6th Grade - Gateway 2

The materials reviewed for Grade 6 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 thoroughly addressed by setting explicit expectations for understanding or interpreting. For example, 6.RP.A.3 specifically calls for tape diagrams and double number lines to show student understanding in regards to ratios. There is one number line in Digits.
• Each lesson is launched with a real-world situation, emphasizing application but not supporting building conceptual understanding.
• One example of building conceptual understanding is topic 6 on the division of fractions.

The materials reviewed for Grade 6 partially meet expectations for attending to the expectation of procedural skill and fluency.

• The fluency standards for Grade 6 are 6.NS.B.2 and 6.NS.B.3. Lesson 7-3 is the only lesson focused on fluently dividing multi-digit numbers (6.NS.B.2).
• Lessons 7-1 through 7-4 address 6.NS.B.3 to fluently add, subtract, multiply and divide multi-digit decimals for each operation.
• Lessons 7-5 and 7-6 compare decimals and fractions.
• Lesson 7-7 solves real-world problems involving the operations with decimals.
• The materials do not include many opportunities for students to practice fluency.

The materials reviewed for Grade 6 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 multi-step application problems.
• There are many real-world type problems, but few multi-step problems within the lessons.
• Students do not have many chances to model their thinking in a variety of instances while solving problems.

The materials reviewed for Grade 6 partially meet the expectations for balance between the three aspects of rigor with the grade.

• Each lesson begins with a launch that includes a real world situation and conceptual base.
• 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.
• The piece missing is enough practice for fluency of dividing multi-digit numbers; and adding, subtracting, multiplying and dividing multi-digit decimals.

The materials reviewed for Grade 6 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 or in other areas of the curriculum.
• The questioning strategies offered in the program overview guide are the best examples 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 students practice these skills. The teacher would need to help students recognize what practices and skills they are employing to solve problems, and ensure students are using tools appropriately in practicing a 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 6 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, which leads to less depth in the practice of the MP.
• While the essence of standard for MP3 is in lessons in Grade 6, students are not directly prompted to "construct viable arguments."
• 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 4-4, "Do You Understand," 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 6 partially meet the expectations for explicitly attending to the specialized language of mathematics.

• This series does not explicitly attend to the specialized language of mathematics.
• The materials often use vocabulary that is not precise and does not allow for the student to be immersed in the language of mathematics.
• A vocabulary lesson is at the end of each topic. While this structure could support the development of mathematical language, they are isolated lessons.
• The focus questions that conclude each lesson are often based on explaining the vocabulary focus of a lesson. For example, in Lesson 1-2, students need to understand the term "variable" to answer the question, "What does a variable allow you to do that you couldn't do before?"