## Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do not meet expectations for alignment to the CCSSM. The instructional materials partially meet expectations for focus and coherence in Gateway 1 as they 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 do not 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.

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## 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

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Gateway One Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 partially meet expectations for focus on major work and coherence in Gateway 1. For focus, the instructional materials do not assess topics before the grade level in which the topic should be introduced, and they devote the large majority of class time to the major work of the grade. For coherence, the instructional materials include an amount of content designated for one grade level that is viable for one school year, but they partially meet the expectations for the remainder fo the indicators in this criterion.

### Criterion 1a

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do not assess topics before the grade level in which the topic should be introduced. In the instances where the material is above grade level, the material could easily be omitted or modified by the teacher to address the grade-level 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 meet expectations for assessing grade-level content. Most of the assessments provide material that is appropriate for Grade 2. In the instances where the material is above grade level, the material could be omitted or modified by the teacher to address the grade-level standards. Probability, statistical distributions, similarity, transformations, and congruence are not within these assessments.

The following are examples where the assessment questions are representative of alignment to the Grade 2 expectations:

• In the Topic 1 Lesson 1.5, Digital Quick Check item 1 says, “Which subtraction sentence goes with the story? Emma has 11 dolls and 5 bears. How many more dolls does she have than bears?” (2.OA.1)
• The Topic 2 Performance Task, page 68, assesses 2.OA.1 (Use addition and subtraction within 100 to solve one and two step word problems) and 2.NBT. 7 (Add and subtract within 1000, 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.) A rubric is included with the task.
• The Topic 6 Performance Task, page 184, enables students to apply the mathematics learned in the Topic. 2.NBT.B.5(Fluently add and subtract within 100 using strategies based on place value, properties of operations and/or the relationship between addition and subtraction,); 2.NBT.B.6 (Add up to four two-digit numbers using strategies based on place value and properties of operations.) and, 2.OA.1 (Use addition and subtraction within 100 to solve one- and two step word problems involving situations of adding to, taking from, putting together, taking apart and comparing with unknowns in all positions.) A rubric is included with the task.
• Topic 15, Lesson 15.1 - Digital Quick Think: On item 1, students estimate the length of a line using paper clips. (2.MD.3)
• Topic 15, Lesson 15.7 - Digital Quick Think: On item 1, students tell what the difference in length between the left side and the length of the top of the game board. (2.MD.5)

The Assessment items that contain above grade-level standards are noted in the following list:

• In the Online Topics 5-8 Benchmark Test, item 9, students solve an addition and a subtraction problem using the standard algorithm. The standard algorithm is listed in 4.NBT.4.
• In the Topic 7 Unit Assessment, questions 8 and 9, students circle “extra information” or “missing information” then write a number sentence if the problem can be solved. Extra information and missing information are not CCSSM.
• In the Topic 11 Performance Task, question 4, students solve a subtraction problem using the standard algorithm. In order to receive a perfect score of a 3, students must correctly answer all of the problems and demonstrate a clear understanding of each. The standard algorithm is found in 4.NBT.4.
• In the Online Topics 13-16 Benchmark Test, items 3 and 4 reference fifty-cent pieces in determining the answer, which is not included in the Grade 2 standards. The Online End-of-Year Test, item 23 and Topic 13 assessment, item 2 also include a fifty-cent piece. Counting money comes in standard 4.MD.2.
• The Topics 13-16 Benchmark Test, questions 8 and 10 include the use of a half dollar.
• In the Topic 15 Unit Assessment, question 2, students use the paperclip to estimate the length of the toothbrush in the previous problem. Students estimate objects using units of inches, feet, centimeters, and meters. (2.MD.3)
• In the Topics 9-12 Benchmark Test, question 8, students identify a spinner with eight equal parts that has four parts shaded. 2.G.3 states that students partition shapes into two, three, and four equal parts.
• The End-of-Year Test, item 8, includes the use of half dollar coins.
• 2.MD.8 has students solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately. The items below address 4.MD.2 (Use the four operations to solve word problems involving…money, including problems involving simple fractions or decimals, …) and 4.NF.6 (Use decimal notation for fractions with denominators 10 or 100) through the use of money. The expectation is for students to work in dollars and cents. • Online Topic Test 13, items 14-17 and 20 have prompts that use the decimal point in the representation. • Alternate Topic Test 13, item 5 uses a prompt with a decimal point in the representation. • Enhanced Topic Test 13, item 4 includes a prompt with a decimal point in the representation. Items 5 and 9 mix bill and coin values and include the decimal point in the representation. (4.MD.2) • The Performance Task in Topic 13, questions 2 and 4 require an answer with the decimal notation for money. The value of each toy given is written in decimal form. In order to earn three points on the rubric, students must write the correct value of Maria’s coin collection and accurately identify one toy that Maria can buy and one toy that she cannot buy using decimal notation. Money in decimal form is found in 4.MD.2. • The End-of-Year Test, item 23 includes a prompt with a decimal point in the representation. ### 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 78 percent of class time to the major work of Grade 2. ### 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 2 meet expectations for spending a majority of instructional time on major work of the grade. • Topics 1 through 11 and Topic 15 of 16 topics are devoted to major work of the grade, which is approximately 75 percent. • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is approximately 122 out of 157 lessons, which is approximately 78 percent. • The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is approximately 26 out of 34 weeks, which is approximately 76 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 78 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. 5/8 + - Criterion Rating Details The instructional materials reviewed for enVisionMATH California Common Core Grade 2 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. However, the instructional materials partially meet expectations for making connections between major and supporting work, being consistent with the progressions in the Standards, and fostering coherence through connections at a single grade. ### 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 2 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. There are examples where supporting work engages students in the major work of the grade, but there are also multiple instances where supporting work is treated separately and does not engage students in the major work of the grade. Lessons that connect supporting content to the major work on the grade include: • Topic 12 addresses Geometry standards 2.G.1, 2.G.2 and 2.G.3. Lesson 12-5 connects to the major work of 2.OA.2. (Add and subtract within 20.) Students represent and solve problems, for example, in Practice Item 1 on page 402: Use square tiles to cover the rectangle. Write number sentences to tell how you counted by rows and columns. Count by rows: ___ Count by columns: ___” Students are expected to write 6 + 6 = 12 and 2 + 2 + 2 + 2 + 2 + 2 = 12. • In Topic 13, the Problem-Based Interactive Learning, Independent Practice, and Quick Check connect money (2.MD.8) to the major work of place value as students skip count by 5s and 10s to find the value of a set of coins. (2.NBT.2) • Lesson 13-1 connects supporting work 2.MD.8 to major work 2.NBT.2. On page 421, there is a quarter, dime, nickel, and two pennies shown. Students add to find the value of the collection as 42 cents. • In Lesson 16-1, students count by 5s on analog and digital clocks. (2.MD.7) This connects to major work 2.NBT.2. • In Lesson 16-8, students solve one-step word problems using addition and subtraction. (2.OA.1) On page 538, students are given a picture graph about Meytal’s closet. Students are asked, “What type of clothing is there the least of in the closet?" And, “How many more pants than shirts are in the closet?” (2.MD.10) Examples of missed opportunities to connect supporting content to the major work on the grade include: • Teacher Edition Lesson 13-4, page 431, contains the problem, “Suppose the pig contains one dollar bill, one penny, one nickel and two dimes. What is the total value of the money in the pig? Where do you put the dollar sign and decimal point when writing money amounts?” Representations using decimal notation align to 4.NF.6. • Lessons 14-1 and 14-2 address money. (2.MD.8) Students subtract within 100 in one-step word problems. (2.OA.1) There is a missed opportunity to have students do two-step word problems as stated in 2.OA.1. Students solve the word problems based on two-digit subtraction problems using the standard algorithm. (4.NBT.4) ### 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 2 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 166 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 112 lessons that are listed in the Table of Contents. Lessons are structured to contain a Math Background, Problem Based Interactive section, Develop the Concept: Visual section with two or three activities, Guided Practice problems, Independent Practice problems, Close/Assess and Differentiated problems, and Leveled Homework. 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 at the beginning of the year as well as the end of the year, Basic Fact Timed Test, and Benchmark Tests every fourth Topic. The publisher provides some information about the suggested time to spend on each lesson or the components within a lesson. The Implementation Guide has a chart that suggests time frames of 50-75 minutes per day. Morning Math is recommended but is not incorporated into the daily math block. The Morning Math time incorporates concepts and skills ranging from the Common Core Review to Quick Checks. ### 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 2 partially meet expectations for the materials being consistent with the progressions in the standards. The instructional materials reviewed for Grade 2 are partially consistent with the progressions in the standards. Although students are given extensive grade-level problems and connections to future work are made in the Skills Trace, future grade-level content is not always clearly identified within the lesson or Topic for the teacher or student. The exception is the Topic titled, Step up to 3rd Grade, where the materials are clearly identified as Grade 3 materials. The Grade 2 materials have instances where future grade-level content is present and not identified as such. For example: • In Lesson 13-3, a decimal point is taught as a vocabulary word. In Grade 4, the standard states, “Use decimal notation for fractions with denominators of 10 or 100. Use the four operations to solve word problems involving distances, …, and money.” (4.NF.6, 4.MD.2) • In Lesson 13-4, page 432, decimal points are used to solve money problems. A dollar bill, a fifty-cent piece, a dime, and a penny are shown. Students are to count and write1.62. (4.MD.2)

The materials do not always meet the full intent of the standards and do not always provide extensive work to students for each standard. For example:

• 2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.3 is addressed in one lesson, 5-6 (Even and Odd Numbers). The standard states, "There are two parts to the standard: determining odd/even by pairing objects and writing equations." In the Independent Practice, pages 145-146, teachers are guided to have students use cubes: “Children may have difficulty solving the exercises without visual support. Encourage them to use connecting cubes to solve the exercises.” On page 144, the teacher directions state, “In this lesson you will learn how to tell if a number is odd or even. If the number is even, you will write a number sentence to show the two equal parts and the total number of cubes.” In the lesson, students do not count by 2s to determine if a number is even.
• 2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally-spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. 2.MD.6 is addressed in Lessons 8-6 (adding using a number line) and 9-6 (subtracting using a number line). In the two lessons, students are given the number lines with the units included. Students do not create a number line with equally-spaced points, and rulers as number lines are not taught until Topic 15. This is a missed opportunity to use rulers when adding and subtracting within 100 in Topics 8 and 9.
• For 2.NBT.1b, there is one lesson, 10-1: Building 1000. The standard states, “The numbers 100, 200, 300, …, 900, refer to one, two, …, or nine hundreds (and 0 tens and 0 ones).” From this lesson, page 301, students understand the value of hundreds and can move to the next lesson putting numbers such as 245 into in the correct place of 2 hundreds and 4 tens and 5 ones in a place-value table.
• For 2.NBT.3, there is one lesson, 5-2: Reading and Writing Numbers. The standard states, “Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.” The lesson works on reading and writing two-digit numbers but not on expanded form or numbers greater than 90.
• For 2.NBT.9, there is one lesson, 11-9: Models for Subtracting with Three-Digit Numbers. The two previous lessons, 11-7 and 11-8, teach subtraction by estimation first, then base-ten blocks alongside the standard algorithm. Lesson 11-9 uses the standard algorithm. The materials do not provide extensive work to students addressing 2.NBT.9.
• For 2.MD.2, there is one lesson, 15-6: Measuring Length. The students start the lesson measuring with non-standard units. The lesson moves to students measuring using inches, feet, and yards. To have students understand that it takes more inches than feet is necessary, but it is not built upon in the lesson. Also, students do not have sufficient practice measuring inches and feet and are not responsible in the standards for yards.
• For 2.MD.4, there is one lesson, 15-8: Comparing Lengths. As both metric and customary measurements are being used in this cluster, centimeters were used to compare not inches, feet, and meters as stated in the standard.

### 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.
1/2
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 partially meet the expectations for fostering 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.

• In Topic 2, students “Add and subtract within 20” (2.OA.B) by working on addition facts involving 0, 1, 2, using the doubling strategy, considering near doubles, and making 10 to add.
• In Topic 4, students “Work with equal groups of objects to gain foundations for multiplication” (2.OA.C) by repeated addition, building arrays, and drawing pictures.
• In Topic 5, students “Use place-value understanding and properties of operations to add and subtract” (2.NBT.B) by grouping objects into tens and ones, comparing two-digit numbers using symbols, and identifying and writing numbers that are 10 more and 10 less than a given number.

Materials do not 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.

• There are missed opportunities to connect 2.OA.1 with 2.MD.10. Topics 1 and 16 are taught independently and do not make a connection between any other cluster within Grade 2.
• There are missed opportunities to connect 2.NBT.B to 2.NBT.A or 2.OA. Materials address parts of a standard at a time and do not connect those parts together or connect those to other standards.

## Rigor & Mathematical Practices

#### Does Not Meet Expectations

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Gateway Two Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do 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 do not meet the expectations for practice-content connections by meeting expectations on explicitly attending to the specialized language of mathematics and partially or not meeting expectations for the remainder of the indicators in the criterion.

### 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
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Criterion Rating Details

The instructional materials for enVisionMATH California Common Core Grade 2 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
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Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 2 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 8 Lesson 8-4, the Overview of the PBIL states, “In this activity, children use connecting cubes to model adding two two-digit numbers and then record the sum. They will decide if regrouping is needed.” The Independent Practice directions state, “Use connecting cubes and your workmat. Add. Did you need to regroup? Circle yes or no.” There are four problems within the Independent Practice that has students using cubes to demonstrate conceptual understanding independently.
• In Topic 10 Lesson 10-2, the Overview of the PBIL states, “Children will use place-value models to represent numbers up to 1,000. The Independent Practice directions state, “Write the numbers. Use models and your workmat if needed.” Students do not use place-value models independently to represent numbers as the pictures are given for the numbers and are shown in the exact same order of hundreds, tens, and then ones for all problems. Students can count the pictures and place the corresponding number in the chart.
• In Topic 11 Lesson 11-4, the Overview of the PBIL states, “In this activity, children will use place-value blocks to add three-digit numbers.” The Independent Practice directions state, “Add. Regroup if needed. Use models and your workmat to help you.” Students do not demonstrate adding three-digit numbers independently using place-value blocks as they fill in a template of a given problem.

### 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
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Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 2 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 standards 2.OA.2 and 2.NBT.5, Fluently add/subtract single digits and add/subtract within 100.

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

• In Topic 4 Lesson 4-3, students use a picture to create an array to represent repeated addition. The Guided Practice includes opportunities for students to practice repeated addition by creating arrays to represent the given story problem.
• In Topic 8 Lesson 8-2, students use counters on a place-value chart to show regrouping when adding two-digit numbers. The Guided Practice includes four opportunities for students to practice regrouping.
• In Topic 8 Lesson 8-7, students add three two-digit numbers. The Guided Practice includes opportunities for students to practice adding two numbers in the ones place first and then adding the last number in the ones place to find the sum of the ones place. Students decide if they need to regroup to find the solution.

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

• In Topic 8 Lesson 8-5, students use a place value chart to find sums. The Independent Practice includes six opportunities for students to demonstrate regrouping independently when adding two-digit numbers.
• In Topic 9 Lesson 9-5, students use a place value chart to find differences. The Independent Practice includes eight opportunities for students to demonstrate regrouping independently when subtracting two-digit numbers.
• In Topic 11 Lesson 11-10, students find differences of three-digit numbers. The Independent Practice includes opportunities for students to demonstrate regrouping independently when subtracting three-digit numbers.

### 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
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Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 2 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 instructional materials provide opportunities for working with the applications of mathematics through routine problems within the Problem Solving lessons and the Problem Solving section within all lessons.

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 4 Lesson 1-4, students write an addition number sentence to represent a story problem. Independent Practice problem 4 states, “There are 4 children with balloons. If each has 3 balloons, how many balloons are there in all?” The problem has a blank repeated addition number sentence below the story problem. The students fill in the blanks with the numbers.
• In Topic 8 Lesson 8-9, students write an addition number sentence to represent a story problem. Independent Practice problem 4 states, “Tina picks 39 blueberries. She picks 14 strawberries. How many pieces of fruit does Tina pick?” The problem has a blank addition number sentence below the story problem. The students fill in the blanks with the numbers.
• In Topic 11 lesson 11-9, students write a subtraction problem in a place-value template to solve a story problem. Problem Solving problem 6 states, “Jeff has 517 baseball cards. He has 263 football cards. How many more baseball cards than football cards does he have?” The problem has a blank place value template with a subtraction symbol next to the story problem. The students fill in the blanks with the numbers.

### 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
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Indicator Rating Details

The instructional materials for enVisionMATH California Common Core Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Lessons included components such as Daily Common Core Review, Problem-Based Interactive Learning, Develop the Concept: Visual, Guided and Independent Practice, and Problem Solving. These components are designed to develop conceptual understanding, procedural skills, and application skills.

All three aspects of rigor are present independently throughout each topic in the materials. For example in Topic 9:

• In Lesson 9-2, students develop conceptual understanding of regrouping in subtraction when using a place value template to solve a subtraction problem.
• In Lesson 9-3, students practice fluency of subtracting within 100 when solving subtraction problems.
• In Lesson 9-6, students apply knowledge of subtraction while using a number line to solve a story problem.

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

• In Topic 15 Lesson 15-2, students develop conceptual understanding of the length of an inch by using a ruler while applying that knowledge to solve the story problem.
• In Topic 10 Lesson 10-3, students develop conceptual understanding of place value when working with place-value models, while practicing the procedural skill of addition when solving the equation.
• In Topic 7 Lesson 7-2, students practice procedural skill of subtraction within a 100 while writing a number sentence to solve a story problem.

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
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Criterion Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do not meet expectations for practice-content connections. The instructional materials explicitly attend to the specialized language of mathematics, but they partially or do not meet expectations for the remainder of the indicators in this criterion. 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
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. Overall, the MPs are identified and used in connection to the content standards, but the materials do not always use the MPs to enrich the mathematics content. In the materials, the connections between the MPs and the content standards are not always clear.

• There are multiple places for finding the MPs in the materials: Content Guide in the Program Resources Tab, the beginning of each Topic, sometimes in the Math Background section within each Topic, and at the beginning of each lesson.
• Within each lesson there is a check list of MPs, but not all of the checked MPs are explicitly labeled within the lesson itself.
• In the Content Guide and the check lists, the MPs are labeled and addressed. Within enVisionMATH California Common Core Grade 2 lessons, the MP is abbreviated.
• MP1 - Make Sense of Problems (no perseverance)
• MP2 - Reason Quantitatively or Reason Abstractly (treated separately)
• MP3 - Communicate or Critique the Reasoning of Others (treated separately)
• MP4 - Model with Mathematics
• MP5 - Use Appropriate Tools
• MP6 - Attend to Precision
• MP7 - Use Structure
• MP8 - Check for Reasonableness or Make Generalizations (treated separately)
• In Math Background (page 1D) for Topic 1, the teacher note states, “Mathematical Practices: Make Sense of Problems - Remind children to first read a story problem in its entirety at least once, and then to think about it one sentence at a time.” The portion of MP1 about perseverance is not addressed.
• In Lesson 11-2, MPs 1 and 5 are listed. MP1 is identified in the lesson (page 394, item 15), but MP5 is not identified. Even though MP5 is not explicitly identified, there is a note for teachers that states, “How do the blocks help you understand the number 243? How can you show 200 using place-value blocks?”
• In Lesson 16-1, MP7 is on the check list but not explicitly denoted within the lesson. In the Topic 14 Overview, MP7 is checked, but no lesson identifies the MP as being used in teaching. In Lesson 15-5, MP7 is checked, but nowhere in the lesson is the MP explicitly taught.

### Indicator 2f

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

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

• MP1: In Lesson 4-1 exercise 12, the teacher note states, “Make Sense of Problems: Encourage children to eliminate incorrect answers. Remember that repeated addition sentences always have equal addends. Which addition sentences do not have equal addends?” Students do not make sense of the problem and persevere in solving it as the teacher leads them to a specific answer. In Lesson 8-1 exercise 13, the teacher’s note states, “Make Sense of Problems: Encourage children to look for important words such as more and in all that give clues about whether to add or subtract.” Students do not make sense of the problem on their own due to the reminders provided by the teacher.
• MP4: In :esson 7-1, the teacher note states, “MP4 Model with Mathematics: Using little ten frames helps children see that subtracting tens is similar to subtracting ones.” Students fill in the numbers in subtraction equations provided for the students, and the suggested use of ten frames is a tool for helping student find the solution to the subtraction equation.
• MP5: In Lesson 3-1, the teacher note states, “MP5 Use Appropriate Tools: Connecting cubes will help children understand the concepts of 0-less-than, 1-less-than, and 2-less-than.” Students do not get to choose which tool to use. In Topics 4 and 5, students use tools chosen by the materials (part-part-whole mats, two-colored counters, and base-ten blocks).
• MP8: In Lesson 8-5, the teacher note states, “Repeated Reasoning: Ask how many children plan to write 25 first in the frame and how many plan to write 27 first. Discuss why the sum will be the same regardless of the order.” In this exercise, students make use of structure (MP7), not MP8. In the CCSSM, part of MP7 states, “Young students, for example, might notice that three and seven more is the same amount as seven and three more, ….”

### 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.
0/2
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 do not meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Materials have few, if any, prompts for students to both construct viable arguments and/or analyze the arguments of others. Students are not given problems that are conducive to public explanations of their solutions. Students are given guided practice to follow steps and then given individual work that imitates the guided-practice problems. On occasion, there is a whole group discussion, but students do not critique the reasoning of others during the discussion. Examples include:

• In Lesson 5-7, MP3 is cited; “Communicate: Children explain the correspondence between verbal descriptions and the data from the chart.” However, students do not critique the reasoning of others.
• In Lesson 8-1, Visual Learning presents the problem, “What is the sum of 37 + 6?” The answer that students are expected to give is 43 based on the Place Value Mat of 4 tens and 3 ones. There is a teacher note on “Prevent Misconceptions: Some children may think that adding two-digit numbers will always require regrouping. Talk about how the example would have been different if the number sentence was 37 + 2 = __.” This is a missed opportunity for student to share the strategies they used, the answers they got, and critique the reasoning of others.
• In Lesson 11-3 Quick Check exercise 5, page 346A, students circle a three-digit number in each box, estimate the sum of the numbers and tell if the sum is more than or less than 500, explaining how they know. The explanation is for the teacher as there are no directions to share strategies and critique others’ reasoning once the teacher has evaluated the Quick Check.
• In Lesson 13-1 Small Group Interaction, page 419, students work in pairs. One partner takes five coins and places them on the workmat. Each person adds the value of the collection and records the answer on their worksheet. Partners then repeat together taking five coins and placing them on the workmat. Four pulls need to be made. Students are given no direction to share strategies and critique others’ reasoning while they are doing this activity.
• In Lesson 16-3 Quick Check Master, question 4 is identified as MP3 Writing to Explain. Students are to “Look at the calendar. Choose a date and write it on the line. Write a story problem about a special day that is after this date.” This is a missed opportunity to get to the full depth of MP3 as students do not share their reasoning with classmates and critique the given reasoning.

### 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
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Indicator Rating Details

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 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 throughout the material 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.

Materials provide little assistance to teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

• Lesson 4-1 exercise 2, page 102, is an Error Intervention. “If children have difficulty seeing that repeated addition sentences have equal groups, then have them model the sentences with counters on the page.” This is a missed opportunity for teachers to use MP3 to share strategies and critique other’s thinking about addition in relation to equal groups.
• In Lesson 6-1 page 157, “Critique the Reasoning of Others: Encourage students to examine if their partner’s reasoning makes sense.” In the Small Group Interaction, one partner is to think of a two-digit number and build that number using base-10 blocks. Students are to then add a multiple of ten to the number created. Children record their answer on the worksheet. There are no directions for teachers to encourage children to give the partner feedback or ask how they know if the answer given is correct.
• In Lesson 8-2 exercise 5, page 220A, teacher directions for Quick Check Master state, “Writing to Explain: Children should write a two-digit number and a one-digit number on the table in the appropriate places. They should write an explanation of how they found the sum.” No direction for teachers to have students share their explanations and critique others is given for MP3.
• In Lesson 10-3 page 305, the teacher note for MP3 states, “By listening and reacting to volunteers, students will understand the different forms and how the forms are similar.” The teacher is to Pose the Problem: “What are three different ways to write the number 519? Lead a class discussion, inviting children to share their answers.” This is a missed opportunity for teachers to have students share their answers as well as the reasoning used to arrive at the answer and what other students think of the given reason.
• In Topic 12 Math Background, the following explanation on how to use MP3 within the topic is provided, “Mathematical Practices: Communicate - Encourage children to share their observations about shapes with one another. By describing what they see, they will be identifying the various properties of the shapes.” Critiquing others’ reasoning is not mentioned.

### Indicator 2g.iii

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

The instructional materials reviewed for enVisionMATH California Common Core Grade 2 meet expectations for explicitly attending to the specialized language of mathematics.

• Each lesson includes a list of vocabulary in the Lesson Overview, at the beginning of each lesson. The identified vocabulary words appear at times within the blue script that teachers may use and the words are highlighted in the student book.
• Each Topic includes two-sided vocabulary cards in the Teacher Edition in the Printable Resources section. Each card has a word on one side and its definition and/or representation on the other. The Teacher Edition includes vocabulary activities at the start of each topic. For example, in Topic 11 in Math Background Vocabulary Activities, page 333D says, “Trading Places: Write three digits from 0 to 9 on the board. Have children arrange the 3 digits to make as many numbers as possible. Ask them if the order of the digits makes a difference and have them explain their reasoning. Then have them determine the greatest and least numbers in the group. Ask them to explain how they know which is the greatest and which is the least. Model the use of place-value vocabulary throughout the discussion.”
• Each Topic Opener has My New Math Words followed by a Vocabulary Cards activity. In Topic 6 Mental Addition, the Topic Opener on page 155 lists My New Math Words as mental math, tens digit,and next ten with their definitions. On page 156 in Topic 6, the Vocabulary Cards activity directions state, “Cards can always be used as flashcards and for playing the matching game. Have children create large vocabulary cards with visuals to add to the classroom word wall.”
• Correct vocabulary is sometimes not used. Examples include, use of number sentence instead of using equation, and bar graphs on page 258A are represented by histograms.

## Usability

#### Not Rated

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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

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

Report Published Date: Wed Oct 24 00:00:00 UTC 2018

Report Edition: 2015

Title ISBN Edition Publisher Year
enVisionMATH California Common Core - Grade 2 9780328792696 Pearson 2015

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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

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## 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.

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