The instructional materials reviewed for the Grade 4 Math in Focus do not meet the expectation for this indicator due to assessment of statistical distributions and similarity, congruence, and transformations. Additionally, there are several instances where future grade level work is covered and assessed. The following evidence describes both the chapter tests and the chapter reviews.

• In chapter 5, all questions from the assessment assess Grade 6 material of mode, mean and median (items 1-12).
• In chapter 14, questions 5, 7, 8, 11 and 12 assess rotational symmetry.
• In chapter 2, questions 4, 8 and 10 assess greatest common factor and least common multiple, which is a Grade 6 standard.
• The chapter 4 assessment contains questions (items 3, 4, 9, 10, 11 and 12) on line graphs.
• The chapter 7 assessment contains question on decimals including reading, writing, comparing and converting fractions to decimals (items 1-10).
• In chapter 8, the assessment contains questions on addition and subtraction of decimals, which is a Grade 5 standard (items 1-12).
• Benchmark 2 test contains questions on decimals (items 1, 2, 3, 4, 5, 11, 12, 13, 14 and 21)
• End-of-year test question 12 addresses Grade 6 standard on least common multiple, question 16 addresses decimals, and question 20 addresses tessellations.

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 4 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 and on future grade level work.

• Five out 15 chapters (1, 3, 6, 7 and 8) or about 33% of the time is focused on the major work of the grade.
• Six out of 15 chapters (2, 9, 10, 11, 13 and 14) or about 40% of the time is focused on the supporting work of the grade.
• Three chapters (4, 5 and 15) or about 20% of the time is focused on work not related to grade level.
• The content of chapter 4 does not meet the full intent of Grade 4 work. The Grade 4 standard for line plots uses fractions of a unit, and in chapter 4, line plots with whole numbers are the only ones present.
• The content of chapter 5 focuses on probability, which is a Grade 6 standard.
• The content of chapter 15 focuses on tessellations, which are not addressed directly in the standards; however, to complete tessellations students must understand rotations, reflections, and translations, which are Grade 8 standards.
• Off grade-level topics include: tables and line graphs (Grade 3), data and probability (Grade 6), adding and subtracting decimals (Grade 5) and tessellations (not CCSSM).
• There are 118 days of instruction. 24% (28 days) are spent on major work, 19% (22 days) are spent on supporting work, 23% (27 days) are spent on additional work, and 34% (41 days) are spent on work that is in another grade level.
• There are 59 instructional lessons in Grade 4. Thirteen lessons, or 22%, are spent on major work, 24% (14 lessons) are spent on supporting work, 15% (9 lessons), and 39% (23 lessons) are spent off grade level.
• More time is spent on off grade-level work than is spent on the major work of the grade.
• The large amount of future grade level work that is introduced and assessed in the material detracts from the major work of the grade.

The supporting content does not enhance the focus and coherence by engaging students in the major work of the grade. For this indicator, all grade level work that was not major work was considered supporting work. Chapters 2, 9, 10, 11, 13 and 14 represent supporting work of the grade.

• Chapter 2 includes lessons 2.2, 2.3 and 2.4 where the major work of the grade is supported using the four operations.
• The content in chapters 9, 10, 11 and 14 is treated separately from the major work of the grade level.
• In chapter 13 only lesson 13.1 supports the major work of the grade by using fractions.

The amount of content designated for Grade 4 Math in Focus is not viable for one school year. Overall, the amount of time needed to complete the lessons is not appropriate for a school year of approximately 170-190 days.

• There are 59 lessons in the program that cover only 119 days of instruction, many of which are not spent on the major work of the grade.
• This falls about 56 days short of the typical school year.

Grade 4 Math in Focus materials are not consistent with the progressions in the standards. Content is not clearly identified, there are not extensive grade-level problems and concepts are not explicitly related to prior knowledge.

Materials do not develop according to the grade-by-grade progressions and prior and future grade content is not clearly identified.

• Several chapters are above grade level work and are not identified as such in the program, including the teacher and student editions.
• The content in chapter 5 is Grade 5 work, and in the skills trace (found at the front of each chapter) and in the chapter planning guide (found in each chapter) there are not notations explaining how the work is Grade 5 work or how this is related to grade-level work. The same is true of chapters 4, 6, 8 and 15.

Materials do not give students extensive work with grade-level problems.

• Grade 4 Math in Focus has 55 lessons that span approximately 119 days.
• Thirty-six lessons or about 65% of the time is spent on grade-level problems.
• Nineteen lessons or about 35% is spent on work other than grade-level problems.
• On a positive note, students have at least four guided practice problems followed by at least 10 independent practice problems in each lesson.
• Thirty days include work that is not grade level appropriate.
• Four days are spent on work that is not in the CCSSM.

Materials do not explicitly relate grade level concepts to prior knowledge from earlier grades.

• Each chapter contains an initial lesson called "Recall Prior Knowledge." In this lesson, students are recalling prior knowledge from earlier grades and chapters.
• Students are recalling prior knowledge from earlier grades and chapters but it does not directly always trace back to the standards. For example, chapter 6 states "students learned in Grade 3 to express fractions in simplest form, and to add and subtract like fractions;" however, there is not a Grade 3 standard which addresses this skill. Students in Grade 3 are not asked to add and subtract like fractions. The closest Grade 3 standard 3.NF.A.3.B states "Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model."
• If prior knowledge were aligned to the standards and not the text then CCSSM concepts would be explicit. Instead skills and strategies from the series are explicitly referred to in the prior knowledge section.
• Chapter 12 refers back to another chapter in Grade 4 instead of tracing the standard from prior grade levels.

Materials do not foster coherence through connections at a single grade level. The learning objectives are not clearly linked to the CCSSM cluster headings, and the materials do not connect two or more clusters in a domain.

The Grade 4 materials do not include learning objectives that are visibly shaped by CCSSM cluster headings.

• For example in chapter 5, the objectives are to describe a data set using the average or mean and then find the mean, median, mode and range of a set of data. This is not a Grade 4 standard within the CCSSM.
• There is a section in the teacher guide for Grade 4 that indicates CCSSM correlations, however these are not always a correct alignment.
• However, the scope and sequence is not organized by cluster headings in Grade 4.
• There are many chapters that are do not address the learning objectives of CCSSM cluster headings (chapters 4, 5, 6, 8 and 15).

The Grade 4 materials do not include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

• The chapter planning guide contains several references in each lesson from two or more clusters and/or two or more domains; however, a closer look at the activities shows the activities do not truly align to the stated standards.
• For example, chapter 1 lesson 1 states it aligns to both 4.NBT and 4.OA. However, when looking at the lesson it does not ask students to generate a number or shape pattern that follows a given rule.
• A missed opportunity to make connection with finding the area of a rectangle (4.MD.2) and multiplying a fraction by a whole number (4.NF.4).
• The content in chapter 9 misses the opportunity to connect measurement of angles (4.MD.C) with addition of fractions (4.NF.3).