The instructional materials reviewed for Grade 5 do not meet expectations for assessment. For this indicator, the review team examined all components of the cumulative tests, which included the power-up tests, the cumulative tests, 10 extension tests, and the performance tasks. The team was unable to review the benchmark tests as they were not included in the materials. There are two reasons why these materials do not meet the expectations for this indicator. First, approximately half of the questions on the cumulative tests align to standards that are below grade 5, and second, of the remaining questions, there are several instances of questions aligning to standards above grade 5. With the significant number of questions that align to either above or below grade-level standards, omission or modification of the questions would result in a significant impact on the underlying structure of the grade 5 materials. The following list of cumulative tests outlines the questions that are aligned to above grade-level standards and the standards or clusters to which the questions are aligned.

• Cumulative Test 3, after lesson 20, question 3 assesses negative numbers on a number line, which aligns to 6.NS.C.6, “Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.”
• Cumulative Test 4, after lesson 25, question 6 assesses negative numbers, which aligns to 6.NS.C, “Apply and extend previous understandings of numbers to the system of rational numbers.”
• Cumulative Test 6, after lesson 35, question 8 assesses negative numbers, which aligns to 6.NS.C, “Apply and extend previous understandings of numbers to the system of rational numbers.”
• Cumulative Test 7, after lesson 40, question 10 assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”
• Cumulative Test 9, after lesson 50, question 8 assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”
• Cumulative Test 10, after lesson 55, question 4 assesses mean, which aligns to 6.SP.B, “Summarize and describe distributions”, and question 5 assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent”.
• Cumulative Test 11, after lesson 60, question 1 assesses mean, which aligns to 6.SP.B, “Summarize and describe distributions.”
• Cumulative Test 12, after lesson 65, questions 1 and 9 assess probability, which aligns to 7.SP.C, “Investigate chance processes and develop, use, and evaluate probability models,” and question 5 assesses mean, which aligns to 6.SP.B, “Summarize and describe distributions.”
• Cumulative Test 13, after lesson 70, question 8 assesses probability, which aligns to 7.SP.C, “Investigate chance processes and develop, use, and evaluate probability models,” and question 1 assesses mean, which aligns to 6.SP.B, “Summarize and describe distributions.”
• Cumulative Test 15, after lesson 80, question 6c assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”
• Cumulative Test 16, after lesson 85, question 2 assesses integer exponents, which aligns to 6.EE.A.1, “Write and evaluate numerical expressions involving whole-number exponents.”
• Cumulative Test 18, after lesson 95, question 9 assesses median, which aligns to 6.SP.B, “Summarize and describe distributions.”
• Cumulative Test 19, after lesson 100, question 5c assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”
• Cumulative Test 20, after lesson 105, question 12 assesses integer exponents, which aligns to 6.EE.A.1, “Write and evaluate numerical expressions involving whole-number exponents,” and question 15 assesses the use of square roots, which aligns to 8.EE.A, “Work with radicals and integer exponents.”
• Cumulative Test 22, after lesson 115, question 4 assesses the use of ratios, which aligns to 6.RP.A.1, “Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities,” and questions 5 and 6 assess the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.”
• Cumulative Test 23, after lesson 120, question 2 assesses the use of percentages, which aligns to 6.RP.A.3c, “Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent,” question 3 assesses negative numbers, which aligns to 6.NS.C, “Apply and extend previous understandings of numbers to the system of rational numbers,” question 6 assesses mean, which aligns to 6.SP.B, “Summarize and describe distributions,” and question 7 assesses probability, which aligns to 7.SP.C, “Investigate chance processes and develop, use, and evaluate probability models.”
• Power Up Test 22 assesses probability, which aligns to 7.SP.C, “Investigate chance processes and develop, use, and evaluate probability models.”

*Evidence updated 10/27/15

The instructional materials reviewed for Grade 5 do not meet expectations for focus since a majority of time is not spent on major cluster of the grade. The materials suggest a 60-minute class period consisting of a 30-minute block in which students complete written practice problems (distributed practice which does not particularly focus on or extend the new concept taught that day) and a 15-minute power up block. Because of this and the wide range of concepts addressed in the practice, which changes daily, it is difficult to trace the amount of time spent on each concept through this and the power up practice. Users of the text would focus primarily on the new concept lessons as the tool in which to base the review alignment to the major work of the grade level. The materials allot only 15 minutes for the new concept lesson. Upon closer scrutiny of the lessons, the review team found that some of the lessons do not accurately reflect the designated standard. For example:

• The lesson 63 new concept is focused on subtracting like denominators so it does not meet the demands of this cluster. This cluster calls for unlike denominators.
• The lesson 64 new concept is consistent with major work of the grade.
• The lesson 67 new concept reflects the major work of the grade.
• The lesson 68 new concept reflects the major work of the grade level.
• Lessons 81 and 82 ask probability questions.
• Lessons 83 and 89 focus on 3-dimensional solids and the labeled standard only calls for work with shapes that are 2-dimensional.
• Lesson 84 is mean, median, mode and range, which is the work of future grades
• Lesson 88 focuses on transformations and probability experiments, which are Grade 7 and Grade 8 standards.
• Lesson 71 relates decimals to percents which is work above the scope of the grade, appropriate for Grade 6.

The materials overall focuses heavily on geometry concepts. In Grade 5, the geometry standard is considered an additional cluster, diminishing the amount of time spent on the major work of the grade.

The Grade 5 materials do not develop according to the grade-by-grade progression in the standards. The materials address off-grade level content and are not clearly identified as such. They identify the CCSSM focus of the lesson as a standard for mathematical practice rather than as a content standard. Additionally, above grade-level content is inaccurately aligned to either a Grade 5 standard or MP. Therefore, the materials do not meet expectations for focus.

The instructional materials reviewed for Grade 5 do not meet expectations for supporting content enhancing focus and coherence simultaneously. Each of the supporting concepts is addressed in too few lessons to make any impact of support to the major work. A lack of coherence between the major and supporting work is evident in the following examples:

• Lessons 44 and 47 identified in this standard cluster do not even involve conversions to support 5.NBT.B.
• Lesson 47 conversions support 5.NBT.B.5 (multiplication with whole numbers).
• Lesson 65 addresses conversions of decimals but not a very robust connection to computation with decimals.
• Lesson 74, the only lesson identified as connected to 5.MD.B.2, which involves using line plots marked in fractions to solve real-world problems with operations on fractions, only has problems for whole number measurements. Lesson extension activity 4 does connect to operations with fractions (5.NF.A and 5.NF.B), but it is just one lesson and it limits the fractions to those less than one.
• In the focus lesson of lesson 13, multiplication as repeated addition is part of Grade 3 standards and adding and subtracting dollars and cents supports work with decimals, which supports the major cluster 5.NBT.B.
• Lesson 47 concerning conversions supports 5.NBT.B.5 and is an example of a lesson where connections were made. It was concluded, however, that there are an extremely limited amount of examples or questions that had support/additional cluster that supported the major work of the grade level.

The instructional materials reviewed for Grade 5 do not meet expectations for viability for one school year in order to foster coherence between the grades. The curriculum consists of 120 lessons, 12 investigations and 23 cumulative assessment days for a total of 155 days needed to complete the curriculum. Although this is a manageable number of days for a school year, only 68 of the 132 lessons are identified as aligned to the major, supporting and additional work of the grade level. Sixty-four lessons (approximately 48% of the lessons) are aligned to the mathematical practices but not to Grade 5 content standards. Thirty-one of the lessons appear in the first 40 instructional days. For these reasons and the evidence cited in 1b, this curriculum does not cover the major work with enough depth for students to be ready for the work of the next grade level.

The instructional materials reviewed for Grade 5 do not meet expectations for consistency with the progressions in the standards. This is evident through examples below which were based on materials around the progression of grade-by-grade content, the access in materials to grade-level problems and the connections to concepts from prior grades. The materials address a great deal of off-grade level content not clearly identified as such. They identify the CCSSM focus of the lesson as a standard for mathematical practice rather than as a content standard. Additionally, above grade-level content is inaccurately aligned to either a Grade 5 standard or MP. Examples of work that are not consistent with the progressions are:

• In Lesson 1, students describe a rule for a sequence (Grade 4 content) and count up or down to identify missing terms in a counting sequence (Grade 4 content).
• In lesson 2, students find half of an even number (Grade 3, divide by two, two equal shares) and an odd number and describe numbers as even or odd (Grade 2 content).
• In lesson 3, students use money amounts to represent place value (Grade 2 content), write a number in expanded form (Grade 2 content) and use digits to write a number given in expanded form (Grade 2 content).
• In lesson 4, students compare two whole numbers (Grade 1 content) and use a comparison symbol to write a comparison given in words (Grade 2 content).
• In lesson 6, students are asked to identify the commutative property of addition and use it to add several one-digit numbers in any order (Grade 1 content) and use the addition to add two- and three-digit numbers (Grade 4 content).
• In lesson 7, students use words and digits to name numbers through hundred thousands (Grade 4 content).
• In lesson 8, students perform basic subtraction (Grade 1 content) and write two addition facts and two subtraction facts for a fact family (Kindergarten to Grade 2 content).
• In lesson 10, students use subtraction to find a missing addend in an equation containing two or more addends (Grade 1 content), use subtraction to check the answer to a missing addend problem (Grade 1 and Grade 2 content), determine the equation for a word problem (Grade 1 and Grade 2 content).
• In lesson 52, students name numbers through hundred billions which is above grade level content.
• In lesson 105, students work with transformations, which is a Grade 8 standard.
• In lesson 71, students work with percents, which is a Grade 6 standard.

In no instances did the review team find evidence that the authors explicitly made these connections to prior knowledge. Additionally, due to the structure of the curriculum, the amount of time spent in new concept lessons on these concepts is only a small fraction of the entire lesson time, thus preventing work from being extensive. Additional evidence pieces were found in the following:

• 5.NF.B calls for students to apply and extend previous understandings of multiplication and division to multiply and divide fractions so there should be natural connections to what was learned in Grade 4 multiplication and division. Opportunities to do so were missed and the connections were not made.
• When multiplication of a fraction by a fraction was introduced in lesson 76, the only connection to whole number multiplication was in the math background note which discusses the commutative property.

In a few instances the review team found evidence that the authors explicitly made these connections to prior knowledge. They include:

• In the lesson extension activity 5 of lesson 87, a connection to whole number division being the inverse of multiplication is made to fraction division.
• In the lesson 119 extension activity 9, a connection to resizing as with whole numbers is made when multiplying fractions.

These examples were not sufficient to warrant a rating of partially meets. Additionally, due to the structure of the curriculum, the amount of time spent in new concept lessons on these concepts is only a small fraction of the entire lesson time, thus preventing work from being extensive.

The materials reviewed for Grade 5 do not meet expectations for coherence through connections at the grade level. This was evidenced through the absence of CCSSM-aligned learning objectives as found in the following:

• Section 29, lessons 81-84 and 88-90. Since the activities on these pages are not aligned to Grade 5 content, the objectives are not shaped by the CCSSM cluster heading for Grade 5.

Materials do not include learning objectives shaped by CCSSM cluster headings. Each individual lesson contains power up questions, new concept explanation and a written practice that is a spiraling review. All lessons and daily components do not state the CCSSM, MP and learning objectives. Examples include lessons 14, 47 and 72.

Additionally, there was a lack of connections in math problems made between and among clusters in a domain and domains in a grade. This informed the evaluation of instructional materials for this criteria. Examples include:

• Student work with conversion of measurements (5.MD.B) does not connect to place value (5.NBT.1) as evidenced in lessons 74 and 86 and lesson extension activity 4. In fact, the lack of lessons aligned to 5.MD.B precludes any connections that could be made.
• Student work with the multiplication of fractions (5.NF.B) is not connected to 5.NBT.B.5 since the intended focus of the lessons is merely to change the whole number into a fraction and multiply numerators and denominators. Understanding is not established this way (e.g., lesson 86). The work with division of fractions in lesson 87 is more closely related to the intent of the standard.