5th Grade - Gateway 3

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that underlying design of the materials distinguishes between problems and exercises.

The Solve & Share, Look Back, Visual Learning Bridge, and Convince Me! sections contain problem sets that connect prior learning and/or engage students with a problem in which new math concepts are taught. The Guided Practice, Independent Practice, and Problem Solving sections provide problem sets for students to build on their understanding of the new concept. Assessment Practice problems at the end of each lesson provide opportunities for students to apply what they have learned and can be used to determine differentiation. Additional Practice problems are found in the Additional Practice Workbook that accompanies each lesson and support students in developing mastery of the current lesson and topic concepts.

Examples include, but are not limited to:

• In Lesson 5-2, the Solve & Share states, “Kyle’s school needs to buy posters for a fundraiser. The school has a budget of $147. Each poster costs $13. About how many posters can his school buy? Solve this problem any way you choose." The authors state the purpose of this problem as, “Students use mental math with compatible numbers to estimate the quotient with a 2-digit divisor. Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge."
• In Lesson 10-22, Do You Understand? states, “In the line plot of dog weights on the previous page, what does each dot represent? In a line plot, how do you determine the values to show on the number line?” Students must independently apply new learning of line plots.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that design of assignments is not haphazard and exercises are given in intentional sequences.

Lessons are structured to build mastery. First, students are introduced to concepts and procedures with a problem-solving experience in the Solve & Share section. Next, the important mathematics are explicitly explained with visual direct instruction and connected to the problem-solving experience in the Visual Learning Bridge. Finally students are assessed at the end of each lesson so appropriate differentiation can be provided in the Assessment Practice section.

The following is an example of sequential learning from Grade 5, Lesson 2-4: Use Strategies to Add Decimals:

• Step 1: Solve & Share: “Mr. Davidson has two sacks of potatoes. The first sack weighs 11.39 pounds.  The second sack weighs 14.27 pounds. How many pounds of potatoes does Mr. Davidson have in all?” The authors states the purpose of this lesson as, “Students solve a problem by adding two decimal numbers.  Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge." 
• Step 2: Visual Learning Bridge: “A swim team participated in a relay race.  The swimmers’ times for each leg of the race were recorded in a table. What was the combined time for Caleb and Bradley’s legs of the relay race?”  Students are explicitly taught how to line up the addends by place value and use what they know about partial sums to add the hundredths, tenths, ones, and tens.
• Step 3: Assessment Practice: “Choose all expressions that are equal to 12.9." Five expression choices are provided.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide variety in what students are asked to produce.

The instructional materials prompt students to produce answers and solutions within the Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math sections. Students are also given opportunities to produce oral arguments and explanations during lesson discussions. Additionally students critique fictional student work. Finally, students are often prompted to solve problems “any way they choose” which provides opportunities for students to create diagrams and mathematical models.

Examples include, but are not limited to:

• In Lesson 8-5, Question 32 states, “To amend the U.S. Constitution, ¾ of the 50 states must approve the amendment. If 35 states approve the amendment, will the Constitution be amended?” 
• In Lesson 10-4, Question 9 states, “Did the number of Xs above the number line affect Ms. Fazio’s conclusion? Explain." 
• In Lesson 4-3, Question 8, students are shown 5 x 0.5 and asked to “Find the product. Use place-value blocks to help."

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

Manipulatives and other mathematical representations are aligned to expectations and concepts in the standards. Visual manipulatives are embedded within the problem sets to represent ideas and build conceptual understanding. Students and teachers have access to digital manipulatives to build conceptual understanding and solve problems. Examples include, but are not limited to:

• Students have access to place value blocks, lined paper, index cards, decimal place value charts, number lines, decimal grids, counters, centimeter grid paper, money, index cards, decimal models, fraction strips, circle fraction models, unit cubes, coordinate grids, rulers, and protractors.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains an overview with discussion questions to increase classroom discourse, support for the teacher of what to look for, and ways to ensure understanding of the concept. Essential questions found at the beginning of each topic are revisited throughout the topic and teaching strategies for answering the Topic Essential Questions are provided in the Topic Assessment pages. Examples include, but are not limited to:

• In Topic 10, Essential Question, students are asked, “How can line plots be used to represent data and answer questions?”
• In Lesson 2-4, Solve & Share, Discussion Questions, students are asked, “How much does each sack of potatoes weigh? What are you asked to find?  How do you align numbers before adding multi-digit whole numbers?” 
• In Lesson 17-8, Visual Learning Bridge, Discussion Questions, students are asked, “In this problem, do the whole number parts need to change when finding equivalent fractions? Explain.” 

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

Each topic contains a Topic Planner providing an overview of every lesson, which includes: Lesson Objectives, Essential Understanding, Vocabulary, Materials Needed, Technology and Activity Centers, and Math Standards. The Topic Planner also includes lesson resources such as the Digital Student Edition, Additional Practice Workbook, available print materials, Digital Lesson Courseware, and lesson support for teachers. Examples include, but are not limited to:

• Visual Learning Bridge lessons include a Visual Learning Animation Plus for each lesson. 
• Digital math tools and games, technology resources, and PDF work pages available for each lesson are noted.
• Each Lesson Overview includes 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 possible Daily Review pages with Today’s Challenge to be implemented.
• Each lesson activity contains an overview, guidance for teachers, student-facing materials, anticipated misconceptions, extensions, differentiation support based on Quick Checks, and opportunities for further practice in the online materials. 
• Annotations and suggestions on how to present the content within the lesson structure of: Step 1: Engage and Explore; Step 2: Explain, Elaborate, and Evaluate; and Step 3: Assess and Differentiate are provided. The corresponding Launch section explains how to set up the activity and what to tell students.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials contain a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

Materials explain 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. Additionally, Look Back, This Lesson, Look Ahead, and Cross-Cluster Connections are found in the Coherence Section for each lesson. Examples include, but are not limited to:

• In Topic 5, Math Background: Coherence, the Look Ahead states, “In Grade 6, students will learn how to divide whole numbers."
• In Lesson 8-2, Lesson Overview, the Look Back states, “In the last lesson, students learned how to multiply a fraction by a whole number. This Lesson: Students will learn how to multiply a whole number by a fraction. Look Ahead: Students use models to find a fraction of a whole number of things and then to multiply a whole number by a fraction."

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

The Program Overview provides information about using assessments to gather information about students’ prior knowledge. The authors state, “Readiness assessments help you find out what students already know. Formative instruction in lessons inform instruction. Various summative assessments help you determine what students have learned. Rubrics are provided for assessing math practices. Auto-scored online assessments can be customized.” The 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. Review What You Know, found in the Topic Opener, gathers information about prior knowledge and provides an Item Analysis for Diagnosis and Intervention. Examples include, but are not limited to:

• In Grade 5, Readiness Assessment, Item 14 states, “Brandy made 7 batches of cookies. Each batch contained 12 cookies. She put the same number of cookies in each of 5 bags. How many cookies were not put in bags?” (4.OA.3).
• In Topic 7, Review What You Know, Question 11 states, “Liam bought $$\frac{5}{8}$$ pound of cherries. Harrison bought more cherries than Liam. Which could be the amount of cherries that Harrison bought?” Four multiple choice answers are provided. (4.NF.2)

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

Lessons include an Error Intervention section identifying where students may make a mistake or have misconceptions and how to provide support. Additionally, lessons contain side matter in the Teacher Edition that identifies possible misconceptions and ways for teachers to prevent them.  Examples include, but are not limited to:

• In Lesson 15-3, Error Intervention states, “If students have difficulty describing a relationship, then have them create a table to see the corresponding numbers in an organized way."  
• In Lesson 12-5, Visual Learning Bridge, teacher side matter prompts teachers to prevent misconceptions: “Point out that the prefix milli-denotes thousandths.  One thousandth of a liter is 1 milliliter, or 1,000 mL = 1 L."

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide 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, and 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.

Examples include, but are not limited to:

• 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 for enVision Mathematics Common Core Grade 5 meet expectations that materials offer ongoing formative and summative assessments that clearly denote which standards are being emphasized. 

Assessments are located in the Assessment Book or 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. Examples include, but are not limited to:

• In Topic 2, Performance Task, Question 6 states, “Kim recorded her scores for Round 2. To estimate her total, she rounds to the nearest whole number and says, ‘7 + 9 + 7 = 23, so my total is at least 23 points.’ Do you agree? Explain your reasoning." This question is noted as being DOK Level 3 and addresses 5.NBT.4, 5.NBT.7, and MP3.

In Topic 8 Assessment, Question 7 states, “Jenna ran 2 ⅞ kilometers each day for a week. How far did she run in all? Give an estimate, then find the actual amount. Show your work." This question is noted as DOK Level 2 and addresses 5.NF.6.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials provide a detailed Scope and Sequence and the Topic Overview identifies prerequisite skills. Each lesson contains a Daily Review and a Solve & Share Activity that reviews prior knowledge and/or prepares students for the activities that follow. Each lesson contains explicit instructional support for sequencing and scaffolding. Lesson side matter provides guidance on discussion questions, sample student work, and look fors. Step 3: Assess and Differentiate, contains optional activities that can be used for additional practice or support before moving on to the next activity or lesson. Examples include, but are not limited to:

• In Lesson 8-1, Independent Practice, students construct an argument, “Do you think the difference of 1.4 - 0.95 is less than 1 or greater than 1? Explain." To support teachers, side matter states, “If students have difficulty comparing the difference to 1, ask ‘What compatible numbers can you substitute for 1.4 and 0.95? What is the difference of 1.5 and 1? So will 1.4 - 0.95 be greater than or less than 1?’”
• In Topic 9, Math Background: Coherence, students apply understanding of division to divide fractions. In the Look Back section, the materials note the Grade 4 standards needed, ““In Topic 5, students solved problems involving division of whole numbers, including problems that involved interpreting remainders." 

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Additional Practice Materials include a lesson for each topic that includes specific questions for the leveled assignment for all learning ranges, Intervention, On-Level, and Advanced with verbal, visual, and symbolic representations. Response to Intervention strategies for each lesson give teachers “look fors,” suggestions to address the needs of struggling students, and discussion questions. Additional examples within the lesson help students extend their understanding of the concept being taught and include extra problems for the teacher to use. Differentiated Interventions, Reteach to Build Understanding, and Enrichment sections provide reteach scaffolding and concept extensions. Examples include, but are not limited to:

• In Lesson 7-3, Reteach to Build Understanding, Problem 6 states, “Find the sum of $$\frac{3}{8}$$ and $$\frac{1}{4}$$.”
• In Lesson 4-4, Enrichment states, “Hazel is earning money this summer by doing chores for her neighbors. She decides to make a bar graph to help her see how much money she makes at each job each week. Show each amount on the graph. Problem 1, Hazel earns $5.50 each time she walks Ms. Duncan’s dog, Rose. She walks Rose three times each week. Problem 2, Hazel helps Mr. Carson clean his attic two times each week. She earns $6.50 each time. Problem 5, Hazel is going to volunteer at the humane society. She needs to decide which job she should stop doing to make time for her volunteer work. Which job do you think Hazel should stop doing? Why?”

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The Solve & Share, Visual Learning Bridge, Guided and Independent Practice, and Quick Check/Assessment Practice sections provide opportunities for students to apply mathematics from multiple entry points. Materials sometimes ask students to use a specific strategy, but questions within the lesson allow students to use a variety of strategies. Lesson and task narratives provided for teachers offer possible solution paths and presentation strategies for various levels. Examples include, but are not limited to:

• In Lesson 4-9, Solve & Share students are presented with information about deli items and their prices. The question states, “Susan is making sandwiches for a picnic. She needs 1.2 pounds of ham, 1.5 pounds of bologna, and 2 pounds of cheese. How much will she spend in all? Solve this problem anyway you choose. Use models to help." (5.NBT.7)
• In Lesson 3-4, Solve & Share states, “Ms. Silva has 12 weeks to train for a race. Over the course of one week, she plans to run 15 miles. If she continues this training, how many miles will Ms. Silva run before the race? Solve this problem using any strategy you choose.” (5.NBT.5)

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials suggest 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. ELL suggestions are provided in Solve & Share and Visual Learning Bridge activities. Visual Learning support is also embedded in every lesson to support ELL learners. 

Support for other special populations is also provided in the Teacher Edition Program Overview. Resources and a key are provided for Ongoing Intervention during a lesson, Strategic Intervention at the end of the lesson, and Intensive Intervention as needed at 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 are provided through teachers' notes to conduct a short lesson where vocabulary, concept development, and practice can be supported. Online Auto Design Differentiation is also included, and supports the program after a lesson, a topic, assessments, or groups of topics. Teachers can track student progress using Assignment Reports and analyzing Usage Data. Examples include, but are not limited to:

• In Lesson 9-3, Solve & Share, English Language Learner support for Expanding students states, “Have students think about meals or snacks in which they did not eat all the food. For example, they ate only 1 bowl of cereal from a box of cereal or two slices of bread from an entire loaf of bread." Support for Developing ELL students states, “Have students draw a picture of the whole sandwich and indicated serving sizes. Have students complete the statement, ‘This is the whole because _____.’" 
• In Lesson 14-1, Visual Learning Bridge, English Language Learner support states, “Say the term ordered pair and have students repeat it. Look at the ordered pair (1,3) on the grid in Box C. The first number tells how far to go to the right. Point to the 1. Use a hand gesture to indicate going right. The second number tells how far to go up. Point to the 3. Use a hand gesture to indicate going up."

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Materials provide extension activities for each Solve & Share activity. Also, Independent Practice problems contain Higher Order Thinking items. Additionally, Enrichment activities follow the Quick Check Assessment in each lesson which can be used for differentiation. STEM activities are provided in the Activity Center. Finally, Additional Practice contains Advanced problems for students. However, teacher guidance is not provided for advanced students activities. Examples include, but are not limited to:

• In Lesson 6-3, Solve & Share states, “Chris paid $3.60 for 3 colored pens. Each pen costs the same amount. How much did each pen cost? Solve this problem any way you choose." Extension problem states, “How can you use a tool to find the solution for 3.42 divided by 3?” 
• In Lesson 2-2, STEM Activity: Giant Kelp states, “Did you Know? Giant kelp is a type of seaweed that grows so tall that it forms an underwater forest. Each kelp blade may grow about 2 feet a day, up to 175 feet high. Kelp produce their own food using sunlight. Ocean consumers that eat the kelp include sea urchins and kelp crab.” Question 1 states, “Suppose a sea urchin eats 1.30 kilograms of kelp one day and 0.51 kilogram the next day. How much total kelp did the sea urchin eat both days? Shade the hundredths grid to help you."

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

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. Materials include a set number of names used throughout the problems and examples (e.g., Joanne, Tomas, Daria, Nolini, Delbert, Ramon, Li, Gloria, Miguel, Jerome, Chico, and Jila). 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 and a pattern of one character using more/less sophisticated strategies does not occur. 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.