5th Grade - Gateway 3

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson. It is clear when the students are solving problems to learn and when they are completing exercises to apply what they have learned.

Lessons include Solve & Share, Look Back, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice. Additional Practice is in a separate section of the instructional materials, distinguishing between problems students complete and exercises in the lessons. The Solve and Share section serves either to connect prior learning or to engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in Guided Practice.

In the Independent Practice and Problem Solving sections, students have opportunities to build on their understanding of the new concept. Each activity lesson ends with an Assessment Practice in which students have opportunities to apply what they have learned from the activities in the lesson and can be used to help differentiate instruction.

Additional Practice problems are consistently found in the Additional Practice Workbook that accompany each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and topic concepts.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, activities within lessons within the topics are intentionally sequenced, so students have the opportunity to develop understanding leading to mastery of the content. The structure of a lesson provides students with the opportunity to activate prior learning and to build procedural skill and fluency. Students also engage with multiple activities that are sequenced from concrete to abstract and increase in complexity. Lessons close with Problem Solving, which typically has students apply learning from the lesson, and Assessment Practice, which is typically two questions aligned to the daily lesson objective.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce written answers and solutions within Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math, and students produce oral arguments and explanations through discussions that occur in whole group, small group, or partner settings. Students also produce written critiques of fictional students’ work that include models, drawings, and calculation.

In the materials, students use a digital platform (Visual Learning Animation Plus and Practice Buddy) and paper-pencil activities to conduct and present their work. The materials prompt students to use appropriate mathematical language in their written and oral responses, and students use various mathematical representations frequently in their work, even though the representation is often provided for students.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives. For example:

• Manipulatives and other mathematical representations are aligned consistently to the expectations and concepts in the standards. The majority of manipulatives used are measurement and geometry tools that are commonly accessible. In Lesson 9-6, students use fraction strips and number lines when dividing whole numbers and unit fractions. In Lesson 11-2, students use cubes to derive a formula to find the volume of a rectangular prism. Animated versions of the task are also provided as an option.
• The materials have manipulatives embedded within the Visual Learning Bridge, Visual Learning Bridge Animation, and Independent Practice activities to represent ideas and build conceptual understanding. For example, in Lesson 3-1, students use place-value blocks to find the product of whole numbers and powers of 10 using patterns and mental math.

Examples of manipulatives for Grade 5 include:

• Counters, number lines, place-value blocks, bills and coins, pattern blocks, circle fraction models, decimal models, and fraction strips.
• Geometry toolkits containing tracing paper, colored pencils, scissors, index card, unit cube, centimeter ruler, inch ruler, yardstick, meter stick, and coordinate grids/paper.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains a narrative for the teacher that includes Lesson Overviews, suggested questions for discussion, and guiding questions designed to increase classroom discourse, support the teacher in knowing what to look for, and ensure understanding of the concepts. For example, in Lesson 2-5 Solve & Share, the following questions are included: “In which place does 15.33 have a digit that 32.7 does not? What can you do to make the number of digits to the right of the decimal point match?” In Lesson 12-2 Visual Learning Bridge and Classroom Conversation, the following questions are included: “Why might you want to change from one unit of capacity to another? Will the number of fluid ounces be less than or greater than 8? How do you know?”

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

• Each Topic has a Topic Planner that givens an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the CCSSM.
• The Topic Planner also includes Lesson Resources such as the Digital Student Edition, Additional Practice Workbook, Print material available, as well as what can be found in the Digital Lesson Courseware and Lesson Support for Teachers.
• Each lesson opens with a Lesson Overview including an Objective and an Essential Understanding, “I can” learning target statements written in student language, CCSSM that are either being “built upon” or “addressed” for the lesson, Cross-Cluster Connections, the aspect(s) of rigor addressed, support for English Language Learners, and any possible Daily Review pages with Today’s Challenge to be implemented. Within the lesson, technology resources or places to print PDF work pages are embedded.
• Lessons include detailed guidance for teachers for the Warm-Up, Activities, and the Lesson Synthesis.
• Each lesson activity contains an overview, guidance for teachers and student-facing materials, anticipated misconceptions, extensions, differentiation support based on formative assessments called Quick Checks, and opportunities for further practice in the online materials. Guiding questions and additional supports for students are included within the lessons.
• The teacher materials that correspond to the student lessons provide annotations and suggestions on how to present the content within the lesson structure: Step 1 (Engage and Explore), Step 2 (Explain, Elaborate, and Evaluate), and Step 3 (Assess and Differentiate). A Launch section follows which explains how to set up the activity and what to tell students. During the Visual Learning Bridge in Step 2, there are supporting questions and narratives for students.
• The materials are available in both print and digital forms. There are additional online resources that support the material. These opportunities are noted within the lessons. For example, each lesson has an Interactive Practice Buddy that is noted in Step 2 and Step 3, as well as Another Look Videos found in Step 3.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

The Teacher Edition explains how mathematical concepts are built from previous grade levels or topics and lessons as well as how the grade-level concepts fit into future grade-level work.

For example, Topic 7 Overview of Math Background: Coherence states that the work in this topic relates to factors/multiples, finding equivalent fractions,  decomposing mixed numbers, adding and subtracting fractions and mixed numbers with like denominators in Grade 4, solving problems using data from line plots and involving measurements later in Grade 5, and expressions and equations with fractions in Grade 6.

There is also an individual coherence section within each lesson with the sections Look Back, This Lesson, Look Ahead, and Cross-Cluster Connections (where applicable).

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

• In the Online Teacher Edition, Program Overview, Assessment Resources provides information about the use of assessments to gather information about student’s prior knowledge.
• Each grade level includes a Grade Level Readiness assessment that is to be given at the start of the year. This Readiness Test can be printed or distributed digitally. In this assessment, prerequisite skills from the prior grade necessary for understanding the grade-level mathematics are assessed.
• The Daily Review is designed to engage students in thinking about the upcoming lesson and/or to revisit previous grades' concepts or skills.
• Prior knowledge is gathered about students through Review What You Know assessments found in the Topic Opener. Each assessment has an Item Analysis for Diagnosis and Intervention. In these assessments, prerequisite skills necessary for understanding the topics in the unit are assessed and aligned to standards so the teacher can re-teach if needed.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Lessons include Error Intervention that identifies where students may make a mistake or have misconceptions. There are questions for the teacher to ask along with what to assign for reteaching the concept or skill. For example, in Lesson 11-1, the Error Intervention gives the following guidance: “If students struggle to make a model, then demonstrate how to make the first layer. To work on the bottom layer, make three rows with three cubes each. This layer is three cubes long by three cubes wide. Have students work on the second layer.”

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure, consisting of Solve & Share, Visual Learning Bridge, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice, provides students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently, with partners and in groups, where review, practice, and feedback are embedded into the instructional routine. In addition, Practice problems for each lesson activity reinforce learning concepts and skills and enable students to engage with the content and receive timely feedback. Discussion prompts in the Teacher Edition provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Each Topic includes a "Review what you know/Concept and Skills Review” that includes a Vocabulary review and Practice problems. This section includes review and practice on concepts that are related to the new Topic.

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 12 and 16 provide review of prior topics as an assessment. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores.

Different games online at Pearson Realize support students in practice and review of procedural skills and fluency.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for assessments clearly denoting which standards are being emphasized.

Assessments are located in a separate book or the online portion of the program and can be accessed at any time. For each topic there is a Practice Assessment, an End-Unit Assessment, and a Performance task. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials include a detailed Scope and Sequence of the course, including pacing. The Topic Overview in the Teacher Edition includes Coherence which enhances scaffolding instruction by identifying prerequisite skills that students should have. Each lesson is designed with a Daily Review and a Solve and Share Activity that reviews prior knowledge and/or prepares all students for the activities that follow.

In lessons, there are the following explicit instructional supports for sequencing and scaffolding: the Lesson Overview, questions and extensions for the Solve & Share, Prevent Misconceptions in Visual Learning Bridge, Revisit the Essential Question in Convince Me!, Error Intervention during Guided Practice, and item-related support during Independent Practice and Problem Solving. This information assists a teacher in making the content accessible to all learners.

Lesson narratives often include guidance on where to focus questions in all lesson activities, sample student work, and guidance on what to look for. Optional activities are often included in Step 3 (Assess and Differentiate) that can be used for additional practice or support before moving on to the next activity or lesson.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure of Step 1 (Problem-Based Learning), Step 2 (Visual Learning), and Step 3 (Assess and Differentiate) includes guidance for the teacher on the mathematics of the lesson, possible misconceptions, and specific strategies to address the needs of a range of learners. Embedded supports include:

• The Additional Practice Materials include a lesson for each topic that includes specific questions for the leveled assignment for all learning ranges.These three levels of problems are I (Intervention), O (On-Level), and A (Advanced) and include verbal, visual, and symbolic representations.
• There are Response to Intervention strategies in each lesson. These sections give teachers “look fors” and suggestions to address the needs of students who are struggling. Questions for the teacher to ask are also included.
• Each lesson has at least one Additional Example. These help students extend their understanding of the concept being taught. It includes an extra problem for the teacher to use.
• Each lesson has Differentiated Interventions for a wide range of learners, which include Reteach to Build Understanding (provides scaffolding to reteach) and Enrichment (extends concepts from the lesson).
  

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Solve & Share, Visual Learning Bridge, Guided and Independent Practice, and Quick Check/Assessment Practice provide opportunities for students to apply mathematics from multiple entry points. Though there may be times when the material asks a student to use a specific strategy, there are still questions within the same lesson that allow for students to use a variety of strategies.

The lesson and task narratives provided for teachers offer possible solution paths and presentation strategies from various levels. For example:

• In Lesson 1-4 Solve & Share, students use place value to show how time is written as a decimal. Students may represent this scenario any way they choose allowing for all students to participate in the task while also focusing instruction on the mathematical concept of place value.
• In Lesson 2-5 Convince Me!, students discuss different strategies for subtracting decimals. Students can represent this in different ways, by using a standard algorithm, number lines, estimation, or using place value knowledge. The teacher is encouraged to look for multiple strategies as students use precision.
• In Lesson 4-1, students solve a story problem where they can apply their knowledge of multiplying decimals by powers of 10. The teacher is encouraged to look for multiple solution paths, and examples of different solution paths or student explanations for counting methods are provided to help the teacher anticipate student solution strategies.
• In Lesson 4-5, Question 17, students use multiplication equations to represent decimal models. Multiple strategies can be provided as this question is considered a quick-check question for prescribing differentiation.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet 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.

The ELL Design is highlighted in the Teacher Edition Program Overview and describes support based on the student’s level of language proficiency: emerging, expanding, or bridging, as identified in the WIDA (World-Class Instructional Design and Assessment) assessment. An ELL Toolkit provides additional support for English Language Learners.

Two ELL suggestions are provided for every lesson, one in Solve and Share and another in Visual Learning Bridge. Also, Visual Learning support is embedded in every lesson to support ELL learners. Examples include:

• In Lesson 2-1 includes English Language Learners' Tips for Emerging: "Read the problem to students. Ask students to identify the cost of the three pieces of software. Ask which operation is needed to find the total cost of the software;” Expanding: “Reread the problem with students. Ask students which words indicate which operation is use to find the total cost of the software;” and Bridging: “Ask students to reread the problem with a partner. Have them find the total cost and explain their method.”
• In each topic opener, there is information provided to include specific ELL supports as needed. For example, in Topic 6, the materials provide ELL support using Visual Learning through the program, ELL instruction in lessons, a Multilingual Handbook, and an ELL Toolkit.
• Visual learning infused throughout the program provides support for English Language Learners. This includes Visual Learning Animation Plus online, Visual Learning Bridge for each lesson, and the Animated Glossary. These use motion and sound to reduce language barriers. Questions are read aloud, visual models are provided, and motion and sound definitions of mathematical terms are provided.
• The Multilingual Handbook is included with a Mathematics Glossary in multiple languages.
• An English Language Learners Toolkit is a resource that provides professional development and resources for supporting English Language Learners.
• For Visual Learning in Lesson Practice, Pictures With a Purpose appear in Lesson Practice to provide information that is related to math concepts or real world problems to support student understanding.

Support for other special populations noted in the Teacher Edition Program Overview include:

• Resources and a key are provided on for Ongoing Intervention (during a lesson), Strategic Information (at the end of the lesson), and Intensive Intervention (as needed anytime).
• The Math Diagnosis and Intervention System (MDIS) supports teachers in diagnosing students needs and providing more effective instruction for on- or below-grade-level students. Diagnosis, Intervention Lessons, and Teacher Support is provided through teachers' notes to conduct a short lesson where vocabulary, concept development, and practice can be supported.
• Online Auto Design Differentiation is included, and the supports within this part of the program include: Differentiation After a Lesson (based on an Online Quick Check where the Interactive Practice Buddy can be utilized), Differentiation after a Topic (based on the online topic assessments where Visual Learning Animations Plus are then assigned), and Differentiation after a Group of Topics (based on the online cumulative benchmark assessments where students can then receive remediation or enrichment). The teacher can track progress using Assignment Reports and analyzing Usage Data.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. All students complete the same lessons and activities; however, there are some optional lessons and activities that a teacher may choose to implement with students.

Opportunities to engage in the content at a greater depth include:

• Extensions found at the end of every Solve and Share.
• Higher Order Thinking items within the Independent Practice and Problem Solving section.
• Enrichment pages as a result of the Quick Checks in every lesson.
• Opportunities to engage in STEM activities during the activity centers.
• Noted Advanced problems to complete during the Additional Practice portions of each lesson.
• Differentiation after a Group of Topics based on the online cumulative benchmark assessments where students can then receive enrichment.

It should be noted that there is no guidance for teachers on engaging advanced students in these activities.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

• The lessons contain tasks including various demographic and personal characteristics. All names and wording are chosen with diversity in mind, and the materials do not contain gender biases.
• The Grade 5 materials include a set number of names used throughout the problems and examples (e.g., Jessie, Salvatore, Clara, Liza, Delbert, Ramon, Li, Yolanda, Hakeem, Jerome, Chico, June). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.
• Characters are often presented in pairs with different solution strategies. There is not a pattern in one character using more/less sophisticated strategies.
• When multiple characters are involved in a scenario they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias. For example, in Lesson 5-4, Question 20 states, “Model with Math: Peter is driving 992 miles from Chicago to Dallas. His sister Anna is driving 1,068 miles from Phoenix to Dallas. Write and solve an equation to find how much farther Anna drives than Peter drives.” There is no differentiation of what roles the characters take that suggests a gender, racial, or ethnic bias.