The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) 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 F (Grade 5) 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: All items align or partially align to grade-level standards.

Mastery Test 4:

• Items in part 1 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
• Items in part 7 assess writing the reciprocal of a fraction which aligns to standards within 6.NS.A.
• Items in part 12 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Mastery Test 5:

• Items in part 4 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.
• Items in part 8 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Mastery Test 6:

• Items in part 1 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
• Items in part 7 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.

Mastery Test 7:

• Items in part 6 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.

Mastery Test 8:

• Items in part 8 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
• Items in part 9 assess finding the area of circles which aligns to standards within 7.G.B.
• Items in part 12 assess finding the volume of a cylinder which aligns to standards within 8.G.C.

Mastery Test 9:

• Items in part 5 assess finding averages which aligns to standards within 6.SP.B.
• Items in part 1 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.
• Items in part 2 assess writing equations with variables which aligns to standards within 6.EE.C.
• Items in part 3 assess solving with variables which aligns to standards within 6.EE.A.

Mastery Test 10:

• Items in parts 4 and 11 assess finding averages which aligns to standards within 6.SP.B.
• Items in part 3 assess solving problems involving probability which aligns to standards within 7.SP.C.

Mastery Test 11:

• Items in part 10 assess finding averages which aligns to standards within 6.SP.B.
• Items in part 6 assess solving problems involving probability which aligns to standards within 7.SP.C.

Mastery Test 12:

• Items in part 4b assess finding averages which aligns to standards within 6.SP.B.

• Items in part 7 assess solving problems involving probability which aligns to standards within 7.SP.C.
• Items in part 1 assess writing equations with variables which aligns to standards within 6.EE.C.

Mastery Test 13: All items align or partially align to grade level standards.

Cumulative Test 1:

• Items in part 5 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
• Items in part 1 assess finding the area of triangles and parallelograms which aligns to standards within 6.G.A.
• Items in part 7 assess determining the value of a variable in an equation which aligns to standards within 6.EE.B.

Cumulative Test 2:

• Items in parts 12 and 17b assess finding averages which aligns to standards within 6.SP.B.
• Items in part 10 assess writing ratio fractions and using ratios to solve problems which aligns to standards within 6.RP.A.
• Items in part 4 assess finding the area of circles which aligns to standards within 7.G.B
• Items in part 24 assess solving problems involving probability which aligns to standards within 7.SP.C.
• Items in part 9 assess finding the volume of a cylinder which aligns to standards within 8.G.C.
• Items in parts 5 and 10 assess finding equivalent ratio fractions and graphing their ordered pairs which aligns to standards within 6.RP.A.
• Items in part 21 assess solving with variables which aligns to standards within 6.EE.A.

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) 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 5.

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 F Correlation to Grade 5 Common Core State Standards for Mathematics” document in Presentation Book 1, pages 437-445, and Presentation Book 2, pages 469-479:

• The percentage of lessons aligned to 5.NBT.A is 64 percent.
• The percentage of lessons aligned to 5.NBT.B is 100 percent.
• The percentage of lessons aligned to 5.NF.A is 58 percent.
• The percentage of lessons aligned to 5.NF.B is 94 percent.
• The percentage of lessons aligned to 5.MD.C is 19 percent.

In book one, there are 232 out of 451 exercises, about 51 percent, that focus on major work. In book two, there are 302 out of 440 exercises, or about 69 percent, that focus on major work. This is 534 out of 891 total exercises, about 60 percent..

• Book one has much less work focusing on major work of grade. This leaves the majority of major work toward the end of year, which may lead to not enough time to develop mastery.

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) 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 120 lessons, 12 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 134 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 6 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 volume, 5.MD.4, which is part of a major cluster, appears in only two exercises (lessons 68.3, 69.6).
• Understanding the concept of volume measurement, 5.MD.3, which is part of a major cluster, appears only in two exercises (lessons 68.3, 69.6).
• Generating two numerical patterns using two given rules, 5.OA.3, appears in only three exercises (lessons 118.2, 119.2, 120.1).

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) 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 5 level work, provide students with extensive work with grade-level problems, or relate Grade 5 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.

• Only 60 percent of the exercises address major work of Grade 5.
• Prior grade-level topics taught and not identified include: 3.NBT.A, place value and rounding (lessons 1-80), 2.NBT.B, addition/subtraction number families (Lessons 1-116), 3.NBT.A, mental math (Lessons 11-106), 4.MD.B, line plots (lessons 103-117), 4.MD.A, area and perimeter (lessons 40-112), 4.MD.C, angles (lessons 54-112), 3.OA.C, multiply and divide within 100 (lesson 1, exercise 4), 2.NBT.A, expanded notation (lessons 1-6), 4.NF.B.C, add and subtract fractions with like denominators (lessons 4-6) and 3.NF.A, recognizing and generating simple equivalent fractions (lesson 11).
• Future grade level topics taught and not identified include: 6.RP.A, percent values (lessons 35-106), 6.RP.A, ratio and proportion (lessons 19-75), 6.EE.A, expressions with variables (begins lesson 35), 6.SP.A, probability (lessons 95-116), 6.EE.C, graphing ratios (lesson 69-120), 6.SP.B, finding averages (lessons 82-117), 6.G.A, finding surface area (lessons 106-112), 7.G.B, finding area of circles (lessons 72- 75) and 8.G.C, solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (lessons 76-80).

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

• Lessons 112-120 are not taught or practiced to the full depth of the standard (MD.B.2).
• Lessons 68 and 69 contain one exercise each that addresses the concept of relating volume to multiplication and addition (MD.C.3 and MD.C.4).
• Lessons 61-120 provide limited work with writing and interpreting numerical expressions (5.OA.1). Students learn "the parentheses are a times sign." Students are not taught how and why parentheses are used and are not introduced to brackets or braces.
• Lessons 90-116 provide limited work with unit conversion (MD.A.1). Students are not given the chance to apply unit conversion to the metric system, which is not only a missed connection, it holds students back from the progression expected to work with decimals and scientific notation in later grades.
• Lessons 62, 102, 104 and 106 provide limited work with line plots (MD.B.2). Students do not make their own measurements or work independently to create a line plot.
• The major work of 5.MD.3 is only addressed in two exercises, or about 20 minutes in the entire school year. This is not enough time for students to understand concepts of volume measurement.
• The major work of 5.MD.4 is only addressed in two exercises or about 20 minutes in the entire school year. This is not enough time for students to master measuring volumes.
• The work of 5.OA.3 is only addressed in three exercises, or about 30 minutes in the entire school year. This is not enough time for students to master generating two numerical patterns using two given rules.
• 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.

• "Coherence in connecting prior work in multiplication to multiplication of fractions or fractions and whole numbers," (5.NF.B ) is not made. For example, in lesson 9, exercise 5, the lesson focuses students on ideas like "the bottom numbers do not have to be the same" and "when you multiply fractions, you don't copy any numbers." No connections are made to previous reasoning or learning with multiplication. Students are not asked to consider or reason about the size of the product relative to the factors.
• When exercises do occur over subsequent lessons, little of the teacher script connects back to a previous day’s learning or understanding.
• Opportunities to extend previous understanding are not made because lessons provide isolated practice of the standards.
• Many of the lessons provide isolated exercises that do not explicitly connect to prior knowledge.

The instructional materials reviewed for Connecting Math Concepts Level F (Grade 5) 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.
• Page 12-13 provides a chart with the Lessons and the CCSSM for Level F.
• Teacher Guide, pages 145-149, shows how the CCSSM are presented in sample lessons.
• A comprehensive listing of the CCSSM and the correlating exercises are found in the backs of Presentation Book 1 and Presentation Book 2.
• CCSSM aligned exercises do not meet the true intent of the standard:
  • 5.OA.A - Students are seldom asked to solve numerical expressions and never asked to write them.
  • 5.MD.C - Students use the formula to calculate volume without having to demonstrate conceptual understanding by counting unit cubes

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

• Student work with multiplying fractions (5.NF.B) does not extend their understanding of the operation of multiplication (5.NBT.B.5).
• Student work with converting units within the metric system is not connected to their work with place value (5.NBT.A.1)