The instructional materials reviewed for Connecting Math Concepts Level D (Grade 3) do not meet the expectations for focus within assessment. For this indicator, the review team examined all mastery tests and both cumulative tests. Overall, the instructional material assesses content from future grades within the majority of the summative assessments. The assessments would not be viable if the above grade level material was omitted, as there are too many assessment questions within the series that are above grade level.

Review Team note: The Level D (Grade 3) teacher guide identifies the cumulative tests as “optional” in two places (pages 3-4); 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 align or partially align to grade level standards.

Mastery Test 2: All items align or partially align to grade level standards.

Mastery Test 3:

• Items in part 5 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.

Mastery Test 4: All items align or partially align to grade level standards.

Mastery Test 5:

• Items in part 3 assess writing numbers in standard form given the word form which aligns to standards within 4.NBT.A.

Mastery Test 6:

• Items in part 5 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
• Items in part 6 assess adding and subtracting fractions with like denominators which aligns to standards within 4.NF.B.

Mastery Test 7:

• Items in Part 6 assess adding and subtracting with numbers greater than 1,000 which aligns to standards within 4.NBT.B.
• Items in part 9 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 8 assess comparing fractions which aligns to standards within 4.NF.A.

Mastery Test 8:

• Items in part 3 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 7 assess comparing fractions which aligns to standards within 4.NF.A.

Mastery Test 9:

• Items in part 5 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
• Items in part 6 assess dividing 3-digit numbers which aligns to standards within 5.NBT.B.

Mastery Test 10:

• Items in part 7 assess dividing 3-digit numbers which aligns to standards within 5.NBT.B.

Mastery Test 11:

• Items in part 4 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
• Items in part 8 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 6 assess finding volume which aligns to standards within 5.MD.C.

Mastery Test 12:

• Items in part 8 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 5 assess adding and subtracting fractions with like denominators which aligns to standards within 4.NF.B.
• Items in part 5 assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.

Mastery Test 13:

• Items in part 4 assess adding and subtracting fractions with like denominators which aligns to standards within 4.NF.B.

Cumulative Test 1:

• Items in part 7 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
• Items in parts 12b and 20 assess adding and subtracting with numbers greater than 1,000 which aligns to standards within 4.NBT.B.
• Items in part 3 assess writing numbers in standard form given the word form aligns to standards within 4.NBT.A.
• Items in part 10 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 13 assess adding and subtracting fractions with like denominators which aligns to standards within 4.NF.B.

Cumulative Test 2:

• Items in parts 11 and 22 assess adding and subtracting decimals which aligns to standards within 5.NBT.B.
• Items in part 4a and 4d assess adding and subtracting with numbers greater than 1,000 which aligns to standards within 4.NBT.B.
• Items in part 2 assess writing numbers in standard form given the word form aligns to standards within 4.NBT.A.
• Items in part 28 assess multiplying 1-digit numbers by multi-digit numbers other than tens is a topic that aligns to standards within 4.NBT.B.
• Items in part 30 assess adding and subtracting fractions with like denominators which aligns to standards within 4.NF.B.
• Items in part 30 assess adding and subtracting fractions with unlike denominators which aligns to standards within 5.NF.A.
• Items in part 8 assess comparing fractions which aligns to standards within 4.NF.A.
• Items in part 15 assess dividing 3-digit numbers which aligns to standards within 5.NBT.B.
• Items in part 23 assess finding volume which aligns to standards within 5.MD.C.

The instructional materials reviewed for Connecting Math Concepts Level D (Grade 3) do not meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 3.

To determine this, two perspectives were evaluated: 1) the number of lessons aligned to major work by cluster and/or standard. 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 percent of lessons aligned to major work clusters according to “Level D Correlation to Grade 3 Common Core State Standards for Mathematics” document in Presentation Book 1, pages 528-537, and Presentation Book 2, pages 449-460:

• The percentage of lessons aligned to 3.OA.A is 92 percent.
• The percentage of lessons aligned to 3.OA.B is 48 percent.
• The percentage of lessons aligned to 3.OA.C is 77 percent.
• The percentage of lessons aligned to 3.OA.D is 57 percent.
• The percentage of lessons aligned to 3.NF.A is 74 percent.
• The percentage of lessons aligned to 3.MD.A is 28 percent.
• The percentage of lessons aligned to 3.MD.C is 35 percent.

In book one, there are 212 out of 581 exercises, about 36 percent, that focus on major work. In book two, there are 360 out of 502 exercises, about 72 percent, that focus on major work. This is 572 out of 1083 total exercises, or about 53 percent.

• Book one has much less work focusing on the major work of grade. This leaves a majority of the major work toward the end of the year, which may lead to not enough time to develop mastery of that concept.
• There are several missed opportunities during the skip counting exercises. If the skip counting exercises were linked to multiplication, they could be counted as major work.

The instructional materials reviewed for Connecting Math Concepts Level D (Grade 3) do not meet the expectations for having an amount of content designated for one grade level as viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is appropriate for a 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 to prepare students for learning in future grades.

• The curriculum supplies 130 lessons, 13 mastery tests, and 2 cumulative tests. Although remedial worksheets are provided to support students struggling on concepts after each mastery test, these do not comprise the same amount of material as is contained in each lesson. These materials, if each mastery test is conducted in one lesson period (45-60 minutes) would be completed over 145 instructional days.
• A substantial number of unaligned exercises focus on skills and understandings not included in CCSSM and/or mastery of above level standards from Grade 4 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.
• Measuring area by counting unit squares, 3.MD.6, which is part of a major cluster, appears in only four exercises (lessons 28.8, 34.5 92.8 and 95.9).
• Partitioning shapes into parts with equal areas, 3.G.A.2, appears only in one exercise (lesson 121.3).
• Understanding division as an unknown-factor problem, 3.OA.B.6, appears only in three exercises (lessons 124.8, 125.8, 126.8).

The instructional materials reviewed for Connecting Math Concepts Level D (Grade 3) do not meet the expectations for materials being consistent with the progressions in the standards. Overall, the instructional materials do not identify or connect prior or future grade-level work to Grade 3 work, provide students with extensive work with Grade 3 work, or relate Grade 3 level concepts explicitly to prior knowledge from earlier grades.

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

• Prior grade level topics taught and not identified include 2.OA.B addition and subtraction number families (lessons 1-20), addition and subtraction facts (lessons 2-35); 2.MD.C telling time (beginning lesson 53); and 2.MD.D picture and bar graphs (beginning lesson 61).
• Future grade level topics taught and not identified include 4.NF.B addition and subtraction of fractions with like denominators (beginning lesson 54); 5.NF.A addition and subtraction of fractions with unlike denominators (beginning lesson 54); 5.NBT.B three-digit division (lessons 65-117); 5.MC.C calculating volume (lessons 101-112); 4.NBT.B multiplying multi-digit numbers (lessons 65-117); 5.NBT.B adding and subtracting decimals (lessons 17-104); 4.MD.A converting measurements (lessons 19-118); and 4.NF.A comparing fractions with unlike denominators (beginning lesson 62).

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

• The addition/subtraction work that builds from lessons 1-39 as independent work and continues through lesson 130 begins with numbers in the second grade range and focuses on the standard algorithm. The depth of the standard is not met by including place value, properties of operations and the relationship between addition and subtraction.
• Multiplication and division (3.OA.A) is taught with emphasis on learning fact families and little time is spent on conceptual understanding. Students are not asked to model/draw equations or problems.
• Students are not asked to create line plots (3.MD.B.4).
• Standard 3.OA.B.6 is addressed in only three exercises.
• Standard 3.OA.D.8 is addressed in only 17 exercises.
• Standard 3.MD.B.4 is addressed in only six exercises.
• Standard 3.MD.C.6 is addressed in only four exercises.
• Standard 3.G.A.2 is addressed in only one exercise and two activities in practice software.
• Students who fail parts of the mastery test can be assigned Remedies aligned to standards below the current grade level to complete during independent practice, so these students would not be working with grade-level problems. Opportunities for enrichment of grade-level work do not exist in the program.

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

• Prior knowledge to other grade levels is not referred to in the curriculum.
• Coherence in connecting prior work in creating 10s/100s, place value with addition/subtraction or other place value work is not made (3.NBT.A). Students work primarily with number lines to identify nearest 10s (Teacher Edition, pages 123-124).
• The standard 3.MD.B.3 addressed in 61 exercises over 51 lessons does not make connections to multiplication/division when using scaled bar graphs.
• When exercises do occur over subsequent lessons, little of the teacher script connects back to a previous day’s learning/understanding.
• Opportunities to extend previous understandings are not made because lessons provide isolated practice of the standards.

The instructional materials reviewed for Connecting Math Concepts Level D (Grade 3) do not meet the expectations for fostering coherence through connections at a single grade level.

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

• Lessons are composed of exercises that are unrelated. In cases where there could be connections made, they are still treated as separate exercises.
• Lessons and exercises are not marked with CCSSM.
• Pages 12-13 provides a chart with the lessons and the CCSSM for Level D.
• Pages 170-180 of the Teacher Guide shows how the CCSSM are presented in sample lessons.
• A comprehensive listing of the CCSSM and the correlated exercises are found in the back of Presentation Book 1 and Book 2.
• CCSSM aligned exercises do not meet the true intent of the standard:
  • 3.OA.D Addition/Subtraction Word Problems (lessons 6-64) presents number families for sentences that compare two letters.
  • 3.OA.D Addition/Subtraction Number-Family Tables (lessons 30-50) presents column addition and subtraction using number-family tables.
  • 3.OA.A Division Problems (beginning lesson 76) teach using the traditional algorithm instead of conceptual models.
  • 3.MD.B.4 Students are never asked to both make measurements with a ruler and create a line plot using this data

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

• Partitioning shapes (3.G.2) and its relationship to visual fraction models (3.NF.A) is not presented in any of the 130 instructional lessons but do appear in the Level D Practice Software Block 5 Activities 2 and 5, which is not part of the core instructional materials.
• Scaled picture and bar graphs (3.MD.B) is not connected with the context of solving multiplication and division problems (3.OA.C) in lessons 61-130.