The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that they assess grade-level content, and if applicable, content from earlier grades. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

Assessments are found in the Teacher Guide and the Assessment Sourcebook. Topic Assessment and Performance Tasks are provided at the end of every unit to assess student understanding of standards taught in the Topic. Cumulative/Benchmark Assessments are given after a group of topics have been taught. Customizable Digital Assessments allow teachers to edit, add questions, and build tests from scratch.

Questions assessing grade-level content include, but are not limited to:

• Topic 2 Assessment, Question 9, states, “Amber bought a hardcover book for $23.70 and a paperback for $6.91. How much did she spend in all? If she paid with 2 twenty-dollar bills, how much change did she get?” Students perform operations with decimals to hundredths (5.NBT.7).
• Topic 14, Performance Task, states, “Omar’s mother is a paleontologist. She digs up and studies dinosaur bones. Omar is helping at the dig site. The Dinosaur Bone Dig 1 grid shows the location of the tent and the triceratops skull Omar’s mother found.” Students name a point on the coordinate plane to solve real-world problems (5.G.2). 
• Topics 1-12, Cumulative Assessment, Question 11, states, “Bottles of water are packaged with 24 bottles per case. A store has 365 cases to sell. How many bottles of water does the store have to sell?” Students fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5).

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet  expectations for spending a majority of instructional time on major work of the grade. 

Evidence includes, but is not limited to:

• The approximate number of Topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 16, which is approximately 75%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 92 out of 108, which is approximately 85%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 122 out of 148, which is approximately 82%. 

A lesson level analysis is most representative of the instructional materials since the lessons include major work, supporting work connected to major work, and assessments embedded within each topic. As a result, approximately 85% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are used to support major work of the grade and are connected to the major standards/clusters of the grade.

Examples of connections between supporting and major work of the grade include, but are not limited to:

• In Lesson 10-1, students read line plots (5.MD.2) and solve problems using operations with fractions (5.NF.2). Question 14 provides a line plot of weights of melons in fractional form and states, “Use the information shown in the line plot. What is the total weight of the 4 heaviest melons?”
• In Lesson 10-2, students make line plots (5.MD.2) using understanding of ordering fractions and decimals (5.NBT.3). Question 8 provides a data table of heights of tree saplings in fractional form and states, “Martin’s Tree Service purchased several spruce tree saplings. Draw a line plot of the data showing the heights of the saplings.”
• In Lesson 10-3, students solve problems with data in line plots (5.MD.2) using operations with fractions (5.NF.2 and 5.NF.6). Question 7 provides a line plot of rainfall in fractional inches and states, “Write and solve an equation for the total amount of rainfall, r, Susannah recorded.”
• In Lessons 12-1 and 12-8 students convert customary units of length (5.MD.1) to solve problems involving multiplication and division (5.NBT.5 and 5.NBT.6). Lesson 12-8, Question 9 states, “Marcia walked 900 meters on Friday. On Saturday, she walked 4 kilometers. On Sunday, she walked 3 kilometers, 600 meters. How many kilometers did Marcia walk over all three days?”
• In Lesson 12-5, students convert metric units of capacity (5.MD.1) using patterns of multiplying and dividing powers of 10 (5.NBT.2). Question 24 states, “Carla makes 6 liters of punch. She pours the punch into 800 mL bottles. How many bottles can she fill?”
• In Lesson 13-3, students interpret numerical expressions (5.OA.2) that involve operations with whole numbers and decimals (5.NBT.5). Question 12 states, “A four story parking garage has spaces for 240 + 285 + 250 + 267 + cars. While one floor is closed for repairs, the garage has spaces for 240 + 250 + 267 cars. How many spaces are there on the floor that is closed? Explain.”

Instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 148 days. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. 

• There are 108 daily content-focused lessons. According to the Pacing Guide, “Each core lesson including differentiation, takes 45-75 minutes.” 
• There is a Topic/Vocabulary Review and Assessment for each of the 16 topics, which are suggested to take two days per topic.
• There are eight 3-Act Math activities where students solve problems using mathematical modeling, which are found in odd-numbered topics and are allotted one day each.

According to the Pacing Guide, additional time can be spent on the following resources (TE 23A):

• Lesson Resources: More days can be spent on some lessons for conceptual understanding, skill-development, and differentiation.
• Additional Resources: More days can be spent on the Math Diagnosis and Intervention System and the 10 Step-Up Lessons used after Topic 16.
• Assessments: More days can be spent on the Readiness Test, Review What You Know, Cumulative/Benchmark Assessments, and Progress Monitoring Assessments (Forms A, B, and C). 

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations for the materials being consistent with the progressions in the Standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems. All grade-level standards are present in the Teacher Edition Program Overview “Grade 5 Common Core Standards.”

The instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. The Teacher Edition contains a Topic Overview Coherence: Look Back, which identifies connections to content taught in previous grades or earlier in the grade, indicating the relevant topics and/or lessons. In addition, Overview Coherence: Look Ahead includes connections to content taught later in the grade and in future grades, topics, or lessons. For example, the Teacher Edition, Topic 4 Overview, Math Background: Coherence, includes:

• “Look Back, Grade 4: In Topic 3, students used strategies and properties to multiply 1-digit numbers by numbers with up to 4 digits. In Topic 4, they did the same to multiply two 2-digit whole numbers. Some of the whole-number strategies, such as partial products, are applied to decimals in Grade 5, Topic 4. Earlier in Grade 5, Lesson 3-1, students discovered to find the product of powers of 10, they should look at the number of zeros and then place the number of zeros on the end of the factor, and that the decimal moves to the right when multiplying decimals by a power of 10.”
• “Connections within Topic 4 include: Students multiply decimals by powers of 10 and estimate products of whole numbers and decimals. Students use number sense to place the decimal point in the product after multiplying as if the decimals were whole numbers.”
• “Look Ahead: In Topic 6, students use what they learn about multiplying with decimals when they divide with decimals. In Topic 12, students use what they learn about multiplying decimals by powers of 10 to convert from one metric unit of measurement to another. In Grade 6, students fluently multiply decimals using the standard algorithm.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve & Share, Visual Learning Bridge, and Convince Me! sections, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to the Independent Practice. During Independent Practice, students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example, students engage in extensive work with Cluster 5.NF.A grade-level problems in Topic 7: Use Equivalent Fractions to Add and Subtract Fractions, including:

• In Topic 7, 3-Act Math, students watch a video of a girl baking banana bread with the measurements for the recipe given. Students make predictions: “Is the red bowl big enough?” Students discuss what information would be needed to solve the problem, and the teacher provides the necessary information so the students can model the solution.
• In Lesson 3, Convince Me!, students use number sense to analyze the information given in the problem to explain why equivalent fractions that use different numbers in the numerator and denominator can have the same value. The question states, “In the example above, would you get the same sum if you used 12 as the common denominator? Explain.”
• In Lesson 7, Problem Solving, Question 18 states, “Paul said, ‘I walked $$2\frac{1}{2}$$ miles on Saturday and $$2\frac{3}{4}$$ miles on Sunday.’ How many miles is that in all?”

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. In the Math Background: Coherence section for each Topic, the Teacher Edition provides explicit connections to prior learning, but standards are not provided. Additionally, some lesson Look Back sections detail connections to previous grades.

Connections to prior grade-level learning include, but are not limited to:

• In Topic 3, Math Background Coherence: Fluently Multiply Multi-Digit Whole Numbers, the Look Back states, “In Grade 4, Topic 1, students learned to round whole numbers. Then throughout Grade 4, they used rounding and compatible numbers to estimate computations with all four operations. They used estimates to check reasonableness of computations.”
• In Topic 7, Math Background Coherence: Use Equivalent Fractions to Add and Subtract Fractions, the Look Back states, “In Grade 4, Topic 7, students learned how to find all the factors of a number and to identify and list multiples”.
• In Lesson 9-1, the Look Back states, “In Grade 4, students extended their understanding of division to recognize $$\frac{a}{b}$$ as a multiple of $$\frac{1}{b}$$, that is $$\frac{a}{b}=a$$x$$\frac{1}{b}$$.”
• In Lesson 11-1, the Look Back states, “In previous grades, students have learned about measuring length, weight or mass, capacity, and area by using manipulatives and standard units of measurement.” In this lesson students find the volume of solid figures.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Examples include, but are not limited to:

• The Topic Planner states Topic 2: “Focuses on developing understanding of addition and subtraction of decimals using models, strategies and understanding of decimal place value (5.NBT.A and 5.NBT.B).” For example, in Lesson 2-2, “students estimate decimal sums and differences using rounding and compatible numbers.”
• Lesson 8-1, the Mathematics Objective states, “Multiply a fraction by a whole number.” This is shaped by 5.NF.B: “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.” 
• Lesson 11-2, the Mathematics Objective states, “Find the volume of rectangular prisms using a formula.”  This is shaped by 5.MD.C: “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”  

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include, but are not limited to:   

• Lesson 4-1 connects 5.NBT.A to 5.NBT.B when students use what they learned about place value patterns to multiply decimals by powers of 10.  
• Lesson 11-4 connects 5.MD.5c to 5.NBT.5 when students solve problems involving volumes of rectangular prisms to developing fluency in multiplication. 
• Lesson 15-2 connects 5.OA.3 to 5.NBT.5 when students identify relationships between patterns using their understanding of multiplication of whole numbers.

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Each lesson is structured to include background information for the teacher and problems and questions that develop conceptual understanding. Examples include, but are not limited to:

• Conceptual understanding for each topic is outlined in the Teacher Edition’s section Math Background: Rigor. For example, the Topic 8 Overview explains multiplying fractions. The Conceptual Understanding states, “Various models are used to develop understanding of multiplying two fractions. One very useful model is an area model. Using an area model also helps develop understanding of finding the area of a rectangle with fractional side lengths.” 
• The Teacher Edition contains a Rigor section for each lesson explaining how conceptual understanding is developed in the lesson. In Lesson 2-2=3, the Rigor section states, “Students use place-value blocks to show how decimals can be added or subtracted. They use tens and ones blocks to show part of a whole and they combine or remove blocks, regrouping as needed”  
• Each lesson begins with a Visual Learning Bridge activity that provides the opportunity for a classroom conversation to build conceptual understanding for students.  For example, Lesson 1-2 states, “Students extend their understanding that each place has a value equal to 10 times the value of the place to its right, and develop the understanding that each place has a value equal to $$\frac{1}{10}$$ of the value of the place to its left.”  Teachers are prompted to ask the following questions, “In 1,440,000, which digit has the greatest place value? Why does the 1 have a greater value than either 4?”
• Each lesson is introduced with a video: Visual Learning Animation Plus, to promote conceptual understanding. For example, the Lesson 4-5 video states, “How can you model decimal multiplication?”  The scenario begins with the following: “A farmer has a square field that is 1 mile wide by 1 mile long. Her irrigation system can water the northern 0.5 mile of her field. If her tomatoes are planted in a strip 0.3 mile wide, what is the area of her watered tomatoes?”   
• Each lesson contains a Convince Me! section that provides opportunities for conceptual understanding. For example, in Lesson 7-10, students use estimation to determine the reasonableness of answers: “Estimate $$8\frac{1}{3}-3\frac{3}{4}$$. Tell how you got your estimate. Susi subtracted and found the actual difference to be $$5\frac{7}{12}$$. Is her answer reasonable? Explain.”

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade-level. Problem sets provide opportunities to practice procedural fluency. Regular opportunities for students to attend to Standard 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. Examples include, but are not limited to:

• Each topic contains a Math Background: Rigor page with a section entitled “Procedural Skill and Fluency.” In Topic 3, this section states, “Topic 3 carefully develops understanding and fluency with using the standard multiplication algorithm for whole numbers. Students start by multiplying 1-digit numbers by 2-, 3-, and 4-digit numbers in Lesson 3-3. This is extended to multiplying two 2-digit numbers in Lesson 3-4 and then to multiplying two 2-digit numbers in Lessons 3-5 and 3-6. Finally, students practice the multiplication algorithm for all of these in Lesson 3-7. The procedure involves multiplying one place at a time.”
• Fluency Practice Activities are found at the end of Topics 3 through 16 to support multi-digit multiplication. In Topic 3, the Fluency Activity states, “Solve each problem. Then follow multiples of 10 to shade a path from START to FINISH. You can only move up, down, right, or left.”  For example, “70 x 89 = __."
• The Performance Task for Topic 3 provides students the opportunity to demonstrate fluency of using the standard algorithm when multiplying. Students are given information on how much elephants eat daily and asked, “How much does Maxie eat in 2 weeks? Complete the computation below." Students calculate 308 x 14.
• Students can practice fluency skills when accessing the Game Center Online at PearsonRealize.com.

he instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of grade-level mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

Materials provide opportunities for students to solve a variety of problem types requiring the application of mathematics in context. Additionally, the materials support teachers by explaining how the students will apply concepts they have learned within each topic in the Math Background: Rigor section of the Topic Overview. 

Students are provided opportunities to work with routine problems presented in context that require application of mathematics.  Examples include, but are not limited to:

• In Lesson 3-8, the Visual Learning Bridge states, “In 1980, a painting sold for $1,575.  In 2015, the same painting sold for 5 times as much. What was the price of the painting in 2015?”
• In Lesson 9-7, the Solve & Share section states, “Organizers of an architectural tour need to set up information tables every $$\frac{1}{8}$$ mile along the 6-mile tour, beginning $$\frac{1}{8}$$ mile from the start of the tour.  Each table needs 2 signs. How many signs do the organizers need?”

Students are provided opportunities to work with non-routine problems presented in context that require application of mathematics.  Examples include, but are not limited to:

• In Lesson 9-5, Visual Learning Bridge, students engage in non-routine applications of dividing a unit fraction by a whole number: “Half of a pan of cornbread is left over.  Ann, Beth, and Chuck are sharing the leftovers equally. What fraction of the original cornbread does each person get?” (5.NF.7c)
• In Lesson 9-7, Question 3 states, “Tamara needs tiles to make a border for her bathroom wall.  The border will be 9 feet long and $$\frac{1}{3}$$ foot wide.  Each tile measures $$\frac{1}{3}$$ foot by $$\frac{1}{3}$$ foot.  Each box of tiles contains 6 tiles.  How many boxes of tiles does Tamara need?  Write two equations that can be used to solve the problem.” (5.NF.7c)
• In Lesson 11, the Performance Task states, “Hiroto works in a sporting goods store. #1  Hiroto stacks identical boxes of golf balls to form a rectangular prism. Each box is a cube. Part A:  How many boxes are in the Golf Ball Display? Part B: Explain how the number of boxes you found in Part A is the same as what you would find by using the formula V=l x w x h.” (5.MD.C) 

Students are provided opportunities to independently demonstrate the use of mathematics flexibly in a variety of contexts. Examples include, but are not limited to:

• In Lesson 3-8, Question 5 states, “A hardware store ordered 13 packs of nails from a supplier.  Each pack contains 155 nails. How many nails did the store order?” 
• In Lesson 5-5, Question 17 states, “The Port Lavaca fishing pier is 3,200 feet long.  There is one person fishing for each ten feet of length. Write and solve an equation to find how many people are fishing from the pier."
• In Lesson 6-6, the Visual Learning Bridge states, “Ms. Watson is mixing 34.6 fluid ounces of red paint and 18.2 fluid ounces of yellow paint to make orange paint. How many 12-fluid ounce jars can she fill? Use reasoning to decide.”
• In Topic 9, the Performance Task states, “Guadalupe likes to bake.  The recipe shown is for blueberry scones with a lemon glaze. Last week, Guadalupe only wanted to make a small batch of scones.  So, she used only half of each amount in the recipe. How much baking powder did Guadalupe use? Write and solve a division equation to answer the question.” 

The instructional materials for enVision Mathematics Common Core Grade 5 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.  

All three aspects of rigor are present independently throughout the program materials. Examples include, but are not limited to:

• Conceptual Understanding is needed to solve in Lesson 5-5. Students use conceptual understanding of place value and area models to divide 3-digit dividends by 2-digit divisors. Question 1 is solved by making a model, “If the orchard has 200 seedlings and 12 are planted in each row, how many rows will be filled? Draw place value blocks to show your answer.”   
• Fluency is practiced in Lesson 3-4, Questions 7-14. Students use the standard algorithm to multiply 2-digit numbers. In Question 7, students solve, “53 x 17." 
• Students apply mathematics to solve problems in context.  In Lesson 8-9, Question 3, students solve, “Isabel is buying framing to go around the perimeter of one of her paintings.  Each inch of framing costs $0.40. What is the total cost of the framing for the painting?” The question displays a picture with a length of $$10\frac{1}{4}$$ inches and a width of $$6\frac{1}{4}$$ inches.

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include, but are not limited to:

• In Lesson 3-3, students use conceptual understanding of regrouping when using the standard algorithm to multiply 2, 3, and 4-digit numbers by 1-digit. To solve Question 13, students find the product and use estimation to determine reasonableness of their estimate for “2204 x 6."
• In Lesson 4-4, students use conceptual understanding of place value to fluently multiply decimals.  Question 22 states, “The airline that Vince is using has a baggage weight limit of 41 pounds. He has two green bags, each weighing 18.4 pounds, and one blue bag weighing 3.7 pounds. Are his bags within the weight limit? Explain.”
• In Lesson 12-5, students use their understanding of metric units to convert capacity in context. Question 24 states, “Carla makes 6 liters of punch. She pours the punch into 800 mL bottles. How many bottles can she fill?”
• In Lesson 16-2, students use their understanding of ordered pairs to solve problems in context. Question 2 states, “Suppose you have a graph of speed that shows a lion can run four times as fast as a squirrel. Name an ordered pair that shows this relationship. What does this ordered pair represent?”

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade-level.

All eight Standards for Mathematical Practice (MPs) are clearly identified throughout the materials. Math Practices are identified in the Topic Planner by lesson. In addition, Math Practices and Effective Teaching Practices (ETP) are identified for each topic, within each lesson, and for specific problems. For example, in Topic 5:

• The Topic Planner states, “MP.1, and MP.5 are addressed in Lesson 3.”
• The Math Practices and ETP addresses MP6: “Attend to precision. Students attend to precision when calculating answers to division problems. (e.g., p. 212, Item 9).”
• In Lesson 5-5, Mathematical Practice states, “MP.5 Use Appropriate Tools Strategically: Students use tools, such as money, place-value blocks, and area models to divide by 2-digit divisors. Also MP.2, MP.4.”

The MPs are used to enrich the mathematical content and are not treated separately. A Math Practices and Problem Solving Handbook is available online at PearsonRealize.com.  This resource provides a page on each math practice for students and teachers to use throughout the year. Math Practice Animations are also available for each practice to enhance student understanding. For example:

• MP1: In Lesson 7-6, Question 24, students make sense of problems and persevere in solving them. For example: “Cal has $12.50 to spend. He wants to ride the roller coaster twice and the Ferris wheel once. Does Cal have enough money? Explain. What are 3 possible combinations of rides Cal can take using money he has?”
• MP2: In Lesson 2-2, Question 21, students reason abstractly and quantitatively. For example: “The size and shape of the Golden Gate Park are often compared to the size and shape of Central Park, About how many more acres does Golden Gate Park cover than Central Park?”
• MP3: In Lesson 8-2, Question 8, students critique the reasoning of others. For example: “Janice said that when you multiply a fraction less than 1 by a nonzero whole number, the products is always less than the whole number. Do you agree? Explain."
• MP4: In Lesson 5-2, Question 23, students model with math,. For example: “The sign shows the price of baseball caps for different pack sizes. Coach Lewis will buy the medium-size pack of caps. About how much will each cap cost? Write an equation to model the problem.”
• MP5: In Lesson 14-1, Solve & Share, students understand how to use ordered pairs to clearly identify a point on the coordinate grid. For example: “On the first grid, plot a point where two lines intersect. Name the location of the point. Plot and name another point. Work with a partner. Take turns describing the locations of the points on your first grid. Then plot the points your partner describes on your second grid. Compare your first grid with your partner’s second grid to see if they match.” 
• MP6: In Lesson 1-5, Solve & Share, students attend to precision when ordering decimals. For example: “What are the lengths of the ants in order from least to greatest?” 
• MP7: In Lesson 3-6, Question 22, students look for structure in place-value relationships in order to solve multiplication problems. For example: “Trudy wants to multiply 66 x 606. She says that all she has to do is find 6 x 606 and then double that number. Explain why Trudy’s method will not give the correct answer. Then show how to find the correct product.” 
• MP8: In Lesson 15-2, Convince Me!, students use repeated reasoning when they analyze patterns and make generalizations. For example: “Do you think the relationship between the corresponding terms in the table Jack created will always be true?”  Students explain why the pattern extends beyond 5 weeks. 

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. 

Materials attend to the full meaning of MP1, MP2, MP6, MP7, and MP8. Examples include, but are not limited to:

• MP1: In Topic 1, 3-Act Math, students make sense of the problem. Students watch a short video about 4 kids pressing buzzers at virtually the same time after 3 seconds. After the video students have a brief discussion about what they noticed about the video. Then the teacher poses the question, “Who hit the button closest to 3 seconds?” Students have to make sense of the information they are given in order to solve the problem and then persevere in order to find the answer.
• MP2: In Lesson 2-2, Solve & Share, students reason abstractly and quantitatively using the properties of addition and compensation to mentally add and subtract decimals. For example, “Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software? Use mental math to solve.” 
• MP6: In Lesson 4-5, Question 17, students attend to precision. For example, “Write a multiplication equation to represent this decimal model.”
• MP7: In Lesson 1-2, Solve & Share, students use the structure of the place value system to determine the relationship between digits in multi-digit whole numbers. For example, “The population of a city is 1,880,000.  What is the value of each of the two 8s in this number? How are the two values related?” A character on the page explains in a text bubble, “You can use place value to analyze the relationship between the digits of a number.”  
• MP8: In Lesson 2-4, Solve & Share, students look for and express regularity in repeated reasoning when adding decimals by using strategies similar to those used to add whole numbers. For example, “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? Solve this problem any way you choose.”  

Materials do not attend to the full meaning of MP4 because students are given a model or told what model to use rather than having to model their mathematical thinking. Examples of questions labeled MP4: Model with Math that do not attend to the full meaning of the standard include, but are not limited to:

• In Lesson 3-3, Question 17 states, “Last year, Anthony’s grandmother gave him 33 silver coins and 16 gold coins to start a coin collection.  Now Anthony has six times as many coins in his collection. How many coins does Anthony have in his collection. Complete the bar diagram to show your work.”
• In Lesson 8-2, the Visual Learning Bridge states, “Claudia has 8 yards of fabric.  She needs $$\frac{3}{4}$$ of the fabric to make a banner.  How many yards of fabric does she need?”  Teachers are prompted to ask students, “Why are there 8 squares in the model?”
• In Lesson 9-3, Question 13 states, “Write and solve a division equation to find the number of $$\frac{1}{3}$$ pound hamburger patties that can be made from 4 pounds of ground beef.”  The full intent of the mathematical practice is not met because students are given a pre-drawn bar model on the page to help them solve.  

Materials do not attend to the full meaning of MP5 because students are given tools rather than being able to choose a tool to support their mathematical thinking. Examples of questions labeled MP5 that do not attend to the full meaning of the standard include, but are not limited to:

• In Lesson 1-1, the Solve & Share states, “A store sells AA batteries in packages of 10 batteries. They also sell boxes of 10 packages, cases of 10 boxes, and cartons of 10 cases. How many AA batteries are in one case? One carton? 10 cartons? Solve these problems any way you choose." The full intent of the mathematical practice is not met because students are given pictures of place-value blocks and a character on the page has a text bubble that states, “You can use appropriate tools, such as place-value blocks, to help solve the problems.  However you choose to solve it, show your work!” 
• In Lesson 5-3 the Solve & Share states, “A parking lot has 270 parking spaces. Each row has 18 parking spaces. How many rows are in this parking lot? Solve the problem any way you choose.”  The full intent of the mathematical practice is not met because students are given graph paper and a character on the page has a text bubble that states, “You can use appropriate tools such as grid paper, to solve the problem. Show your work.”  
• In Lesson 14-4, Question 9, “What tool would you choose for drawing a line segment between points on a coordinate grid? Explain your thinking.”  The Teacher prompt states, “Remind students that a tool, like a ruler or straightedge can be used to draw a line segment." The full intent of the mathematical practice is not met because students are reminded that a ruler or straightedge would be the appropriate tool to use.

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

The Solve & Share activities, Visual Learning Bridge problems, Problem Sets, 3-Act Math activities, Problem Solving: Critique Reasoning problems, and Assessment items provide opportunities throughout the year for students to both construct viable arguments and analyze the arguments of others.

Student materials consistently prompt students to construct viable arguments. Examples include, but are not limited to:

• In Lesson 2-2, Question 19 states, “The cost of one DVD is $16.98, and the cost of another DVD is $9.29. Ed estimated the cost of the two DVDs to be about $27. Is his estimate higher or lower than the actual cost? Explain."
• In Lesson 3-5, the Visual Learning Bridge states, “Last month a bakery sold 389 boxes of bagels. How many bagels did the store sell last month? Find 12 x 389.” The next question in the Convince Me! section states, “Is 300 x 10 a good estimate for the number of bagels sold at the bakery? Explain."
• In Lesson 7-2, the Solve & Share states, “Sue wants $$\frac{1}{2}$$ of a rectangular pan of cornbread. Dena wants $$\frac{1}{3}$$ of the same pan of cornbread. How should you cut the cornbread so that each girl gets the size portion she wants? Solve this problem any way you choose.” The next question in the Look Back section states, “Is there more than one way to divide the pan of cornbread into equal-sized parts? Explain how you know."

Student materials consistently prompt students to analyze the arguments of others. Examples include, but are not limited to:

• In Lesson 1-2, Question 16 states, “Paul says that in the number 6,367, one 6 is 10 times as great as the other 6. Is he correct? Explain why or why not."
• In Lesson 7-1, the Visual Learning Bridge states, students are presented with this scenario, “Mr. Fish is welding together two copper pipes to repair a leak. He will use the pipes shown. Is the new pipe closer to $$\frac{1}{2}$$ foot or 1 foot long? Explain.” The next question in the Convince Me! section states, “Nolini says that if the denominator is more than twice the numerators, the fraction can always be replaced with 0. Is she correct? Give an example in your explanation.”
• In Lesson 7-2, Problem Solving, Question 22 states, “Irene wants to list the factors for 88. She writes 2, 4, 8, 11, 22, and 44, and 88. Is Irene correct? Explain.”
• In Lesson 16-4, Question 10 states, “Mr. Herrera’s class is studying quadrilaterals. The class worked in groups, and each group made a “quadrilateral flag. Marcia’s group made the red flag. Bev’s group made the orange flag. Both girls say their flag shows all rectangles. Critique the reasoning of both girls and explain who is correct.”

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others in a variety of problems and tasks presented to students. Examples include, but are not limited to:

• In Lesson 4-5, Visual Learning Bridge, students solve, “Nita says that the product of an even number and an odd number is always even. Is she correct?”  In the Convince Me!, students solve, “Does multiplying by 8 also always result in an even product? Explain.” Teachers guidance includes: “Students explain that a number multiplied by 8 results in an even number because 8, a multiple of 2, can be divided by 2 with none left over.  Ask students to explain why multiplying by any even number results in an even product.” 
• In Lesson 6-5, Convince Me! states, “Is 3.6 ÷ 1.2 equal to, less than, or greater than 36 ÷ 12? Explain.'' Teacher guidance includes: “Since 3.6 ÷ 1.2 = $$\frac{3.6}{1.2}$$, multiplying the dividend and divisor by the same number to get an equivalent quotient is similar to multiplying the numerator and denominator of a fraction by the same number to get an equivalent fraction.”
• In Lesson 8-6, Convince Me! states, “The fractions on the right ($$\frac{5}{8},\frac{5}{6}$$) refer to the same whole. Kelly said, ‘These are easy to compare. I just think about $$\frac{1}{8}$$ and $$\frac{1}{6}$$.’ Circle the greater fraction. Explain what Kelly was thinking.”  The Teacher’s Edition notes in the margin state, “Students explain a possible reason for Kelly’s thinking to help deepen their understanding of how to compare fractions with unlike denominators. Point out that it is always true that if two fractions have the same numerator (e.g. $$\frac{5}{6}$$ and $$\frac{5}{8}$$) the fraction with the lesser denominator is the greater fraction.” 
• In Lesson 15-1, the Visual Learning Bridge states, “Lindsey has a sage plant that is 3.5 inches tall. She also has a rosemary plant that is 5.2 inches tall. Both plants grow 1.5 inches taller each week. How tall will the plants be after 5 weeks? What is the relationship between the height of the plants?” The next section, Convince Me!  states, “If the patterns continue, how can you tell the rosemary plant will always be taller than the sage plant?” The teacher edition states, “Students explain their reasoning about the relationship between the two patterns in terms of the context. Reiterate how much the two plants grow each week and the difference between the plants’ heights at the beginning."
• In Lesson 16-3, Question 13 states, “Construct Arguments: Draw a quadrilateral with one pair of parallel sides and two right angles. Explain why this figure is a trapezoid.” The teacher edition states, “Emphasize that in order for the figure to be trapezoid, the figure needs to have only one pair of parallel sides. If needed, remind students that a figure with two pairs of parallel sides is a parallelogram." 

The instructional materials reviewed for enVision Mathematics Common Core Grade 5 meet expectations that materials explicitly attend to the specialized language of mathematics.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Examples include, but are not limited to:

• Each topic contains a Vocabulary Review providing students the opportunity to show their understanding of vocabulary and use vocabulary in writing.
• The Teacher Edition provides teacher prompts to support oral language. For example in Topic 7, the Oral Language prompt states, “Before students complete the page, you might reinforce oral language through a class discussion involving one or more of the following activities. Have students define terms in their own words. Have students say math sentences or ask math questions that use the words." 
• The Game Center at PearsonRealize.com contains an online vocabulary game. 
• A vocabulary column is provided in the Topic Planner that lists words addressed with each lesson in the topic. In Lesson 9-4, the Vocabulary List includes: Unit Fraction. This word is also listed in the Lesson Overview. 
• Online materials contain an “Academic Vocabulary” and an “Academic Vocabulary Teacher’s Guide” section. The guide supports vocabulary instruction by providing information on how teachers can develop word meaning and build word power. The Academic Vocabulary section provides a variety of academic words with definitions and activities to help students learn the words. For instance, when clicking on the word, horizontal, the definition is provided: “Straight across from side to side.” Next, the word is used in context: “Does the figure have a horizontal line of symmetry? Where is it?” Lastly, students are provided a task to help build word power: “Use the word in a sentence."
• A glossary exists in both the Student Edition and the Teacher’s Edition Program Overview. In the glossary, distributive property is defined as: “Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. Example: 3 x (10 + 4) = (3 x 10) + (3 x 4)."
• Visual Learning Bridge activities provide explicit instruction in the use of mathematical language.The words are highlighted in yellow and a definition is provided. 
• A bilingual animated glossary is available online which uses motion and sound to build understanding of math vocabulary.

The materials use precise and accurate terminology and definitions when describing mathematics, and support students in using them. Examples include, but are not limited to:

• In Lesson 2-1, the Visual Learning Bridge states, “Compatible numbers are numbers that are easy to compute mentally." Further explanation is provided with an example, “Add 11.45 + 9.55 first because they are easy to compute mentally. $11.45 + $9.55 = $21. $21 + $3.39 = $24.39." 
• In Lesson 12-3, the Visual Learning Bridge states, “1 ton is equal to 2,000 pounds." The materials display. “1 ton (T) = 2,000 pounds (lb).” Next, students practice with the new term in the Problem Solving portion of the lesson, “What would be the most appropriate unit to measure the combined weight of 4 horses?”
• In Lesson 15-1, Visual Learning Bridge, students learn about corresponding terms. Materials prompt teachers, “Say corresponding terms and have students repeat it. Display these number sequences. 0,3,6,9,12,15. 0,4,8,12,16, 20. Point to pairs of corresponding terms, each time saying corresponding terms as you point."
• In In Lesson 16-1, Visual Learning Bridge, students classify triangles based on the lengths of their sides and their angle measures.  During Independent Practice, students “Classify each triangle by its sides and then by its angles.”

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 the visual design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Student print and digital materials follow a consistent format. Tasks within a lesson are numbered to match the teacher guidance. The print and visuals on the materials are clear without any distracting visuals. Student practice problem pages include space for students to write their answers and demonstrate their thinking. In the student’s digital textbook, audio support is provided for Solve & Share and Convince Me! problems. Vocabulary is highlighted when used in the textbook, provided in bold print in independent practice, and an icon reminds students that vocabulary can be found in the glossary.

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 partially meet expectations that materials contain a teacher’s edition with full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The Teacher Edition Program Overview includes resources to help teachers understand the mathematical content, the overarching philosophy of the program, a user’s guide, and a content guide. Additionally, each topic contains a Professional Development Video explaining the mathematical concepts of the lessons with examples that are clearly explained. 

A Math Background is provided for each topic and lesson identifying the connections between previous grade, grade level, and future-grade mathematics. However, these do not support teachers in understanding the underlying Mathematical Progressions.

The Assessment Source Book, Teacher Edition, and Mathematical Practices and Problem Solving Handbooks provide answers and sample answers to problems and exercises presented to students. However, there are no adult-level explanations to build understanding of the mathematics of these tasks.

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 provide a list of lessons in the teacher's edition, cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter, and unit.

The Teacher Edition Program Overview provides a visual showing the number of lessons per topic by domains. It also provides a Pacing Guide showing how many total days, by topic, the material will take. Support for lessons requiring additional time is provided: “Each Core lesson, including differentiation, takes 45-75 minutes. The Pacing Guide above allows for additional time to be spent on the following resources during topics and/or at the end of the year."  A resource list is provided.

The instructional materials for enVision Mathematics Common Core Grade 5 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

A Home-School Connection letter to families and caregivers is provided for each topic. The letter provides an overview of what students will be learning and an activity that the family can complete together. These letters are available in both Spanish and English.

The instructional materials for enVision Mathematics Common Core Grade 5 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials draw on research to explain and contextualize instructional routines and lesson activities. The Teacher Edition Program Overview contains specifics about the instructional approach. Additionally, the Teacher Edition Program Overview explains Instructional Routines. Examples include, but are not limited to:

• The Efficacy Research section states, “First, the development of enVision Mathematics started with a curriculum that research has shown to be highly effective."
• The Research Principles for Teaching with Understanding section states, “The second reason we can promise success is that the enVision Mathematics fully embraces time-proven research principles for teaching mathematics with understanding. One understands an idea in mathematics when one can connect that idea to previously-learned ideas (Hiebert et al., 1997). So, understanding is based on making connections, and enVision Mathematics was developed on this principle."
• Problem Solving Lessons are explained: “Throughout enVision Mathematics, the eight math practices are infused in lessons. Each Problem Solving lesson gives special focus to one of the eight math practices. Features of these lessons include the following: Solve & Share, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Performance Task, and Additional Practice."

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 partially meet expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

End of Topic Assessments and Topic Performance Tasks contain a Scoring Guide assigning point values to each question. However, there is no rubric or sample answers to assist the teacher in scoring student written responses.

Assessments can be taken online where they are automatically scored, and students are assigned appropriate practice, enrichment, or remediation based on their results.  However, teachers must interpret the results on their own and determine materials for follow-up when students take print assessments.

The instructional materials for enVision Mathematics Common Core Grades 3, 4, and 5 do not include opportunities for students to monitor their own progress. Materials do not provide support or components for students to monitor their progress.

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. 

The instructional materials for enVision Mathematics Common Core Grade 5 provide opportunities for teachers to use a variety of grouping strategies.

Materials include teacher-led instruction that present limited options for whole-group, small-group, partner, and/or individual work. When suggestions are made for students to work in small groups, there are no specific roles suggested for group members, but teachers are given suggestions and questions to ask to move learning forward. The Visual Learning Bridge Animation Plus focuses on independent work, while the Pick a Project and 3-Act Math activities have opportunities to work together in small groups or partners.

The instructional materials for enVision Mathematics Common Core Grade 5 encourage teachers to draw upon home language and culture to facilitate learning.

The Teacher Edition Program Overview includes Supporting English Language Learners, which contains ELL Instruction and Visual Learning. English Language Learners' support for each lesson is provided for the teacher throughout lessons to provide scaffolding for reading, as well as differentiated support based on student language proficiency levels (emerging, expanding, or bridging). The Home-School Connection letters for each topic are available in both English and Spanish. There is also an English Language Learners Toolkit available that consists of Professional Development Articles and Graphic Organizers.

The instructional materials for enVision Mathematics Common Core Grade 5 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Teachers and students have access to tools and virtual manipulatives within a given activity or task, when appropriate. Pearson Realize provides additional components online such as games, practice, instructional videos, and links to other websites. In the print Teacher Edition, there are statements in each lesson noting when resources are available online.

Examples include, but are not limited to:

• Animated videos explaining each of the eight Math Practices are provided. At this time only Spanish versions of these videos are provided at Pearsonrealize.com.
• An Animated Glossary embedded in the program helps students internalize the meaning of key concepts, and sometimes visual models are provided.
• The Interactive Additional Practice book provides opportunities for students to engage in the Mathematical Practices.
• Problem-Based Learning activities provide repeated opportunities for students to use precise language to explain their solutions (MP6).
• Visual Learning Animation Plus videos provided at the beginning of each lesson in the Visual Learning Bridge is an interactive way for students to understand conceptually.

The digital instructional materials for enVision Mathematics Common Core Grade 5 are web-­based and compatible with multiple internet browsers. In addition, materials are “platform neutral” and allow the use of tablets and mobile devices.

The digital materials are platform neutral and compatible with multiple operating systems, such as Windows and Apple, and are not proprietary to any single platform. Materials are also compatible with multiple internet browsers such as Internet Explorer, Firefox, Google Chrome, and Safari. Finally, materials are compatible with various devices including iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

The instructional materials for enVision Mathematics Common Core Grade 5 include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology. Examples include, but are not limited to:

• PearsonRealize.com offers online assessments and data which are found in ExamView. Teachers can assign and score material, and analyze assessment data through dashboards.
• PearsonRealize.com offers online fluency games and other program games requiring procedural skills to solve problems.
• Virtual Nerd offers tutorials on procedural skills, but there are no assessments or opportunities to practice procedural skills within the tutorials.
• Skill and Remediation activities in the Topic Readiness online assessment tab include tutorials and opportunities for students to practice procedural skills using technology. There is also a Remediation button to see online activities.

The instructional materials for enVision Mathematics Common Core Grade 5 can easily be customized for individual learners and  include digital opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. 

Teachers can select and assign individual practice items for digital student remediation based on the Topic Readiness assessment. Teachers can also create and assign classes online for students through the Accessible Student Edition. Closed Captioning is included in STEM and 3-Act Math videos. Examples include, but are not limited to:

• Math problems in the digital Student Edition have a read aloud option. Students press the speaker button to have it read aloud. 
• Some lessons and resources are provided in English and Spanish for students such as the Math Practice Animations, Interactive Additional Practice, Game Center, and Animated Glossary.  
• Students have access to digital Math Tools to solve problems in the digital Student Edition such as counter stamps, place value block stamps, erasers, shapes, number lines, grids, fraction strips, and decimal strips.   

The instructional materials for enVision Mathematics Common Core Grade 5 can be easily customized for local use and provide a range of lessons to draw from on a topic. 

There are digital materials correlated to the topic lesson of the print materials. Also, teachers can create and upload files, attach links, and attach documents from Google Drive that can be assigned to students. Additionally, teachers can create assessments from a bank of test items or teacher-written items and assign them to students.

The instructional materials for enVision Mathematics Common Core Grade 5 include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

At PearsonRealize.com, teachers can assign a discussion from a list of prompts under the  “Discuss” tab. Teachers can also go to "Classes" and attach files for students.