The instructional materials reviewed for enVision Mathematics Common Core Grade 3 meet expectations that they assess grade-level content, and if applicable, content from earlier grades. In instances where above-level content is assessed, questions could easily be omitted or modified by the teacher. 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:

• Topic 9, Assessment, Question 1, states, “Find the sum of 458 and 342. Use place value and find the sums of the hundreds, tens, and ones.” Students use place value understanding to perform multi-digit arithmetic (3.NBT.2).
• Topic 12, Performance Task, Question 3, states, “Divide the number line into the number of equal parts of the cake. Then mark a dot on the number line to show the part of the cake that Bruno frosted. Write the fraction that he frosted.” Students represent a fraction on a number line (3.NF.2).
• Topics 1-8, Cumulative Assessment, Question 12, states, “Louise made the shape from tiles. What is the area of the shape. Explain.” The shape has four whole squares and six diagonal halves of squares around the outside. Students use understanding of multiplication and addition related to area (3.MD.6).

Questions assessing content above grade level that can be omitted or modified include:

• Topic 2, Performance Task, Question 6, states, “Carlos reads 10 pages every day. The book he is reading has 46 pages. How many days will it take him to finish his book? Complete the chart and explain your answer.” This question requires students to calculate with remainders in the solution (4.NBT.6).
• Topics 1-4, Cumulative/Benchmark Assessment, Question 3, states, “A coach brought a cooler with 20 bottles of water for the baseball team. Each player gets the same number of bottles of water. There are 9 players on the team. Which statement is true?” This question requires students to calculate with remainders in the solution (4.NBT.6).

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 14 out of 16, which is approximately 88%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87 out of 104, which is approximately 84%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 144, which is approximately 80%. 

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 84% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 Lessons 7-1 through 7-4, students interpret data in scaled picture graphs and bar graphs (3.MD.3) to solve two-step problems using multiplication and division (3.OA.8). Lesson 7-1, Question 8 states, “How many more points were scored on October 10 and 24 combined than on October 3 and 17?”
• In Lesson 8-5, students round whole numbers (3.NBT.1) to determine the reasonableness of answers (3.OA.8). Question 17 states, “Zoe says 247 rounded to the nearest hundred is 300 because 247 rounds to 250 and 250 rounds to 300. Is Zoe correct? Explain.”
• In Lesson 15-3, students identify attributes of shapes (3.G.1) using area as an attribute (3.MD.7b). Question 11 states, “Explain which of the shapes at the right you can cover with whole unit squares and not have any gaps or overlays.”
• In Lesson 10-2, students use place-value to find multiples of whole numbers and 2-digit multiples of 10 (3.NBT.3) in multiplication problems (3.OA.3). Question 21 states, “Juanita buys 7 sheets of postage stamps at the post office. Each sheet has 20 stamps. How many stamps does she buy in all? Explain how you solved the problem. Tell why you chose that method”.
• In Lesson 12-6, students measure to the nearest half inch and use a line plot to share results (3.MD.4) representing fractional measurements on a number line (3.NF.2). Question 11 states, “Draw a number line from 0 to 2. Label the wholes. Divide each whole into thirds. Label each fraction.”
• In Lesson 15-1, students describe quadrilaterals (3.G.1) using fractional parts (3.NF.1). The Solve & Share Activity states, “The area of each small triangle on the paper represents a unit fraction of the whole square each of your quadrilaterals represents.”

Instructional materials for enVision Mathematics Common Core Grade 3 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 144 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 104 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 3 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 3 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 5 Overview, Math Background: Coherence, includes:

• “Look Back, Grade 2: In Topic 2, students began to work in equal groups of objects arranged in arrays. They learned to find the total number of objects by writing equations using rows or columns. Earlier in Grade 3, Topic 1, students developed conceptual understanding of multiplication and division. In Topic 2, students used arrays to understand multiplication facts. In Topic 4, students used the relationship between multiplication and division to learn division facts.”
• “Connections within Topic 5 include: In Lessons 5-1 and 5-2 students use multiplication tables to find patterns, products, and unknown factors. All Topic 5 lessons use the strategies of multiplication tables, breaking apart, and skip counting.”
• “Look Ahead: Students continue working towards being able to demonstrate fluency with multiplying and dividing within 100. In Topic 6, students develop an understanding of the relationship between multiplication and area. In Topic 7, students use multiplication to draw and interpret scaled picture and bar graphs. In Grade 4, Topics 3 and 4, students multiply and divide larger numbers using strategies and properties. In Topic 7, students work with factors and multiples.”

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 follow a consistent lesson structure that includes a topic project, and in every other topic there is a 3-Act Mathematical Modeling Task. Topic Lessons include Solve & Share, Visual Learning Bridge, and Convince Me! sections, where 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 with extensive work with grade-level problems for 3.OA.5 in Topic 3: Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8 (3.OA.5) as they engage in activities, including:

• In Topic 3, 3-Act Math, students watch a video of a teacher handing out water and juice boxes on a field trip. Students make predictions on “How many bottles of water did the students drink?” Students determine what information is needed to solve the problem, and are given additional information about juice boxes and water in order to model the solution.
• In Lesson 3-3, Convince Me!, students use the distributive property to find the product of unknown facts by breaking the unknown fact into the sum of two known facts. The question states, “Use a 5’s fact and a 1’s fact to find 6 x 9. Draw two arrays. Explain your drawings.”
• In Lesson 3-5, Problem Solving, Question 26 states, “Mr. Ling walks 5 miles each day. How many total miles does he walk in one week? Explain.”

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 1, Math Background Coherence: Understand Multiplication and Division of Whole Numbers the Look Back states, “In Grade 2, Topic 2, students explored even and odd numbers and used arrays to find totals. They also learned to write equations for arrays using rows or columns.”
• In Topic 6, Math Background Coherence: Connect Area to Multiplication and Addition the Look Back states, “In Grade 2, Topic 2, students began to work with equal groups of objects arranged in arrays. They also learned to find the total number of objects by writing equations using rows or columns.” 
• In Lesson 8-1, Look Back, “In Grade 2, students learned to add within 1,000, using models or strategies.” In this lesson, students solve addition problems using the commutative, associative, and identity properties of addition.
• In Lesson 14-1, Look Back, “In Grade 2, students learned to tell time to the nearest 5 minutes and they learned about patterns with 5 as a factor in Topic 2.” In this lesson students apply knowledge of counting by 5s and 1s to tell time to the nearest minute.

The instructional materials for enVision Mathematics Common Core Grade 3 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 3: “Focuses on using known facts and properties of multiplication to learn the multiplication facts with factors of 3, 4, 6, 7, and 8 (3.OA.B)”. For example, in Lesson 3-6, “students use the Associative (Grouping) Property of Multiplication to multiply with three factors.”
• In Lesson 5-1, the Mathematics Objective states, “Use the multiplication table and the distributive property to find patterns in factors and products.”  This is shaped by 3.OA.B: “Understand properties of multiplication and the relationship between multiplication and division”.
• In Lesson 14-3, the Mathematics Objective states, “Solve word problems involving addition and subtraction to measure quantities of time.” This is shaped by 3.MD.A: “Solve problems involving measurement and estimation.”  

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 2-2 connects 3.OA.A to 3.OA.D when students represent and solve problems involving multiplication while solving problems involving the four operations that include identifying and explaining patterns in arithmetic.   
• Lesson 6-2 connects 3.MD.C to 3.OA.A when students find areas of rectangles on grids using arrays.  
• Lesson 8-1 connects 3.NBT.A to 3.OA.D when students use place value understanding and properties of operations to perform multi-digit arithmetic to solve two step word problems.  
• Lesson 14-3 connects 3.MD.A to 3.NBT.A when students solve problems involving time using strategies based on place value and properties of operations to add and subtract.  

The instructional materials for enVision Mathematics Common Core Grade 3 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. The Topic 2 Overview explains Multiples of 2, 5, 9, and 10, as well as the Identify Property of Multiplication and the Zero Property of Multiplication. The Conceptual Understanding section states, “Deep understanding of these properties is important as students will use them throughout their work in mathematics, including equation solving and fraction equivalence.”
• The Teacher Edition contains a Rigor section for each lesson explaining how conceptual understanding is developed in the lesson. In Lesson 1-1, the Rigor section states, “Students explore the relationship between addition and multiplication. Multiplication is used in various applications throughout this lesson.”
• Each lesson begins with a Visual Learning Bridge activity that provides the opportunity for a classroom conversation to build conceptual understanding for students. In Lesson 1-4, students use their knowledge of multiplication to help understand and solve division problems. Teachers are provided the following prompts to facilitate discussion and conceptual understanding: “Why do you need 3 equal groups? What is the total number of toys? What part of the diagram shows the total? Why is the bar divided into 3 equal parts? How is division different from multiplication?”
• Each lesson is introduced with a video: Visual Learning Animation Plus, to promote conceptual understanding. The Lesson 12-5 video states, “How can you use a number line to represent fractions greater than 1?” The scenario begins by saying, “A marsh rabbit hopped $$\frac{7}{4}$$ the length of a rabbit trail. How can you show this on a number line?”  It then explains how number lines can represent fractions greater than one whole. Students are asked to divide each whole into fourths and explore the value of fraction units using an interactive number line.  
• Each lesson contains a Convince Me! section that provides opportunities for conceptual understanding. In Lesson 2-3, students are asked to use appropriate tools to solve the following, “How would you use counters to show 7x1? How many counters would you have in all?”  Students use counters to show their understanding of the Identity Property of Multiplication. 
• Each lesson contains a Do You Understand? section that makes a connection to previous learning that provides opportunities for conceptual understanding. In Lesson 1-2, “Students explore the relationship between equal groups on a number line and multiplication.” Teachers facilitate student understanding by asking, “On the previous page, why do you skip count by 3s on the number line?  On the previous page, why do you make five jumps on the number line? How would the jumps on the number line look different if there were 4 pens in each gift bag?”

Practice problems provide students opportunities to independently develop conceptual understanding. Examples include, but are not limited to:

• In Lesson 4-4, students use multiplication facts to find related division facts with a multiplication table. (3.OA.2)
• In Lesson 2-3, Visual Learning Bridge, students use their understanding of properties to apply procedures accurately for multiplying by 1 and 0, for example: “How would you use counters to show 7x1? How many counters would you have in all? (3.OA.1)
• In Lesson 8-2, Solve & Share, students “Explain how you can test to see if the relationship among the three sums that are next to each other is a pattern.”  Students use an addition table provided on the page. (3.OA.9)

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

Within the Teacher’s Edition of the lessons, if the lesson focuses on procedural skills and fluency, it is stated in the Lesson Overview page.  For example, Lesson 9-6 focuses on procedural skill and fluency. In regards to procedural skill, “Students add and subtract 3-digit numbers from other 3-digit numbers with one or more zeros using a variety of strategies.”  In terms of fluency, “Students’ fluency in place value, addition and subtraction, and regrouping benefits them as they continue to become more adept at using other strategies. The 3-digit subtraction problems in this lesson provide a challenge as students learn to regroup with zeros” (Teacher’s Edition, page 357 A).  

The Game Center Online at PearsonRealize.com provides opportunities for practicing fluency skills.

The Visual Learning Bridge integrates conceptual understanding with procedural skills.  Addition Fluency and Practice pages are in the Teacher Edition and Ancillary Books as well as online with the Practice Buddy Additional Practice.  Each topic ends with Fluency Practice/Assessment Worksheets.  

Problem sets provide opportunities to practice procedural fluency. Regular opportunities for students to attend to Standard 3.NBT.2: adding and subtracting within 1,000, and to Standard 3.OA.7: multiplying and dividing within 100, are provided.

The instructional materials develop procedural skill and fluency throughout the grade-level. 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 5 this section states, “Fluency with multiplication and division within 100 is an expectation in this topic. There are many relevant patterns in a multiplication table that are important in building fluency. For example, noticing that 4 x 8 = 8 x 4 reinforces the Commutative Property of Multiplication. Students can also notice that if one factor is doubled, the product is also doubled. These patterns can become a powerful strategy for learning more difficult facts. Students continue to use the Distributive Property extensively in Topic 5. Students also use the relationship between multiplication and division to find quotients.”
• Each lesson contains a Visual Learning Bridge which provides instruction on  procedural skills. In Lesson 7-3, the Visual Learning Bridge states, “Greg made a table to show the amount of money he saved each month from tutoring. Use the data in the table to make a bar graph." Students practice graphing coordinates from a table. 
• Fluency Practice Activities are found at the end of Topics 5, 6, 7, 8, 11, 13, and 15 to support multiplying and dividing within 100. In Topic 5, the Fluency Activity provides a numbered chart and states, “Partner 1 and Partner 2 each point to a black number at the same time. Both partners multiply those numbers.”
• The Performance Task for Topic 9 provides students the opportunity to fluently add and subtract within 1,000.  Students are presented with a table that contains names of children and the amount of green and silver tokens they earned while playing a board game. Students are asked questions about the table, including: “How many tokens did each friend win in all? The board game comes with a total of 500 green tokens. After each friend earns his or her tokens, how many green tokens are left?”
• Students can practice fluency skills when accessing the Game Center Online at PearsonRealize.com.

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade-level. Examples include, but are not limited to:

• In Topic 6, Fluency Practice Activity, students practice fluently dividing to find the quotients that are odd numbers during a partner activity, this also includes an online game and an interactive practice buddy. (3.0A.C)
• In Topic 7, Fluency Practice Activity, students practice fluently multiplying numbers within 100 during a partner activity, this also includes an online game and an interactive practice buddy. (3.0A.C)
• In Lesson 5-2, Question 6-7, students fill in missing factors and products in multiplication charts provided.
• In Lesson 5-3, Question 11, students use strategies to find the product: “_____ = 5 x 9." 
• In Lesson 9-3, students estimate and then find the sum of the following three numbers stacked vertically using the standard algorithm: “164 + 68 + 35."
• The Performance Task for Topic 9 provides students the opportunity to fluently add and subtract within 1,000.  Students are presented with a table that contains names of children and the amount of green and silver tokens they earned while playing a board game.  Students are asked questions about the table, including: “How many tokens did each friend win in all? The board game comes with a total of 500 green tokens.  After each friend earns his or her tokens, how many green tokens are left?”

The instructional materials for enVision Mathematics Common Core Grade 3 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 1-5, Visual Learning Bridge, teachers guide students to solve, “June has 10 strawberries to serve her guests.  If each guest eats 2 strawberries, how many guests can June serve?” Then, Guided Practice Question 1 states, “There are 3 boxes with 2 toys in each box.  The total number of toys can be expressed as 3 x 2 = 6. What is meant by 6 ÷ 3 = 2? What is meant by 6 ÷ 2 = 3?” (3.OA.3)
• In Lesson 11-3, Solve & Share, students solve, “An aquarium had 75 clownfish in a large water tank. The clownfish represented in the graph were added to this tank.  How many clownfish are in the tank now? Write and explain how you found the answer.” (3.OA.8)

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 6-7, Visual Learning Bridge, students solve, “Janet is painting a door. She needs to paint the entire door except for the window. What is the area of the part of the door that needs paint?” Students are provided a picture of a 4 by 9 foot door with a 2 by 2 foot window. (3.OA.8)
• In Topic 7, Performance Task, Question 3, students are given a picture graph showing how many different color balloons Miles used to make different animals at a birthday party.  Students are also given a bar graph showing how many of each balloon color Miles has used. Students use the Balloons Bought picture graph and the Balloons Used bar graph to determine, “How many balloons does Miles have left?” (3.OA.3)

Students are provided opportunities to independently demonstrate the use of mathematics flexibly in a variety of contexts, especially where called for by 3.OA.3. Examples include, but are not limited to:

• In Topic 2, Performance Task, students solve, “Ms. Harris awards points to her students for reading books in the book club.  There are three levels of books. The table shows the points for each level. Students who earn 50 points get a prize.” Part A, “Luke has earned 15 points.  All of the books he read were at the same level. What level were the books he read? Explain.” 
• In Lesson 3-1, Question 11, students solve, “Paige bakes 5 cupcakes. She puts 7 jelly beans on each cupcake. How many jelly beans does Paige need? Use the bar diagram to help write an equation.” 
• In Lesson 4-2, Additional Practice, students solve, “You have 18 erasers and use 3 erasers each month. How many months will your erasers last? Identify the quotient, dividend, and divisor." 
• In Lesson 5-4, Question 7, students solve, “Bonnie buys 6 paperback books every month.  She buys 2 hardcover books every month. How many books does she buy in 4 months?”

The instructional materials for enVision Mathematics Common Core Grade 3 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 Lesson 3-1, Solve & Share. Students use conceptual understanding of the distributive property to solve, “Find two ways to break the array below into two smaller arrays. What multiplication equation can you write for each array? What is the total? Tell how you decide."
• Fluency is practiced in Lesson 9-2, Questions 5-12. Students use regrouping to add 3-digit numbers. Question 8 states, “118 + 335."
• Students apply mathematics to solve problems in context.  In Lesson 9-7, the Visual Learning Animation states, “Nancy has $457 in her savings account and wants to have $500 by the end of the year. Christopher has $557 in his savings account and wants to have $600 by the end of the year. Who needs to save more money by the end of the year?”

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 6-4, students develop conceptual understanding of area by counting unit squares and then apply their understanding of multiplication and division to determine the areas of squares and rectangles in context.  Question 8 states, “Jen’s garden is 4 feet wide and has an area of 28 square feet. What is the length of Jen’s garden? How do you know?”
• In Lesson 9-3, Visual Learning Bridge, students are shown how to use partial sums or column addition to add.  Students then apply this mathematical learning in context when solving, “Different kinds of birds are for sale at a pet store.  How many birds are for sale. Find 137 + 155 + 18.”  
• In Lesson 12-6, students use their understanding of fractions to fluently measure the length of objects to the nearest half inch. Then students use their knowledge of number lines, to create a line plot.  Question 5 states, “Measure the lengths of the pieces of yarn at the right to the nearest half inch. Write the length for each piece." Question 7 states, “Make a line plot to show the measurements of the yarn."
• In Lesson 16-3, students develop conceptual understanding of perimeter and polygons by writing equations with variables that represent unknown side lengths.  Students apply the definitions and attributes of common shapes in the writing of equations. Independent Practice, Question 11 states, “These plane figures each have equal sides that are whole numbers. One figure has a perimeter of 25 inches. Which could it be? Explain.”  Students must choose from a triangle, pentagon, hexagon.

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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. Math Practices and Effective Teaching Practices (ETP) are also provided for each topic, within each lesson, and for specific problems.

• In Topic 3, the Topic Planner states, “MP.3, MP.6, and MP.7 are addressed in Lesson 1.”
• In Topic 3, the Math Practices and ETP addresses MP1: “Students make sense of problems and identify information to use to explain their solution. (e.g., p. 84, Item 14).”
• In Lesson 3-4, Mathematical Practice states, “MP.7 Look For and Make Use of Structure: Students will use known multiplication facts and skip counting to solve problems. Also MP.1."

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 3-2, Question 14, students make sense of problems and persevere in solving them. For example: “James needs to buy supplies for his trail walk.  What is the total number of cereal bars James needs to buy? Explain how you used the table to find the answer?”
• MP2: In Lesson 5-6, Question 9, students reason abstractly and quantitatively. For example: “Mrs. Kendel is making a model house. The footprint for the house is shown at the right. What is the total area? Explain your reasoning."
• MP3: In Lesson 14-5, Convince Me!, students critique the reasoning of others. For example:  “Jason says, ‘I think it is better to find the measurement of the fishbowl by filling the fishbowl with liters of water instead of emptying the fishbowl into liter beakers.’ Is Jason correct?”
• MP4: In Lesson 1-1, Convince Me!, students connect repeated addition with multiplication and use strategies to solve a real-world problem. For example:  “Suppose Jessie won 5 bags of 8 goldfish. Use math you know to represent the problem and find the number of goldfish Jessie won.”  
• MP6: In Lesson 8-5, Solve & Share, students attend to precision. For example:  “Think about ways to find numbers that tell about how much or about how many. Derek has 277 stickers. What number can you use to describe about many stickers Derek has? Explain how you decided."
• MP7: In Lesson 10-4, Question 6, students look for and make use of structure. For example: “How can you find the total amount for each student? Think about properties or patterns you know."
• MP8: In Lesson 5-5, Solve & Share, students look for both general methods and shortcuts as they apply math they know when writing and solving multiplication and division problems. For example: “Write a real-world division story for 28 ÷ 4. Then write another real-world story that shows a different way to think about 28 ÷ 4."

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. 

Materials do not attend to the full meaning of MP4 because students are given a model rather than having to model with mathematics. 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 1-4, Visual Learning Bridge, students solve, “Three friends have 12 toys to share equally.  How many toys will each friend get?” Students are given the bar model that is split into three sections with four toys in each section. 
• In Lesson 9-2, Convince Me!, students “Show how to use place-value blocks to find 128 +235 using regrouping.” Students are instructed to model a problem using a specific method. 
• In Lesson 9-5, Visual Learning Bridge, students solve, “Mike and Linda play a game. Linda has 528 points. Mike has 349 points. How many more points does Linda have than Mike? Find 528 - 349." Students are directed to model 528 with place-value blocks. Teachers are prompted to ask, “Which place-value blocks did you use to show 528?” 

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 1-3, the Solve & Share states, “Mark has 12 sports cards.  He arranges the cards with an equal number in each row. Find ways Mark can arrange his cards." Teachers are instructed to provide counters for the students to use, so students are not given the opportunity to choose their tool.
• In Lesson 4-1, the Solve & Share states, “Use 24 counters to make arrays with equal rows. Write multiplication and division equations to describe your arrays.” Students are told which tool to use.
• In Lesson 10-1, the Solve & Share states, “Companies package their goods in a variety of ways. One company packages a case of water as 2 rows of 10 bottles. How many bottles are in each of the cases shown in the table below? Explain your thinking." Students are given pre-drawn place value blocks and a number line and are therefore not choosing the tool. 

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

• MP1: In Lesson 8-7, Solve & Share, students make sense of problems and persevere in solving them. For example, “Sara collected 220 cans on Monday, 80 cans on Tuesday, and 7 cartons with 8 cans each on Wednesday to recycle. Pierre collected 112 cans. About how many more cans did Sara collect than Pierre?” 
• MP2: In Lesson 1-5, Question 11, students use reasoning to find the number of groups when dividing. For example, “An ice cream store plans to make 8 new flavors each year. How many years will it take for the store to make 80 flavors? Write and solve an equation."
• MP6: In Lesson 8-5, Solve & Share, students attend to precision when considering how to round numbers. For example, “Think about ways to find numbers that tell about how much or about how many.  Derek has 277 stickers. What number can you use to describe about how many stickers Derek has? Explain how you decided.” A note on the page says, “Think about whether you need to be precise.” 
• MP7: In Lesson 1-3, Question 7, students use the structure of arrays to find and write multiplication equations. For example, “Chen arranged 16 berries in the array shown below. Use counters to help complete the table to show other arrays Chen can make with the same number of berries."
• MP8: In Lesson 3-6, Question 19, students generalize strategies to multiply using the associative property of multiplication to represent and solve problems. For example, “There are 7 mockingbird nests at a park with eggs in them. What is the greatest number of eggs there could be at this park? What is the least number of eggs there could be?”

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 6-1, the Solve & Share states, “Look at Shapes A-C on Area of Shapes Teaching Tool. How many square tiles do you need to cover each shape? Show your answer below. Explain how you decided. Can you be sure you have an accurate answer if there are gaps between the tiles you used? Explain.”
• In Lesson 7-3, Question 7 states, “Construct Arguments: Which two kinds of movies received about the same number of votes? Explain how to use your bar graph to find the answer."
• In Lesson 8-4, the Visual Learning Bridge states, “A store is having a sale on jackets. A jacket is on sale for $197 less than the original price. What is the sale price?” Students are shown two ways to solve the problem, one with counting back on the number line and another with counting up on the number. The next question in the Convince Me! section states, “Which of the two ways above would you use to solve 762 - 252? Explain.” 

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

• In Lesson 3-1, Question 12 states, “Critique Reasoning: Fred wants to separate the rows of the array below into a 2 x 4 array and a 3 x 4 array. Can Fred do this? Explain?”
• In Lesson 8-4, Convince Me! states, “Which of the two ways above would you use to solve 762-252?  Explain.” 
• In Lesson 9.6, Problem Solving, Problem 18 states, “The students at Cleveland School are collecting soda can tabs. The goal of each class is to collect 500 tabs. So far, the second graders have collected 315 tabs. The third graders have collected 190 more tabs than the second graders. Have the third graders reached their goal? Construct an argument to explain.” (3.NBT.1)
• In Lesson 12-4, Convince Me! states, “Jenna and Benito each marked 1⁄4 on a number line. The length of the part from 0 to $$\frac{1}{4}$$ on Jenna’s number line is shorter than on Benito’s. Did someone make a mistake? Explain your thinking.”

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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 1-4, the Solve & Share states, “Six friends picked 48 grapefruits. They want to share them equally. How many grapefruits should each friend get?” In the teacher edition, during small group, assists teachers to engage students in constructing an argument “Could the answer by 5 grapefruits? Explain.” 
• In Lesson 2-2, the Solve & Share states, “Maria bought 4 packages of bottled water. There are 9 bottles in each package. How many bottles did Maria buy? Explain how you solved this problem." Teachers are prompted to ask, “How did Nikki use counters to represent the number of bottles of water Maria bought? What strategy is represented in her work? How did Ethan use a table to find the number of bottles of water Maria bought?”
• In Lesson 5-2, Question 10 states, “Bill used a multiplication table to find the value of $$\frac{12}{6}$$. His answer was 3. Do you agree? Why or why not?” The teacher edition states, “Ensure that students understand the mistake in reasoning Bill made by showing how to correctly use a multiplication table to find the value of $$\frac{12}{6}$$." 
• In Lesson 12-3, Problem Solving, students construct an argument regarding the following problem: “Jenna and Jamal are making rugs.  They have finished the parts shown. Draw pictures to show each whole rug. Who’s rug will be longer when it is finished? Explain.” Teachers are guided to “Remind students that the size of part of the whole determines the size of the whole.  Because $$\frac{1}{3}$$ of Jamal’s rug is longer than $$\frac{1}{3}$$ of Jenna’s rug, his whole rug will be longer.” 
• In Lesson 14-9, Performance Task, Question 7 states, “Sachi says that the 5th grade singers should begin at 7:40 p.m. Phil says that 5th grade singers should begin at 8:00 p.m. Who is correct?” Teachers are prompted to ask, “What is the total length of time for each of the acts after the break? What is the total amount of time needed to introduce each act? What mistake did Phil make?” 

The instructional materials reviewed for enVision Mathematics Common Core Grade 3 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. In Topic 1, 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." 
• 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 8-5, the Vocabulary List includes: Round and Place Value. These words are 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, distribute, the definition is provided: “to give out shares of something." Next, the word is used in context: “Lisa will distribute the pieces of this pizza equally to 4 friends. How many pieces will each friend get?” 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, multiple is defined as, “The product of a given whole number and any non-zero whole number. Example: 4, 8,12, and 16 are multiples of 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 1-3, Visual Learning Bridge, students learn about arrays. A display shows medals in an array and a character on the page defines an array as, “The medals are in an array. An array shows objects in equal rows and columns.” 
• In Lesson 1-4, the Visual Learning Bridge states, “Three friends have 12 toys to share equally. How many toys will each friend get? Think of arranging 12 toys into 3 equal groups.” A character on the page defines division: “Division is an operation that is used to find how many equal groups there are or how many are in each group."
• In Lesson 6-1, the Visual Learning Bridge states, “Area is the number of unit squares needed to cover a region without gaps or overlaps.” Next, the materials differentiate between a unit square and square units: “A unit square is a square with sides that are each 1 unit long. It has an area of 1 square unit.”

The instructional materials for enVision Mathematics Common Core Grade 3 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 2-2, the Solve & Share states, “Each chicken has 2 legs. How many legs are there in a group of 9 chickens? Show how you decided." The authors state the purpose of this problem as, “Students continue using their knowledge of multiplication to see the patterns that exist in products with whole numbers when 2 or 5 is a factor. Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge."
• In Lesson 14-2, Independent Practice, students apply what they have learned about elapsed time in the lesson to solve problems independently. The directions for this section of the lesson state, “Use clocks or number lines to find the elapsed or end time." 

The instructional materials for enVision Mathematics Common Core Grade 3 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 Lesson 9-1: Add two 3-digit numbers by breaking apart problems into smaller problems:

• Step 1: Solve & Share: “There are 2 bins of oranges. One bin has 378 oranges. The other bin has 243 oranges. Find the sum of 378 + 243. Think about place value.” The authors state the purpose of this lesson as, “Students use what they know about place value and breaking apart numbers to add two 3-digit numbers. Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge." 
• Step 2: Visual Learning Bridge: “Margot counted 243 manatees one year and 179 manatees the next. How many manatees did Margot count all together?” Students are explicitly taught how to break apart numbers using place value to add.
• Step 3: Assessment Practice: “Which shows breaking 622 + 247 apart by place value to find the sum?”

The instructional materials for enVision Mathematics Common Core Grade 3 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 1-3, Question 10, students are shown the equation 8 x 5 = 5 x ____ and then asked to, “Use the Commutative Property of Multiplication to find the missing factor." 
• In Lesson 4-8, Question 17 states, “Rosi and Karen are trying to solve 4 = ? ÷ 8. Rosi says the value of the unknown is 32. Karen says the value of the unknown is 2. Is Rosi or Karen correct? Explain."
• In Lesson 12-3, Question 11 states, “Jenna and Jamal are making rugs. They have the finished parts shown. Draw pictures to show each whole rug. Whose rug will be longer when it is finished? Explain." 

The instructional materials for enVision Mathematics Common Core Grade 3 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 two color counters, number lines, centimeter grid paper, 1-inch grid paper, cubes, paper cups, place value blocks, string/yarn, multiplication table, two color tiles, rulers, fraction strips, egg cartons, clock faces, 1 liter bowls, containers and pans, gram and kilogram weights, metric weights, quadrilaterals, and triangles.

The instructional materials for enVision Mathematics Common Core Grade 3 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 3 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 4, Essential Questions, students are asked, “How can you use known multiplication facts to find unknown division facts? How are multiplication and division related?”
• In Lesson 6-2, Solve & Share, Discussion Questions,  students are asked, “How are the unit squares in each grid different? What information do you need to know about the size of each unit square to solve the problem? How does the size of one unit square in the top of the grid compare to the size of one unit square in the bottom grid? How do the sizes of the unit squares change the area measurement?”
• In Lesson 11-3, Visual Learning Bridge, Discussion Questions, students are asked,“What is the hidden question in the problem? When you estimate to check your answer, what will you round $325 to? Why do you need two operations to solve this problem?”

The instructional materials for enVision Mathematics Common Core Grade 3 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 3 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 3 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 3, Math Background: Coherence, the Look Back states, “Grade 2: Even Numbers and Arrays: In Topic 2, students explored even and odd numbers. They also wrote equations for arrays using rows or columns.”  The authors explain how this is connected to use known facts, equal groups, and multiply with three factors.  
• In Lesson 12-2, Lesson Overview, the Look Back states, “In the previous lesson, students learned that when a region is partitioned into a nonzero number of equal parts, each equal part can be named using a unit fraction. This Lesson: Students continue their study of fractions by learning that a fraction represents multiple copies of a unit fraction.  Look Ahead: Students use what they learned about fractions to determine and draw whole (unit) shapes given one part (unit fraction) of a shape."

The instructional materials for enVision Mathematics Common Core Grade 3 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 3 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 3 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 3 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 3 Readiness Assessment, Question 5 states, “Tanika has 16 tulips. She gives 7 tulips to friends. How many tulips does she have left?" Four multiple choice answers are provided (2.OA.1 and 2.OA.2).
• In Topic 8, Review What You Know, Question 11 states, “Atif puts 45 rocks in a display box. He has 54 rocks in all. Which expression can be used to find how many rocks are not in the display box?” (3.NBT.2)

The instructional materials for enVision Mathematics Common Core Grade 3 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 9-2, Error Intervention states, “If students are having difficulty estimating to the nearest hundred, then say Look at 538.  What digit is in the tens place? Since the digit in the tens place is less than 5, what is 538 rounded to the nearest hundred? Look at 429.  What digit is in the tens place? Since the tens digit is less than 5, what is 429 rounded to the nearest hundred? What is the sum of 500 and 400?”
• In Lesson 5-3, Visual Learning Bridge, teacher side matter prompts teachers to prevent misconceptions: “Remind students that these two ways of multiplying are strategies for finding products.  Point out that both strategies result in the same answer." 

The instructional materials for enVision Mathematics Common Core Grade 3 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 3 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 7, Performance Task, Question 2 states, “How many fewer blue balloons were used than all of the other colors combined? Explain." This question is noted as being DOK Level 2 and addresses 3.MD.3 and MP2.
• In Topic 14, Assessment, Question 4 states, “Name the metric unit that could be used to measure the capacity of a kitchen sink. Then, using that unit, write a reasonable estimate for the capacity of a kitchen sink." This question is noted as DOK Level 2 and addresses 3.MD.2.

The instructional materials for enVision Mathematics Common Core Grade 3 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 3 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 6-3, Error Intervention, students are counting shaded unit squares and writing the area. The materials state, “If students do not write the correct unit for the area of the sticker, then remind them that an area measurement consists of two parts: the number of square units and the name of the square units. ‘Compare the sticker on the previous page with the sticker described in Item 1. Are they the same? How are the two stickers different? What units are used to describe the area of each sticker?’” 
• In Topic 3, Math Background: Coherence, students apply properties of multiplication facts for 3, 4, 6, 7, and 8. In the Look Back section, the materials note the Grade 2 standards needed: “In Topic 2, students explored even and odd numbers. They also wrote equations for arrays using rows or columns."

The instructional materials for enVision Mathematics Common Core Grade 3 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 11-2, Reteach to Build Understanding, students are presented with vocabulary and then guided through a series of problems that have partially completed portions: “Jill is in charge of scheduling fields for the youth soccer leagues. There are 4 leagues with 6 teams in each league. An equal number of teams will play on each of the 3 fields. How many teams will play on each field?” Next, students fill in the following to solve, “Step 1: Find and answer the hidden question. Hidden question: How many _____ are there in all? There are ____ leagues. There are ____ teams in each league. A= 4 x 6. A = _____. There are _____ teams in all."
• In Lesson 11-2, Enrichment, students guess a number based on the following clues: “I am thinking of a 2-digit number. Both of the number’s digits are the same. When you double the number, the resulting product is greater than 50 and less than 80. What number am I thinking of?”

The instructional materials for enVision Mathematics Common Core Grade 3 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:

• Lesson 3-2, Solve & Share, “There are 3 rows of pictures on a wall. Each row has 7 pictures. How many pictures are on the wall?” The helping character in the text states, “You can use appropriate tools. You can draw arrays or make arrays with counters to help solve the problem." (3.OA.5)
• Lesson 7-5 Convince Me!, “Bella has a bakery. She will use the bakery items at the right to make a gift basket worth $40. Bella wants the basket to have more than one of each bakery item. Show one way to make a gift basket." (3.OA.3)

The instructional materials for enVision Mathematics Common Core Grade 3 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 2-2, Solve & Share, English Language Learner support states, “Review the terms data, array, and patterns. Use the terms as you discuss how to find how many bottles of water Maria bought.” Support for Entering ELL students states, “Ask students to read aloud and complete the sentence stem. ‘To find the product of 2 x 9 is to group 9s ____ times.’"
• In Lesson 3-5, Visual Learning Bridge, English Language Learner support states, “Read the problem and point to the dragon. ‘How many sections are there in the dragon’s body? How long is each section?’” Support for Emerging ELL students states, “Draw a dragon on the board and draw lines between each section and write 4 under each section. ‘How many sections? How many feet in each section?’” 

The instructional materials for enVision Mathematics Common Core Grade 3 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 6-7, Solve & Share states, “Mr. Anderson is tiling his kitchen floor. He will not need tiles for the areas covered by the kitchen island or the counter. How many square meters of tiles does Mr. Andersen need?” Extension problem states, “Mr. Anderson is changing the counter to 4 meters by 1 meter. How many square meters of tiles will Mr. Anderson need now?” 
• In Lesson 12-5, Enrichment Activity: What’s in a Name? states, “Each point on the number line has more than one name. Write some of the names for each point on the number line. Label fourths, label halves, and label whole numbers.”

The instructional materials for enVision Mathematics Common Core Grade 3 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., Jessie, Debra, Salvatore, Clara, Lois, Delbert, Marcus, Ramon, Li, Yolanda, Hakeem, Jerome, Forest, Chico, and June). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity. Characters are often presented in pairs with different solution strategies 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 3 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 3 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 3 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 3 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 3 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 3 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 3 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 3 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.