6th Grade - Gateway 1

The instructional materials reviewed for Grade 6 partially meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. To determine this, we looked at the student lessons that were not major work to identify connections and support they provided to the major clusters. We also considered if there were missed opportunities to make strong connections. In the teacher guide, the lessons are correlated to standards, so there was some guidance in determining where connections were being made.

• In general, the standards alignment in the teacher’s guide is accurate, therefore it is a reliable source for determining when lessons that are not major clusters directly support major work.
• The strongest support comes from geometry lessons, specifically area, supporting the major work of expressions and equations, which require the students to use formulas/equations to solve problems.
• There was also significant support linking the number system standards to both expressions and equations and ratios and proportional relationships. Examples include dividing decimals to find equivalent rates, using decimal operations in percent problems, calculating equivalent measurements and writing repeated factors as exponents.
• There were several instances where the supporting work missed opportunities to connect to major work. One example of this is Chapter 8 on statistics could easily have made strong connections to both number system and expressions and equations, but did not.
• However, much of the supporting work is “stand-alone” lessons that do not make connections to major work. Examples include multiple lessons on central tendency, work with data displays and scatterplots, and basic computation such as multiplying decimals.

The instructional materials reviewed for Grade 6 partially meet the expectation to be consistent with the progressions in the standards. Materials do provide all students with extensive work at grade-level problems. However, content from prior grades is rarely identified and materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections are also not made to content in future grades. Overall, the materials in Grade 6 are consistent with the depth and progressions in the standards, but explicit connections to prior or future grade level content are never identified for teachers or students.

Throughout the entire series in the Teacher's Guide, content connections made are within the current course, but they never explicitly tie to prior or future work.

• On the chapter introduction page, students are given a very clear overview of what the chapter will be and helps make connections such as:
  • “Your work with similar figures and scale drawings will lay the foundations for much of the rest of the chapter.”
  • “In 5.2, you will continue your earlier study of probability.”
  • “Since the concepts in this chapter lay the foundation for simplifying and solving equations, they will be revisited throughout the entire course.”
  • “In section 3.1, you learned about the multiple representations of portions, now you will return to the idea of portions as you develop strategies for finding parts of parts.”
• Chapter overviews include a chart with a column of “Concepts Introduced/Reviewed” as well as identifying “Section Content Revisited” but they are within the course.
• Each chapter overview includes “Where is this going?” that makes connections to extensions of the concept later in the year since this curriculum spirals.
• Teacher notes at the beginning of each lesson sometimes include a mathematical background section – these provide information but do not make direct connections to prior or future work.
• When off grade-level material is present, it is sometimes labeled as “preparation for” and it does tie to grade-level work with reasonable connections, but there are no explicit connections made to prior or future standards.
• The materials do address the depth of the standards for the grade level.
• Concept development supports the expected progression of the grade.

1.e.ii

The instructional materials reviewed for Grade 6 meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do consistently give students extensive work with grade-level problems, however there is extensive dependency on peer interactions for learning concepts that could be a significant challenge for many students.

• All students are expected to do the same work.
  • Students have ample opportunity to engage deeply in grade-level work.
  • Every lesson requires student teams to start by solving non-routine problems where clear pathways or expected answers are not obvious.
  • Problems presented are frequently relevant, authentic, and require students to make connections.
  • Some problems develop through multiple extensions throughout the entire course, spiraling back with new connections.
• Working with a collaborative team is the default strategy for helping all students engage in the problems.
• There is a good balance of time devoted to each standard, though a slightly disproportionate amount is allocated to statistics and probability considering it is supporting work and detracts from time that could be spent on the major work of the grade.

1.e.iii

The instructional materials reviewed for Grade 6 only partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades other than noting that certain lessons are “preparation for” a grade-level standard.

• Lessons identified as “preparation for” lessons support grade level work by developing conceptual understanding.
• Some lessons are not aligned to a standard at all, these lessons generally review or build concepts necessary for grade-level standard understanding, which could be explicitly linked to previous standards.
• Connections between concepts are addressed on the chapter introduction page so students can begin to see how content relates (see 1.e.i for examples), though concepts are never explicitly connected to learning from prior grades.
• Within the teacher materials, each chapter contains narrative stating topics that may be “reintroduced” from previous courses.