6th Grade - Gateway 2

The materials reviewed in Grade 6 partially meet the expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Several problems ask the student to apply their knowledge to real-world situations. In module 8 of the student edition on page 208, which deals with percents, students are asked to apply what they know about percents to a story problem involving a real-world situation.

Places where application is evident:

• Each lesson begins with a section called "Motivate the Lesson," which includes a question that puts the mathematics concept into a real-world situation and is meant to engage the student in the learning.
• The examples at the beginning of the lesson are often real-world problems and tie the learning to context.
• In a section titled "Guided and Independent Practice" there are numerous problems that have students apply their knowledge.

Areas in need of improvement:

• Very few problems are multiple-step problems, and when one is, the materials break the work down for the students.
• The performance tasks are lengthy questions, but do not require students to do more than answer a question similar to those on the independent practice and often solvable in one step.
• Many problems are simply word problems that require an algorithm to solve.

The materials reviewed for Grade 6 partially meet expectations for attending to the full meaning of each MP.

In module 4, lesson 4.4, students are guided in MP1 (Make Sense of Problems and Persevere in Solving Them) to solve multistep problems using the following steps: analyze the information, formulate a plan, solve, then justify and evaluate.

In module 1, lesson 1.3 on page 24, students are given a question and directed to give an example if they respond yes or to explain why not if they respond no. (MP3 [Constructing Viable Arguments])

In the student edition, in module 5, lesson 5.1 on page 112, students are given a mathematical estimation (#31) and a real-world scenario for making a prediction (#33.) For each, they are directed to explain their reasoning (MP3) but not to analyze the arguments of others.

The materials reviewed for Grade 6 partially meet the expectation for appropriately prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards. There are places where students are prompted to construct viable arguments and analyze the work of others. When looking beyond the labels of the practices there are many places where the label does not match the problem or the problem covers more than one practice, but only one is listed.

Places where evidence for MP3 is found:

• Student edition, question 12 asks the student if two different numbers could have the same absolute value, why or why not and to explain.
• Student edition questions 21, 29 and 31 all ask the students to explain how they would do something.
• Page CC13 describes MP3 and then shows examples of where it is evident in the book. It can be found in each lesson as an "essential question check-in" and in the "independent practice" section with question headings such as "Critique Reasoning," "Error Analysis," "Justify Reasoning," and "Communicate Mathematical Ideas."
• At the end of each lesson the question analysis lists to which MP the question connects.

Problems with the mathematical practices were also found in the text.

• Some MPs are mislabeled (e.g., page 209, question 20).
• The citations on page CC6-CC9 do not always identify the practice on the correct page (e.g., pages 24 and 468). The practice is not evident any unit in the "assessment readiness" section or in any performance task.

The materials reviewed for Grade 6 partially meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• Exercises 12, 13 and 14 ask students to make a conjecture, communicate mathematical ideas and critique reasoning, respectively.
• The teacher edition also states on page CC7 that MP3 is evident on page 248 in the student book. Exercises 19, 20 and 21 ask students to explain the error, communicate mathematical ideas and critique reasoning, respectively.
• Page CC7 also states MP3 is on page 406. On page 405, the teacher edition lists the specific exercises and the corresponding MP. Exercises 20 and 22 in the student book on page 406 do match MP3 and have the student construct arguments.
• There is a section called "Extend the Math." This only describes part of the activity as the rest of it is online. Only one of 22 activities reviewed had students engaged in looking at and discussing each other's work.
• Each lesson has a whiteboard activity. This is electronic and does not come with the teacher edition. Of the several that were reviewed, only one had language that could engage students in discussion.

The materials reviewed for Grade 6 partially meet the expectation for explicit attention to the specialized language of mathematics.

• Vocabulary is a category in independent practice that attends to MP6. However, there is no counter example category in independent practice in Grade 6.
• Vocabulary is taught with pages entitled "Reading Start-Up" and "Unpacking the Standards." The former is review of previous content and the latter includes current vocabulary and a real-world example. Vocabulary is highlighted when it is introduced.
• A study guide includes a recapitulation of the vocabulary.
• The "H.O.T." questions expect students to respond and explain, using precise language.
• In the teacher edition on page CC9, it states that MP6 is evident on page 13. However, on page 13, question 1, the one requiring "reflection," just asks the student to look at the accompanying data and number line to solve the problem; there is no specific language or vocabulary.
• Vocabulary is not evident in the "assessment readiness" section of any unit.
• Vocabulary is evident in only two of the six performance tasks, units 1 and 3.