## Alignment: Overall Summary

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for alignment to the CCSSM. The instructional materials partially meet expectations for focus and coherence in Gateway 1 as they do not meet expectations for focus and partially meet expectations for coherence. In Gateway 2, the instructional materials partially meet the expectations for rigor and balance, and they partially meet the expectations for practice-content connections. Since the instructional materials do not meet expectations for both Gateways 1 and 2, evidence was not collected regarding usability in Gateway 3.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
10
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

|

## Gateway 3:

### Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for focus on major work and coherence in Gateway 1. The instructional materials do not meet expectations for focus as they assess topics before the grade level in which the topic should be introduced, but they do devote the large majority of class time to the major work of the grade. The instructional materials partially meet the expectations for coherence by including an amount of content designated for one grade level that is viable for one school year and fostering coherence through connections at a single grade.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
0/2
+
-
Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 assess topics before the grade level in which the topic should be introduced. There are assessment items that assess above grade level statistics and probability standards.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 do not meet expectations for assessing grade-level content. Most of the assessments include material appropriate for Grade 5; however, there are seven assessment items that assess above grade-level statistics and probability standards.

In the Teacher Edition, a Topic Test is available for each of the sixteen topics. In Topic 14, the instructional materials assess content that aligns to 6.SP.5. For example:

• In the Topic 14 Topic Test, question 1 states, “As part of a class fundraiser, students received money for each lap they ran around the school’s parking lot. What is the outlier in this set of data?”
• In the Topic 14 Topic Test, question 5 states, “What is the outlier in the set of data for Exercise 4?”
• In Topic 14 Topic Test, question 12 states, “Is there an outlier in this set of data? Explain how you decided.”
• In the Topic 14 Performance Assessment, question 3 states, “Suppose 10 students were absent the last day of the data. How would that change the data?” The sample answer states, “The number of students present would be 12. The range would increase. 12 would be an outlier because it is not close to any of the other data points.”

Examples of the instructional materials assessing grade-level content include:

• In the Topic 2 Topic Test, question 4 states, “Beth worked 33.25 hours last week and 23.75 hours this week. How many total hours did she work? Use mental math to solve.” Students add decimals to hundredths. (5.NBT.7)
• In the Topic 9 Topic Test, question 7 states, “Teri and her friends bought a party-size sandwich that was 7/9 yard long. They ate 2/3 of a yard. What part of a yard was left?” Students subtract fractions with unlike denominators (5.NF.1)
• In the Topic 16 Topic Test, question 6 states, “Which ordered pair is located on the line shown on the graph?” Students find a point on the coordinate plane and write the ordered pair. (5.G.1)

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
+
-
Criterion Rating Details

Students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. The instructional materials devote approximately 70 percent of class time to the major work of Grade 5.

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
+
-
Indicator Rating Details

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

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 11 out of 16, which is approximately 69 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 109.5 out of 156, which is approximately 70 percent.
• The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 22 out of 31, which is approximately 71 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work, and the assessments embedded within each topic. As a result, approximately 70 percent of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for coherence. The instructional materials include an amount of content designated for one grade level that is viable for one school year and foster coherence through connections at a single grade. The instructional materials also miss some connections between major and supporting work and do not clearly identify content from prior and future grade levels.

### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are not always used to support major work of the grade and often appear in lessons with few connections to the major work of the grade.

Throughout the series, supporting standards/clusters are typically taught in isolation and rarely connected to the major standards/clusters of the grade. Students can often complete problems aligned to supporting work without engaging in the major work of the grade. The following examples illustrate missed connections in the materials:

• In Topic 13 Lesson 13-6, students convert metric units of mass. The supporting standard 5.MD.1 has a natural connection to 5.NBT.7 when multiplication and division are used to convert metric units to the hundredths place. This connection is not supported in the lesson as all metric conversions are made with only whole numbers. Problem Solving question 28 states, “Hummingbirds found in North America weigh about 3 grams. How many milligrams is this?”
• In Topic 14 Lesson 14-1, students analyze and create line plots from given data sets. The supporting standard of 5.MD.2 is aligned to this lesson. 5.MD.2 has a natural connection to the major work cluster 5.NF.B, apply and extend previous understandings of multiplication and division to multiply and divide fractions. Throughout the lesson, students create line plots with fractional units, but there is no measurement unit assigned, and they do not use operations to solve problems. Students interpret points on a line plot while using fractional representations but do not use operations to solve problems. Guided Practice question 1 states, “How many giraffes are 14 1/2 feet tall?” The major work of 5.NF.B is not supported by 5.MD.2 in this lesson.

Examples that illustrate connections in the materials include:

• In Topic 3 Lesson 3-6, supporting cluster 5.NBT.B connects to the major cluster 5.OA.A when students interpret story problems, construct bar model diagrams, and write expressions with a letter for the unknown value. Guided Practice question 1 states, “Copy and complete the picture and write an equation. Solve. Sharon’s Stationary Store has 219 boxes of cards. May’s Market has 3 times as many boxes of cards. How many boxes of cards does May’s Market have?”
• In Topic 14 Lesson 14-4, students use powers of 10 in metric conversions (5.MD.1) with place-value strategies involving whole numbers and decimals (5.NBT.7). The supporting standard 5.MD.1 connects to the major work standard 5.NBT.7.
• In Topic 8 Lesson 8-3, students write and evaluate numerical expressions that include decimals (5.OA.1). Independent Practice question 9 states, “Evaluate each expression. 112.5 - (3.3 / 0.6) x 2” The supporting standard 5.OA.1 connects to the major work standard 5.NBT.7.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
+
-
Indicator Rating Details

Instructional materials for enVisionMATH California 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 162 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.

The instructional materials consist of 108 lessons that are listed in the Table of Contents. Lessons are structured to contain a Daily Review, Develop Concept-Interactive, Develop Concept-Visual, Close/Assess and Remediate, and Center Activities.

The instructional materials consist of 54 reteaching lessons and assessments that are listed in the Table of Contents. These include Reteaching, Topic Tests, Performance Assessments, Placement Test, Benchmark Tests, and End-of-Year Test.

The publisher does not provide information about the suggested time to spend on each lesson or the components within a lesson. The Implementation Guide has a chart that suggests times for a multi-age classroom. The lessons within the multi-age classroom are structured differently than a single-age classroom. The multi-age lessons are structured to contain Problem Based Interactive Learning, Guided Practice, Center Activities, Independent Practice, Small Group Strategic Intervention, and Digital Assignments/Games. The suggested time for the multi-age lesson is 50-75 minutes per lesson.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 5 partially meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials do not clearly identify content from prior and future grade levels and do not use it to support the progressions of the grade-level standards.

Prior and future grade-level work is not clearly identified within each lesson. For example:

• In Topic 1 Lesson 1-2, the Teacher Edition lists the standard 5.NBT.3a as the focus of the lesson. Students represent fractions as decimals to the hundredths place. This is prior grade-level content aligned to 4.NF.2.
• In Topic 3 Lesson 3-3, the Teacher Edition lists the standard 5.NBT.5 as the focus of the lesson. Students use manipulatives and other strategies to multiply two digits by two digits. This is prior grade-level content aligned to 4.NBT.5.
• In Topic 14 Lesson 14-1, the Teacher Edition lists the standard 5.MD.2 as the focus of the lesson. Students find the outlier from a set of given numbers. This is future grade-level content aligned to 6.SP.5.

Some of the lessons include a section in the Teacher Edition called, Link to Prior Knowledge. The Link to Prior Knowledge poses a question or strategy that has previously been learned for students to connect to the current lesson. The Link to Prior Knowledge does not explicitly identify standards from prior grades. For example:

• In Topic 9 Lesson 9-4, the Link to Prior Knowledge states, “How can you represent the fraction that measures each length of string? (Sample answers: Use fraction strips, use a number line, or draw a picture.)” The publisher does not connect this prior knowledge to a specific prior grade level.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

The majority of lessons within the 16 topics focuses on and provides students with extensive opportunities to practice grade-level problems. Within each lesson, students practice grade-level problems within Daily Common Core Review, Practice, Reteaching, Enrichment, and Quick Check activities. For example:

• In Topic 2 Lesson 2-4, the Teacher Edition lists the standard 5.NBT.7, Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used, as the focus of the lesson. Students subtract decimals to hundredths using concrete models or drawings and strategies based on place value. Guided Practice question 3 states, “Use hundredths grids to add or subtract. 2.73 - 0.94”
• In Topic 5 Lesson 5-3, the Teacher Edition lists the standard 5.NBT.6, Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models, as the focus of the lesson. Students find whole-number quotients of whole numbers as well as illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Guided Practice question 1 states, “Use the model to find the quotient. 288/12”
• In Topic 9 Lesson 9-7, the Teacher Edition lists the standard 5.NF.1 as the focus of the lesson. Students add and subtract fractions with unlike denominators. Independent Practice question 10 states, “2/3 - 7/12 = ___”

The instructional materials contain a Common Core State Standards Skills Trace for each topic that can be found the Printable Resources section of the Program Resources Document. This document contains the grade-level standards for each topic and the standards from previous and future grade levels that are related to the standards focused on in the specified topic. The document states the specific topic numbers from previous and future grades to which the grade-level standards are related.

• In Topic 8, the skills trace lists the standard 5.OA.1 as the focus of the topic. This standard is linked to a “Looking Back” list where it lists the standards 4.OA.2 and 4.OA.5 as the focus in Topics 1 and 2 within the Grade 4 instructional materials. The standard 5.OA.1 is also linked to a “Looking Ahead” list where it lists the standards 6.EE.2b, 6.EE.2c and 6.EE.3 as the focus in Topic 1 within the Grade 6 instructional materials.

### Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to 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.
2/2
+
-
Indicator Rating Details

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

Each topic is structured by a specific domain and the learning objectives within the lessons are clearly shaped by CCSSM cluster headings. For example:

• In Topic 5 Lesson 5-7, the lesson objective states, “Students will find one-digit quotients where the divisor is a two-digit number.” This is shaped by the cluster 5.NBT.B, Perform operations with multi-digit whole numbers and with decimals to hundredths.
• In Topic 12 Lesson 12-2, the lesson objective states, “Students will count cubic units and use volume formulas to find the volume of rectangular figures.” This is shaped by the cluster 5.MD.C, Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
• In Topic 13 Lesson 13-3, the lesson objective states, “Students will convert from one unit of customary weight to another and apply this skill to compare quantities.” This is shaped by the cluster 5.MD.A, Convert like measurement units within a given measurement system.

Instructional materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade in cases where the connections are natural and important.

• In Topic 7 Lesson 7-1, cluster 5.NBT.A connects to cluster 5.NBT.B when students solve division problems using powers of 10. Guided Practice question 2 states, “Use mental math to find each quotient. $$126.4\div 10^2$$”
• In Topic 16 Lesson 16-3, domain 5.G connects to domain 5.OA when students use coordinate graphs to explore relationships between two rules. Independent Practice question 6 states, “Complete the table at the right and graph the data using sunflower for the x-axis and corn for the y-axis.”

## Rigor & Mathematical Practices

#### Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for rigor and mathematical practices. The instructional materials partially meet expectations for rigor by meeting expectations on giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. The instructional materials also partially meet the expectations for practice-content connections by meeting expectations on explicitly attending to the specialized language of mathematics and prompting students to construct viable arguments and analyze the arguments of others.

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
6/8
+
-
Criterion Rating Details

The instructional materials for enVisionMATH California Common Core Grade 5 partially meet expectations for rigor and balance. The instructional materials meet expectations for giving attention to the development of procedural skill and fluency and balancing the three aspects of rigor. However, the instructional materials partially meet expectations for giving attention to conceptual understanding and applications.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
1/2
+
-
Indicator Rating Details

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

The instructional materials present a Problem-Based Interactive Learning activity (PBIL) and a Visual Learning Bridge (VLB) within each lesson to develop conceptual understanding. However, the PBIL and VLB are teacher-directed and do not offer students the opportunity to practice conceptual understanding independently through the use of pictures, manipulatives, and models.

Overall, the instructional materials do not consistently provide students opportunities to independently demonstrate conceptual understanding throughout the grade level.

• In Topic 1 Lesson 1-5, the Overview of PBIL states, “Students will learn to compare decimals through the thousandths place.” In the teacher-directed PBIL activity, students use a place-value chart to compare decimals to the thousandths place. The Develop the Concept: Visual section of the lesson shows three separate steps to compare decimals without place-value charts. Step 1 states, “Write the numbers, lining up the decimal points. Start at the left. Compare digits of the same place value.” The directions for the Independent Practice state, “Copy and complete. Write $$\gt$$, $$\lt$$, or = for each circle.” Students do not demonstrate the conceptual understanding of comparing decimals to the thousandths place independently as $$\gt$$, $$\lt$$, and = are shown as sample answers in the 12 problems in the Independent Practice.
• In Topic 3 Lesson 3-3, the Overview of PBIL states, “Students extend the addition of partial products to the standard algorithm to multiply two-digit numbers by multiples of ten.” In the teacher-directed PBIL activity, students use the area model to represent the product of 90 x 23. The directions for the Independent Practice state, “In 10 through 30, multiply to find each product.” Students do not demonstrate the conceptual understanding of multiplying two-digit numbers independently as products are shown as sample answers in the 21 problems in the Independent Practice.
• In Topic 9 Lesson 9-5, the Overview of PBIL states, “Students formulate a method for adding fractions with unlike denominators.” In the teacher-directed PBIL activity, students use tape diagrams to represent the sum of 1/4 and 3/8. The directions for the Independent Practice state, “In 7 through 22, find each sum. Simplify, if necessary.” Students do not demonstrate the conceptual understanding of adding fractions with unlike denominators independently as sums are shown as sample answers in the 16 problems in the Independent Practice.
• In Topic 11 Lesson 11-4, the Overview of PBIL states, “Students find a fraction of a fraction.” In the teacher-directed PBIL activity, students fold paper to demonstrate finding 1/4 of 1/2. The Develop the Concept: Visual section of the lesson describes the procedural steps of multiplying fractions. The directions for the Independent Practice state, “In 7 through 31, find each product. Simplify if necessary.” Students do not demonstrate the conceptual understanding of multiplying fractions independently as products are shown as sample answers in the 25 problems in the Independent Practice.

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
+
-
Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 5 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials provide regular opportunities for students to attend to the standard 5.NBT.5, Fluently multiply multi-digit whole numbers using the standard algorithm.

The instructional materials develop procedural skill and fluency throughout the grade level.

• In Topic 3 Lesson 3-4, the Develop the Concept: Visual section of the lesson develops procedural skill when modeling the standard algorithm for multiplication of a two-digit number by a two-digit number in three separate steps. Step 2 states, “Multiply by the tens. Regroup. 38 x 12” The Independent Practice section includes a template for filling in the numbers to the partial products when practicing the standard algorithm for multiplication.
• In Topic 12 Lesson 12-3, the Develop the Concept: Visual section of the lesson models finding the combined volume of non-overlapping right rectangular prisms. The materials develop procedural skill when students multiply multi-digit numbers in the formula for volume.
• In Topic 13 Lesson 13-3, students develop procedural skill and fluency when using the standard algorithm for multiplication when converting units of weight. Problem Solving problem 1 states, “The world’s heaviest lobster weighted 44 pounds, 6 ounces. How many ounces did the lobster weigh? Describe the steps you took to find your answer?”

The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level.

• In Topic 3 Lesson 3-5, the Independent Practice section of the lesson provides multi-digit multiplication practice problems for students to demonstrate knowledge of procedural skill. Problem 24 states, “35 x 515”
• In Topic 4 Lesson 4-1, the Common Core Review provides students with a multi-digit multiplication word problem. Problem 2 states, “Meg buys 12 bags of sunflower seeds. Each bag has 58 seeds. How many seeds does Meg buy?”
• In Topic 4 Lesson 4-7, the Common Core Review provides students with a multi-digit multiplication word problem. Problem 4 states, “Kevin buys a car. His car payment is $248 per month. After 55 payments, how much has Kevin paid?” ### Indicator 2c Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade 1/2 + - Indicator Rating Details The instructional materials for enVisionMATH California Common Core Grade 5 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. Each topic includes at least one Problem Solving lesson that can be found at the end of the topic. These lessons offer students opportunities to integrate and apply concepts and skills learned from earlier lessons. Within each individual lesson, there is a section titled, Problem Solving, where students practice the application of the mathematical concept of the lesson. However, the applications of mathematics in Problem Solving are routine problems. The instructional materials have few opportunities for students to engage in non-routine application throughout the grade level. Examples of routine applications, where a solution path is readily available, are: • In Topic 2 Lesson 2-7, students use addition and subtraction to solve a multi-step word problem. Independent Practice problem 4 states, “Elias saved$30 in July, $21.50 in August, and$50 in September. He spent $18 on movies and$26.83 on gas. How much money does Elias have left?”
• In Topic 4, Stop and Practice, students determine if a statement involving decimals is true or false and explain their reasoning. Number Sense problem 24 states, “The difference of 15.9 and 4.2 is closer to 11 than 12.”
• In Topic 9 Lesson 9-7, students solve word problems involving addition and subtraction of fractions with unlike denominators. Problem Solving problem 26 states, “Tara made a snack mix with 3/4 cup of rice crackers and 2/3 cup of pretzels. She then ate 5/8 cup of the mix for lunch. How much snack mix is left?”
• In Topic 11 Lesson 11-6, students solve real-world problems involving multiplication of fractions and mixed numbers. Problem Solving problem 25 states, “The city plans to extend the Wildflower Trail 2 1/2 times its current length in the next 5 years. How long will the Wildflower Trail be at the end of 5 years?”
• In Topic 11 Lesson 11-12, students use multiplication of mixed numbers to solve a word problem. Independent Practice problem 7 states, “Tina is making a sign to advertise the school play. The width of the sign is 2 2/3 feet. If the length is 4 1/2 times as much, then what is the length of the sign?”
• In Topic 14 Lesson 14-5, students use division and addition to solve a multi-step word problem. Independent Practice problem 14 states, “Students at Gifford Elementary collected stamps from various countries. The students collected 546 stamps from Africa, 132 from Europe, and 321 from North and South America. If a stamp album can hold 24 stamps on each page, how many pages will the stamps completely fill?”

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
+
-
Indicator Rating Details

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

Lessons include components that serve to develop the three aspects of rigor. These include a Daily Common Core Review, Problem-Based Interactive Learning, Develop the Concept: Visual, Guided and Independent Practice, and Problem Solving. All three aspects of rigor are present independently throughout each topic in the materials. For example, in Topic 11:

• In Lesson 11-5, students develop conceptual understanding of multiplying fractions when creating area models to model the solution.
• In Lesson 11-10, students practice the procedural skill of multiplying by a reciprocal to find a quotient. Independent Practice problem 12 states, “In 12 through 16, use multiplication to find each quotient. 3 divided by 1/5”
• In Lesson 11-11, students apply knowledge of dividing unit fractions by a non-zero whole number to solve word problems. Problem Solving problem 11 states, “Sue has 1/2 gallon of milk. She needs to pour 4 glasses of milk. What fraction of a gallon should she put in each glass?”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

• In Topic 2 Lesson 2-4, students develop conceptual understanding of adding and subtracting decimals while practicing the procedural skill of the standard algorithm of addition and subtraction of decimals when using hundredths grids to solve a problem. Independent Practice problem 9 states, “In 9 through 18, add or subtract. Use hundredths grids to help. 0.1 + 0.73”
• In Topic 8 Lesson 8-3, students practice procedural skill of following the order of operations to solve a word problem. Problem Solving problem 19 states, “Soledad solves the problem below and thinks that the answer is 92.3. Jill solves the same problem, but thinks that the answer is 67.5. Who is correct? [(65 + 28.2) - (7.8 + 5.5)] = 12.4”
• In Topic 14 Lesson 14-3, students develop conceptual understanding of creating line plots displaying a set of fractional measurements and use information on the line plot to solve word problems. Problem Solving problems 10-13 state, “For 10-13, use the data set at the right. Marvin’s Tree Service purchased several spruce tree saplings. The saplings had the heights listed in the table. 10. Draw a table to organize the data. 11. What is the height of the shortest sapling? 12. How many saplings are 27 1/4 tall? 13. Draw a line plot of the data.”

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/10
+
-
Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for practice-content connections. The instructional materials explicitly attend to the specialized language of mathematics and prompt students to construct viable arguments and analyze the arguments of others. The instructional materials partially meet expectations for identifying and using the mathematical practices to enrich mathematics content within and throughout the grade and assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
+
-
Indicator Rating Details

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

Mathematical Practice standards are identified in three places within the Teacher Edition: Problem Based Interactive Learning activity, Guided Practice exercises, and Problem-Solving exercises. Throughout the teacher and student editions, there is a symbol that indicates that one or more MP is being used. Key phrases such as “Look for Patterns,” “Use Tools,” and “Reason” identify which practice is being highlighted. At the beginning of each lesson, all eight mathematical practices are listed. A check mark is placed beside each practice that is to be addressed within the lesson.

An example of an MP that is identified but does not enrich the mathematical content includes:

• In Topic 7 Lesson 7-1, MP1 is identified with the icon and the key word “Persevere." Question 8 states, “If Shandra wanted to cut the cloth into 100 strips, how wide would each strip be?”

An example of MPs that are identified and enrich the mathematical content include:

• In Topic 9 Lesson 9-1, MP6 is identified with the icon and the key word “Be Precise.” Question 22 states, “Which is a prime number?” Four answer choices are given for the students. Teachers are given information that reads, “Remind students to review the definition of a prime number.”
• In Topic 9 Lesson 9-2, MP4 is identified with the icon and the key word “Model.” Question 26 states, “Draw a diagram that could be used to build a cube.” Teachers are given information that reads, “Remind students that, when looking at the cube in Exercise 26, there are faces that they cannot see in the drawing.”

An example where the MPs are incorrectly labeled:

• In Topic 9 Lesson 9-6, MP7 is identified with the icon and the key word “Use Structure.” Question 26 states, “ Find the perimeter of the figure below.” A triangle with side lengths is shown.

Overall, all eight math practices are included within the curriculum and are not treated as separate standards. However, the standards are not used to enrich the content. They are aligned to some of the problems as an explanation to what math practice students might need to use to solve the problem.

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 do not meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of each of the eight MPs. The MPs are defined in both the topic and lesson narratives, as appropriate, but are not fully attended to when students interact with the aligned problems in the materials.

The materials do not attend to the full meaning of three or more MPs. Examples that demonstrate this include:

MP1 Make sense of problems and persevere in solving them.

• In Topic 12 Lesson 12-3, MP1 is identified for question 12 in the Problem Solving section. Question 12 states, “A carpenter is cutting out wooden blocks in the shape shown below. How much wood is needed for one block?” It is a multiple-choice question, and the teacher is given information on how to make sense of the problems by reminding students to use problem-solving skills and strategies.
• In Topic 14 Lesson 14-4, MP1 is identified in the PBIL section. Students use organized data on a line plot to find solutions to questions such as, “What was the difference between the greatest amount of rain in a day and the least amount of rain in a day?” This requires the subtraction of like denominators and does not require perseverance to solve.

MP4 Model with mathematics.

• In Topic 13 Lesson 13-2, MP4 is identified for question 28 in the Problem Solving section. Question 28 states, “One tablespoon (tbsp) equals 3 teaspoons (tsp) and 1 fluid ounce equals 2 tablespoons. A recipe calls for 3 tablespoons of pineapple juice. A jar of pineapple juice has 12 fluid ounces. How many teaspoons of juice are in the jar?” The teacher is told to “encourage students to draw a picture to help them solve this problem.”
• In Topic 14 Lesson 14-5, MP4 is identified for question 12 in the Problem Solving section. Question 12 states, “Write and solve an equation to find the total number of hours, h, astronauts spent in space during the Gemini and Apollo space programs combined.” There is a chart given for this problem. The teacher is prompted to question the students about the chart to guide them as they answer this question.

MP5 Use appropriate tools strategically.

• In Topic 12 Lesson 12-3, MP5 is identified for question 9 in the Problem Solving section. Question 9 states, “Sarah is wrapping a gift for her friend and uses a ribbon to tie both boxes together. What is the volume of the combined boxes?” Two pictures of boxes are given with dimensions. Students do not use or choose a tool to solve the problem.
• In Topic 13 Lesson 13-4, MP5 is identified for question 19 in the Problem Solving section. Question 19 states, “What is the equivalent length of the bumblebee bat in centimeters?” A labeled picture with the measurement of the bat given in millimeters is included. This is a multiple-choice question, and students do not use or choose a tool to solve the problem.

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

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

Students justify their work and explain their thinking; however, evaluating and critiquing the work of others are found less often in the materials. Students critique the reasoning of in problems that ask them if they agree or disagree with a statement or solution.

Student materials prompt students to both construct viable arguments and analyze the arguments of others. Examples that demonstrate this include:

• In Topic 6 Lesson 6-1, Problem Solving Question 40 states, “Construct Arguments. Marcia and David each multiplied 5.6 x 10 and 7.21 x 100. Marcia got 0.56 and 0.721 for her products. David got 56 and 721 for his products. Which student multiplied correctly? How do you know?”
• In Topic 10 Lesson 10-3, Guided Practice Question 6 states, “Construct Arguments. Kyle used 9 as an estimate for 3 1/6 plus 5 7/8. He added and got 9 1/24 for the actual sum. Is his answer reasonable?”
• In Topic 15 Lesson 15-2, Guided Practice Question 3 states, “Construct Arguments. Can a right triangle have an obtuse angle in it? Why or Why not?”

Examples where there are missed opportunities to construct viable arguments and analyze the arguments of others include:

• In Topic 1 Lesson 1-3, Problem Solving Question 30 states, “Frank reasoned that in the number 0.558, the value of the 5 in the hundredths place is ten times as great as the 5 in the tenths place. Is this correct? If not, justify your reasoning.” Students only justify their answer if they disagree with the claim.
• In Topic 11 Lesson 11-1, Problem Solving Question 21 states, “Jo said that when you multiply a nonzero whole number by a fraction less than 1, the product is always less than the whole number. Do you agree?” Students critique the reasoning of others; however, they are not asked to justify their conclusion.

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The Teacher Edition contains a Mathematical Practice Handbook which defines each math practice and includes question stems for each MP to help the teacher engage students. MP3 offers the following questions stems: “How can I use math to explain why my work is right?”, “How can I use math to explain why other people’s work is right or wrong?”, and “What questions can I ask to understand other people’s thinking?”

The materials label multiple questions as MP3 or parts of MP3; however, those labeled have little information assisting teachers to engage students in constructing viable arguments or to critique the reasoning of others. The information that the materials provide is not specific and are often hints or reminders to give students while they are solving a problem.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. For example:

• In Topic 1 Lesson 1-1, Problem Solving Question 31 states, “Critique Reasoning. 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.” No teacher guidance is given for this question.

Examples where teachers are supported, although generally, to assist students in constructing viable arguments and analyzing the arguments of others include:

• In Topic 2 Lesson 2-5, Problem Solving Question 28 “Critique Reasoning. Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct? Tell how you know.” Teacher guidance for this MP is “If students have difficulty understanding how Juan’s answer is not correct, ask: If you add two numbers less than 5, will their sum be greater than 80?”
• In Topic 6 Lesson 6-6, Problem Solving Question 33 “Construct Arguments. Mary Ann ordered 3 pens and a box of paper on the Internet. Each pen cost $1.65 and the paper cost$3.95 per box. How much did she spend?” Teacher guidance for this MP is “Remind students that they may need to obtain information that is not given explicitly in the problem.”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 5 meet expectations for attending to the specialized language of mathematics.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

• Within the Yearlong Curriculum Guide, a list is provided for the Key Math Terms that are used each month of the school year.
• The teacher and student editions include a Review What You Know section at the beginning of every topic. This section reviews vocabulary used in prior topics along with introducing the vocabulary in the current topic. Students complete this activity by inserting the correct vocabulary word into a sentence to correctly identify its definition.
• Within Review What You Know, the new vocabulary listed for Topic 7 includes: dividend, decimal, divisor, and quotient.

The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them.

• In the Student Edition, vocabulary terms can be found highlighted in yellow within the Visual Learning Bridge across the top of the pages. A definition in context is provided for each term and is used in context during instruction, practice, and assessment.
• In the Implementation Guide, Teacher Edition, as well as the Student Edition, a complete Glossary is included and can be referred to at any time.
• No examples of incorrect use of vocabulary, symbols, or numbers were found within the materials.

Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of Mathematics.

## Usability

#### Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

### Indicator 3g

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. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains 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.
N/A

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

### Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

### Indicator 3q

Materials encourage students to monitor their own progress.
N/A

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

### Indicator 3u

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 (e.g., modifying vocabulary words within word problems).
N/A

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
N/A

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

### Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

## Additional Publication Details

Report Published Date: 10/24/2018

Report Edition: 2015

Title ISBN Edition Publisher Year
enVisionMATH California Common Core - Grade 5 9780328792726 Pearson 2015

## About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

## Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

## Advancing Through Gateways

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
• Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

X