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.

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).

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.

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).

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.

• Natural and mathematically important connections are generally not made in these materials. For example, there are 48 lessons in the Grade 2 program that focus on solving word problems involving money (2.MD.C.8). Working with money provides an opportunity for a natural connection to place value, as 10 pennies (ones) equal 1 dime (ten); 10 dimes (tens) equal 1 dollar (hundred). Instead, much of the work in these lessons focuses on simply counting coins, and/or adding and subtracting money amounts using a vertical method (traditional algorithm). Another mathematically important connection that is missed in these materials is working with addition and subtraction on the number line (2.MD.B.6); this work complements adding and subtracting within 100 and 1000 and understanding the relationship between addition and subtraction (2.NBT.B.5, 7, 9). However, the Grade 2 materials rely heavily on the traditional algorithm for addition and subtraction within 100 and 1000.