The instructional materials reviewed for Grade 4 do not meet expectations for assessment. For this indicator, the review team examined all components of the cumulative tests, which included the power-up tests, the cumulative tests, 10 extension tests, and the performance tasks. The team was unable to review the benchmark tests as they were not included in the materials. There are two reasons why these materials do not meet the expectations for this indicator. First, a significant number of the questions on the Cumulative and Power Up tests align to standards that are below grade 4, and second, of the remaining questions, there are several instances of questions aligning to standards above grade 4. With the significant number of questions that align to either above or below grade-level standards, omission or modification of the questions would result in a significant impact on the underlying structure of the grade 4 materials. The following list of cumulative tests outlines the questions that are aligned to above grade-level standards and the standards or clusters to which the questions are aligned.

• Cumulative Test 10, after lesson 55, questions 3, 5, and 10 assess working with numerals larger than 1,000,000, which is above expectations for 4.NBT.A, “Generalize place value understanding for multi-digit whole numbers”, and 4.NBT.B, “Use place value understanding and properties of operations to perform multi-digit arithmetic,” where the expectation is to work with numerals less than or equal to 1,000,000.
• Cumulative Test 11, after lesson 60, question 7 assesses writing a number larger than 1,000,000, which is above expectations for 4.NBT.A.2, “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons”, where the expectation is to work with numerals less than or equal to 1,000,000.
• Cumulative Test 14, after lesson 75, question 7 assesses locating negative numbers on a number line, which aligns to NS.C.6, “Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.”
• Cumulative Test 16, after lesson 85, question 6 assesses fractions with a denominator of 13, which is above expectations for 4.NF, “Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.”
• Cumulative Test 19, after lesson 100, question 5 assesses median, which aligns to 6.SP.B, “Summarize and describe distributions.”
• Cumulative Test 21, after lesson 110, question 2 assesses rounding to the nearest 100,000,000, which is above expectations for 4.NBT.A, “Generalize place value understanding for multi-digit whole numbers,” where the expectation is to work with numerals less than or equal to 1,000,000.
• Cumulative Test 22, after lesson 115, assesses the interpretation of a circle graph, which is a type of graph that is beyond expectations for the Common Core State Standards for Mathematics.
• Cumulative Test 23, after lesson 120, question 2 assesses finding the area of a triangle, which aligns to 6.G.A.1, “Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems,” and questions 3 and 8 assess the use of rates and percentages, which aligns to 6.RP.A, “Understand ratio concepts and use ratio reasoning to solve problems.”

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 4 do not meet expectations for focus. The materials suggest a 60-minute class period consisting of a 30-minute block in which students complete written practice problems (distributed practice which does not particularly focus on or extend the new concept taught that day) and a 15-minute power up block. Because of this and the wide range of concepts address in the practice which changes daily, it is difficult to trace the amount of time spent on each concept through this and the power up practice. This leaves one to focus primarily on the new concept lessons as the tool in which to base the review alignment to the major work of the grade level. The materials allot a mere 15 minutes for the new concept lesson. An in-depth look at the major work of the grade in 4.OA, 4.NBT and 4.NF lead the review team to the following.

4.OA.A:

• Of the 11 lessons designated as major work in the text, only two, lesson extension activity 3 (multiplicative comparisons) and lesson 94 (two-step word problems) are actually major work.
  • Lesson 94 is only partially aligned since much of the lesson does not deal with the word problems, but rather 2-step equations set up to solve in an algebraic fashion. The other nine lessons are mostly single-step word problems, not multi-step as the standard indicates, and therefore more a review.

4.NBT:

• For 4.NBT.A, nine lessons involve the major work of generalizing place value for multi-digit numbers.
• For 4.NBT.B, the addition and subtraction computation lessons up to lesson 25 are mostly review. Roughly 15 lessons can be considered major work. Multi-digit multiplication doesn't begin until lesson 44; prior to that, the lessons involve multiplication facts (five lessons). The multi-digit multiplication or division lessons cannot be considered to be part of the major work as they all involve teaching procedures that should not be addressed until Grades 5 and 6.

4.NF:

• For 4.NF.A and 4.NF.B, approximately 18 lessons could be considered in the realm of major work, however too many of the lessons are reviewed which does build throughout the year. Unfortunately, it takes far too long to actually get to the meat of the major fraction work and the few lessons (104, 107, 109, 115 and 116) which directly reflect the major work come at the end of the year. This reflects only one lesson multiplying fractions by a whole number (lesson extension activity 6) and one lesson adding and subtracting fractions with a common denominator (lesson 107).
• For 4.NF.C, four lessons address this standard and within two of these lessons, decimals to the thousandths are addressed which is above the scope of Grade 4. In summary, approximately 48 of the 132 lessons (120 lessons and 12 investigations) align to the major work of the grade level. This amounts to roughly 36% of the lessons addressing the major work of Grade 4.

In addition, specific misalignments were found in the following:

• In lesson 91, new concept exceeds standards by going to 1000th place with decimals.
• In lesson 96, is labeled as aligned to 4.OA.A, however the new concept is focused on finding averages in data. This is not reflective of the major work of this grade level.
• In lesson 97, within the lessons' written practice, a percent question (question 3) and writing a mixed number as a decimal to the thousandths place (question 4) is found.
• Lesson 99 asks for the square root of 25 and to write a number from Roman numerals in the power up portion.
• Lesson 111 focuses on volume, which is a Grade 5 standard.
• Lessons 112 and 115 focus on reducing fractions to the simplest form but asks to reduce fractions that have a 9 and a 7 as the denominator. The expectations in Grade 4 are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.
• Lesson 117 focuses on rounding whole numbers through hundred millions. Expectations are limited to whole numbers less than or equal to 1 million.
• Lesson 119 focuses on fractions with different denominators. It is not aligned because Grade 4 standards are adding and subtracting with like denominators. This is more appropriate for Grade 5.

The instructional materials reviewed for Grade 4 do not meet expectations for supporting content enhancing focus and coherence simultaneously. A lack of coherence between the major and supporting work is evident in the following examples:

• In lesson 40, capacity is taught in isolation and therefore does not support the major work of the grade. In section 10, one of the 11 lessons reference alignment to additional standards.
• In lesson 92, classifying quadrilaterals and angles is taught in isolation.
• In lesson 55 about prime and composite numbers, students find multiples of numbers by multiplying, on a multiplication table and find the factors of a number by drawing arrays, identify numbers as prime or composite, and work only with finding factors of numbers to 12. There is no real connection or support to multi-digit multiplication (4.NBT.B) because in actuality, multiplying multi-digit numbers is introduced in Lesson 44, which is prior to the lesson in which factors and multiples are explored. Multi-digit multiplication is presented only using procedure.
• The work in this standard cluster requires students to use a line plot to display fractional measurement data and solve problems which link to addition and subtraction of fractions (4.NF.A). However, lessons identified in this standard cluster mostly involve pictographs, line graphs, bar graphs and circle graphs (investigation 6). Only extension lesson 7 addresses the line plot with fractional measurement data.

The following examples serve as lessons where connections were made, but it was concluded that there are an extremely limited amount of examples or even questions that had support or an additional cluster that supported the major work of the grade level. In lesson 68, question 30 supports 4.NBT.A; lesson 95, question 30B supports 4.OA.A.

The instructional materials reviewed for Grade 4 do not meet expectations for viability of materials for one year in order to foster coherence between the grades. The curriculum consists of 120 lessons, 12 investigations and 23 cumulative assessment days for a total of 155 days needed to complete the curriculum. Although this is a manageable number of days for a school year, only 48 of the 132 lessons identified as aligned to the major work of the grade level can actually be considered major work. Most lessons are either a review of previous content or address work above grade level. None of the lessons dealing with multiplication and division can be considered major work as the strategies taught align with Grade 5 and Grade 6 work respectively. Additionally, 23 lessons (approximately 17% of the lessons) are aligned to the MP, but not also aligned to Grade 4 content standards. For these reasons and the evidence cited in 1b, this grade does not cover the major work with enough depth for students to be ready for the work of the next grade level.

The instructional materials reviewed for Grade 4 do not meet expectations for consistency with the progressions in the standards. This is evident through examples below which were based on materials around the progression of grade-by-grade content, the access in materials to grade-level problems and the connections to concepts from prior grades. The materials address a great deal of off-grade level content which is not clearly identified as such, other than identifying the CCSSM focus of the lesson as a MP rather than a content standard. Additionally, above grade level content is inaccurately aligned to either a Grade 4 standard or MP. Examples of work that are not consistent with the progressions are:

• Although one method cited in multiplying 2-digit numbers in lesson 44 (4.NBT.B) is a partial product strategy, the multiplication procedure is taught as method 2. This is more appropriately presented in Grade 5.
• Lesson 50 involves adding decimal numbers (a Grade 5 standard). While the major work in division is to be presented using strategies and the relationship between multiplication and division, instead the division work is presented by teaching the procedural skill of long division, which shouldn't be presented until Grade 6.
• Lesson 35 concerns naming a mixed number, which is a Grade 5 standard. This displaces grade level content.
• Lesson 62 teaches exponents, which is future material that is not identified.
• The new concept in lesson 73 is geometric transformations which is a standard in Grade 8.
• In lesson 11, students review addition. There is no grade level correlation provided based on problems in the lesson. This is reviewing content that should be mastered in Grade 1 and Grade 2.
• In lesson 6, students review subtraction based on the problems given. This also focused on Grade 1 and Grade 2 content without identifying it as such.
• In lesson 41, the new concept is subtracting across zeros with three-digit problems. This is expected to be mastered in Grade 3.

The majority of the major work focus in 4.NF doesn't occur until after Lesson 102 and therefore not much time is allotted for grade-appropriate work in this cluster. Additionally, due to the structure of the curriculum, the amount of time spent in new concept lessons is only a small fraction of the entire lesson time, thus preventing work from being extensive. A majority of the lessons are either below grade level review or extend above grade level expectations. Lessons 22, 26, 36, 37 and 74 review previous grade level concepts. Lessons 85 and 91 go beyond the scope of Grade 4 by introducing thousandths.

Additionally, connections between concepts are not clearly articulated to teachers. The curriculum materials do not connect between grade levels explicitly identified, so teachers are not made aware of how what they are currently teaching relates to what students learned in Grade 3, although sections do list pre-requisite skills needed for the lesson. For example, in Grade 3, fractions are identified and explored using models, but in the Grade 4 materials these concepts are taught again as new concepts (e.g., lessons 22, 26, 103), with no mention that this is a review from Grade 3 to teacher or student.

In no instances did the review team find evidence of explicit connections made to prior knowledge. Additionally, due to the structure of the curriculum, the amount of time spent in new concept lessons on these concepts is only a small fraction of the entire lesson time, thus preventing work from being extensive.

The materials reviewed for Grade 4 do not meet expectations for coherence through connections at the grade level. This was evidenced through the absence of CCSSM-aligned learning objectives as found in the following:

• The identified objective in lesson 15 is to use money amounts to represent subtraction of two-digit numbers with regrouping (Grade 2 content).
• The identified objective in lesson 20 is to use a number line to round a number to the nearest ten (Grades 2 and 3); and to round money amounts to the nearest dollar and to the nearest 25 cents (Grade 4 rounds to any place).
• Lesson 22 objectives deal with naming fractions and adding money which is not aligned to 4.NF.A.
• Lesson 26 objectives state drawing pictures representing halves, thirds and fourths, which is not aligned to 4.NF.A.
• Lesson 36 objectives reference naming and comparing fractions of a dollar which is not aligned to 4.NF.A.
• Objectives in lessons 112 and 114 reference writing a reduced form of a fraction and simplifying which is not aligned to 4.NF.A.
• The objectives in Lessons 70, 74, 89, 116, 119 and 120 do not align to the 4.NF.B cluster.

Additionally, a lack of connections in math problems made between and among clusters in a domain and domains in a grade informed the evaluation of instructional materials for this criteria. Materials do not connect domains where they are natural and important. The series is set up as individual lessons focusing on a specific skill. These skills are randomly reinforced throughout the year within the written practice portion of the lesson but the questions/skills are always in isolation. There is no evidence of purposeful domain connection. Examples where connections were missed include:

• Lesson 45 focus is on parentheses and the associative property as well as naming line segments. These concepts are not connected mathematically in this lesson.
• In lesson 49, students solve equal grouping problems and solve comparison problems. These concepts are addressed separately yet could be connected.
• Student work with conversion of measurements (4.MD.1 and 4.MD.2) does not relate to multiplicative comparisons of 4.OA.A, specifically:
• Lesson 40 work with converting capacities does not specifically illustrate the multiplication connection but lesson 77 work with converting weight/mass does involve connecting the "times as many" work as they use multiplication to convert from one unit to the other. Unfortunately, those are the only two lessons involving this part of 4.MD.A. The other lessons designated as 4.MD.A do not pertain to this.

A few connections are made, but not enough to meet or partially meet expectations.

• Lessons 109, 115 and 116 are the only lessons in which the objectives do indicate alignment to 4.NF.A
• In Lesson 75, there is some attempt at connecting angle measurement to a fraction of the full 360-degree measure of a circle, connecting 4.MD.C to 4.NF.3, but it isn't followed through in subsequent lessons 81, lesson extension activity 4 or in lesson 92, lesson extension activity 5.