## Alignment: Overall Summary

The instructional materials reviewed for Grade 2 do not meet the expectations for alignment to the CCSSM. In Gateway 1, the instructional materials do not meet the expectations for focus on major work because of assessing too many above, grade-level topics and devoting an insufficient amount of time to the major work of the grade. The materials also do not meet the expectations for coherence because they do not make sufficient connections between the standards. Since the materials do not meet expectations for focus and coherence in Gateway 1, they were not reviewed for evidence of rigor and the mathematical practices in Gateway 2.

|

## Gateway 1:

### Focus & Coherence

0
7
12
14
1
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
N/A
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

#### Does Not Meet Expectations

+
-
Gateway One Details

### Criterion 1a

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

### 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 for Connecting Math Concepts Level C (Grade 2) do not meet expectations for assessing material at grade level. Most of the program’s thirteen mastery tests and two cumulative tests include items beyond the scope of expectations for Grade 2, including adding and subtracting 3-digit numbers using a traditional algorithm, multiplication concepts, finding area and perimeter, and measurement conversions. It would not be possible for teachers or districts using this program to remove or amend the misaligned items without disrupting the overall structure and design of the grade level program.

Review Team note: The Level C (Grade 2) teacher guide identifies the cumulative tests as “optional” (page 3); however, the publisher orientation session identified these assessments as a required component of the grade level program. Therefore, the cumulative tests are included in this review.

Mastery Test 1:

• Items in parts 2-5 assess standards from previous grades, including writing numerals 1-20 (K.CC.A.3) and fact fluency within 10 (1.OA.C.6). This review is appropriate for the beginning of the year.
• All items in parts 1, 6 and 7 assess Grade 2 standards, focusing on writing numbers within 1000, identifying the value of digits, and 2-digit addition within 100.

Mastery Test 2:

• Items in parts 3, 8 and 12 assess learning from Grade 1, including three single-digit addends (1.OA.A.2), a 2-digit number + 10 (1.NBT.C.5), and counting and writing numbers within 100 (1.NBT.A.1). This review is appropriate for the beginning of the year.
• Items in parts 1, 2, 4, 5, 6, 7, 9, 10 and 11 assess Grade 2 standards, focusing on fluency within 20, counting money, writing expanded form, skip-counting, and 2-digit addition and subtraction within 100.
• Items in parts 3 and 6 assess learning that is not specifically required by the CCSSM, including counting backwards and skip-counting by nines.

Mastery Test 3:

• Items in Parts 1-4 and 6-9 assess Grade 2 standards, focusing on fluency within 20, skip-counting by fives, writing numbers within 1000, counting coins, using expanded form, and exploring place value.
• Part 5 calls for students to put three 2-digit numbers in order from least to greatest. This is not the intent of 2.NBT.A.4.
• Part 9 calls for students to count paper money and coins to find the total value; while counting coins is within expectations for 2.MD.C.8, students should be doing this work within the context of word problems.

Mastery Test 4:

• Items in Parts 1, 2, 4, 7, 8 and 11 assess Grade 2 standards, focusing on understanding subtraction, comparing numbers, 2-digit addition, measuring in standard units, writing numbers, and mentally adding 10 to 2- and 3-digit numbers.
• Some items call for students to count by fours which is not specifically required by the CCSSM.
• Items in Parts 3, 6, and 9 call for students to represent situations with more than one unknown or calling for more than one variable. This is not appropriate for Grade 2.

Mastery Test 5:

• Part 9 assesses students’ ability to identify basic shapes (K.G. and 1.G).
• Items in Parts 1, 2, 6, 7 and 8 assess Grade 2 standards, focusing on fluency within 20, counting coins, measuring with standard units, completing equations based on drawings, and subtraction with 2-digit numbers.
• Parts 3 and 4 assess learning that is not part of CCSSM: write a comparison statement with three values and represent a word problem with two variables.
• Part 5 calls for students to use multiplication (3.OA.A.1).

Mastery Test 6:

• Items in Parts 1, 3, 6 and 7 assess Grade 2 standards, focusing on fluency within 20, completing equations based on a drawing, and identifying 2D and 3D shapes.
• Parts 2, 4 and 5 assess learning that is not part of Grade 2 CCSSM, calling for students to represent word problems with more than one variable and compare variables.

Mastery Test 7:

• Items in Parts 1, 2, 3, 5 and 7 assess Grade 2 standards, focusing on addition within 100, fluency within 20, counting money, completing equations based on a drawing, and solving an equation for the unknown addend.
• Parts 4 and 6 assess learning that is not part of Grade 2 CCSSM, calling for students to represent word problems with more than on variable.

Cumulative Test 1:

• Items in Parts 1-5, 7, 9, 10, 14-17, 19, 21 and 22 assess Grade 2 standards; these items are a review of parts of Mastery Tests 1-7.
• Parts 6, 8, 11, 12 and 20 assess learning that is not part of Grade 2 CCSSM, calling for students to represent word problems with more than one variable; order three 2-digit numbers; and write comparison statements with three values.
• Some items call for students to count by fours, and nines which is not specifically required by the CCSSM.
• Part 13 assesses multiplication facts (3.OA).

Mastery Test 8:

• Items in Parts 1, 3, 5 and 7 assess Grade 2 standards, focusing on fluency within 20, 3-digit addition and subtraction within 1000, adding and subtracting multiples of ten, and finding the unknown number in an equation.
• Parts 4 and 6 assess future learning: rounding to the nearest ten (3.NBT.A.1); and finding perimeter (3.MD.D.8).
• Part 2 assesses learning that is not part of Grade 2 CCSSM, calling for students to represent word problems with more than one variable.

Mastery Test 9:

• Items in Parts 2, 3, 5 and 8 assess Grade 2 standards, including fluency within 20, solving word problems, and telling time in five-minute intervals.
• Items in Parts 3 and 5 call for students to represent and solve word problems within and beyond 100. 2.OA.A.1 only calls for solving word problems within 100.
• Parts 4, 6, 7 and 9 assess future learning: multiplication (3.OA); addition/subtraction within 1000 using an algorithm (3.NBT.A.2); and rounding (3.NBT.A.1).
• Part 1 calls for students to write labels for questions in word problems, not an explicit standard in Grade 2 CCSSM.

Mastery Test 10:

• Items in Parts 1 and 3 assess Grade 2 standards, focusing on fluency within 20.
• Parts 2, 4-7 assess future learning: multiplying to find the value of coins and solving unknown-factor equations (3.OA.A.1); telling time to the nearest minute (3.MD.A.1); comparing measurements with different units (4.MD.A); and adding and subtracting dollars and cents (5.NBT.B.7).

Mastery Test 11:

• Items in Parts 1, 6 and 8 assess Grade 2 standards, focusing on fluency within 20, addition within 100/1000, and solving equations to find the unknown number.
• Parts 2, 4, 5, 9 and 10 assess future learning: perimeter and area of rectangles (3.MD); multiplication arrays (3.OA); comparing measurements with different units (4.MD); and adding and subtracting dollars and cents (5.NBT.B.7).
• Part 7 calls for students to rewrite an amount given in cents, using "$" and the decimal point correctly. This is not an explicit part of 2.MD.C.8 and should not be a stand-alone lesson. Mastery Test 12: • Items in parts 1, 4 and 6 assess Grade 2 standards, focusing on fluency within 20, measuring length and finding the difference between lengths, and comparing 3-digit numbers in standard and expanded form. • Parts 2 and 5 assess future learning: multiplication concepts (3.OA); and solving word problems with prices given in dollars and cents (5.NBT.B.7). Mastery Test 13: • Items in parts 1, 2, 4-6, 8-10 and 12-14 assess Grade 2 standards, focusing on solving word problems within 100, measuring lines and making a line plot, making number families to decompose numbers, addition and subtraction within 100/1000, analyzing and interpreting a bar graph, naming parts of an equally partitioned shape, identifying shapes, and identifying numbers as even or odd. • Parts 7, 10 and 11 assess future learning: elapsed time (3.MD.A); writing multiplication facts for a given array (3.OA); and comparing measurements with different units (4.MD). Cumulative Test 2: • Parts 1, 2, 4, 9, 12-16, 17 and 23 assess Grade 2 standards; these items are a review of parts of Mastery Tests 8-13. • Parts 6, 8, 10, 11, 15 and 18-21 assess future learning: multiplication concepts (3.OA); telling time to the nearest minute (3.MD); finding area and perimeter (3.MD); rounding (3.NBT.A); comparing measurements with different units (4.MD); and solving word problems with prices given in dollars and cents (5.NBT.B.7). • Parts 3, 7, and 22 assess learning that is not part of Grade 2 CCSSM. ### Criterion 1c - 1f Coherence: Each grade's instructional materials are coherent and consistent with the Standards. 1/8 + - Criterion Rating Details The instructional materials for Connecting Math Concepts Level C (Grade 2) do not meet expectations for coherence and consistency with the standards. The program includes minimal opportunities for students and/or teachers to make connections between supporting content and the major work of the grade, even in places where there are natural connections between standards. The amount of content in this grade level program is not viable for a school year, due to the large amount of lesson content that is from future grades. Students using this program as designed would not develop a solid foundation needed to understand and master grade-level content. The Level C program is not consistent with the progressions in the CCSSM: the instructional materials do not clearly identify work that is above level, and the above grade-level work is not an appropriate extension or reinforcement of grade level standards; all students do not have opportunities to engage extensively with grade level work, due to the amount of content from future grades; and there is no mention of building on students’ prior knowledge. These instructional materials treat learning objectives and standards as individual pieces that rarely interact, with no visible connections to the language from CCSSM cluster headings. Activities within exercises sometimes connect two or more grade-level clusters, but these are randomly placed and are not explicitly called out as important or natural connections. Overall, the Level C instructional materials do not attend to coherence. ### 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 for Connecting Math Concepts Level C (Grade 2) partially meet expectations for using supporting content to enhance focus and coherence by engaging students in the major work of the grade. The grade level program includes some exercises where supporting content naturally connects to major work; however, there are many places in the materials where natural connections are missed. Connections between CCSSM Supporting Work and Major Work are never identified in the teacher presentation books or the teacher guide. Connecting Math Concepts is a “direct instruction” program, where teachers are encouraged to use instructional materials as written, with little to no deviation from the prescribed presentation script. The teacher guide states: “The script for each lesson indicates precisely how to present each structured activity. Follow the specified wording in the script.” (page 28). This structured presentation discourages teachers from making unidentified connections explicit for students. • Each lesson consists of a series of discrete exercises, with each exercise addressing a different standard. A typical lesson includes exercises targeting up to three different domains, routinely moving back and forth between domains and clusters without making connections explicit for students or teachers, even where natural connections are evident. • Telling and writing time (2.MD.C.7) allows an opportunity for Grade 2 students to practice the major work of skip-counting by fives (2.NBT.A.2). There are 54 exercises in the Level C program that focus on telling and/or writing time. However, much of this work exceeds the expectations of Grade 2 by including analog and digital times that are to the nearest minute. • Solving word problems involving money (2.MD.C.8) supports the major work of representing and solving problems within 100 (2.OA.A.1) and addition and subtraction fluency within 100 based on place value (2.NBT.A.1, 2.NBT.B.5). The Level C program focuses on this skill in 50 exercises; however, many of these exercises do not meet the expectations of the Grade 2 standard. 2.MD.C.8 calls for problem solving with dollar bills, quarters, dimes, nickels, and pennies; some exercises included word problems that use dollars as the unit, with no focus on monetary value; some exercises only focus on using the$ and ₵ symbols, with no problems or computation work; and some exercises have students adding and subtraction dollar and cent amounts written with decimals using the standard algorithm (5.NBT.B.7).
• As Grade 2 students generate and represent data on line plots (2.MD.D.9), they connect to the major work of measuring the length of objects (2.MD.A.1). The four exercises in Level C that explore this content make this important connection; however, the measurement unit in all four exercises is centimeters. Teachers using this program should seek out supplemental lessons that call for students to measure and represent length data with other units of measurement. As Grade 2 students represent and interpret data in picture and bar graphs (2.MD.D.10), they connect to the major work of solving word problems with addition and subtraction (2.OA.A-B). The Level C program includes thirteen exercises devoted to this content. Three exercises focus on reading a picture graph, but students never draw one themselves. Nine exercises focus on reading a bar graph, and two exercises have students making a bar graph—all teacher-directed. Nine exercises engage students in interpreting data in picture and bar graphs by answering questions; however, most are low-level questions such as “Which has the most/least?” and “How many ____ are ____?”, rather than the put-together and compare problems called out in 2.MD.D.10. None of the graphing exercises include take-apart problems.

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
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Indicator Rating Details

The instructional materials for Connecting Math Concepts Level C (Grade 2) do not meet expectations for designating a viable amount of grade-level content for one year. At face value, the amount of content, including lessons and assessments, is viable for one school year of approximately 140-190 days; however, due to the large amount of content that is not aligned to the grade level, there is not enough instruction at the depth required by Grade 2 standards to prepare students for learning in future grades.

• This grade level program contains 130 lessons, lessons, 13 mastery tests, and 2 cumulative tests, spanning approximately 145 days, which is a sufficient number for a standard school year. The teacher guide (page 7) states: "The ideal goal is to teach one lesson each period. If students are not firm on content that is being introduced, you will need to repeat parts of lessons or entire lessons.” This possibility of reteaching lessons is within reason for a typical school year.
• On page 7 of the teacher guide, the publisher identifies two starting points: lesson 1 for students who are new to the Connecting Math Concepts program; and lesson 11 for students who have completed Level A or passed the Level B Placement Test. For students starting instruction at lesson 11, the program will span approximately 135 days, plus any repeated lessons. This number is low for a typical school year.
• The Grade 2 program is designed to be taught daily; a 50-minute period for structured work is suggested each day, as well as 20 minutes of independent work (teacher guide, page 5). The material allocated for instruction each day is reasonable for this suggested amount of time.
• The Level C instructional program consists of a total of 1,158 exercises; 298 of these exercises (26 percent) focus on objectives that do not align with Grade 2 CCSSM expectations. A substantial number of unaligned exercises focus on skills and understandings not included in CCSSM and/or mastery of above level standards from Grade 3 and beyond (see report for Indicator 1b); this focus on above grade-level objectives takes time and focus away from foundational grade level understandings. Teachers using this program would need to make significant modifications to the daily lessons and/or omissions that would affect the integrity of the grade level program.

### 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.
0/2
+
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Indicator Rating Details

The instructional materials for Connecting Math Concepts Level C (Grade 2) do not meet expectations for following the learning progressions outlined in the CCSSM. These materials include a substantial amount of above grade-level content, which does not allow for students to have extensive time exploring grade-level problems. The tendency of the lessons and exercises to move quickly beyond grade-level expectations does not allow these materials to meet the full depth of the Grade 2 standards. In addition, connections between prior, current, and future concepts are not clearly articulated in the student or teacher materials.

i. Materials do not develop according to the grade-by-grade progressions. Prior or future content is not clearly identified.

• The first ten lessons of the program “are designed to acquaint new students with the conventions that continuing students learned in Level B” (teacher guide, page 7). The activities students engage in are an appropriate review of prior knowledge and skills; however, these lessons and exercises do not contain any references to Grade 1 standards.
• As explained in previous indicators (see 1b and 1d), the Connecting Math Concepts Level C program contains a significant amount of above grade-level work, moving students quickly beyond the expectations of Grade 2 standards and unduly interfering with the major work of the grade (2.OA.A-B, 2.NBT, 2.MD.A-B). Multiplication (3.OA) is introduced as early as Lesson 32. Grade 2 standards call for students to add and subtract within 100 and 1000, using strategies based on place value and properties of operations. The Level C materials call for students to add and subtract 3- and in some cases 4-digit numbers with a standard algorithm (3.NBT.A.2, 4.NBT.B.4). Students’ work with understanding and solving word problems in this program also extends beyond grade-level expectations, due to the number of exercises that call for students to tackle word problems beyond 100 (3.OA.D.8, 4.OA.A.3).

ii. Materials do not give students extensive work with grade-level problems.

• The teacher guide states: “CMC Level C instruction meets all requirements of the [CCSSM] for second grade” (page. 2). While it is true that all Grade 2 standards are addressed in the program, not all major standards are explored extensively. Place value work in understanding hundreds, tens, and ones (2.NBT.A.1) only occurs within exercises in 34 lessons; work with comparing 3-digit numbers based on place value (2.NBT.A.4) is only explored within exercises in 13 lessons; estimating lengths using standard units (2.MD.A.3) is only explored within exercises in 6 lessons; and representing addition and subtraction within 100 on a number line (2.MD.B.6) is only explored within exercises in 15 lessons.

iii. Most materials do not explicitly relate grade-level concepts explicitly to prior knowledge from earlier grades

• There is an emphasis in the CMC Level C program on addition and subtraction within 20, which aligns with CCSSM expectations (2.OA.B.2). However, very little time is devoted to exploring properties and mental strategies that are necessary for Grade 2 students to compute efficiently, flexibly, and accurately. As noted in the K-2, Operations and Algebraic Thinking Progressions document: “Fluency in each grade involves a mixture of just knowing some answers, knowing some answers from patterns (e.g., “adding 0 yields the same number”), and knowing some answers from the use of strategies. It is important to… [recognize] that fluency will be a mixture of these kinds of thinking” (page 18).

### 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.
0/2
+
-
Indicator Rating Details

The instructional materials for Connecting Math Concepts Level C (Grade 2) do not meet expectations for fostering coherence within the grade. Both the teacher and student materials lack explicit connections to support student learning, due to the overall structure of the program and the exclusion of language from CCSSM cluster headings.

The materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings.

• The lesson materials do not emphasize references to or language from domain or cluster headings. The Common Core State Standards Chart (TG, pages 12-13) and Level C Correlation (Presentation Book 1, pages 490-499, Presentation Book 2, pages 404-412) list the domains and cluster headings, but do not give any attention to how the cluster headings relate to the lesson content. The Scope and Sequence of the Level C program (teacher guide, pages 10-11) lists the different tracks, organized by skill(s), included in the 130 lessons. This chart lists the program’s “tracks” for this level, including: Number Families, Column Addition/Subtraction, Mental Math, Money, Multiplication, Measurement, and Missing Addend. The Planning Pages for each series of five lessons (Presentation Books) identify only the individual standards that align with each lesson, not the cluster headings.
• The exercises within lessons are presented as Student Learning Objectives on the Planning Pages in the Presentation Books. These objectives do not meaningfully relate the exercises to the standards; rather, the learning objectives simply name what students are doing in each exercise. For example, Student Learning Objectives for Lesson 95 include: Mentally add and subtract and count by a variety of numbers; Use the symbols >, <, or = to compare units of measure; Solve addition and subtraction money problems; Solve addition and subtraction facts with a small number of 6; Count by twos, fours, fives, nines, and tens and identify the missing factor; Tell time to the minute; Figure the area of a rectangle; Complete work independently.
• Lessons are not aligned at the cluster level and do not focus on larger ideas. Lessons are comprised of a series of 7-12 disparate exercises, with each exercise taught separately from the previous one. Problems and activities sometimes connect two or more clusters within a lesson; however, these are randomly placed and do not serve as an important or natural connection. For example, in lesson 83 (Presentation Book 2, pages 79-84) the tasks in this lesson are placed in no certain order: estimation (Column Problems); mental math/counting (subtract tens, count by fours); column addition (carrying to the hundreds); comparison word problems (unit names); tell time (to the five minutes); multiplication (rows of like coins); addition/subtraction facts (small number of four); and money. This lesson moves from Number and Operations in Base Ten (NBT) to Operations and Algebraic Thinking (OA), back to NBT, then to OA, then to Measurement and Data (MD), back to OA and finally to MD. There is no statement made in the lesson script that explains how students are learning one concept to get to an understanding of another concept.

Materials rarely connect two or more clusters in a domain or two or more domains in a grade when appropriate.

### 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.
0/4
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Criterion Rating Details

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
0/4
+
-
Indicator Rating Details

The instructional materials for Connecting Math Concepts Level C (Grade 2) do not meet expectations for spending class time on the major work of the grade. Many of the exercises not aligned to major work focus on skills and understandings that are explored in future grades. In determining the percentage of materials that align to or directly support major work of the grade, any exercises that partially aligned to major work of the grade were included as exercises fully aligned to major work of the grade. Even with these partially-aligned exercises included, the percentage of exercises was approximately 65 percent. Given that the calculated percentage is an overestimate for the percentage of materials aligned to major work of the grade and Grade 2 materials should be closer to 85 percent aligned to major work of the grade, the Level C materials don’t allocate enough instructional time to clusters and standards that make up the major work of Grade 2.

The Level C program consists of 130 lessons, with each lesson made up of a series of 7-12 exercises. The lessons are not organized into chapters or units, and the amount of instructional time for each exercise is not indicated in the program materials. To review materials for this indicator, the team considered two perspectives: (1) the number of lessons aligned to major work by cluster and/or standard (as reported in Presentation Book 1, page 490-499 and Presentation Book 2, page 404-413); and (2) the number of exercises aligned to major work (based on reviewer analysis). The review team found the second perspective to be the most accurate, as it indicates an amount of class time devoted to major work each day. A third perspective was not evaluated because the materials spiral and are not organized into units or chapters.

• The percentage of lessons aligned to 2.OA.A.1 is 72 percent. While this program does include a strong focus on problem solving, a significant portion of the work in Level C involves equations beyond 100.
• The percentage of lessons aligned to 2.OA.B.2 is 99 percent. The program materials have a strong emphasis on addition and subtraction facts within 20, which is the required CCSSM fluency for Grade 2. Teachers using this program should note: much of the work is timed practice, with minimal focus on strategies to develop fact fluency.
• The percentage of lessons aligned to 2.NBT.A is 94 percent. Much of the time devoted to this cluster is around 2.NBT.A.2, which calls for students to count within 1000, and skip-count by fives, tens, and hundreds; a significant amount of class time is spent skip-counting by twos, fours, and 9nines, which is not a part of this standard. Only 34 of 130 lessons focus on 2.NBT.A.1, and only 13 of 130 lessons focus on 2.NBT.A.4; Grade 2 students would benefit from more lessons devoted to understanding place value and comparing multi-digit numbers.
• The percentage of lessons aligned to 2.NBT.B is 99 percent. The Level C program devotes a significant amount of time to adding and subtracting multi-digit numbers, including adding more than two addends. However, most of this work calls for students to use a standard algorithm to add, rather than strategies based on place value and properties of operations as called for in 2.NBT.B.5 and 2.NBT.B.7. Some lessons have equations that extend past 1000, or call for students to add more than two 3-digit numbers. Teachers using this program will need to seek out additional materials to address 2.NBT.B.9, as only 5 of 130 lessons call for students to explain why addition and subtraction strategies work.
• The percentage of lessons aligned to 2.MD.A is 32 percent. This is a significant concern, as students using these materials will not have enough time to develop measurement skills and understandings necessary for future learning.
• The percentage of lessons aligned to 2.MD.B is 20 percent. Teachers using this program should consider supplementing instruction with additional lessons focused on solving word problems involving lengths, and representing whole numbers, as well as sums and differences, on the number line.
• The percentage of lessons aligned to 2.MD.C, which supports Grade 2 work with word problems and skip-counting, is 37 percent. Level C devotes an appropriate amount of time to this cluster.
• The percentage of lessons aligned to 2.MD.D, which supports Grade 2 work with measurement and solving word problems with addition and subtraction, is 9 percent. Teachers using this program will need to find supplementary materials to explore representing and interpreting data.
• An analysis of Lessons 1-65 revealed that 441 of 627 exercises are fully or partially aligned to or support major work, which calculates to 70 percent. This number is just above the minimum expectation for Indicator 1b for Grade 2.
• An analysis of Lessons 65-130 revealed that 311 of 531 exercises are fully or partially aligned to major work, which calculates to 56 percent. This amount of exercises devoted to major work is below the prescribed 65-85 percent.
• An analysis of the program as a whole revealed 752 of 1,158 exercises aligned to or supporting major work, which calculates to 64.9 percent. This is the minimum prescribed amount; this includes a number of exercises that are only partially aligned to Grade 2 CCSSM.
• Many of the exercises not aligned to major work focus on skills and understandings that are explored in future grades, according to the CCSSM: adding and subtracting beyond 100 and with more than two 3-digit numbers using columns (algorithm) (3.NBT.A.2, 4.NBT.B); solving word problems with sums and differences greater than 100 (3.OA.D.8, 4.OA.A.3); working with multiplication concepts (3.OA); telling time to the nearest minute (3.MD.A.1); working with area and perimeter (3.MD.C-D, 4.MD.A.3); measurement conversions and equivalent measurements (4.MD.A); and solving word problems with money amounts written in decimal form (5.NBT.B).

## Rigor & Mathematical Practices

#### Not Rated

+
-
Gateway Two Details
Materials were not reviewed for Gateway Two because materials did not meet or partially meet expectations for Gateway One

### 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.

### 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.
N/A

### 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.
N/A

### 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
N/A

### 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.
N/A

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
N/A

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
N/A

### Indicator 2g

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

### 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.
N/A

### 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.
N/A

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
N/A

## 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 3aa - 3z

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

### 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

### 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
abc123

Report Published Date: 2016/01/25

Report Edition: 2013

Title ISBN Edition Publisher Year
978‑0‑02‑103576‑2
978‑0‑02‑103577‑9
978‑0‑02‑103578‑6
978‑0‑02‑103591‑5
978‑0‑02‑103592‑2
978‑0‑02‑103594‑6
978‑0‑02‑103597‑7
978‑0‑02‑114898‑1

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria 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 review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria 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.

## Math K-8

K-8 K-8

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. 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).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, 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.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, 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.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.