The instructional materials for Connecting Math Concepts Level B (Grade 1) do not meet expectations for assessing material at grade level. Most of the program’s 12 mastery tests and two cumulative tests include items beyond the scope of expectations for Grade 1, including understanding place value with 3-digit numbers, adding and subtracting 3-digit numbers, and identifying and counting money. 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 B (Grade 1) 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:

• All items in parts 1-4, and 7 assess Grade 1 standards, focusing on writing numbers within 120 and completing +1/+10 equations.
• Parts 5-6 appropriately review Kindergarten counting skills.
• Part 8 calls for students to count backward which is not specifically required by the CCSSM .

Mastery Test 2:

• All items in parts 1-7 assess Grade 1 standards, calling for students to write and understand 2-digit numbers, complete +0/+1/+2 and -1 equations.
• Part 8 appropriately reviews counting by tens (K.CC.A.1).
• Part 9 calls for students to count backward which is not specifically required by the CCSSM.
• Part 10 calls for students to read and decompose 3-digit numbers (2.NBT.A.3).

Mastery Test 3:

• All items in parts 1-8 assess Grade 1 standards, calling for students to write addition and subtraction facts and “turnaround equations,” write equations to solve word problems within 20, complete -0/+0, +1/1+, +10 equations, understand tens and ones in a 2-digit number, and work column equations with no regrouping.
• Part 9 is not fully aligned to CCSSM as items call for students to count by 100s and count backward, which are not specifically required by the CCSSM.
• Part 10 is partially aligned Grade 1 standards, as it calls for students to identify ones and tens in 2-digit numbers, but then extends to identifying ones, tens, and hundreds in 3-digit numbers (2.NBT.A.1).

Mastery Test 4:

• Parts 2 and 5 assess Grade 1 standards, calling for students to find the missing number and/or write equations in number (fact) families using addition and subtraction, and complete +1/-1, 1+ equations.
• Parts 1, 3 and 4 call for students to work with place value and operations with 3-digit numbers (2.NBT.A-B).

Mastery Test 5:

• Parts 3, 7, 8 and 9 assess Grade 1 standards, calling for students to find the missing number and/or write equations in number (fact) families using addition and subtraction, complete +2/-2, 2+ equations, and complete equations with three addends.
• Part 1 is partially aligned to Grade 1 standards, as students are asked to listen to and write 1-, 2-, and 3-digit numbers.
• Parts 2, 4, 5 and 6 assess content beyond Grade 1, calling for students to write and solve equations for word problems beyond 20 (2.OA.A.1 and beyond), write equations with 2-/3-digit numbers in columns (2.NBT.A-B), count coins (2.MD.C.8), and write expanded form for 3-digit numbers (2.NBT.A.3).

Mastery Test 6:

• Parts 2, 3 and 5 assess Grade 1 standards, calling for students to count on to solve equations with 1- and 2-digit numbers, and complete addition and subtraction equations within 10 and 20.
• Parts 1, 4, 6 and 7 assess content beyond Grade 1, calling for students to write and solve equations for word problems beyond 20 (2.OA.A.1 and beyond), count coins (2.MD.C.8), write expanded form for 3-digit numbers vertically (2.NBT.A.3), and add and subtract 3-digit numbers (2.NBT.B.7, 3.NBT.A.2).

Cumulative Test 1:

• Parts 1-3, 7-8, 10-13 and 15-17 assess Grade 1 standards, calling for students to write and decompose 2-digit numbers, complete +0/+1/+2, +10 equations, write “turnaround equations,” write the four related facts in a number (fact) family and find missing numbers in families using addition or subtraction, count on to complete 2-digit + 1-digit equations, and complete equations within 20.
• Parts 4, 5 and 9 are partially aligned to Grade 1, calling for students to write numbers, write and solve equations for given word problems, and find sums and differences. Some items in these parts extend beyond the limitations stated in Grade 1 standards (2.NBT.A.3, 2.NBT.B.7, 3.NBT.A.2).
• Parts 6 and 14 assess content beyond Grade 1, calling for students to write expanded form for 3-digit numbers horizontally and vertically (2.NBT.A.3), and count coins (2.MD.C.8).

Mastery Test 7:

• Parts 1 and 2 assess Grade 1 standards, calling for students to find missing numbers in families using addition or subtraction, and use a visual model to support addition.
• Part 3 calls for students to count paper money.
• Parts 4, 5 and 6 assess content beyond Grade 1, calling for students to add three 2-/3-digit numbers and subtract 2- and 3-digit numbers (2.NBT.B), and count coins (2.MD.C.8).

Mastery Test 8:

• Parts 2, 3 and 5 assess Grade 1 standards, calling for students to use a visual model to complete equations, and add and subtract within 20.
• Part 6 is partially aligned to Grade 1, calling for students to add with 2-digit numbers. One item extends beyond the limitations stated in Grade 1 standards, as it includes three addends (2.NBT.B.6).
• Part 1 calls for students to write dictated dollar/cents amounts using appropriate symbols, which is not an explicit CCSSM expectation.
• Parts 4 and 7 assess content beyond Grade 1, calling for students to count coins (2.MD.C.8), and add and subtract money amounts written in decimal form (5.NBT.B.7).

Mastery Test 9:

• Parts 4, 6 and 7 assess Grade 1 standards, calling for students to compare numbers, recognize and identify shapes, and complete equations within 20.
• 2 of the 5 items in Part 5 assess a Grade 1 standard, calling for students to add two 2-digit numbers within 100; the other items include 3-digit numbers, extend beyond 100, and include three addends (2.NBT.B).
• Parts 1 and 3 assess content beyond Grade 1, calling for students to write and solve word problems beyond 20 (2.OA.A), and write equations to find the difference in 2 given measurements (2.MD).
• Part 2 calls for students to write dictated dollar/cents amounts using appropriate symbols.

Mastery Test 10:

• Parts 3 and 5 assess Grade 1 standards, calling for students to identify faces on 3-dimensional objects, and complete equations within 20.
• Part 1 calls for students to write dictated times with correct notation, without looking at a clock; only 4 of the 8 items are within the scope of 1.MD.B.3.
• Parts 2, 4 and 6 assess content beyond Grade 1, calling for students to find missing numbers in families beyond 20 (2.NBT.B), add and count money (2.MD.C.8), and do column addition with 3-digit numbers and/or three addends beyond 20 (2.NBT.B, 3.NBT.A.2).

Mastery Test 11:

• Parts 1, 5 and 7 assess Grade 1 standards, calling for students to identify faces on 3-dimensional objects, and complete addition and subtraction equations within 20.
• Parts 2, 3 and 6 assess content beyond Grade 1, calling for students to write and solve equations with word problems beyond 100 (beyond 2.OA.A.1), tell time beyond the hour/half-hour (2.MD), and write expanded form with 3-digit numbers (2.NBT.A.3).
• Part 4 calls for students to write number families from given equations with 2- and 3-digit numbers, which is loosely connected to 2.NBT.B.9.

Mastery Test 12:

• Parts 5, 7 and 10 assess Grade 1 standards, calling for students to recognize faces on 3-dimensional objects, and complete addition and subtraction equations within 20.
• Parts 1, 8 and 9 are partially aligned to Grade 1 standards; some items extend beyond Grade 1 expectations (3.NF.A, 2.MD).
• Parts 2, 3, 4 and 6 assess content beyond Grade 1, calling for students to find missing numbers in families beyond 20 (2.NBT.B), write even and odd numbers (2.OA.C.3), and complete addition and subtraction equations beyond 20 with unknowns in all positions (2.NBT.B).

Cumulative Test 2:

• Parts 2, 3, 5, 12, 17, 24, 25, 27 and 28 assess Grade 1 standards, calling for students to complete number (fact) families within 20, write “turnaround equations,” complete addition and subtraction equations within 20, record data, and recognize and identify shapes.
• Parts 1, 4, 7, 15 and 23 are partially aligned to Grade 1 standards; some items extend beyond Grade 1 expectations (2.NBT.A.3, 2.NBT.B, 3.NF.A, 2.MD).
• Parts 6, 9, 10, 11, 13, 14, 16, 18, 19, 20, 21 and 26 assess content beyond Grade 1, calling for students to add and subtract 2- and 3-digit numbers beyond 100 (2.NBT.B.7), write and solve measurement word problems beyond 20 (2.MD.B), write even and odd numbers (2.OA.C.3), write fractions (3.NF.A), write column equations to find the difference between given measurements (2.MD.B), count coins and paper money (2.MD.C.8), write expanded form of 3-digit numbers (2.NBT.A.3), compare two expressions beyond the standards set out in 1.NBT.B.3, and complete equations beyond 20 with unknowns in all positions (2.NBT.B).
• Part 8 calls for students to write dictated dollar/cents amounts using appropriate symbols, which is not an explicit CCSSM expectation.

The instructional materials for Connecting Math Concepts Level B (Grade 1) 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 1 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 15 lessons of the program “are designed to review facts and other information presented in Level A” (Teacher’s Guide, page 5). 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 Kindergarten standards.
• As explained in previous indicators (see 1b and 1d), the Connecting Math Concepts Level B program contains a significant amount of above grade-level work, moving students quickly beyond the expectations of Grade 1 standards and unduly interfering with the major work of the grade (1.OA, 1.NBT, and 1.MD.A). For example, multiple exercises focus on understanding 3-digit numbers and their expanded form, as well as counting by 100s (2.NBT.A). Grade 1 standards call for students to add and subtract within 20, and then extend their understanding of addition to numbers within 100. The Level B materials call for students to add and subtract 3-digit numbers with a standard algorithm (2.NBT.B, 3.NBT.A.2). Student 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 understand and solve word problems beyond 20 (2.OA.A).

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

• The teacher guide states: “The CMC Level B program addresses all standards specified in the [CCSSM] for first grade” (page 5). The team noted three Grade 1 standards that are part of the major work of the grade that are not addressed in any of the 125 lessons. Students engaging with this program would not have extensive work with solving word problems with three addends (1.OA.A.2), comparing 2-digit numbers based on place value (1.NBT.B.3), and measuring objects by iterating units (1.MD.A.2). The teacher guide does note that teachers need to use the Student Practice Software to cover these standards (page 10-11), but there are no instructional notes for teachers in the scripted lessons explaining how to incorporate this technology into daily instruction. In addition, the planning pages for each series of five lessons lists the Student Practice Software activities as “Additional Practice.”

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 B program on addition and subtraction within 20 and practicing fact fluency within 10 which aligns with CCSSM expectations (1.OA.C.6). However, very little time is devoted to exploring properties and mental strategies that are necessary for Grade 1 students to compute quickly and accurately. As noted in the K-2, OA 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).