8th Grade - Gateway 2

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

• There are multiple representations used including verbal descriptions, graphs, number lines, tables and equations.

• Conceptual understanding is not attended to thoroughly by setting explicit expectations for understanding or interpreting.

• Each lesson is launched with a real-world situation, but they often emphasize application instead of building conceptual understanding. For example, Lesson 6-1 has a launch about when two runners will pass one another, and later there is a problem about comparing the lengths of two shark species. These lessons begin to support the development of conceptualizing systems of equations, but are not deepened in order for students to develop a solid understanding.

The materials reviewed for Grade 8 partially meet expectations for attending to the expectation of procedural skill and fluency. The fluency standards for Grade 8 are 8.EE.C.7 and 8.EE.C.8.B.

• Solving linear equations in one variable (8.EE.C.7) is taught in lessons 2-1, 2-2, 2-4 and 2-5. There are not many practice problems designed to promote fluency with this skill.

• Topic 6 addresses 8.EE.C.8.B on solving systems of two linear equations in two variables, and there are not many practice problems designed to promote fluency with this skill.

The materials reviewed for Grade 8 partially meet the expectations for spending sufficient time working with engaging applications of the mathematics without losing focus on the major work of each grade.

• The enrichment project for each unit is the major resource for application with multi-steps.

• Within the lessons there are many real-world type problems, but few multi-step problems.

• Students are often asked to determine the answer or explain (conceptual understanding) a problem, but do not have many chances to model their thinking in a variety of instances while solving problems.

The materials reviewed for Grade 8 partially meet the expectations for balance between the three aspects of rigor with the grade.

• Each lesson begins with a launch that is a real-world situation and conceptually based. In the "Got It" sections, there are problems that are procedural and applications of the mathematical topic.

• There is an attempt to balance conceptual and procedural work.

• There are not enough problems to support developing fluency, particularly in solving linear equations in one variable and estimating solutions by graphing the equations.

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

• While the MPs are included and labeled in the launch of each lesson and the focus question, they are not identified anywhere in the in-class teaching notes and are missing in other areas of the curriculum.

• The questioning strategies offered in the program overview guide are the best example of how to assist the educator to lead their students into applying the MPs to enrich the mathematics content.

• Each lesson has students using a variety of MPs to enrich the lesson, but need explicit teacher support in order to ensure these students practice these skills. For example, the teacher would need to help students recognize what practices and skills they are employing to solve problems, and to show students that they are using tools appropriately and practicing that standard.

• MP4 on modeling is referred to often, but these lessons miss the opportunity to also practice MP5, which requires students to select the appropriate tool in order to solve real-world problems.

The materials reviewed for Grade 8 partially meet the expectations for prompting students to construct viable arguments and analyzing the arguments of others.

• Materials have students constructing arguments through certain routine problems such as reasoning, reflecting, writing and error analysis.

• These problems appear in each lesson in the same manner, so the depth of the practice is not able to fully develop.

• While the essence of Standard for MP3 is in lessons in Grade 8, students are not directly prompted to "construct viable arguments."

• The attempt is there to prompt students to construct viable arguments with some of the questions used in each lesson, but the ability to have true mathematical discourse in the lessons is not strong.

• The "Do You Understand" section attempts to do this with reasoning and error analysis questions.

• Students are prompted to construct arguments through some of the questions in each lesson, but in many cases parts of the answers are already given to the students in advance and they do not need to think deeply about the answer. For example, in the Lesson 8-6, there is an error analysis on writing an equation for a situation and students have to find the error. This question does not require the students to fully reason and construct arguments because they have already been told it is incorrect.

The materials reviewed for Grade 8 partially meet the expectations for explicitly attending to the specialized language of mathematics.

• This series falls short in explicitly attending to the specialized language of mathematics.

• It often uses vocabulary that is not precise and does not allow for the student to be completely immersed in the language of mathematics.

• At the end of each topic is a vocabulary lesson. While this structure could support the development of mathematical language, they are presented as isolated lessons.

• The focus questions to end each lesson are often based on explaining the vocabulary focus of a lesson. For example, in lesson 7-3, students must understand the term "linear function" in order to answer the focus questions, "What are linear functions? How are linear functions useful?"