Materials considered for review for this indicator were STEM projects. The instructional materials reviewed for Grade 4 do not meet the expectations for this indicator. The review team found that the instructional materials assess grade level content beyond the scope of the grade. The out of grade level standards assessed are not Mathematically reasonable for this grade level.

STEM materials that assess grade level content beyond Grade 4.

• Rocket Apogee STEM Project on pages 71 – 94 of the teacher STEM project edition
  • This project asks students to find angle measurements of right triangles using the tangent ratio. While it is noted that this is above grade level, this is not to be addressed until high school according to HSG.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles; and HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
  • This project asks students to identify outliers and calculate averages. These are not to be addressed until Grade 6 according to 6.SP.B.5.C.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
    

• 3D GEO STEM project on pages 95 – 108 of the teacher STEM project edition
  This project recommends students use Euclidean construction for geometric structures. While it is noted that this is above grade level, this is not to be addressed until HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
  

Review Team Note: A separate supplemental digital assessment database is available for an additional purchase cost. The review team did not analyze this supplemental digital assessment database as evidence for indicator 1a due to the fact that this additional component is not provided as part of the core materials.

*Evidence updated 10/27/15

The materials do not spend the majority of class time on the major cluster of each grade. A total of 72 activities/lessons are provided, and some may be repeated or take additional class periods. However, of the 72 activities/lessons, only 45 are aligned to major work of the grade, according to the table of contents. If the 45 lessons were fully aligned, 62.5% of the time is spent on the major work. Looking more closely, the percent of time spent on major work is below 62.5%. The lessons are labeled as aligned to major work of the grade, but the activities in the lessons do not actually align. Examples of this misalignment can be found in:

• ART page 81, denominators of 60, and ART page 96, denominators of 36. These examples are not the denominators that should be present in the Grade 4 standards.
• Pages 1-28 in ART do not fully align with the intent of the standards.
• There is little work with multi-step problems, work is often single- and double-digit, and there is little interpretation of the multiplicative comparison.
• The depth of work on OA.C.5 in pages 67-78 lacks connections to algebraic patterns.
• On page 31, the standard 4.OA.A.2 is not supported with the question-and-answer format that is presented. The standard asks for students to solve problems within a word problem by showing their thinking through drawings and equations, but this page is simply rote memory format without asking students to demonstrate thinking through drawings or equations.
• The standard 4.NBT.A.1 is not fully addressed with the lessons on pages 87-96. The lesson only briefly mentions that place value of a number is 10 times the place value to its right. The student work is identifying place value of numbers through multiple choice, matching numbers with their word form, and multiplying and dividing numbers by 10. There is no effort to connect that the place value is 10 times the place to the right in the number.
• Only 12 of the 34 lessons in the student book adequately cover major clusters. The following are not adequately covered:
  • 4.OA.A.2 (pages 15-31). Only 2 problems use drawings.
  • 4.NBT.A.1 (pages 80-96). Half of the pages are identifying place value and half are multiplying and dividing by tens, neither of which is 4.NBT.A.1.
  • 4.NBT.A.3 (pages 117-141). Five of the student pages are estimating, not just rounding.
  • 4.NBT.B.5 (pages 160-179). These lessons use fluency for multiplication with larger numbers, a Grade 5 standard.
  • 4.NBT.B.6 (pages 180-203). These lessons use fluency for division with larger numbers, a Grade 6 standard.
  • 4.NF.B.4.A (pages 298-309). Not all the pages include pictures or models.
  • 4.NF.B.4.B (pages 310-319). These lessons are not based on any true understanding; they simply use a procedure with multiplication.
  • 4.NF.B.4.C (pages 327-328). The drawings are supposed to help students solve the problems but students are asked to draw the picture after getting an answer.
  • 4.NF.C.7 (pages 355-372). The lessons lack opportunities to have students give justification of conclusions/answers.

Because of these misalignments, the actual time spent on major work would be less than the amount of time noted according to the table of contents.

The instructional materials for supporting content reviewed for Grade 4 do not meet expectations. The following evidence exemplifies a lack of coherence between and among content standards.

• The ART lesson on page 152 does not support the major work of 4.NF and there is a misrepresentation of a line plot.
• The identification of factors does not support major work because it is out of context, both in teacher edition on page 48, and in the student edition on page 29.
• The ART Lesson on page 19 does not meet standard and also seems forced content to connect with the Olympics (4.OA.B.4).
• In the ART lesson on pages 136-139, there are no recording equivalents in a two-column table and there is no generating conversion table or listing number pairs (4.MD.A.1).
• ART page 152 does not correctly utilize or represent a line plot (4.MD.B.4). The standard in this cluster requires students to use a line plot to display measurements in fractions of a unit and to solve problems involving addition and subtraction of fractions, connecting it directly to the 4.NF clusters.

The instructional materials for Grade 4 do not meet expectations for the amount of content designated for the year as viable for one school year in order to foster coherence between grades.

• For instance, 4.OA.A should have lessons that allow for in-depth work. There are seven lessons between the three resources labeled with standards in 4.OA.A out of the 72 total lessons.
• Beyond that, not all of these lessons are fully aligned to 4.OA.A. The STEM lesson "Plan your Escapement" has connections to 4.MD, which are not made and do not fully address interpretation of equations, multiplicative comparisons, and solving multi- step problems.
• The STEM lesson "Rocket Apogee" has many instances of above grade-level work on tangent ratio, base distance and altitudes.

The instructional materials for Grade 4 do not meet expectations for consistency with the progressions in the standards. Evidence of denominators outside of the scope of Grade 4 are scattered throughout. For example:

• ART page 81.
• ART pages 90 and 96. The use of terms such as "improper fraction" and "reduce" are not consistent with the language in the progressions.

Additional evidence of pieces that lacked consistency with the progressions can be found on:

• Teacher edition page 162 is the only example found for the use of arrays and the area model. This is not substantial enough to develop and explain understanding of this representation as way to solve multi-digit multiplication.
• The STEM Lesson "3-D Geometry" is beyond the scope of Grade 4 mathematics.
• Connections between unit fractions and addition of fractions and adding with the same denominators are not fully developed. These connections as well as the understanding of the size of the whole, from Grade 3, are missing in all three resources.
• Teacher edition pages 234-297 rush to procedures and do not build on the conceptual understanding of fractions from Grade 3 standards.
• The mathematical practices are not indicated nor aligned throughout lessons and instead are provided their own set of activities at the end of the book. This exact same set of activities appears in all teacher editions, Grades 3-5.

The instructional materials reviewed for Grade 4 do not meet expectations for fostering coherence through connections at a single grade. Learning objectives are written and either address learning at the individual standard level or simply restate the cluster. In other instances the objectives are written as activities so say what the students will be doing, not what they will learn. For examples, see teacher edition, pages 333 and 434 and STEM page 2, "Plan your Escapement."

Each lesson is taught in isolation, as a standard or a cluster of standards within the same domain. There is no evidence of lessons/activities where standards exist across domains. For example, there are missing 4.NF and 4.MD connections, and 4.MD and 4.OA connections throughout the resources.