Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 1 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.

See Rating Scale
Understanding Gateways

Alignment

|

Does Not Meet Expectations

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Does Not Meet Expectations

+
-
Gateway One Details

The instructional materials for Connecting Math Concepts Level B (Grade 1) do not meet expectations for Gateway 1: Focus on Major Work and Coherence. Students are assessed on multiple topics from future grades on a majority of the twelve mastery tests and both of the cumulative tests. Overall, 61 percent of the program’s lesson exercises are partially or fully aligned to the major work of Grade 1; this is below the prescribed 65-85 percent, which would not allow students learning with this program to fully develop the grade-level skills and understandings required by the CCSSM. The Level B program does not attend to the coherent design of Grade 1 CCSSM. Lessons are made up of a series of isolated exercises, with no discernible pattern or intent to make connections across content with/for students. The few connections that do exist seem coincidental, and are not fully developed. 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 B 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 Connecting Math Concepts Level B (Grade 1) instructional materials do not meet expectations for Gateway 1, and therefore, evidence will not be collected for Gateway 2.

Criterion 1a

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

The instructional materials for Connecting Math Concepts Level B (Grade 1) do not meet expectations for focus on grade-level materials and sufficient time on the major work of the grade. Most of the program’s 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. The Level B materials do not meet expectations for spending class time on the major work of the grade. Overall, the program materials devote approximately 61 percent of daily exercises to major work of the grade, which is below the prescribed 65-85 percent. These materials allocate too much instructional time to skills and understandings from future grades, as well as topics that are not included in the CCSSM.

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 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.

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
+
-
Criterion Rating Details

The instructional materials for Connecting Math Concepts Level B (Grade 1) do not meet expectations for focus on grade-level materials and sufficient time on the major work of the grade. Most of the program’s 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. The Level B materials do not meet expectations for spending class time on the major work of the grade. Overall, the program materials devote approximately 61 percent of daily exercises to major work of the grade, which is below the prescribed 65-85 percent. These materials allocate too much instructional time to skills and understandings from future grades, as well as topics that are not included in the CCSSM.

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 B (Grade 1) do not meet expectations for spending the majority of class time on the major work of the grade. Overall, the program materials don’t allocate enough instructional time to clusters and standards that make up the major work of Grade 1, instead spending too much time on future grade-level work.

The Level B program consists of a series of 125 lessons, with each lesson divided into 8-12 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 276-282, Presentation Book 2, page 296-302, Presentation Book 3, page 388-396); 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 1.OA.A is 28 percent. This presents a significant concern, as representing and solving problems within 20 merits more time and attention than it is given in this program. While there is a strong focus on problem solving, much of this work is beyond 20. Also, no lessons focus on 1.OA.A.2, which calls for solving word problems that call for adding three whole numbers with a sum less than or equal to 20.
  • The percentage of lessons aligned to 1.OA.B is 60 percent. The time devoted to this cluster: “Understand and apply properties of operations and the relationship between addition and subtraction” is appropriate. The materials do attend to unknown addend problems (1.OA.B.4), but often do this beyond the Grade 1 CCSSM expectation of sums and differences within 20.
  • The percentage of lessons aligned to 1.OA.C is 100 percent. This program has a strong emphasis on addition and subtraction facts within 20.
  • The percentage of lessons aligned to 1.OA.D is 98 percent. This program includes an emphasis on number families and understanding that numbers within families have a relationship (1.OA.D.8). There is not enough emphasis on 1.OA.D.7 (17 of 125 lessons); teachers using this program should seek out supplemental instructional materials to engage students in understanding the meaning of the equal sign and determining if addition and subtraction equations are true or false.
  • The percentage of lessons aligned to 1.NBT.A is 100 percent. There is a strong emphasis on counting in this program, although students are often expected to count beyond 120.
  • The percentage of lessons aligned to 1.NBT.B is 70 percent. All of the time devoted to this cluster is around 1.NBT.B.2, which calls for students to understand place value in 2-digit numbers; it should be noted that some of these lessons call for students to focus on place value with 3-digit numbers. There is no attention given to 1.NBT.B.3; teachers using this program will need to seek out supplemental materials to explore comparing 2-digit numbers based on the meaning of the tens and ones digits.
  • The percentage of lessons aligned to 1.NBT.C is 100 percent. These grade level materials devote a significant amount of time to adding and subtracting within and beyond 100, but these exercises emphasize the use of an algorithm to perform these operations, rather than the concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction as outlined in 1.NBT.C.4. There is adequate time devoted to mentally finding 10 more and 10 less than a given number without counting (1.NBT.C.5). There is a minimal focus (11 of 125 lessons) on subtracting multiples of ten from multiples of ten, as called for in 1.NBT.C.6.
  • The percentage of lessons aligned to 1.MD.A is 4 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 1.MD.C.4, which supports 1.OA, is 3 percent. Teachers using this program should consider supplementing instruction with additional lessons focused on representing and interpreting data.
  • An analysis of lessons 1-60 revealed that 439 of 649 exercises are fully or partially aligned to or support major work, which calculates to 68 percent. This number is barely within expectations for Indicator 1b for Grade 1.
  • An analysis of Lessons 61-125 revealed that 338 of 630 exercises are fully or partially aligned to major work, which calculates to 54 percent. This amount of exercises devoted to major work is well below the prescribed 65-85 percent.
  • An analysis of the program as a whole revealed 777 of 1,279 exercises aligned to or supporting major work, which calculates to 61 percent. This is below the prescribed 65-85 percent.
  • Many of the exercises not aligned to major work focus on skills and understandings that are explored in future grades, according to the CCSSM: counting, recognizing and writing numbers beyond 120, identifying and decomposing 3-digit numbers, expanded notation with 3-digit numbers, adding and subtracting beyond 100 and with 3-digit numbers using columns (algorithm), comparing 3-digit numbers (2.NBT); solving word problems with sums and differences greater than 20 (2.OA); identifying and counting money, measuring with a ruler, finding the difference in two given measurements, telling time beyond the hour/half-hour (2.MD), and solving word problems with money amounts written in decimal form (5.NBT.B).

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 B (Grade 1) 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 B 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 B 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 B (Grade 1) 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.
  • As Grade 1 students organize, represent, and interpret data (1.MD.C.4), they practice the major work of solving word problems using addition and subtraction (1.OA) as they answer “how many more/less?” and/or “how many total?” (adding three one digit numbers). The four exercises devoted to this content include this connection. However, the work with data exceeds the expectation of the Grade 1 standards, as more than three data categories are used in three of the four lessons.
  • Telling and writing time (1.MD.B.3) allows for an opportunity for Grade 1 students to practice the major work of reading and writing numbers (1.NBT.A). There are 32 exercises in the Level B program that focus on telling and writing time. However, much of this work exceeds the expectations of Grade 1 by including analog and digital times that are not to the hour and half-hour.

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
+
-
Indicator Rating Details

The instructional materials for Connecting Math Concepts Level B (Grade 1) 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; 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 1 standards to prepare students for learning in future grades.

  • This grade level program contains 125 lessons, 12 mastery tests, and 2 cumulative tests, spanning approximately 140 days, which is a sufficient number for a standard school year. The teacher guide (page 5) 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 5 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 16 for students who have completed Level A or passed the Level B placement test. For students starting instruction at lesson 16, the program will span approximately 125 days, plus any repeated lessons. This number is too low for a typical school year.
  • The Grade 1 program is designed to be taught daily; a 50-minute instructional period is suggested each day, with 40 minutes of structured work and 10 minutes of independent work (teacher guide, page 5). The material allocated for instruction each day is reasonable for this suggested amount of time.
  • The first half of the instructional program (lessons 1-60) consists of a total of 649 exercises; 208 of these exercises (32 percent) focus on objectives that do not align with Grade 1 CCSSM. The second half of the instructional program (lessons 61-125) consists of a total of 630 exercises; 202 of these exercises (32 percent) focus on objectives that do not align with Grade 1 CCSSM. The majority of unaligned exercises focus on mastery of above level standards from Grades 2-3 (see report for Indicator 1b). This focus on above grade level objectives takes time and focus away from foundational grade level understandings. These lessons would require significant modifications and/or omissions that would affect the integrity of the grade level program. Teachers using these materials would need to make significant modifications and/or omissions to the content of lessons in order to prepare students for future mathematics learning.

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
+
-
Indicator Rating Details

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).

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 B (Grade 1) do not meet expectations for fostering coherence within the grade.

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

  • 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 lesson materials do not emphasize references to or language from domain or cluster headings. The Common Core State Standards Chart (teacher guide, page 10-11) and elaborations (teacher guide, page 94-97) 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 B program (teacher guide, page 8-9) lists the different tracks, organized by skills, included in the 125 lessons. This chart lists skills such as: counting: forward and backward; number family strategy; column addition with carrying; comparison word problems, classifying statements; and coins and bills. 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 66 include: "Say two addition and two subtraction facts for number families; find missing numbers in number families; Count forward or backward from a given number; Say how many of each coin equals a dollar; Identify 2-dimensional shapes; Solve subtraction facts; Solve 2-digit and 3-digit addition and subtraction problems; Use a centimeter ruler and count a part in a whole and count on for the whole to solve equations; Solve addition and subtraction facts; Write the symbols for word problems in columns and solve; and Complete work independently."
  • Lessons are not aligned at the cluster level and do not focus on larger ideas. “Each lesson is composed of exercises from 6 to 9 tracks that present various (sometimes unrelated) skills” (teacher guide, page 32). Lessons are comprised of a series of 8-12 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 28 (presentation book 1, page 162-167) the topics covered throughout this lesson are placed in no certain order: mixed counting; number families (commutative property); digits (hundreds, tens, ones); facts (1 plus, plus 1); place value addition (3-digit numbers); facts (plus/minus mix); number families; word problems (writing & solving); and column problems. This lesson spans over the domains of: pperations and algebraic thinking, and numbers and operations in base ten without any listed reason by the publisher for doing so. 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.

  • The program includes exercises that loosely connect two or more clusters, although these do not appear consistently throughout the year. For example, lesson 41 exercise 8 calls for students to use an understanding of place value (1.NBT.A) to add two 2-digit numbers (1.NBT.C); however, teachers using this program should note that this series transitions to the same type of work with 3-digit numbers for a greater number of lessons than the work with 2-digit numbers. A second example occurs in the extensive work with number families, where students use addition and subtraction (1.OA.C) to determine how three numbers are related, and to find an unknown number in a given family (1.OA.B). Teachers using this program should take time when planning instruction to create opportunities to make explicit connections like these on a regular basis.

Gateway Two

Rigor & Mathematical Practices

Not Rated

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.
0/8

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.
0/2

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.
0/2

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
0/2

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.
0/2

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
0/10

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
0/2

Indicator 2f

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

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

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.
0/2

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
0/2

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

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.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

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.
0/2

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.
0/2

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.
0/2

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).
0/0

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.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

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.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

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).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

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.
0/0

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.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

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.
0/0

Indicator 3ad

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.).
0/0

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.
0/0

Additional Publication Details

Report Published Date: Mon Jan 25 00:00:00 UTC 2016

Report Edition: 2013

Title ISBN Edition Publisher Year
null 978-0-02-103574-8 null null null
null 978-0-02-103575-5 null null null
null 978-0-02-103588-5 null null null
null 978-0-02-103589-2 null null null
null 978-0-02-103590-8 null null null
null 978-0-02-103593-9 null null null
null 978-0-02-103596-0 null null null

About Publishers Responses

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

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

Educator-Led Review Teams

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

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

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

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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