4th Grade - Gateway 3

The underlying design of the materials does distinguish between problems and exercises, thereby meeting 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 513 SE is an Independent Practice, and pages 511–512 SE are Math in My World and Guided Practice.
• All lessons contain practice exercises that allow students to apply what they have learned. These exercises are broken down into approaching level, on level, and beyond level.
• Test Practice is used to diagnose student errors. In Chapter 4, students have to draw area models to multiply.
• 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 the 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 135–138 and 37–40 in the Teacher’s Edition.

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

• The problems in My Math are purposefully designed and organized. Connections are made and directly stated in the “What’s the Math in this Chapter?” and “Making Connections” sections at the beginning of each chapter in the Teacher’s Edition.
• Teachers are also directed in the lessons to point out the connections. Examples occur on pages 4–6, 189E–189F, 321E–321F and 478 in the Teacher’s Edition.
• 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.
• The design of the assignments is done in an intentional sequence. For example, the sequence starts with place value, addition and subtraction, and then moves into multiplication and division before working on primes and factors which then segue to fractions.

There is a variety in what students are asked to produce, which meets 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 math providing a model first and then moves on to students producing answers using other strategies besides always using a model.
• Some opportunities are given in the problem-solving sections for students to create arguments about someone else’s work. Examples include pages 237–238.
• Students are required to justify their answers on some of the Independent Practice and Homework. Examples include pages 503–504.
• Students are asked to produce a variety of work throughout the materials. For example, Independent Practice found on page 513 SE.
• Math in My World, page 517 SE, helps students see math in a real world context and students are producing solutions in a grade-appropriate manner.
• Throughout the materials, students are using mathematical models, for example page 539 SE, problems 2–7. During some HOT problems students are asked to explain their thinking, for example, page 804 SE, problem 26.

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 561 build it) and on homework assignments (for example, page 565 homework helper).
• The digital website has tools containing virtual manipulatives.
• Page 657 SE is an example of using base ten blocks to represent fractions.
• Another example is page 527 SE in Homework Helper where 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 page 241B, 445B, and 387B.
• 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, page 581 TE, 827–828 TE, 595–596 TE, and 115–116 TE) and ways to incorporate mathematical practices are also noted (for example, page 579 TE).

Each lesson contains differentiation suggestions and ELL support (for example, TE page 583A). • Exit tickets identify common misconceptions/errors (for example, page 584 TE).

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.

There are answer keys for most of the student problem sets, exit tickets, homework and tests. Some problems state "see students’ work" or "see students’ models" as the answer key (some examples of this are on pages 115–116 TE, 351–352 TE).

In the Online piece, there is a section called PD. Under PD, there is a section called content videos. These videos do help understand the mathematics a little better and also give the teacher a little better understanding of how to present the information to the students.

Each lesson contains a section called Diagnose Student Errors to help the teachers understand where students may have misunderstandings. For example, see pages 145–146 TE and 15 –152 TE.

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 9, page 555A TE. 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 572 TE).
• Some lessons identify common errors that students make (for example, pages 581-582 TE).
• There are Common Error sections for the teacher to help catch errors students are making and correct them. Examples of this are on pages 571–572 TE, 827–828 TE, 595–596 TE, and 115–116 TE.

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 also contains a Problem of the Day that reviews learning from previous units. For example, Chapter 9, lesson 3, page 573A TE.
• Some lessons provide ideas for Exit Slips (for example page 592 TE).
• Teachers can also create assessments/practice online through the Manage and Assign tab.
• Each chapter has a review section designated to diagnose, prescribe and self-monitor for students. Each problem is outlined by standard, and intervention activities and strategies are aligned to students’ errors/misconceptions.
• Teachers can use the application cards and exit slips as formative assessments and ways to provide feedback for student learning (examples on pages 731–732 TE and 827–828 TE).
• 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.
• Independent Practice provides students the opportunity to practice and teachers the opportunity to provide feedback immediately to students.
• Each lesson also has homework pages. For example, see Chapter 8, lesson 1, page 489 SE.

The materials meet the expectations for having assessments that clearly denote which standards are being emphasized.

• The “Am I Ready” that begins each chapter has student exercises broken down by standard (for example, page 625 TE).
• “Check my Progress” in each chapter identifies concepts being assessed but not standards.
• Chapter Review at the end of each unit identifies standards and provides intervention support (for example, pages 681–682 TE).
• A chapter test correlation of questions and the standards can be found online. It is called the Chapter Assessment Question Correlation.

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 675A TE).
• Think-Pair-Share is suggested for formative assessment (for example, page 680 TE).
• All lessons sequentially practice the new learning, apply the learning, and extend the concepts.
• Materials provide practice for students using Foldables, Vocabulary Cards, and Math Words. For example, see pages 131–134 TE.
• Suggestions for follow-up are located within the Test Practice—Diagnose Student Errors. For example, see pages 469–470 TE.
• 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 TE.

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 and ELL Learner Support (for example, page 673A TE).
• Each chapter has a project (for example, page 624 TE) and additional projects are available online under Project-Based Learning.

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 (for example, page 673A TE).
• Each lesson contains ELL Differentiation Support (for example, page 641A TE).
• A multilingual glossary is available online.
• 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, page 661A TE).
• Enrichment 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 (for example, pages 680 and 765 TE).
• Within the Investigate and Model the Math Section, students are exposed to a variety of places, people, and pictures. Jargon is varied throughout the text (i.e., party favors/souvenirs/decorations). For example, see pages 161–162 SE.
• 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.
• Within the student editions a variety of demographics and personal characteristics are present. For example, see pages 125 SE, 154 SE, 179 SE, and 190 SE.