack of lessons addressing the full depth. For example, there are four lessons listed for 5.MD.B.2; however, only one lesson actually aligns to the full depth of the standard. Lesson 8-6 has students creating line plots using 1/8, 1/4, and 1/2. The other three lessons only have students creating line plots using 1/2, a Grade 3 standard. Another example is 5.OA.A.1, using parentheses and brackets in equations and expressions. While there are 50 exposures to this standard according to the online tracker, only four of the exposures are Focus lessons. None of those four lessons teaches students how to use parentheses or brackets; they just expect students to be able to use them. There are only two lessons for division, three for multiplication, three sharing multiplication, one for addition, one for subtraction and two sharing addition and subtraction. The other two lessons are not aligned to the standard. When looking at 5.NBT.6, finding whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, there are 110 exposures according to the spiral tracker; however, there are only 13 lessons. Of those, only one lesson includes in-depth work with four-digit dividends with two-digit divisors. (Nine of the 13 lessons are misaligned.)

Everyday Mathematics Grade 5 materials do not provide extensive work with grade-level standards. For example, the instructional materials do not provide extensive work with the following standards:

  • 5.NBT.A.1: The spiral tracker lists 9 instances of lessons aligning to this standard, however only five lessons were found to be aligned.
  • 5.NBT.A.3- There are nine Focus lessons aligned to this standard.
  • 5.NBT.B.4- There are five Focus lessons aligned to this standard.
  • 5.NF.A.1: The spiral tracker lists 11 instances of lessons aligning to this standard, however only 6 lessons were found to be aligned and only one of those focuses on subtraction.
  • 5.NF.B.5- There are ten Focus lessons aligned to this standard.
  • 5.NF.B.7- There are only three Focus lessons aligned to this standard.
  • In lessons where prior knowledge is needed, it is not stated 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 based on the spiral trace. They also tell when the student will use the skill/concept again in the future of that unit. The spiral tracker is listed by lessons and not connecting standards. It does a little better job at the beginning of each unit explaining the spiral trace and what will occur by the end of the unit, but not any further and not connecting to the next standard.
Indicator 1F
01/02
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.

The instructional materials reviewed for Grade 5 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 there are 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 2-2, "Exponents and Powers of 10," is shaped by 5.NBT.A.
  • Lesson 3-12, "Solving Fraction Number Stories," is shaped by 5.NF.A.
  • Lessons 4-8 and 4-9, "Solving Problems on a Coordinate Grid," are shaped by 5.G.A.
  • Lesson 6-11, "Division of Decimals by Whole Numbers," is shaped by 5.NBT.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 6-4 shows connections between 5.MD.1 5.MD.2, 5.NF.2 and 5.NF.1 However, the lesson is divided into parts, and the parts only truly address one standard at a time.

Criterion 1.3: Coherence
05/08
Indicator 1C
01/02
Indicator 1D
02/02
Indicator 1E
01/02
Indicator 1F
01/02
Overview of Gateway 2

Rigor & Mathematical Practices

The instructional materials reviewed for Grade 5 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.

Gateway 2
v1.0
Gateway 2

Rigor & Mathematical Practices
09/18
0
10
16
18
Criterion 2.1: Rigor
05/08
Criterion 2.2: Math Practices
04/10
Does Not Meet Expectations

Criterion 2.1: Rigor
05/08
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.

The instructional materials reviewed for Grade 5 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. 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.

Indicator 2A
01/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

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, these fall short by not providing higher-order, thinking questions to truly determine students' understandings.

Cluster 5.MD.C calls for conceptual understanding of volume and how volume relates to multiplication and addition.

  • There are 12 focus lessons on volume. Many of the lessons are directed and explicit, so students do not have many opportunities to struggle with the understanding of the mathematics. There is only one Open Response lesson on volume in the year. There are some missed opportunities to connect conceptual understanding of measurement of volume to multiplication and addition.
  • Cluster 5.NF.B focuses on applying and extending previous understanding of multiplication and division to multiply and divide fractions.
  • Lessons 3.10-3.12 provide several opportunities to develop understanding, including use of manipulatives. "Fraction Capture" provides opportunity for students to create different combination of fractions to sum to a given fraction. Overall, however, the student work in these lessons prompts and promotes students to work with mathematics in a procedural manner.
  • The Professional Development box on Teacher Edition page 446 discusses development of understanding in Lessons 5.1-5.4. These lessons provide students ample time and opportunity to work with a variety of solving problems with fractions using several strategies. Although many strategies are addressed in a procedural way, the amount of time spent on these strategies may provide an excellent foundation for developing understanding.

Clusters 5.NBT.A and 5.NBT.B focus on understanding the place value system and performing operations with multi-digit whole numbers and decimals to hundredths.

  • In Lessons 4.1-4.5 students are frequently told how to think, sort, and label during problems, thus detracting from developing an understanding. The Teacher Questions for the "Fraction of" game in Lesson 4.2 allow students the opportunity to make mathematical sense of diagrams/manipulatives which could lead to understanding, and students are given time to express their thinking.
  • In Lessons 6.1 and 6.3, the Math Journal provides problems to probe student understanding; however, problems simply address student "why?" without providing a task that challenges their thinking. Repetition of mathematical problems detracts from developing conceptual understanding.

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

  • On page 23 of the Teacher Edition, the Professional Development box explains that, in Grade 5, students should find the area of rectangles with fractional side lengths using tiling and applying the formula for area. The box emphasizes that students are not expected to use the area formula until later in the year.
  • On page 414 of the Teacher Edition, the Professional Development box explains that the purpose of the lesson is to expose the class to several different decimal subtraction algorithms. The box emphasizes that the "most reliable or efficient algorithm may vary from student to student" and that students do not need to master every algorithm.
Indicator 2B
02/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials reviewed for Grade 5 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The instructional materials include activities to build fluency multiplying multi-digit whole numbers using the standard algorithm, 5.NBT.5.

  • The online spiral tracker shows 5.NBT.B.5 has 104 exposures within the curriculum. There are 13 Focus lessons that explicitly teach students the traditional algorithm for multiplying multi-digit problems. There are several exposures to the standard algorithm each day.
  • Students complete some mental problems, play a game, complete Math Boxes and are assigned a homework page. Frequently, this standard is covered in the Math Boxes problems, games, and homework problems.
  • Lesson 2.4 introduces the standard algorithm and shows several examples of how it connects to other strategies (including area models). Students continue their work with the standard algorithm through Lesson 2.9. Students do not multiply with 2 multi-digit numbers until Lesson 2.7.
  • Students may need more time and practice to develop fluency. Students do get additional time with multi-digit multiplication using the standard algorithm in Unit 8. 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 fifth grade. 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
01/02
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

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 another. Each unit contains a two-day "Open Response" lesson which engages students in application of mathematics. For example, lesson 6-5 has students engaging in application of the mathematics where students are asked to figure out how much breakfast casserole is shared with a class of Grade 5. Online, in the resource section, some "Projects" are available; however, several of the "Projects" have students doing activities which do not align to standards, such as Mayan math, Ancient Civilizations math, and Magic Computation Tricks.

Standard 5.NF.6 has 59 exposures within the curriculum and is listed as the focus of 13 days of Focus lessons.

  • The Focus portions of Lessons 3-13, 3-14, 5-5, 5-6, 5-7. 5-9, 5-10, 5-12, 7-1, 7-2, 7-3, 8-1 and 8-3 are aligned to 5.NF.6.
  • Standard 5.NF.6 is focused on solving real-world problems involving multiplication of fractions and mixed numbers. However, there is not enough instruction or practice of application of solving real-world problems involving multiplication of fractions and mixed numbers.
  • On the Lesson 3-13 Math Journal worksheet "Fraction-Of Problems," students are solving routine one-step word problems. This worksheet is aligned to 5.NF.6, but students are not multiplying fractions and mixed numbers.
  • On the Lesson 7-1 Math Journal worksheet "Multiplying Mixed Numbers," students are given one-step routine word problems to solve and one multiplication problem to use to write a word problem. These word problems do not require true application of the standard given that the title tells students what to do with the only two numbers in each of the word problems.
  • Lesson 7-3 provides scaffolded application problems involving area and multiplication of mixed numbers by integers, not mixed numbers and fractions.
  • Lesson 8-1 has a practice sheet with an alignment to 5.NF.B.6, but none of the word problems on the page require multiplying a fraction and a mixed number.
  • On the Lesson 8-3 Math Journal worksheet "Buying a Fish Tank," students are given a multi-step word problem. However, the problem is scaffolded, and students are not provided an opportunity to multiply a fraction and a mixed number.

Standard 5.NF.7.C has 30 exposures within the curriculum and is listed as the focus of three days of Focus lessons.

  • The Focus portions of Lessons 5-13, 5-14, and 7-4 are aligned to 5.NF.7.C.
  • On the Lesson 5-13 Math Journal worksheet "Solving Fraction Division Problems," students are given one-step word problems requiring division of a fraction by a non-zero whole number. In this lesson, the word problems are very similar, and the directions and problems are so scaffolded that true application of the standard is not achieved.
  • In Lesson 5-14, students continue to work the same types of one-step word problems that they encountered in Lesson 5-13. Additionally, students are asked to write one-step word problems to match division problems. Students are not provided with a variety of single- and multi-step contextual problems, including non-routine problems that truly require application of the standard.
  • In Lesson 7-4, students again solve one-step word problems and write one-step word problems to match division problems. Students are not provided with a variety of single- and multi-step contextual problems, including non-routine problems.
  • Student work with this standard focuses on routine problems. Even when students are writing their own word problems, the provided sample answers are typically one-step routine problems. For example, the "Multiplying and Dividing Fractions" Math Journal in Lesson 7-10 gives a one-step sample word problem involving drinks. Both of the sample answers for the "Fraction Division Problems" Math Journal in Lesson 7-4 are about meatloaf.
Indicator 2D
01/02
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.

The Grade 5 Everyday Mathematics instructional materials partially meet the expectations for balance. Overall, the three aspects of rigor are neither always treated together nor always treated separately within the materials. The instructional materials meet expectations for procedural skill and fluency; however, 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 2.1: Rigor
05/08
Indicator 2A
01/02
Indicator 2B
02/02
Indicator 2C
01/02
Indicator 2D
01/02

Criterion 2.2: Math Practices
04/10
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Grade 5 do 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 does not meet expectations. Overall, in order to meet the expectations for meaningfully connecting the content standards and the MPs, the instructional materials should carefully pay attention to the full meaning of every practice standard, especially MP 3 in regards to students critiquing the reasoning of other students and the use of correct vocabulary throughout the materials.

Indicator 2E
01/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Grade 5 partially meet the expectations for identifying the MPs and using them to enrich the mathematics content.

The MPs are identified in the grade 5 materials for each unit and the focus part of each lesson.

  • For Unit 3, page 217 discusses how MP5 and MP8 unfold within the unit and lessons.
  • For Unit 5, page 433 identifies which MPs are in the focus parts of the lessons within the unit.
  • For Unit 6, page 553 discusses how MP6 and MP7 unfold within the unit and lesson.
  • For Unit 7, page 657 explains the development of MP2 and MP8 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
00/02
Materials carefully attend to the full meaning of each practice standard

The Grade 5 Everyday Mathematics instructional materials do not meet the expectation for carefully attending to the full meaning of each practice standard. 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 MPs is not met.

  • MP1: Lesson 1-2, citing MP1, asks students which facts they know and which ones they still need to learn; this is not having them making sense of problems or preserving in solving them. Lesson 1-8 has the teacher explaining when mathematicians have a new problem to solve. They think about how they have solved similar problems in the past; this is not having students engage in MP1. Lesson 2-8 cites MP1 when having the teacher demonstrate how to solve a problem; this is not the students making sense of problems or preserving in them.
  • MP4: Lesson 2-2 is cited with MP4, but students are told what model to use.
  • MP 4: Lesson 6-13 has students “share something about the class line plot”. Students are told what model to use and do not make assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
  • MP5: In Lesson 1-6, MP5 is cited. However, students are not choosing a tool to use; they are just being asked a question about a tool. Lesson 2-6 cites MP5; however, students are told which tool to use.
  • MP6: In Lesson 1-7, MP6 is cited, but reminding students of the importance of packing without gaps or overlaps is not the student attending to precision. Lesson 2-3 cites MP6; the teacher telling the students to always think about if their answer makes sense is not the students attending to precision.
  • MP7: In Lesson 2-1, MP7 is cited; the teacher explaining that a pattern is a mathematical structure and helps in problem solving is not having students look for and make use of structure. Lesson 2-5 cites MP7; the question asks "Do you notice any patterns in the steps of U.S. traditional multiplication?" This tells the students there is a pattern or structure to see taking away the intent of students looking for the structure and making use of it. A better question would simply be to ask "what do you notice?"
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
01/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

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 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; MP 3 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:

  • In Lesson 1-3, the teacher's guide provides the following student question: "Why is it important to make sense of others' mathematical thinking?" This question does not require students to analyze the evidence of others as indicated in the materials.
  • In Lesson 2-9, on Math Journal page 59, problem 5 asks students which method they used to multiply and why?
  • In Lesson 3-9, problem 5 on the Math Journal "Addition and Subtraction Number Stories" activity asks students to explain how they solved the problem.
  • In Lesson 3-9, problem 5 on the Math Journal worksheet asks students to explain Morton's reasoning.
  • In Lesson 3-14, teachers are told to "Look for partnerships using a successful strategy and have them share their strategies and representation." Although the selected students will explain their thinking, the other students will not. Also, students will not be analyzing the evidence of others.
  • In Lesson 3-14, on page 307 of the teacher's guide, teachers are told "(a)fter each strategy is shared, encourage other students to explain it in their own words." Although students may critique the reasoning as they are providing explanation, they are not prompted to do so by the materials.
  • In Lesson 5-14, on page 531 of the teacher's guide, teachers are told to "(h)ave students restate others' ideas in their own words to make sure that they understand why the quotients is larger than the dividend." Although students may critique the reasoning as they are providing restated idea, they are not prompted to by the materials.
  • In the Math Message Follow-Up for Lesson 8-11, students are simply sharing their answers and explaining how they used the graph to make their predictions.
Indicator 2G.ii
01/02
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.

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 5 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:

  • In the Math Message Follow-Up for Lesson 1-6, students are asked to share ideas that they discussed with partners. Teachers are told to encourage them to "explain their own thinking clearly and to ask questions to be sure that they understand each other's thinking;" however, the questions are not provided for the teacher.
  • In the Math Message Follow-Up for Lesson 3-6, students are sharing how they solved the math message. Teachers are told to "(b)e sure the discussion covers the following two strategies;" however, the materials do not offer assistance to teachers to ensure that the two strategies are incorporated into the discussion.
  • Lesson 3-11 has students discussing their models and solutions to fair share problems; however, there is no guidance to the teacher on how to prompt rich mathematical discourse.
  • In the Math Message Follow-Up for Lesson 6-8, teachers are told to ask students to share their conjectures and arguments. The teacher guidance states that teachers should "(e)xpect most to argue that 2.4*1.8 is greater than 2.4 because 1.8 is greater than 1." However, the teacher guidance does not offer any suggestions on how to guide the conversation if most students do not provide that conjecture.
  • In the Math Message Follow-Up for Lesson 8-3, teachers are told to have students share their conjectures, but teachers are not given guidance to help students form the conjectures.
Indicator 2G.iii
01/02
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Grade 5 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 2-5, includes "For beginnings ELLs, use visual aids and role play to scaffold comprehension of explanations."
  • Everyday Math comes with a Reference book that uses words, graphics, and symbols to support students in developing language.
  • Correct vocabulary is often not used. For example, "Turn-around fact" is used rather than the term commutative property, number sentence is used instead of equation, "name-collection box" instead of equivalent equations or equivalent expressions, "number model" instead of expression, and trade-first subtraction.
  • Some units have a heavy load of required mathematical vocabulary. In Unit 7, there are 39 vocabulary words needed for students in Grade 5 to understand the unit. Some of these words include corresponding terms, fathom, hierarchy, great span, joint, relationship, subcategory and others. In contrast, unit 6 only has 14 vocabulary words for the unit which is a much more manageable number for students in Grade 5.
Criterion 2.2: Math Practices
04/10
Indicator 2E
01/02
Indicator 2F
00/02
Indicator 2G
Read
Indicator 2G.i
01/02
Indicator 2G.ii
01/02
Indicator 2G.iii
01/02
Overview of Gateway 3

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Gateway 3
v1.0
Gateway 3

Usability
NE = Not Eligible. Product did not meet the threshold for review.
NE
0
22
31
38
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Not Rated

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
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.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
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.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3A
00/02
Indicator 3B
00/02
Indicator 3C
00/02
Indicator 3D
00/02
Indicator 3E
Read

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
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.
Indicator 3H
00/02
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.
Indicator 3I
00/02
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.
Indicator 3J
Read
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).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3F
00/02
Indicator 3G
00/02
Indicator 3H
00/02
Indicator 3I
00/02
Indicator 3J
Read
Indicator 3K
Read
Indicator 3L
Read

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3M
00/02
Indicator 3N
00/02
Indicator 3O
00/02
Indicator 3P
Read
Indicator 3P.i
00/02
Indicator 3P.ii
00/02
Indicator 3Q
Read

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
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).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3R
00/02
Indicator 3S
00/02
Indicator 3T
00/02
Indicator 3U
00/02
Indicator 3V
00/02
Indicator 3W
00/02
Indicator 3X
Read
Indicator 3Y
Read

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
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.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
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.
Indicator 3AD
Read
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.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3AA
Read
Indicator 3AB
Read
Indicator 3AC
Read
Indicator 3AD
Read
Indicator 3Z
Read
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