5th Grade - Gateway 3

The underlying design of the materials does distinguish between problems and exercises to meet the expectations for this indicator.

• The design of the materials distinguishes between problems and exercises. In My Math, exercises are labeled as Independent Practice and Practice while problems are labeled Math in My World and Guided Practice. For example, page 159 in the SE is an Independent Practice, and pages 157–158 in the Student Edition are Math in My World and Guided Practice.
• All lessons contain practice exercises, which allow students to apply what they have learned. These exercises are broken down into approaching level, on level, and beyond level.
• In the Write About It section, exercises provide opportunity for students to reflect on a topic and build understanding needed to answer the chapter Essential Question.
• Math in My World provides new mathematics. The independent practice gives a chance for the child to practice the new learning with guidance from a teacher. The homework provides yet another opportunity to use the new skill on your own. Examples are on pages 175–176 and 391–392 in the Teacher’s Edition.

The design of assignments is not haphazard; exercises do seem to be given in intentional sequences meeting the expectations for this indicator.

• The problems in My Math are purposefully designed and organized. Connections are made and directly stated in the Teacher’s Edition. This is directly stated in the “What’s the Math in this Chapter?” section at the beginning of each chapter and also in the “Making Connections” section at the beginning of each chapter.
• Teachers are also directed in the lessons to point out the connections.
• The sequence in lessons usually goes from a more concrete example using manipulatives or models to more abstract types of problems.
• Due to the intentional layout of the materials, the “What’s the Math in This Chapter” section provides the reason for lessons being presented as they are. It shows the link between prior knowledge and new information to be learned.

There is a variety in what students are asked to produce meeting the expectations for this indicator.

• Students are asked to produce many types of answers throughout the work they do.
• Math in My World usually has the student work through the mathematics by providing a model first and then moves students to producing answers using other strategies besides always using a model.
• Independent practice and Homework provide opportunities for students to work on fluency in producing answers. It also has a section for problem solving that gives the student the chance to model what they have learned and explain their thinking. For examples, see pages 45–46 and 257–258.
• Some opportunities are given in the problem solving sections for students to create arguments about someone else’s work. Examples are on pages 273–274.
• Students are required to justify their answers on some of the Independent Practice and Homework. Examples include pages 327–328.
• Students are asked to produce a variety of work throughout the materials. For example, Independent Practice, as found on pages 363–364 in the Student Edition.
• Math in My World, on page 379 in the Student Edition, helps students see math in a real world context, and students are producing solutions in a grade-appropriate manner.

The manipulatives are almost always faithful representations of the mathematical objectives they represent and, when appropriate, are connected to written models meeting the expectations for this indicator.

• Manipulatives are appropriately used and explained in both the student book (for example, page 707, “draw it”) and on homework assignments (for example, page 711–712 SE).
• The digital website has tools containing virtual manipulatives.
• Page 27, in the Student Edition, is an example of using base ten blocks to represent fractions.
• Another example is page 614, in the Student Edition, in Guided Practice. The number line is used to compare and order fractions.
• The Teacher Edition contains Model the Math sections which provide teachers the materials needed to model the math. Examples are on pages 551B, 651B, and 771B.
• For Math in My World, there is a visual model that is an appropriate representation.

Materials meet the expectations for containing a teacher edition that has ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

• The teacher edition contains ample annotations and suggestions. Common Errors are noted (for example, pages 57–58, 337–338, 413–414, and 727–728 in the Student Edition) and ways to incorporate mathematical practices are also noted (for example, pages 727–728 in the Student Edition).
• Each lesson has an online presentation to mirror instruction in the text to support and enhance student learning.
• In the Teacher’s Edition, there are many scripted parts of the lesson with expected or anticipated student responses to help guide the teacher.
• Each lesson contains a section called Diagnose Student Errors to help the teachers understand where students may have misunderstandings. For example, see pages 743–744 and 875–876 in the Student Edition.

The materials meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

• Each unit contains an "Am I Ready Quiz" which identifies whether students have necessary skills for success in the unit, and an online version is available. For example, see chapter 4, page 245 in the Student Edition. Differentiated instruction is then provided based on the answers given by the students.
• The Teacher Assessment book also contains a pretest for each unit to determine if students already know the standards being taught in the unit.

Materials meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• Some lessons contain test practice problems which identify common errors and misconceptions (for example, page 812 Student Edition).
• Some lessons identify common errors that students make (for example, see page 842 Student Edition).
• There are Common Error sections for the teacher to help catch errors students are making and correct them. Examples of this are on pages 57–58, 117–118, and 343–344.

The materials meet the expectations for providing opportunities for ongoing review and practice, with feedback for students in learning both concepts and skills.

• Each lesson begins with a Common Core quick check that reviews the previous day's learning.
• Each lesson contains a Problem of the Day that reviews learning from previous units (for example, chapter 7, lesson 7, page 519A Student Edition). Some lessons provide ideas for Exit Slips (Student Edition page 862).
• Teachers can also create assessments/practice online through the Manage and Assign tab.
• Teachers can use the application cards and exit slips as formative assessments and ways to provide feedback for student learning (examples on pages 365–366 and 445–446).  
• There are Check My Progress sections in order for the student and the teacher to have formative assessment and an opportunity for feedback from the teacher.
• Lessons provide practice pages, for example, chapter 7, lesson 2, page 489 in the Student Edition.
• Each lesson also has homework pages, chapter 7, lesson 2, page 491 in the Student Edition.

Within the teacher materials, the summative and formative assessments meet the expectations for clearly denoting which standards are being emphasized.

• Am I Ready beginning each chapter has student exercises broken down by standard (for example, page 789).
• Check my Progress in each chapter identifies concepts being assessed but not standards.
• The Chapter Review at the end of each unit identifies standards being taught and provides intervention support (Student Edition, pages 783–784).
• The summative assessments themselves do not clearly denote which standards are being assessed, but under the assess tab in the online portion there is a complete breakdown of all assessments and the standards they are assessing.  It is called Chapter Assessment Question Correlation Grade 5. 

Materials meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Teachers are given Cognates to help ELL learners (for example, page 807A TE).
• Collaborative Conversation is suggested for MP7 (Student Edition, pages 807–808).
• All lessons sequentially practice the new learning, apply the learning, and extend the concepts.
• The lessons are sequenced to build from conceptual understanding, using concrete and pictorial representations for more abstract representations.  
• Most lessons have an RTI Differentiated Instruction page at the end. These provide the additional instruction for students approaching level, on level, and beyond level. Assessments are also provided at these same levels.
• Each lesson provides ELL support and differentiated instruction support. For example, see Chapter 10, lesson 5, page 661A in the Student Edition.
• A concern does exist that struggling students may not reach the depth of the standards for the grade level.

The materials meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

Differentiated Instruction is provided for each lesson (for example, page 811A TE) and ELL Learner Support (for example, page 811A TE).

Each chapter has a project (Student Edition, pages 787–788), and additional projects are available online under Project-Based Learning.

Most lessons have an RTI Differentiated Instruction page at the end. These provide the additional instruction for students approaching level, on level, and beyond level. These pages describe different strategies for working on the content. For example, see page 491A.

The materials meet the expectations for suggesting support, accommodations, and modifications for English language learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

• ELL Instructional Strategies are provided in lessons (page 807A TE).
• Each lesson contains ELL tiered Differentiation Support (page 811A TE).
• Spanish versions of the Parent Letter for each chapter are available online.
• A multilingual glossary is available online.
• At the end of most lessons, there is a section called RTI Differentiated Instruction. These provide the additional instruction for students approaching level, on level, and beyond level.
• Additionally, some materials can be printed in Spanish and Arabic.

Materials meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

• Each lesson has a Beyond Level Extension. For example, see Chapter 11, lesson 2, page 811A.
• Enrich worksheets are available online. Project-based learning activities are available online.
• Online games are available.
• There is also a differentiated test (test forms 3A and 3B) for those students performing beyond level.

Materials meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Student artwork is featured on each volume cover, and information about the artists is provided. Pictures of students from various backgrounds are pictured in the text (page 813, 819).
• The names and situations in the story problems represent a variety of cultural groups and genders.  
• The problems include real-world situations that apply to a variety of cultural and gender groups. For example, see pages 158, 170, 176, and 180 in the Student Edition.