The instructional materials reviewed for Grade 4 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 detail supporting work in the instructional materials.

• Topic 7 is focused on factors and multiples and somewhat supports the major work of the grade. The connections to the major work are weak. If this topic was earlier in the materials the connections would be stronger since the connections are one-digit by one-digit or one-digit by two-digit multiplication. However, no instruction in Topic 7 is explicitly tied to multiplication/division strategies (e.g., splitting a number into factors, using associative property to rearrange); connections to creating common factors is mentioned in the teacher guide but not tied to instruction in this topic.
• Topic 13 is focused on conversion of measurements 4.MD.A and does support the major work of the grade. Lesson 13-1, Lesson 13-2, Lesson 13.3 and Lesson 13.6 connect measurement standards to operations with fractions (4.NF).
• Topic 14 is focused on generating and analyzing patterns 4.OA.C. This topic is treated separately and does not support the major work of the grade.
• Topic 15 is focused on angles and angle measurement, 4.G.A. This topic is treated separately and does not support the major work of the grade.
• Topic 16 is focused on lines, angles, and shapes (4.G.A). This lesson is treated separately from major work.

The instructional materials reviewed for Grade 4 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 5th grade" where the materials are clearly identified as Grade 5 materials. The Grade 4 materials have some instances where future grade-level content is present and not identified as such. For example:

• Lessons 3-7, 3-8, 3-9, and 4-10 align to using a procedure for multiplication, which is 5.NBT.5.
• Lessons 5-8 and 5-9 align to using a procedure for division, which is 6.NS.2.
• Lessons 11-1 and 11-2 have students finding the outlier in a set of data, which is 6.SP.5c.

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

• 4.OA.3, "Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding" is the focus of three lessons. Within these three lessons (6-3, 6-4 and 6-5), some of the problems are one-step problems. A few other lessons do list 4.OA.3 as a supporting standard; however, they do not have multistep problems in the lessons.
• 4.NBT.5, "Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models" is the focus of three lessons. One of the lessons (3-1) teaches students to write zeros after the product of the first two numbers if you are multiplying by a power of 10. For example, for 3 x 50, you would multiply 3 x 5 and then add one zero to get the answer. There is no connection made to place value, which could lead to misconceptions later for students.
• 4.NF.2 is the focus of three lessons, and this standard encompasses the major work of comparing fractions with unlike numerators and unlike denominators.
• 4.NF.5 is mentioned in two lessons, and when further examining those lessons, the standard is not present in lesson 12-5 and is briefly mentioned in the examples in lesson 12-4.

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 4 domains are as follows: 5 out of 16 topics address number and operations in base ten; 4 out of 16 topics address number and operations - Fractions; 3 out of 16 topics address operations and algebraic thinking; 3 out of 16 topics address measurement and data; and 1 out of 16 topics address geometry.

The materials 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 4, explaining connections to the content within the topic, and explaining what will come later in Grades 4 and 5. An example can be found on pages 325c-325d for Topic 6.
• Individual lessons also include coherence headings. An example is in lesson 6-1 on page 327A that includes the heading, "Coherence: In Topic 2, students developed fluency in adding and subtracting whole numbers. In Topics 3 and 4, ... In this lesson, students use these skills to solve problems involving comparisons."
• In lesson 9.1, for 4.NF.B, students are extending their simple equivalent fraction knowledge to add fractions using models.
• In lesson 1.4, for 4.NBT.A, students are extending their knowledge of number lines to round whole numbers.

The instructional materials reviewed for Grade 4 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 2 is 4.NBT.B, Use place value understanding and properties of operations to perform multi-digit arithmetic, and 4.OA.A, Use the four operations with whole numbers to solve problems. Lesson objectives in Topic 2 include: L4 - Use place value and an algorithm to subtract whole numbers and L6 - Use previously learned concepts and skills to reason abstractly and make sense of quantities and their relationships in problem situations.
• A similar example for Topic 15 can be found on pages 765I - 765J.

The materials for Grade 4 enVision Math 2.0 partially foster coherence through grade-level connections. Most lessons in the Grade 4 program focus within a single domain and cluster. Of 109 lessons, 70 lessons focus within a single cluster and domain.

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