5th Grade - Gateway 3

The design of the materials reviewed for Grade 5 meet the expectation for this indicator by providing students with ongoing opportunities to practice previously learned skills alongside their learning of new content. These materials use problem sets and application problems to develop their understanding of new mathematics. These materials use homework, application problems and fluency sessions to practice previously learned concepts.

• Problems sets within the lessons include guidance on how to select and sequence the exercises.
• Fluency exercises within the lessons include guidance on the purpose of each activity allowing the teacher to determine the necessary activities for the students.
• "How to Implement A Story of Units" provides information for the teacher on the purpose for each lesson section.
  • "The primary goal of the problem set is for students to apply the conceptual understanding(s) learned in the lesson." (page 12)
  • "The bank of fluency activities for each lesson is intentionally organized so that activities revisit previously-learned material to develop automaticity, anticipate future concepts, and strategically preview or build skills for the day's Concept Development." (page 23)
  • "The homework gives students additional practice on the skills they learn in class each day. The idea is not to introduce brand-new concepts, but to build student confidence with the material learned in class." (page 13)
  • "A Story of Units doesn't wait months to spiral back to a concept. Rather, once a concept is learned, it is immediately spiraled back into the daily lesson structure through fluency and applications." (page 9)

The materials reviewed for Grade 5 meet the expectations of this indicator by using intentional sequences in the design.

• Problem sets, exit tickets and homework relate to the mathematical concept developed in the lessons each day.
• Once a concept is developed, it is spiraled back into the daily structure within the fluency and application portion.
• The sequence of topics within each module is intentional going from working with a variety of concrete and pictorial representations to more abstract work with numbers and computation.
• For example, module 1 goes from decimals on the place-value chart to place-value patterns, then to rounding, and then to addition, subtraction, multiplication and division of decimals.
• Progressions are clear and obvious, as in mastering whole-digit operations before moving on to operations on fractions.

The materials reviewed for Grade 5 meet the expectations of this indicator by providing a variety in what students are expected to produce.

• Students are expected to produce answers and solutions throughout the fluency sections and some of the problem sets.
• Students are expected to provide arguments and explanations within the problem sets, exit tickets and homework.
• Students are asked to provide a variety of mathematical responses.
• Arguments and explanations are the basis for the debriefing section of each lesson.
• The "Read, Draw, Write" procedure requires students to represent the problem in a drawing and make connections between the drawing and the equations.
• Throughout the modules and lessons students produce a variety of solutions, using concrete, pictorial and abstract representations.
• In Module 2, for example, students are asked to use place-value knowledge to solve multiplication problems (2.A.10); to write out reasoning why a strategy will or will not work (2.A.11); draw representations of multiplication, including ways to use the distributive property to solve harder multiplication (2.B.10); and to use an area model to solve multiplication problems (2.B.50).

The materials reviewed for Grade 5 meet the expectations of this indicator by using manipulatives and models as faithful representations of the mathematics they are used to represent.

• The materials use a limited set of concrete and pictorial models throughout the program.
• Each module lists suggested tools and representations that apply to the mathematics in the module.
• An example of how manipulatives are used occurs in module 4, lesson 2, in which square sheets of paper are used to help clarify the relationship between fractions and division. Later, counters and drinking straws are used to further this understanding (4.C.4).

The materials reviewed for Grade 5 meet the expectations for this indicator by supporting teachers in using questions to guide mathematical development.

• Materials provide quality-suggested questions throughout the debriefing section of each lesson. For example, in module 4, students are asked, "Did you see other solutions that surprised you or made you see the problem differently?" and "Look at Problems 1(e) and 1(f). We know that 4 fifths and 1 seventh aren't equal, so how did we get the same answer?"
• Quality questions are also included in the concept development portion, application problems and problem sets of the lessons.

The materials reviewed for Grade 5 meet the expectations for this indicator by including a teacher's edition with ample and useful annotations and suggestions on how to present the content.

• The concept development sections include a sample script to help the teacher understand what might happen when presenting the material. These scripts can sometimes mask the mathematical concepts at hand, leading teachers to think that this script is exactly what should happen. A summary of the process and concept before the script would be useful.
• Within the lessons, aside from the teacher script and wording in the teacher directions, most lessons have pictures and representations with annotations, demonstrating the concepts pictorially for the teacher, to provide guidance about how to present the content.
• There are answer keys for all the student problem sets, exit tickets, homework and tests, including written annotations to show what student work should look like.
• There are also boxes in the sidebar of many lessons that annotate information about how to present content to students.
• There is a repeated process for solving word problems called the "Read, Draw, Write" approach, which the manual explains in the module overview.

The overview of each module has several suggestions for delivering instruction.

The materials reviewed for Grade 5 meet the expectations for this indicator by including adult-level explanations and examples of mathematical topics so that teachers can improve their own knowledge of the subject, if necessary.

• In the teacher edition for each module, there is an overview section that has narrative information about the math content of the module.
• In each module, at the start of each topic, there is another section of narrative that gives a mathematical explanation of the math content in the topic.
• These topic-level explanations and overviews include mathematical coherence within and between grade levels.
• "How to Implement A Story of Units" includes adult-level explanations of the models and representations used.

The materials reviewed for Grade 5 meet the expectations for this indicator by including strategies to identify and address common student errors and misconceptions.

• Each summative assessment includes a chart showing "progression toward mastery" to help teachers with the coherence towards mastery.
• On page 13, "How to Implement A Story of Units" says this about addressing errors and misconception: "Distractors for such questions are written to illuminate common student errors and misconceptions."
• The student debrief section of the lesson is intended to invite the students to reflect and process the lesson. Strategies include partnering to guide students in conversation to debrief the problem set and process the lesson.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need support. In particular, the "Multiple Means of..." notes tend to focus on student misconceptions.

The materials reviewed for Grade 5 meet the expectations for this indicator by including ongoing review and practice.

Ongoing review and practice is included within fluency section of lessons.

• Exit tickets can provide feedback depending upon teacher use.
• Review and practice also within the problem sets and homework that are included in every lesson.
• The summative assessments contain rubrics to provide feedback to the teacher and student as to a student's progression toward mastery.

The materials reviewed for Grade 5 meet the expectations for this indicator by including strategies to help teachers sequence and scaffold lessons.

• The lessons are sequenced to build from conceptual understanding, using concrete and pictorial representations to more abstract representations.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options and materials.
• Lessons and mathematical topics are sequenced according to the CCSSM progressions of learning.
• A description of the module sequence and layout is provided.

The materials reviewed for Grade 5 meet the expectations for this indicator by including strategies for meeting the needs of a range of learners.

• The lessons are sequenced to build from conceptual understanding, using concrete and pictorial representations to more abstract representations.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options, and materials.
• "How to Implement A Story of Units" describes a variety of scaffolds and accommodations (page 13).

The materials reviewed for Grade 5 meet the expectations for this indicator by providing tasks with multiple entry-points that can be solved in a variety of ways.

• Application problems, problem sets, and homework are included in almost all lessons. These problems can be solved in a variety of ways. Students can choose their own solution strategy and/or representation.
• The embedded tasks show the students multiple representations using drawings, charts, graphs, or numbers or words to solve.

The materials reviewed for Grade 5 meet the expectations for this indicator by including support for the English Language Learner (ELL) and other special populations in order for them to actively participate.

• Notes on multiple means of engagement give teachers suggestions about meeting the needs of ELL students. These margin notes include sentence starters, physical responses and vocabulary support.
• On pages 14-20 of "How to Implement A Story of Units," there are suggestions for working with ELL students and students with disabilities. Page 14 states, "It is important to note that the scaffolds/accommodations integrated into A Story of Units might change how a learner accesses information and demonstrates learning; they do not substantially alter the instructional level, content, or performance criteria. Rather, they provide students with choices in how they access content and demonstrate their knowledge and ability."

The materials reviewed for Grade 5 meet the expectations for this indicator by offering instructional support for advanced students.

• Notes on multiple means of engagement give teachers suggestions about meeting the needs of advanced students.
• The curriculum specifies that not all pieces of each section of a lesson must be used, so advanced students could be asked to tackle problems or sections that a teacher does not use for all students.
• "How to Implement A Story of Units" provides teachers with suggestions for working with above-grade level students (page 20).

The materials reviewed for Grade 5 meet the expectations for this indicator by providing a balanced portrayal of various demographic and personal characteristics.

• The names and situations in the story problems represent a variety of cultural groups.
• The application problems include real-world situations that would appeal to a variety of cultural and gender groups.
• There is a balanced approach to the use of gender identification.