8th Grade - Gateway 2

The materials reviewed for Grade 8 partially meet the expectations for developing conceptual understanding of key mathematical concepts.

• Each lesson is launched with a real-world situation, and these often support application practice and do not build conceptual understanding.
• Problems are solved for students, and they are shown each step in prescribed process. The materials have few conceptual problems.
• There are strategies provided for teachers to help students understand concepts better, but few problems for students to explore on their own.
• Lessons include practice with procedural work and homework assignments include application.
• There are inconsistencies among chapters and concepts on how much conceptual understanding is presented.
• Lesson 5.1 introduces solving systems of equations through tables to build conceptual understanding, but the rest of the chapter focuses on procedures.
• Lesson 4.4 on understanding slope-intercept form begins with a problem situation about two boys walking at a constant rate but this problem only describes vocabulary of y intercept, x intercept and slope intercept form. The students are not asked to solve a problem using this vocabulary except in rote problems.
• There are a variety of representations used.
• Practice problems are intermingled with contextual problems, tables and number work with scaffolding. Many questions ask for the answer without having students explain or justify.

The materials reviewed for Grade 8 partially meet the expectations for giving attention to individual standards for developing procedural skills and fluency.

• Procedural skills are evident throughout the chapters; however, most problems are skills-based without attending to conceptual understanding.
• There are instances where students are engaged in problems that require procedural skills and fluency.
• Most of the problems in the lessons and over half of the homework is typically devoted to procedural skills and fluency.
• Fluency is built from practicing the procedures shown to the students in the examples of the lessons.
• Lesson 8.3 builds a conceptual understanding of rotation and then works on procedural fluency of rotating shapes.
• In chapter 9 students are asked to justify their ideas about transformations as they are working on doing the transformations.
• Each chapter has a lot of repeated practice for building procedural fluency.

The materials reviewed for Grade 8 partially meet the expectations for having the Standards for Mathematical Practice (MPs) identified and used to enrich mathematics content.

• The MPs for each chapter are listed on the chapter at a glance page.
• The MPs are there as a structure to design procedural problem work.
• The lessons do not allow students to construct meaning from the MP.
• During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices.
• The lessons do not always match the practices that are listed. For example, chapter 2 says MP1 is spotlighted. The problems are small, scaffolded and the application of a procedure. The students are not applying problem solving strategies or having to persevere through long problems.
• Instances that support MPs include lesson 9.2: Construct arguments, where students have to identify similar triangles and justify how they can prove it; Lesson 5.2: Model mathematics, which sets up systems using bar models; and Lesson 6.2: Model mathematics, which addresses multiple representations of a function, such as words, equations, tables and graphs.

The materials reviewed for Grade 8 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• The materials are scaffolded to the point where true, rich discussion may not be possible.
• For example, in lesson 5.3, the teacher edition states, "Best Practices--You may want to ask volunteers to show how this system of equations could be solved using the substitution method." This statement implies that this strategy may or may not be employed. It in no way encourages teachers to use this authentic discussion daily.
• In most lessons, there are hints to the teacher that would prompt some analysis to begin discussions such as in lesson 6.2; teachers have a prompt telling them to have a student explain in their own words the "Caution" in the example problem.
• Many of the "Best Practices" boxes provide suggestions to teachers that ask the students to think about what is presented.
• In Lesson 4.4, it prompts teachers to have students verify the slope by using two points or in Lesson 5.2, the prompt is to solve it in another way.
• Some of the "Think Math" strategies could help students construct viable arguments but there is no guarantee that these strategies will be utilized by teachers.