• The instructional materials reviewed for Course 3 partially meet the expectations for the non-major content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. In some cases, the non-major work enhances and supports the major work of the grade level, while other areas could be stronger.

  Non-major clusters of the Grade 8 are:

  • 8.NS.A - Know that there are numbers that are not rational, and approximate them by rational numbers.
  • 8.SP.A - Investigate patterns of association in bivariate data.
  • 8.G.C - Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

  Evidence of non-major content enhancing focus and coherence and supporting a partially meet's score are:

  • 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 5, lesson 2 by having students work with Irrational Numbers so that they are able to fully understand the major work of the Pythagorean Theorem by working with square and cube roots.
  • 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 6, Lesson 1 by having students work with square and cube root symbols so they are able to fully comprehend and solve problems involving right triangles.
  • 8.SP.A supports 8.EE and 8.F in Module 7 - Chapter 15, Lessons 1-3 by having students work with grade level vocabulary supporting the major work and interpreting and analyzing scatter plots to determine the relationship between the two variables.

  Examples of missed opportunities:

  • 8.G.C has no support of major work noted.
  • Supports of the major work are not often specifically called out as a support. Often times the connections are there, but a teacher would need to know the cohesiveness on their own to be able to make the connections for the students.

  Though the supporting standards have made some connections to major work, they are not specifically written as such, and the non-major clusters of this grade are taught in isolation and miss some opportunities to engage students in the major work of Grade 8, which is why this team supports a partially meets score.

  In chapter 15, slopes and intercepts are interpreted as constant rates of change and initial values in the data, which supports major work of Grade 8.
• Opportunities to connect student-derived formulas for volume with nonlinear functions (8.F.5) were missed.
• In chapter 13, 8.EE.A, which is major work, is supported by 8.G.C.9.

The instructional materials reviewed for Course 3 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grade standards is clearly identified; however above grade-level standards are not clearly marked as such. There is ample practice for students to engage deeply with with the problems related to the Grade 8 standards, but no connections are explicitly made to prior or future content in the Teacher Implementation Guide or the student text.

Some examples of areas where identification of standards from lower grades is beneficial and supports a partially meets rating along with a an example of not meeting the full depth of the standard:

• Lower grade-level material is clearly identified in the grade level outline found in the Teacher Implementation Guide on page FM-30. They are also identified and explained in the same resource at the beginning of each lesson.
• Chapter 5, pages 281-310, titled "The Real Number System" starts with 7.NS.3, a below grade-level standard, as indicated in the pacing guide and in the chapter overview, Teacher Implementation Guide page 281A. This standard is included, as stated by publisher, to review the sets of natural numbers, whole numbers, integers, and rational numbers.
• Occasionally, the lessons do not seem to go to the full depth of the standards.
  • Chapter 5 which is suppose to cover 8.NS.1 and 8.NS.2 does not cover 8.NS.2 as deeply as suggested in the standards. 8.NS.2 states, "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of the expressions (e.g., pi squared)." The lesson and skills practice only asks the students to compare or place numbers on a number line to the hundredths place. This is not a common occurrence in the curriculum for this grade.

The instructional materials reviewed for Grade 8 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

Some examples of giving all students extensive work with grade-level problems, but not of varying abilities and supports a partially meets rating:

• There is ample practice for each standard. Every lesson has guided practice with a script for the teacher to follow. This portion has the students conceptually developing the skill being taught and are given practice problems as well. Along with the guided practice are assignments. The number of assignments and number of problems varies per lesson. In addition there are skill practice pages to accompany each lesson as well. The number of skill pages also varies with each lesson.
• The Teacher Implementation Guided does not list any lessons or ideas for differentiated instruction except when it talks about the Mathia Software product. No differentiated or extension lessons in the Student Text, Students Skills Practice book, or the Student Assignment book were found by the reviewers.

The instructional materials reviewed for Grade 8 do not meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, no support materials were found that relate grade-level concepts explicitly to prior knowledge from earlier grades.

• The Teacher Implementation Guide is a wrap around of the Student Text. In the margins of the Teacher Implementation Guide, the authors have reworded the question asked in the student text but these does not seem to add anything to the instruction. The margins also have steps for the teachers to follow, ways to groups students (i.e., "Have students complete questions 2 and 3 with a partner. Then share the responses with a class," page 5), and guiding questions to ask students. However, it does not clearly make connections between previous knowledge and new concepts. There are not any indicators that knowledge is being extended.
• The warm-up sections for each lesson listed would be an ideal place to include connections to prior standards covered in this curriculum. For instance:
  • Chapter 10, lesson 4, when equations of perpendicular and parallel are introduced.
  • Chapter 12, lesson 2, students are asked to write a linear system to represent each graph, yet there are no discussion questions that could guide discussion to perpendicular and/or parallel linear equations.

The instructional materials reviewed for Course 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

• The Chapter titles are clearly labeled and aligned to the standards without a need for much interpretation.
  • Chapter 2 - Linear Functions (8.F)
  • Chapter 4 - Multiple Representations of Linear Functions (8.EE)
  • Chapter 6 - Pythagorean Theorem (8.G.B)
  • Chapter 9 - Similarity (8.G.A)

The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 3.

• For the majority of the work, most standards were taught and covered within one Unit out of the entire series and not aligned with any other concept throughout the year.
• There are no connections identified by publisher. However, there are connections within the Grade 8 standards that are just not noted or stated by the publisher.

Some examples of where connections were made and support a partially meets rating is:

• Chapter 3, "Slope: Unit Rate of Change," lessons 1 and 5 connect 8.EE.B.5 and 8.F.A by having students determine the rate of change from graphs by using the formal definition of rate of change and using rise/run formula. Students will compare the rates of graphs, compare the steepness of four lines on the same graph and relate the steepness of the lines to the magnitudes of their rates of change.
• Chapter 4, "Multiple Representations of Linear Functions," lessons 1 through 3 connect 8.EE.C.7.B and 8.F.A by having students, given linear equations written in standard form, complete tables by evaluating each equation and solving for the value of either x or y. The points are graphed and then used to calculate slope. Finally, the students convert the standard form linear equations into slope-intercept form.
• Chapter 6, "Pythagorean Theorem," lesson 1 connects 8.NS.A and 8.EE.A.2 by having students determine the area of a larger square and the sum of the areas of the two smaller squares to prove they are equal. Students also use the Pythagorean Theorem to solve for the length of unknown sides of right triangles set in a variety of contexts. In lessons 2 through 6, 8.EE.A.2 and 8.G.B are connected by having students use the Pythagorean Theorem to determine that the diagonals in a rectangle and square are congruent along with the diagonals of a trapezoid only when the figure is isosceles.