Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 4 do not meet the expectations for alignment to the CCSSM. The instructional materials partially met 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 did not meet the expectations for Gateway 2 as they did 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
11
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
9
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

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Gateway One Details

The instructional materials reviewed for Grade 4 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.

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 4 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 4 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 4 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, and Unit Assessments which assess the Grade 4 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 104-115 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 182 of lesson 2-10, the Assessment Check-In focuses on 4.G.2, right angles, and gives additional questions for the students who excel.

All unit assessment items are on Grade 4 level. There are no scoring rubrics provided for the educators; however, all assessments do provide answer keys.

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 4 Everyday Mathematics materials do meet expectations for devoting the large majority of class time to the major work of the grade level. The Grade 4 Everyday Mathematics engages students in the major work of the grade about 88 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 4 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 4.NBT and 4.NF and cluster 4.OA.A.

The Grade 4 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 8-13 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 5-10 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 ninety-two lessons out of the 104 are focused on the major work. This represents approximately 88 percent of the lessons.
  • Eleven lessons out of the 104 are focused on the supporting work of the grade. This work was treated separately from the major work of the grade.
  • One lesson out of the 104 is focused on off, grade-level work. Lesson 4-3 focuses on 5.OA.A.1, using parentheses in numerical expressions and evaluating the expressions.
  • Two lessons out of the 104 focus on other content. In Lesson 1-8, students try to figure out a code for muffin orders. In Lesson 2-6, students measure two dogs with dog treats and then with paper clips.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
5/8
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Criterion Rating Details

The instructional materials reviewed for Grade 4 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 measurement and data 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 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 4 materials partially 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 4 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.

The supporting work is treated separately about half the time. There were approximately 42 of the 104 lessons which were focused on supporting work and approximately 21 of the lessons supported major work. 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 1-13 connects supporting standards 4.MD.1 and 4.MD.3 with 4.NBT.4 and 4.NBT.5, major work of the grade.
  • Lesson 2-13 connects supporting standard 4.OA.5 with 4.NBT.4 and 4.NBT.5, major work of the grade.
  • Lesson 5-9 connects supporting standard 4.MD.4 with 4.NF.3 and 4.NF.3.C, major work of the grade.
  • Lesson 7-8 connects supporting standards 4.MD.1 and 4.MD.2 with 4.NBT.5 and 4.NBT.6, major work of the grade.

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:

  • Lesson 2-10 is focused on Classifying Triangles. The focus portion of this lesson is aligned to 4.G.2 with no explicit connection to major work of the grade.
  • Of the five lessons that include Focus portions citing 4.MD.5, only one lesson, Lesson 6-11, includes a connection to major work of the grade. For example, Lesson 6-9 is focused on Measuring Angles. The lesson focuses on supporting standards 4.MD.5, 4.MD.5.A, 4.MD.5.B, and 4.MD.6.
  • Lesson 7-9 includes an "Identifying Figurate Number Patterns" Math Journal worksheet that is aligned to major work 4.NBT.6, but the worksheet does not focus on finding whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. The focus of this lesson is on supporting standards 4.OA.5 and 4.MD.3.

Indicator 1d

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

The instructional materials reviewed for Grade 4 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 112 days of lessons (104 lessons total) and another 16 days allowed for assessment, making 128 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 Friday's as a Flex Day for games and intervention work. With Fridays being included as Flex Days, this curriculum allows for approximately 32 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.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 4 partially meet the expectations 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 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 4 materials have one instance where prior, grade-level content is present and not identified as such. Lesson 4-3 focuses on 5.OA.1, using parentheses in numerical expressions and evaluating expressions. Often the sample answers include off, grade-level answers, and this is not identified for the teachers. For example, on page 128, the math masters answer key for page 54 shows students using parentheses in their answers, 5.OA.1. While the problems could be solved without using the parentheses, this could lead teachers to believe they must be included in the answer.

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, in Grade 4, there are 11 standards devoted to fractions (not including decimals), all of which are major work; there are 33 lessons for fractions. 

Everyday Mathematics Grade 4 materials do not provide extensive work with some grade-level standards. In particular, there are only two lessons fully aligned to 4.NF.4a. Although lesson 8-13 is identified to address 4.NF.B.4a, the lesson would only accomplish this if a student gave a particular answer to the problem posed in the Math Journal on page 311.  Thus, the lesson was not counted as fully aligned to the standard.  

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 4 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 1-1, "Place Value in Whole Numbers," is shaped by 4.NBT.A.
  • Lesson 3-3, "Number Lines and Equivalence," is shaped by 4.NF.A.
  • Lesson 6-6, "Measuring Angles," is shaped by 4.MD.C.
  • Lesson 7-10, "Solving Multistep Fraction Number Stories," is shaped by 4.NF.B.

While the materials have many instances where two or more domains are connected, often the connections are only surface-level connections. For example, in lesson 4-13, it shows connections between 4.NBT.2,4.NBT.3 4.NBT.5, 4.NF.6, and 4.NF.7. 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

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Gateway Two Details

The instructional materials reviewed for Grade 4 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 4 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.

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

The spiral tracker cites many instances of exposure to 4.NF.A, 4.NF.B and 4.NF.C, all of which require the development of conceptual understanding. Analysis of the lessons indicate only 13 lessons for 4.NF.A, 19 lessons for 4.NF.B, and 9 lessons for 4.NF.C. When looking at the lessons, the majority of the lessons do not develop conceptual understanding but instead give students a procedure to follow. Frequently, they work to develop conceptual understanding is through the math boxes, math journal, and games in the lessons. The teacher-provided directions and questions often remove the opportunity for students to develop conceptual understanding and create a procedural approach.

  • In the lessons on fractions, there is one open response lesson in unit 5 about fractions. Students spend two days discussing a word problem about inheriting land. However, there is only one answer to this question and one entry point to the problem.
  • In lesson 3-4, students are required to develop a rule for finding equivalent fractions. Instead of working with number lines and models, they are introduced to standard multiplication to find the equivalent fraction. With the way this lesson is set-up, students are simply employing a rule to find the answer.
  • In lesson 3-7, students are required to put fractions in order. The first page is done with the use of visual fraction models. The second page is done with number lines. However, only one problem gives any fractions on the number line to help students reason about their size.

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

  • On page 242 of the Teacher Edition, the Professional Development box reminds teachers to develop understanding instead of pushing multiplication by 1 (and explains why).
  • On page 326 of the Teacher Edition, the Professional Development box has strong commentary on the development of the unit. However, the box indicates an intentional emphasis on math facts in an attempt to build towards understanding.

There are many missed opportunities for the daily math message to provide a problem which would lead to student questioning and conceptual understanding of key topics. For example, lesson 5-5 is about adding tenths and hundredths; while the math message is about tenths and hundredths, students only write the "number model." This could have been a rich problem filled with mathematical discourse before the lesson to build conceptual understanding, but instead it is treated very procedurally.

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 4 partially meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. While lessons do exist to work on fluencies required at the fourth grade level, the lessons do not build upon each other to help students reach fluency, particularly with 4.NBT.4.

The instructional materials lack activities to build fluency adding and subtracting multi-dgit whole numbers using the standard algorithm. There are two lessons on the standard algorithm, which is the first time students are exposed to the standard algorithm. The online spiral tracker shows 81 exposures to 4.NBT.B.4 in focus lessons. When analyzing the lessons, many of the instances noted in the tracker show multiple exposures for the same lesson. Some of the lessons are not having students add and subtract multi-digit numbers. In lesson 1-5, students are rounding and then adding using friendly numbers. Lesson 1-10 has students converting yards, feet, and inches which involves multiplication but does not have students adding or subtracting. In chapter one, where the tracker showed 21 exposures, there are only eight actual lessons, and of those, only two align to the stated standard, lessons 1-7 and 1-9.

There are some places where fluency is given attention in the materials.

  • Most lessons in the materials have a "Mental Math and Fluency" piece which allows for students to practice fluencies required in Grade 4.
  • Several online games help students with the expectation of fluency, including: Baseball Multiplication, Multiplication Top-It, Beat the Computer, and Multiplication Bingo. It is important to note none of the online games have students practicing division.
  • Online is a reference sheet called "Do Anytime Activities" with suggestions to help students practice fluencies at home.
  • There is a fact check in the assessment book for teachers to mark when mastery of facts is accomplished.
  • Math Boxes are used during each lesson which consist of an average of six problems for students to complete. These problems do not connect to each other and are pulled from several different clusters and/or domains for students to complete for practice and maintenance of previous skills.

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. 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 create fruit baskets using multiple fruits. Online in the resource section, some "Projects" are available to help students with application of math.

Standard 4.OA.3 has 106 exposures within the curriculum and is listed as the focus of 14 days of Focus lessons.

  • The Focus portions of Lessons 1-5, 1-6, 1-7, 1-9, 4-2, 4-12, 5-13, 6-5 (2 days), 6-8, 7-7, 7-12, 8-1, and 8-9 are aligned to 4.OA.3.
  • Lesson 1-5 is aligned to 4.OA.3. The Focus portion of the lesson addresses estimation, but the problems are scaffolded and center more on the different strategies that were introduced in the lesson than on computation. The Math Masters "Using Estimation Strategies" worksheet includes a family note that states "Today students explored different ways of estimating...While all methods of estimation are equally valid, some may be more helpful than others for answering specific kinds of questions." The note never mentions computation, and the directions state "Read the number stories. Choose an appropriate estimation strategy."
  • Lesson 1-6 also focuses on estimation. The "World's Tallest Buildings" Math Journal provides five multi-step word problems. These problems require students to provide estimates and answers. However, on page 46 of the Teacher's Lesson Guide, teachers are told to do the following: "Referring students to the Guide to solving Number Stories on page 26 of the Student Reference Book, guide a discussion of the problem-solving process." This procedure for students to follow when solving number stories along with the scaffolding accompanying the problems detracts from the true application of the standard.
  • The focus portion of Lesson 4-2 is also aligned to 4.OA.3. Again, this lesson is addressing estimation without a focus on computation. The Math Journal activity "Finding Estimates and Evaluating Answers" requires students to write estimates and then "(u)se a calculator to solve the problem."
  • The Focus portion of Lesson 4-12 also addresses estimation. Although the Math Journal "Solving Multistep Multiplication Number Stories" does provide four multi-step word problems, the Teacher's Lesson Guide again scaffolds the problem solving and detracts from the true application of the standard (page 398).
  • The focus portion of Lesson 5-13 includes a "Planning a School Fair" Math Journal activity. The activity includes five problems, but only one of the five problems is not scaffolded for students.
  • The Focus portion of Lesson 6-8 addresses solving division number stories with remainders. Students complete the "Interpreting Remainders" Math Journal activity. The activity is very scaffolded. The top of the worksheet has bulleted steps for how to solve each problem, and three of the four word problems are scaffolded for students.
  • Lesson 7-12 includes a "Shopping at the Stock-Up Sale" Focus activity. This activity includes four word problems. Although the problems are multi-step, the word problems are very brief, and the context is very thin.
  • Lesson 8-1 includes "Cracking a Number Story Code" Focus activity. The activity requires students to solve eight multi-step word problems to crack a code.

Standard 4.NF.3.D has 76 exposures within the curriculum and is listed as the focus of 15 days of Focus lessons.

  • The Focus portions of Lessons 5-3, 5-4, 5-7, 5-8, 6-12, 7-6, 7-11, 7-12, 8-5, 8-6, 8-7, 8-8, 8-9, 8-10, and 8-11 are aligned to 4.NF.3.D.
  • The Focus portion of Lesson 5-3 focuses on fraction addition number stories. True application of the standard is not achieved because the problems are clearly identified as addition problems, so students know that they simply need to add the two fractions in the word problems. Also, on the "Fraction Addition" Math Journal worksheet, the problems are scaffolded, and students are required to use different strategies to solve each of the two word problems. Also, the worksheet includes three fraction addition problems which also clue the student to add the numbers.
  • The Focus portion of Lesson 5-4 focuses on mixed number addition problems. True application of the standard is not achieved because the problems are clearly identified as addition problems, so students know that they simply need to add the two fractions in the word problems. Also, on the "Adding Mixed Numbers" Math Journal worksheet, the problems are scaffolded, and students are required to use different strategies to solve each of the two word problems. Also, the worksheet includes four mixed number addition problems which also clue the student to add the numbers.
  • The Focus portion of Lesson 5-7 focuses on fraction subtraction number stories. True application of the standard is not achieved because the problems are clearly identified as subtraction problems, so students know that they simply need to subtract the two fractions in the word problems. Also, on the "Fraction Subtraction Number Stories" Math Journal worksheet, the problems are scaffolded, and students are required to use different strategies to solve each of the two word problems. Also, the worksheet includes four fraction subtraction problems which also clue the student to subtract the numbers.
  • The Focus portion of Lesson 5-4 focuses on mixed number subtraction problems. True application of the standard is not achieved because the problems are clearly identified as subtraction problems, so students know that they simply need to subtract the two fractions in the word problems. Also, on the "Subtracting Mixed Numbers" Math Journal worksheet, the problems are scaffolded, and students are required to use different strategies to solve each of the two word problems. Also, the worksheet includes four mixed number subtraction problems which also clue the student to add the numbers.
  • The Focus portion of Lesson 6-12 focuses on addition and subtraction number stories with fractions and mixed numbers. The "Fraction Number Stories" Math Journal activity provides six word problems. Although they are routine problems, some of them are multi-step. Some of the problems contain additional questions for students to answer after answering the original question, but this follow-up question is separate from the original question.
  • Lesson 7-6 includes a "Three-Fruit Salad" activity which requires students to create a recipe. This multi-step application problem has multiple solutions and entry points for students.
  • Lessons 7-12 and 8-7 are focused on Decimal Number Stories. The included word problems in Lesson 7-12 are all focused on money, and the connection to fractions is only made when students convert decimals to fractions, and in Lesson 8-7 the decimals are all "simple" (tenths). The connection to standard 4.NF.3.D is only made if students follow the procedure to solve the problems that has been introduced in the focus portion of the lesson.
  • Lesson 8-10 includes a "Making Sparkling Punch" activity. The application of addition and subtraction of fractions is limited because only two of the five ingredients in the recipe are fractions.
  • Lesson 8-11 includes a "Puppy Feeding Guidelines" activity which allows students to apply both standards 4.NF.3.D and 4.NF.4.C.

Standard 4.NF.4.C has 64 exposures within the curriculum and is listed as the focus of 15 days of Focus lessons.

  • The Focus portions of Lessons 6-13, 7-2, 7-3, 7-4, 7-5, 7-6 (2 days), 7-10, 7-11, 7-12, 8-7, 8-8, 8-9, 8-10, and 8-11 are aligned to 4.NF.4.C.
  • The Focus portion of Lesson 6-13 focuses on multiplying a fraction by a whole number. Four of the five problems on the "Making Lip Balm" Math Journal worksheet are scaffolded, requiring students to fill in the blanks for addition and multiplication equations.
  • The Focus portion of Lesson 7-2 focuses on multiplication number stories. True application of the standard is not achieved because the problems are clearly identified as multiplication problems, so students know that they simply need to multiply two numbers. On the "Baking Muffins" Math Journal worksheet, the fractions are all multiplied by either three or four. Most of the problems are of the same type making the activity routine.
  • Lesson 7-3 is aligned to 4.NF.4.C. On the "Multiples of Unit Fractions" Math Journal, there are only two word problems. The seven other problems on the page cue students to solution methods to the word problems and do not allow for true application of the standard.
  • In Lesson 7-4, the problems on "The Walking Club" Math Journal are too scaffolded to allow application of the standard. Each problem prompts students to write a multiplication equation.
  • The Focus portion of Lesson 7-5 focuses on multiplying mixed numbers by whole numbers. True application of the standard is not achieved because the problems are clearly identified as multiplication problems, so students know that they simply need to multiply the two numbers in the word problems. Also, on the "Solving Number Stories" Math Journal worksheet, the problems are scaffolded, and students are required to use different strategies to solve each of the two word problems. Also, the worksheet includes four multiplication problems with an integer and a fraction which also clue the student to multiply the numbers.
  • Lesson 7-6 includes a "Three-Fruit Salad" activity which requires students to create a recipe. This multi-step application problem has multiple solutions and entry points for students.
  • Lesson 7-10 includes a "Burning 100 Calories" activity. Although the problems have thin contexts, students are able to choose their own solution methods.
  • Lessons 7-12 and 8-7 are focused on Decimal Number Stories. The included word problems in Lesson 7-12 are all focused on money, and the connection to fractions is only made when students convert decimals to fractions and, in Lesson 8-7, the decimals are all "simple" (tenths). The connection to standard 4.NF.4.C is only made if students follow the procedure to solve the problems that has been introduced in the Focus portion of the lesson.
  • In Lessons 8-7 through 8-11, contexts are often expected but require application of the standard. For example, Lesson 8-11 includes a "Puppy Feeding Guidelines" activity which allows students to apply both standards 4.NF.3.D and 4.NF.4.C. Often multiple problems focus on the same context, for example sewing, allowing problems to become more procedural and require less true application.

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 4 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. 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 leads students to a specific procedure. Contexts are frequently thin, and problems are posed in a way in which students can solve them by relying on 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
5/10
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Criterion Rating Details

The instructional materials reviewed for Grade 4 do not meet the expectations for practice-content connections. 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 4 partially meet the expectations for identifying the MPs and using them to enrich the mathematics content.

The MPs are identified in the Grade 4 materials for each unit and the focus part of each lesson.

  • For Unit 3, page 219 discusses how MP3 and MP4 unfold within the unit and lessons.
  • For Unit 5, page 429 identifies which MPs are in the focus parts of the lessons within the unit.
  • For Unit 6, page 541 discusses how MP5 and MP7 unfold within the unit and lessons.
  • For Unit 8, page 751 discusses how MP1 and MP4 unfold within the unit and lesson.
  • Within the lessons, there 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. In a lesson, this can be seen in 2-8, page 168 TE.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

The Grade 4 Everyday Mathematics instructional materials partially meet the expectation for treating each MP in a complete, accurate, and meaningful way. The lessons give teachers limited guidance on how to implement the standards.

Below are examples of where the full intent of the MP is not met.

  • MP1: Lesson 8-1 cites MP1 and says "students will be solving stories that are more challenging but use the skills they already now;" however, in looking at the problems they are limited to two-step problems, a Grade 3 standard, which would not require students to persevere necessarily. Lesson 2-7 cites MP1; however, simply asking students "what happens when we go from a larger unit of time to a smaller unit" is not having students persevere in a problem. Lesson 3-2 cites MP1; telling students they should only use one color at a time and record a fraction to describe each of the different ways they find does not have student's persevering with problems.
  • MP2: Lesson 1-2 cites MP2 but has students writing numbers in expanded form; this does not have students reasoning abstractly and quantitatively.
  • MP4: Lesson 2-9 and 3-1 cite MP4; however, telling students how to model the problem does not meet the intent of practice. Lesson 3-6 cites MP4 and tells the students to use a visual fraction model, again not meeting the intent.
  • MP5: Lesson 1-1 cites MP5; however, the students are told to use calculators. Lesson 2-7 cites MP5 and again tells students which tools to use. Lesson 7-4 cites MP5, use tools appropriately; however, in the lessons, students are given the tools with which they are to work and not allowed to choose the tools.
  • MP6: Lesson 1-5 cites MP6; having students discuss real-life situations in which an estimate might be useful is not having students attend to precision. Lesson 2-3 cites MP6; however, reminding students that 2 and 7 are factors of 14 and asking for the other factor pair is not having students attend to precision. Lesson 3-9 cites MP6; students answering "what strategy did you use when comparing fractions and try to make a match" is not necessarily having students attend to precision.
  • MP8: Lesson 7-5 cites MP8, but in the lesson, there is no indication students are looking for structure when playing "Divide and Conquer."

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
+
-
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 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. MP3 is not even called out until Unit 3 as a focus practice standard and then doesn't show up until lesson 6. Here, it is labeled next to the directions "Invite students to justify their conclusions." 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:

  • In the Unit 8 assessment on page 835, question 5, students are asked to explain how they solved problem 4. However, students are not asked to work with other students and really explain and defend their thinking.
  • Math Journal page 72, problem 5, asks students if they agree with Sharita's reasoning; Sharita is a fictional student.
  • Math Masters, page 111, problem asks students if they agree with Margot's reasoning; Margot is a fictional student.
  • The first problem on the "Sharing Veggie Pizza" Math Masters in Lesson 3-5 homework has two answers, and students must choose the right answer. Students do not provide an explanation for their choice other than to add on to the provided drawing.
  • In the Lesson 3-13 Math Message Follow-Up, teachers are told to "(h)ave students explain how they knew which decimal was larger." However, students are not given an opportunity to work with other students and really explain and defend their thinking.
  • In Lesson 3-13, on page 305, the summarize problem asks students the following: "How can you help Vanna see her mistake?" A follow-up question states "What incorrect reasoning do you think Vanna used to get her answer?" These questions do not allow students to truly analyze the thinking of others because they are told that the thinking is incorrect.

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
+
-
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 4 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 3-6 states "Justify their conclusions." The missed opportunity here is for teachers to guide students in a rich discussion about what strategies they used and why.
  • Lesson 3-7 states "have the students justify their conclusion," but teachers are not given guidance to help students explore their justifications or the justifications of others.
  • Lesson 3-10 cites MP3, and again it asks students to justify. Teachers are not given guidance to help students explore their justifications or the justifications of others.
  • Lesson 4-11 has students explain how they solved the problem. Again, there is not instruction or guidance for the teacher to help the students explore the explanations of others.
  • During the "Solving an Area Problem with Fractions" activity in Lesson 8-9, the teacher guide states on page 807 to "(h)ave partnerships solve Problem 1 and discuss responses as a class," but teachers are not given guidance to facilitate this conversation.

Indicator 2g.iii

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

The instructional materials reviewed for Grade 4 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 5-5 includes "For beginning ELLs use visual aids and restatements to make task directions comprehensible and to explain word meanings."
  • 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. For example, in Unit 2, there are 39 vocabulary words needed for the students in Grade 4 to understand the unit. In contrast, Unit 7 only has 5 vocabulary words for the unit which is a much more manageable number for students in Grade 4.
  • 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, trade-first subtraction.  Other non-mathematical vocabulary includes “close-to estimation”, “mirror image”, “rectangular numbers”, and “equivalent names”. 

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 978-0-02-130758-6 null null null
null 978-0-02-137658-2 null null null
null 978-0-02-140942-6 null null null
null 978-0-02-141001-9 null null null
null 978-0-02-143064-2 null null null
null 978-0-02-143092-5 null null null
null 978-0-02-143096-3 null null null
null 978-0-02-143697-2 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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