The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 5 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The examples from Primary Mathematics Common Core Edition Grade 5 where connections are made between major and supporting work are not always noted in the Teacher’s Guide. Some examples of where the materials make connections between supporting and major work include:

• In Unit 8, Lesson 5a (Teacher’s Guide 3B, page 204/Student Textbook, page 128) students convert measurements involving decimals (5MD.A) which supports and connects to the work of 5.NBT.A, understanding the place-value system.
• In Unit 8, Lessons 8.5a and 8.5b, students convert a decimal measurement to a smaller unit or a compound unit and convert a measurement unit to a larger unit as a decimal (supporting standard, 5.MD.1). There are natural connections made to the major work of multiplication of decimals (5.NBT.5). Student Textbook, page 54, #1a says, “Express 0.75 m in centimeters. 0.75 m = 0.75 x 100 cm = _____ cm” The connection is not noted in the Teacher’s Guide.
• In Unit 10, Lesson 10.2a, students work with line plots (supporting standard, 5.MD.2), which is connected to the major work of adding and subtracting fractions with unlike denominators (5.NF.1). Student Workbook 5B, page 73, #1 says, “The following are measurements of the amount of time it took to do an activity to the nearest twelfth of an hour - 1 2/3, 1 5/6, 1 1/2, 1 1/3, 1 2/3, 1 2/3, 1 1/4, 1 7/12, 1 3/4, 1 5/6, 1 1/4, 1 5/12.” [Students need to plot the measurements and answer questions related to the measurements.] This connection is not noted in the Teacher’s Guide.

Examples where units and/or lessons did not make connections between major and supporting work include:

• Unit 2, Lessons 1a and 1b addresses operations and algebraic thinking (5.OA) without any connection to major work of Grade 5, such as 5.NBT.A and 5.NBT.B.
• In Unit 11, students work with two-dimensional figures and subcategories of categories and classify 2-D figures based on properties (supporting standards 5.G.3,4) without connections to major work of the grade.

The instructional materials for Primary Mathematics Common Core Edition Grade 5 partially meet expectations for the materials being consistent with the progressions in the standards. Overall, materials develop according to the grade-by-grade progressions of the standards; however, some of the content within Grade 5 reflects standards above grade level. Materials make connections to previous grades; however, content from future grades is not identified. For example:

• In Unit 1, the mathematics includes finding the lowest common multiple and greatest common factor of pairs of numbers (6.NS.4). For example, “Find the lowest common multiple of each set of numbers. (a) 3 and 5; (b) 6 and 8; (c) 4, 6, and 9” in Student Workbook 5A, page 14.
• In Unit 1, the mathematics includes finding the prime factorization of a number (6.EE.1). For example, “List the composite numbers between 47 and 51 and show the prime factorization of each” in Student Workbook 5A, page 15.
• In Unit 2, the mathematics includes applying the order of operations to expressions with and without parenthesis (6.EE.2). For example, “Find the value of each of the following. (a) 7 x 9 + 1 ÷ 1 - 6 x 3; (b) (108 + 12) ÷ 5 x 6; (c) 60 ÷ 5 + 24” in Student Workbook 5A, page 31.
• In Unit 6, the mathematics includes ratios that align with Grade 6 CCSS (6.RP.1, 6.RP.2, 6.RP.3). For example, “The ratio of Gary’s mass to Andy’s mass is 4:5. Their total mass is 117 kg. (a) Find Andy’s mass. (b) Find Gary’s mass” in Student Workbook 5A, page 174.

The Grade 5 Teacher’s Guides (5A and 5B) include a Developmental Continuum (5A-page vii-xi and 5B page vii-xi) that contains an overview of topics and skills for each grade level, K-5, but no specific standards are indicated. Standards specific to units and lessons are listed in the introduction to each unit. There are no connections to future grade-level content. In each Teacher’s Guide, there is a Notes section at the beginning of each lesson that includes work learned in previous grade levels as well as the connection to the current work in the lesson. For example:

• Unit 1 in Teacher’s Guide 5A, page 4 states, “In Primary Mathematics 3A, students learned to relate 4-digit numbers to the place-value concept. In Primary Mathematics 4A, the place-value concept was reinforced and extended to 6-digit numbers. In this lesson, the place-value concept will be extended to hundred billions, or numbers with 12 digits.”
• Unit 7 in Teacher’s Guide 5B, page 13 states, “In Primary Mathematics 3A, students learned to round numbers of up to four digits to the nearest ten, hundred, or thousand. In Primary Mathematics 4A, they learned to round larger numbers to the nearest hundred, thousand, ten thousand, and hundred thousand. In Primary Mathematics 4B, students learned to round decimals to a whole number and to one decimal place. In this lesson, students will review rounding decimals to a whole number or one decimal place and extend this to rounding decimals to two decimal places.”
• Unit 10 in Teacher’s Guide 5B, page 142 states, “In earlier levels of Primary Mathematics, students learned how to locate points on both horizontal and vertical number lines. In this lesson, students will learn to graph positive points on a plane by using a coordinate grid.”

In Grade 5, students have extensive work with grade-level problems. In each lesson, students are guided through the topic of the day with problems demonstrated by the teacher, discussion problems (which include problems in the student workbook), assessment problems (which are formative assessment problems in the student workbook), and practice problems (which students complete on their own in the workbook). For example, Unit 3, Lesson 2 Fractions and Division, Textbook 5A, page 63 focuses on 5.NF.3 and gives the students two illustrations with explanation on how 3 divided by 4 is 3/4 and how 5 divided by 4 is 5/4. Students show “another way” to use the standard algorithm for division of 5 divided by 4. Students then complete eight problems, varying from procedural to conceptual/word problems (one problem (#2 on page 64), students need to answer using two methods). The workbook pages that correlate give the students 16 problems to solve using their knowledge learned.

However, as noted previously in this report, the presence of above grade-level work represented in the units detracts from the grade-level work. There are limited opportunities for enrichment and reinforcement of grade-level work.

The instructional materials for Primary Mathematics Common Core Edition Grade 5 partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

The materials for Primary Mathematics Common Core Edition for Grade 5 include learning objectives that are visibly shaped by the CCSSM cluster headings. For example:

• In Unit 8, Lesson 8.5a (Teacher’s Guide 5B, page 78), students convert meters to centimeters, feet to inches, quarts to cups, gallons to quarts, pounds to ounces, kilometers to meters and vice versa (5.MD.1). This lesson is shaped by 5.MD.A, “Convert like measurement units within a given measurement system." For example, Student Textbook 5B, page 55, “Express 4.2 L in liters and milliliters.”
• In Unit 9, Lesson 9.1a (Teacher’s Guide 5B, page 93), students find the volume of solids made up of 1-cm cubes (5.MD.3), which is shaped by 5.MD.C, “Geometric measurement: Understand concepts of volume.” For example, in Student Workbook, page 48, “How many 1-cm cubes are needed to fill a rectangular container that measures 3 cm by 3 cm by 4 cm?”
• In Unit 3, Lesson 3.5a (Teacher’s Guide 5A, page 140), students utilize pictures, models and number lines to multiply a fraction by a whole number (5.NF.4), which is shaped by 5.NF.B, “Apply and extend previous understandings of multiplication and division.”

The materials for Primary Mathematics Common Core Edition Grade 5 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. For example:

• Unit 5, Lesson 5.2a (Teacher’s Guide 5A, page 227) connects the major cluster, “Use equivalent fractions as a strategy to add and subtract fractions” (5.NF.A) to the major cluster, “Apply and extend previous understandings of multiplication and division” (5.NF.B). Students find the area of a composite figure, including sides with fractional lengths. For example, in Student Workbook 5A, page 141, students find the area of figures where some of the figures have side lengths of mixed numbers. (Figure D - 10 1/2 inch sides, Figure E - 8 2/3 inch side)
• Unit 7, Lesson 7.4d (Teacher’s Guide 5B, page 30) connects the major cluster, “Apply and extend previous understandings of multiplication and division” (5.NF.B) to the major cluster, “Perform operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). Students express a fraction as a decimal correct to two decimal places. For example, in Student Textbook 5B, page 27 #22, “Express each fraction as a decimal correct to 2 decimal places: (a) 3/7, (b) 5/8.”
• Unit 9, Lesson 9.1c connects the major cluster, “Use equivalent fractions as a strategy to add and subtract fractions" (3.NF.2) and the major cluster, “Apply and extend previous understandings of multiplication and division" (3.NF.3d).

The materials in Primary Mathematics Common Core Edition Grade 5 include problems and materials that do not make connections with two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

• Unit 4 - Multiply and Divide Fractions (Teacher’s Guide 5A, pages 160-216) contains lessons that focus on one CCSSM cluster. For example, in the first lesson (4.1a, Product of Fractions, Teacher’s Guide 5A, page 165), the mathematics is focused on developing the concept of multiplying a fraction by another fraction (5.NF.B), using pictures, models, and number lines. A natural connection in this unit is, “Use equivalent fractions as a strategy to add and subtract fractions,” (5.NF.B) as students develop multiple strategies to multiply and divide fractions.
• Unit 9 - Volume (Teacher’s Guide 5B, pages 89-123) addresses the major cluster (5.MD.C) without any connection to other domains or clusters. For example, in Lesson 9.2a (Teacher’s Guide 5B, pages 99-102), the mathematics involves finding the volume of rectangular prisms, given the length, width, and height. A natural connection in this unit is the major cluster, “Performs operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). Problems that contain side lengths with decimal values would have connected the work of the major cluster (5.MD.C) with the major cluster (5.NBT.B).

There were three units where the Review lesson made connections with two or more clusters in a domain, or two or more domains in a grade:

• In Units 1 and 2, the Review lessons connect two or more clusters in a domain: “Understand the place value system,” (5.NBT.A) and “Perform operations with multi-digit whole numbers and with decimals to hundredths” (5.NBT.B). For example, in the Unit 1 Review, students are asked to find the value of expressions that include exponents and solve problems that require a “quick estimate.”
• In Unit 3, the Review lesson connects two or more clusters in a domain: “Use equivalent fractions as a strategy to add and subtract fractions,” (5.NF.A) and “Apply and extend previous understandings of multiplication and division to multiply and divide fractions” (5.NF.B). For example, “A piece of wood is 5 ft long. Juan used 3/4 of it to make a shelf. What is the length in feet of wood left?” (Student Workbook, page 94, #12)