The instructional materials reviewed for Grade 4 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A, “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.”. There are also many other sessions in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. For this indicator, all of the identified assessments and end-of-unit assessments for the nine units were reviewed. Units and sessions accompanying above grade-level assessment items are noted in the following list.

• In unit 2, the end-of-unit assessment expects students to describe the shape of the data from a numerical data set, including where the data are concentrated and the highest, lowest, and median values. The scoring rubric indicates that in order to meet expectations, students are to recognize statistical distributions including range, median, mode, and outliers. These expectations align to standards within 6.SP. According to Table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6.
• Problem 2 in the end-of-unit assessment for unit 4 assesses how to find the area of polygons, in this case a kite-shaped figure, using square units. The scoring rubric on page 161, indicates that the question is assessing student ability to find the area of polygons using a square unit of measure and counting them– square units and half units. Finding the area of shapes other than rectangles 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.” This problem could be omitted from the assessment without impacting the structure of the assessment.
• The end-of-unit assessment for unit 7 expects students to clearly show an understanding of volume from the scoring rubric on page 106. This expectation aligns to 5.MD.C, “Geometric measurement: understand concepts of volume,” and all of the sessions in unit 7 could be omitted without significantly impacting the underlying structure of the materials.
• Problem 2 on the end-of-unit assessment for unit 8 expects students to solve division problems with 1-digit and 2-digit divisors by using at least one strategy efficiently. The scoring rubric on page 128 indicates that there are several strategies students could use to demonstrate proficiency (none of which is the standard division algorithm). The inclusion of 2-digit divisors goes beyond the language of 4.NBT.B.6, and the problem could either be omitted or modified to a 1-digit divisor without impacting the structure of the assessment.
• In Unit 9, all problems on the end-of-unit assessment are on the topics of line graphs, constant change, and representing constant change on tables. The scoring rubrics on page 145 indicate that students must be able to read and interpret line graphs involving constant rate of change and to complete tables based on a constant change and represent it with an arithmetic expression. Constant rate of change is a topic that aligns to 6.RP.A., “Understand ratio concepts and use ratio reasoning to solve problems.” Since this is the last unit of the grade-level materials, this unit could be omitted without affecting the structure of the materials.

*Evidence updated 10/27/15

Instructional materials reviewed for Grade 4 do not meet expectations for focus. The majority of class time is not spent on the major clusters of the grade. According to the alignment 62% of the time is spent on major work at the grade. Upon deeper examination of the content in the nine units at the grade level, in five of these units (2, 4, 5, 7 and 9) there is above grade-level content that is being taught and assessed, which accounts for a portion of each of these not being fully aligned. This would even further decrease the amount of material on major work of the grade. For example:

• Lesson 1.1 and 1.2 in unit 9 align with 8.F.
• Lesson 2.4 in unit 9 graphs a linear pattern-Grade 5 work-and in lesson 2.7 the work comparing the two quantities that are graphed with possible expressions and equations is Grade 6 work.
• Unit 7 has 13 lessons and three assessments. Of the 13 lessons, only two are truly aligned to the standards. Lesson 3.1 in investigation 3 is only aligned because five problems on the homework page ask for students to compare fractions to hundredths, the remaining three problems on the page that ask for decimal addition are not aligned and the lesson itself is on volume and nets, which is Grades 5 and 6 work.

Additionally, every 4.NF standard, which is major work at the grade, is covered in unit 6, with two additional lessons (3.1 and 3.2) in unit 7. The two lessons from unit 7 do not match to 4.NF.C.7 and were not included in the following calculation. Therefore in the fraction unit, there are 22 lessons out of 162 total lessons in the program, which allots for 13.5 % of the time, or 15% including the three assessments of fraction. With six major clusters in Grade 4, three of them being 4.NF.A, B and C, this is not enough time to spend on the work of extending equivalence, building fractions and understanding decimals.

The instructional materials reviewed for Grade 4 do not meet expectations for viability of content for the scope of one year. The curriculum consists of 162 total sessions according to the provided pacing in the Investigations and Common Core State Standards Resource. Although this is a manageable number of days for a school year, the review team found that the major work accounts for about 62% of the lessons. The major work of 4.NF is greatly underrepresented in this series. In addition, unit 6 teaches addition of decimals which is above the grade level in three of the 24 lessons that deal with 4.NF.A, 4.NF.B and 4.NF.C.

The instructional materials reviewed for Grade 4 do not meet expectations for consistency with the progressions. The materials do not develop according to the progressions, nor do they give students extensive work with grade-level problems. In the front matter of each unit, there are detailed explanations of the content addressed that appears in a section called mathematics in this unit. Within this section, the "Looking Back" and "Looking Forward" pieces explains content from entering school to future grades within the program. There are not explicit connections to CCSSM, however. For example:

• "Understanding Volume" in unit 7, investigation 3, does not follow the grade-to-grade progression due to the concept being misaligned. Volume is introduced as a standard in Grade 5.
• Investigation 4 in unit 4 is completely not in the grade-to-grade progression because it has lessons on finding the area of special quadrilaterals which is a Grade 6 standard.
• The major work of 4.NF is greatly underrepresented in this series. There are only 22 of 162 sessions that appropriately support number fraction work.
• Unit 6 includes language around extending equivalence understanding in number fraction from Grade 3. There is a small note on page 10 about connections to Grades 2 and 3, but not an explicit connection to the standards. These connections could be enhanced in the next edition.
• In the area of 4.OA.A, only one lesson is focused on multiplicative comparison and this isn't enough to engage the students in this major work. There is an all-around lack of multi-step problem opportunities throughout. For the most part, students are guided through a three-part progression to guide them to solve.