7th Grade - Gateway 2

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings meeting the expectations for this indicator.

• Generally, lessons develop understanding through explicit discussion outlined in the teacher lessons. Conceptual understanding is evident throughout nearly all lessons and lesson plans of teacher instruction. Students are consistently being asked to verify their work and explain for understanding. Teacher questioning during instruction is designed to lead to conceptual understanding.
• Teacher and student prompts often include terms like introduce, discuss, review, demonstrate, compare, explain, challenge, show how, draw, represent, give an example, describe, why, prove, create, notice, etc., that encourage students to demonstrate conceptual understanding.
• Units 1, 3 - 9 and 11 all include work related to the major work clusters that address conceptual understanding (7.NS.A, 7.EE.A).
• Examples of lessons that develop conceptual thinking include:
  • 1.2: Investigating "⅓" through work with hundreds grid to build understanding of terminating versus repeating decimals.
  • 3.1: Develops positive and negative numbers as hot and cold pieces and uses counter model and temperature change model.
  • 4.3: Extending understanding of integer addition and subtraction to rational numbers, using number lines
  • 5.1: Connecting models (counter model, temp change model, number lines) to multiplication of integers
  • 5.2: Building conceptual understanding of sign rules for multiplication/division of integers using patterns on coordinate
  • 8.2: Using patterns in hundreds chart to write equations.
  • 8.3/9.1: Using polygon pieces to write expressions.
  • 9.2: Solving equations using concept of balance and tape diagrams.
• It needs to be noted, however, that beyond the lessons, 12 of the 16 units did not call for students to demonstrate conceptual understanding on the summative assessments.

Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

• Procedural skill and fluency that develop the major clusters that emphasize it (7.EE.A.1, 7.EE.B.2, and 7.NS.A) is evident in 12 of the 16 units.
• Examples found in lessons include:
  • 4.3: Procedural practice of adding and subtracting rational numbers
  • 6.3: Procedural practice multiplying and dividing rational numbers
  • 8.1/8.2: Procedural practice with equivalent expressions
  • 9.3: Procedural practice with solving equations
  • 12.1: Procedural practice of finding percent increase and percent decrease
• Besides an abundance of examples throughout the lessons, there are also skill builder activities in each unit designed to develop procedural skill and lead to fluency.
• In the teacher guide, there are often multiple "Introduce, Explore/Summarize, and Practice” sections depending on lesson content that develop procedural skill and fluency.

The MPs are identified and used to enrich mathematics content within and throughout each applicable grade.

• There is a clear articulation of connection between MPs and content. Materials regularly and meaningfully connect MPs to the CCSSM within and throughout the grade.
• Every unit identifies the MPs used in the unit both on the student and teacher overview page.
• In the teacher guide, each unit specifically relates how the listed standards are used in the unit. These are logical connections and integrated with the content.
• The MPs have also been identified for the quizzes, proficiency challenges, tests, and tasks.
• MPs are not identified within student materials, but are listed on the back cover along with the CCSSM.
• There are some instances of under-identification of the MPs, such as:
  • MP 6 “Attend to Precision” is usually identified in situations where precise language is important, but it is rarely included related to problems where precise calculations are important.

The materials meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the Teacher's Guide, unlike the student's edition, has consistent prompts for teachers to follow and use for promoting mathematical discussions in the classroom.

• Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
• There are multiple examples of the teacher materials assisting in engaging students in both constructing viable arguments and analyzing the arguments of others frequently throughout the program through questioning techniques. Some examples of constructing viable arguments include:
  • 5.3: “How can we justify that these numbers are equivalent?”
  • 8.1: “Why is it necessary to subtract 4 from this number of squares?”
  • 11.1: “How do we know that the values of the ratios are equal?”
  • 11.3: “From the numbers in the table, how do you know which store has the better buy?”
  • 11.3: “Why does the Door-to-Door Pizza graph NOT go through the origin?”
  • 12.1: “Why must these problems have different answers?”
• Some examples of analyzing the arguments of others include:
• • 6.2: “What is Blakely’s shortcut?”
  • 7.1: “What do you think Donny’s aunt means?”
  • 8.1: “What do the lines in Jaime’s sketch mean?”
  • 12.1: “Which estimate do you think is better for the discount of the coat?”
  • 12.1: “How might you determine the original price using Hans’ strategy (…then using Franz’s strategy)?”
  • 12.3: “Jay was unsure how to compute the price he can afford, but he knew it could be more than $92. Do you agree with Jay?”

Materials explicitly attend to the specialized language of mathematics.

• Materials explicitly attend to the specialized language of mathematics.
• Correct mathematical terminology is consistently used, enforced, and reinforced.
• Explicit detail is always used in student-teacher discussion and explanation of process.
• Each unit starts with a vocabulary list of words used in the unit and students have a “resource guide” to refer to. Throughout the unit, these terms are used in context during instruction, practice, and assessment.
• There are student lesson questions which specifically focus on the importance of precise language. For example, in Unit 9, on page 14: 11, it says “… explain why this language is not precise.”
• The terminology that is used in the modules is consistent with the terms in the standards.