The instructional materials reviewed for Primary Mathematics Common Core Edition Grade 3 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 3 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 3, Lesson 1f, students solve word problems involving multiplication and division within 100 (major work, 3.OA.3) with representing data (supporting work, 3.MD.3, 3.MD.4). “A tailor used 21 m of cloth to make dresses. She used 3 m of cloth for each dress. How many dresses did she make?”
• In Unit 11, Lesson 1a, students represent data with pictographs (supporting work, 3.MD.3) and connections are made to multiplying and dividing within 100 (major work, 3.OA.2). “Joanne has counted the number of different types of evergreen trees in a park and put the information into a table [Table inserted in text.] She makes a scaled picture graph to show the number of trees in a nature park. She wants to have no more than about 10 symbols in each row. [Pictograph inserted in text.] If [one tree inserted] represents 4 trees, what does [half tree inserted in text] represent? Why did Joanne choose one symbol for 4 trees? Could she have used a different scale?” (Student Textbook, 3B, page 128). This connection is not noted in the Teacher’s Guide.
• In Unit 9, Lesson 9.1a, students use bar models and shapes (supporting work, 3.G.2) to identify fractional pieces and relate them to a whole (major work, 3.NF.1) “What fraction of each shape is shaded? What fraction is not shaded?” (Student Textbook, 3B, page 86). 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:

• In Unit 2, Lesson 1.1b, students use mental math to subtract within 1,000, supporting standard 3.NBT.2, with no connection to major work of 3.OA.
• In Unit 5, Lesson 5.3a, students measure, estimate, and compare lengths in feet, yards, and inches, supporting standard 3.MD.4, with no connection to major work of 3.OA or 3.NF.
• Unit 12 addresses angles and shapes through three lessons, supporting standard 3.G.1, in isolation.

The instructional materials for Primary Mathematics Common Core Edition Grade 3 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 3 reflects standards above grade level. Materials make connections to previous grades; however, content from future grades is not identified. For example:

• In Primary Mathematics Teacher’s Guide 3A, page 4 in Unit 1, Numbers to 10,000, the Notes state, “Students will learn the terms' standard form and expanded form. 2,435 is the standard form of the number shown. 2,000 + 4000 + 30 + 5 is the expanded form of 2,435, which shows the value of each digit.” The unit goes beyond the grade-level expectation of working with numbers within 1000. (3.NBT.2)
• In Unit 2, Workbook 3A, page 52, students add and subtract beyond 1,000. For example: “A television costs $1790. It costs $800 less than a computer. What is the cost of the computer?” This aligns to 4.NBT.4.
• In Unit 3, Workbook 3A, page 117, students multiply beyond 1-digit numbers (other than multiples of 10) in Workbook 3A. For example: “5 bicycles cost $740. How much does one bicycle cost?” This aligns to 4.NBT.6.
• In Unit 9, Workbook 3B, page 97, students work with fractions whose denominators go beyond those aligned with Grade 3 (2, 3, 4, 6, 8). For example: “A pine tree sapling is 2/5 m tall. A maple tree sapling next to it is 5/10 m tall. Which one is taller?” This aligns to 4.NF.3.
• There are 24 games/activities offered as reinforcement in the back of Teacher Guide 3A. Two of these activities relate to adding/subtracting 4-digit numbers (4.NBT.4.). Two of these activities relate to multiplying/dividing a 3-digit number by a 1-digit number (4.NBT.5.).
• There are eight games/activities offered as reinforcement in the back of Teacher Guide 3B. Five of the eight games/activities relate to money, including adding/subtracting decimal amounts (4.MD.2, 5.NBT.7).

The Grade 3 Teacher’s Guides (3A and 3B) include a Developmental Continuum (3A-page vi-x and 3B page vi-x) 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 (other than subsequent units within the same grade level) with except for Units 8 and 13. 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 3A, page 2 states, “Students should have a basic understanding of place value through hundreds and simple addition and subtraction. They should also be familiar with scaled number lines, that is, number lines in which the divisions stand for quantities greater than 1. In Primary Mathematics 2B, they worked with bar graphs with divisions other than 1.”
• Unit 7 in Teacher’s Guide 3B, page 52 states, “From Primary Mathematics 2A, students should understand the need for standard units of measurement in order to communicate the measure of something. They should also be aware that there are two systems of measurement, a customary one used in the United States, and the metric system used in most of the world and also in the sciences in the United States. They should know which units are used in which system for length and weights.”
• Unit 10 in Teacher’s Guide 3B, page 168 states, “Students should be able to tell time to the half hour, quarter hour, and 5-minute interval using an analog clock face and be able to read and write time using the hour:minute notation.”

Students in Grade 3 do not have extensive work with grade-level problems due to the amount of above grade-level work in the lessons which detracts from the grade-level work. There are limited opportunities for enrichment and reinforcement of grade-level work.

The instructional materials for Primary Mathematics Grade 3 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 Grade 3 include learning objectives that are
visibly shaped by the CCSSM cluster headings. For example:

• In Unit 4 Lesson 1f (Teacher’s Guide 3A, page 252), students solve word problems (one- and two-step problems involving the four operations and identify and explain patterns in arithmetic.” For example, Student Workbook 3A, page 136 says, “A human heart beats 72 times a minute. How many times does it beat in 6 minutes?”
• In Unit 9, Lesson 9.1a (Teacher’s Guide 3B, page 122), students demonstrate understanding of how many fraction pieces make one whole using pictures, models, and numerals (3.NF.1). This is shaped by cluster heading 3.NF.A, “Develop understanding of fractions as a number.”
• In Unit 9, Lesson 9.3b (Teacher’s Guide 3B, page 126), students review the terms “numerator” and “denominator,” compare fractions using models and numerals, and order fractions (3.NF.3). This is shaped by cluster heading 3.NF.A, “Develop understanding of fractions as a number.” For example, in the Student Textbook 3A, page 86, students are given shapes and determine “Which fraction of each shape is shaded? Which fraction of each shape is not shaded?”
• In Unit 13, Lesson 13.1b (Teacher’s Guide 3B, page 232), students find the area of figures by counting the square units (3.MD.6). This is shaped by cluster heading 3.MD.C, “Geometric measurement: understand concepts of area and relate to multiplication and to addition.”

The materials for Primary Mathematics Grade 3 have one example of 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.

• Unit 6, Lesson 6.2b (Teacher’s Guide 3B, page 13) connects two clusters from different domains in the grade. Specifically, “Represent and solve problems involving multiplication and division.” (3.OA.A) and “Solve Problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.” (3.MD.A) For example, Student Textbook 3B, page 14 says, “A fast food outlet sells 45 kg of fruit in each of 7 boxes. What is the total mass of the fruit he has to pack?”

The materials in Primary Mathematics Grade 3 miss connections between 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 9 - Fractions addresses the major cluster, “Develop understanding of fractions as numbers,” (3.NF.A) without connections to other clusters or domains. The mathematics in this unit focuses on recognizing and naming fractions, comparing and ordering fractions with common numerators and common denominators, recognizing and finding equivalent fractions, and finding the simplest form of fractions. Connecting fractions with the measurement and data domain, specifically the major cluster, “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects," (3.MD.A) would be a natural connection.
• Unit 10 – Time, Lessons 10.1a - 10.1e and Lessons 10.2a-10.2b, addresses the major cluster, “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects,” (3.MD.A) without any connections to other clusters or domains. The mathematics in this unit includes telling time to the nearest minute, converting hours, minutes, and seconds in various ways, adding and subtracting hours and minutes, and solving problems involving time intervals. The domain, Number and Operations - Fractions, and specifically cluster, “Develop understanding of fractions as numbers,” (3.NF.A) would be a natural connection for these lessons, providing students the opportunity to develop a sense of 1/4 hour, 1/2 hour and 3/4 hour.