The instructional materials reviewed for Grade 5 partially meet expectations that supporting content enhances focus and coherence by engaging students in the major work of the grade. Some of the supporting work is treated separately and does not support the major work of the grade, and many natural connections are missed.

The following details supporting work in the instructional materials.

• Topic 11 is focused on converting measurements. All but one lesson supports the major work of the grade. However, there are missed connections with powers of ten and decimals, 5.NBT.2.
• Topic 12 is focused on data and is mainly treated separately from the major work of the grade. Lesson 12-3 touches on using operations with fractions, mainly with two types of questions – finding the total and finding the difference between highest value and lowest value.
• Topic 13 is focused on using parentheses and brackets. A few of the problems support the major work of the grade by including decimals and fractions in the problems.
• Topic 14 is focused on graphing on the coordinate plane to solve real world problems. This work is treated separately from the major work of the grades.
• Topic 15 is focused on analyzing patterns and relationships. A few of the problems support the major work by including decimals and fractions in the problems.
• Topic 16 is focused on classifying two dimensional figures and is treated separately from the major work of the grade.

The instructional materials reviewed for Grade 5 partially meet the expectations for being consistent with the progressions in the standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade-level.

Material related to future grade-level content is not clearly identified or related to grade-level work. The exception is the topic titled "Step up to 6th grade" where the materials are clearly identified as Grade 6 materials. The Grade 5 materials have some instances where future grade-level content is present and not identified as such. For example:

• In Topic 2, Lesson 4-6 use a procedure for adding and subtracting decimals instead of building on conceptual understanding.
• Lessons 5-5 and 5-7 address the standard algorithm for division which more closely aligns to 6.NS.2.
• Lessons 12-1 to 12-3 have students finding the outlier in a data set, 6.SP.5c.

The content does not always meet the full depth of standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:

• In Topic 2, all 7 lessons cite 5.NBT.7 for addition and subtraction. Of the 7 lessons, the first 3 focus on using concrete models or drawings and strategies based on place value. In lesson 2-4, students are introduced to the standard algorithm for addition, and in lesson 2-5, students are introduced to the standard algorithm for subtraction, which is continued for addition and subtraction in 2-6. The seventh lesson focuses on the standards for mathematical practice.
• Topic 4 cites 5.NBT.7 for 9 of the 10 lessons for multiplication of decimals, and 6 of those 9 lessons use concrete models or drawings and strategies based on place value. In lessons 4-4 and 4-9, students use the standard algorithm for multiplication. The tenth lesson focuses on the MPs.
• Topic 6 cites 5.NBT.7 for 8 of the 9 lessons for division of decimals, and 4 of those 8 lessons use concrete models or drawings and strategies based on place value. In lessons 6-4, 6-5, 6-7, and 6-8, students use the standard algorithm for division. The ninth lesson focuses on the standards for mathematical practice.
• The last part of 5.NBT.7 states that students should "relate the strategy to a written method and explain the reasoning used." The lessons in Topics 2, 4 and 6 that align to 5.NBT.7 offer few opportunities for students to explain the chosen strategy or reasoning used themselves.

The materials extensively work with grade-level problems, for example:

• All students complete grade-level materials, and suggestions for re-teaching and intervention are included with each lesson and at the end of each topic.
• Online resources include extra, on-level and advanced-practice materials.
• A math and science project is available for each topic taught.
• Homework practice problems are identified in the teacher edition as intervention, on-level, and advanced.
• The numbers of topics focusing on Grade 5 domains are as follows: 6 out of 16 topics address number and operations in base ten; 3 out of 16 topics address number and operations - Fractions; 2 out of 16 topics address operations and algebraic thinking; 3 out of 16 topics address measurement and data; and 2 out of 16 topics address geometry.

The materials generally relate grade-level concepts to prior knowledge within the introduction of each topic, for example:

• "Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 5, explaining connections to the content within the topic, and explaining what will come later in Grades 5 and 6. An example can be found on pages 1c-1d for Topic 1.
• Individual lessons also include coherence headings. An example is in lesson 13-3 on page 747A that includes the heading, "Coherence: Throughout the program, students have been exposed to the meaning of the operations, starting with addition and subtraction ... to write numerical expressions with more than one operation and parentheses."
• In Topic 7, for 5.NF.B, students are extending their knowledge of addition and subtraction of fractions to add/subtract fractions with unlike denominators.
• In Topic 10, for 5.MD.A, students are building on their ability to calculate area to calculate volume.
• In Topic 11, for 5.MD.A, students build on their measurement knowledge to calculate measurement conversions.

However, there are times when critical connections to prior learning are missed or stated incorrectly.

• 5.NF.4/5.NF.7 - The teacher's guide makes links to prior grade work with operations with fractions but does not link prior (or current) grade work with multiplication and division and related models to the work with multiplying and dividing fractions; connections to these operations and decimals may have been particularly useful.
• 5.NBT.6/5.NBT.7 - The teacher's guide combines five topics together and has one column on one page of prior, grade-level standards. This link is focused on Grade 4 work with addition and subtraction and multiplication and division. The visual includes an example of the standard algorithm for division, but this is not the only method students were taught or would primarily have as they transition from Grade 4 to Grade 5. This suggests that this is the way division should be taught in Grade 4 and/or that students may be coming to them in Grade 5 with this as their primary strategy. Fraction multiplication is also included here, but it is not made clear how it connects to the content of Topics 2-6. Little attention is given to the previous conceptual learning students had in 1st-4th grade regarding operations and how this learning development may be connected to where students are headed with their work with division and with operations with decimals.

The instructional materials reviewed for Grade 5 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.

The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.

• The focus of Topic 12 is 5.MD.B, Represent and interpret data. Lesson objectives in Topic 12 include: L1 - Read and analyze line plots and L2 - Organize and display data in a line plot.
• A similar example for Topics 8 and 9 can be found on pages 455I - 455J.

The materials for Grade 5 enVision Math 2.0 do not foster coherence through grade-level connections. Most lessons in the Grade 5 program focus within a single domain and cluster. Of 112 lessons, 101 lessons focus within a single cluster and domain.

• In Topic 1, 0 of the 7 lessons address standards within two or more clusters.
• In Topic 2, 0 of the 7 lessons address standards within two or more clusters.
• In Topic 3, 0 of the 7 lessons address standards within two or more clusters.
• In Topic 4, 0 of the 10 lessons address standards within two or more clusters.
• In Topic 5, 0 of the 8 lessons address standards within two or more clusters.
• In Topic 6, 0 of the 9 lessons address standards within two or more clusters.
• In Topic 7, 0 of the 12 lessons address standards within two or more clusters.
• In Topic 8, 0 of the 9 lessons address standards within two or more clusters.
• In Topic 9, 0 of the 8 lessons address standards within two or more clusters.
• In Topic 10, 0 of the 6 lessons address standards within two or more clusters.
• All 8 of the 8 lessons within Topic 11 address standards in two domains (5.MD and 5.NBT).
• In Topic 12, 2 of the 4 lessons address standards in two domains (5.NF and 5.MD).
• In Topic 13, 0 of the 5 lessons address standards within two or more clusters.
• In Topic 14, 0 of the 4 lessons address standards within two or more clusters.
• In Topic 15, 1 of the 4 lessons address standards in two domains (5.OA and 5.G).
• In Topic 16, 0 of the 4 lessons address standards within two or more clusters.